WATER DROPLET MOVEMENTS ON METHYL-TERMINATED ORGANOSILANE MODIFIED SILICON WAFER SURFACES. A Dissertation. Presented to

Transcription

1 WATER DROPLET MOVEMENTS ON METHYL-TERMINATED ORGANOSILANE MODIFIED SILICON WAFER SURFACES A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Feng Song May, 2008

2 WATER DROPLET MOVEMENTS ON METHYL-TERMINATED ORGANOSILANE MODIFIED SILICON WAFER SURFACES Feng Song Dissertation Approved: Accepted: Advisor Dr. Bi-min Zhang Newby Department Chair Dr. Lu-Kwang Ju Committee Member Dr. Steven S. Chuang Dean of the College Dr. George K. Haritos Committee Member Dr. Edward Evans Dean of the Graduate School Dr. George R. Newkome Committee Member Dr. Jun Hu Date Committee Member Dr. Rex D. Ramsier Committee Member Dr. Igor Tsukerman ii

3 ABSTRACT Water droplet movements on a variety of organosilane modified wettability gradient surfaces were first examined. These gradient surfaces were generated by the contact printing (CP) of octadecyltrichlorosilane (OTS) or octadecylmethyldichlorosilane (OMDS) on silicon wafer surfaces. The experimental results showed that a water droplet as small as a few pecoliters could move toward the higher wettability region on these gradient surfaces. As the droplet size or the gradient scale increased, the droplet velocity increased. The study also confirmed that of the two factors to cause the resistances in droplet movement, contact angle hysteresis (CAH) was always the predominated factor, while the interfacial friction only became more important when the wettability gradient size scaled down to sub-millimeters. To predict the contribution of CAH and interfacial friction in resisting droplet motion, the modes of droplet movement on the gradient surfaces should first be determined. However, under the current experimental conditions (small droplets and short droplet traveling time); it was too challenging to obtain the droplet motion modes on the wettability gradient surface. Alternatively, tracer particles were suspended in large water drops that moved down on inclined OTS surfaces, also generated by CP, and the internal fluidity was deduced from the movement of the tracer particles. The results iii

4 showed that the motion of the water droplet is a combination of sliding, slipping, and rolling. Furthermore, to evaluate the effect of drop size on the drop motion mode, water drop movements on an inclined dimethydichlorosilane (DDS) surface having a low water CAH (i.e. CAH of about 5 as compared to ~ 20 for OTS or OMDS surfaces) were studied. It was experimentally observed, by including tracer particles inside the water drops during the drop movements, which at a lower inclined angle, rolling had a greater contribution to the drop motion; while at a higher inclined angle, sliding contributed more to the drop movement. An analysis based on the ratio of the rotational torque to that of the sliding torque of a water drop on an inclined surface captures the basic trends of the experimental results. Experimental results also showed that a smaller drop exhibits a larger rolling contribution to the drop motion. Under a small ratio (< about 18) of the torques after by considering the effects of both inclined angle and drop size, a complete rolling becomes possible; conversely, a large enough ratio (> about 36) of the torques leads to no rolling with small or even no slipping. When the degree of rolling and the degree of the interfacial slipping sum up to a value less than unity; the sliding of the drop likely accounts for the remaining portion of the droplet velocity. iv

5 ACKNOWLEDGEMENTS The author would like to thank Dr. Bi-min Zhang Newby for her continuous guidance and invaluable support to my research throughout my whole Ph.D study. I also would like to thank all of my committee members: Dr. Steven S. Chuang, Dr. Edward Evans, Dr. Jun Hu, Dr. Rex D. Ramsier, and Dr. Igor Tsukerman, for their invaluable suggestions. v

6 TABLE OF CONTENTS Page LIST OF TABLES...x LIST OF FIGURES... xi NOTATION... xiv CHAPTER I. INTRODUCTION Issues of Droplet Movements Issues on Droplet Movements on Wettability Gradient Surfaces Issues on Generation of Wettability Gradient Surfaces Objectives and Organization of the Dissertation Wettability Gradient Surfaces...7 II. BACKGROUND Water Droplet Movements on Wettability Gradient Surfaces Experimental Studies Analysis Water Droplet Movements on Inclined Solid Surfaces Experimental Studies Theoretical Analysis Boundary Slip of Fluid Flow on Solid Surfaces Experimental Studies Theoretical Analysis...30 vi

7 2.4 Contact Angle and Contact Angle Hysteresis (CAH) Contact Angle Contact Angle Hysteresis (CAH) Friction at Liquid/Solid Interfaces Organosilane Modified Surfaces Formation of Organosilane Self-Assembled Monolayers Deposition Techniques Generation of Wettability Gradient Surfaces Characterization of Organosilane modified Surfaces...44 III. EXPERIMENTAL Materials and Equipment Materials Equipment Preparation of Organosilane Surfaces Stamp Fabrication Substrate Cleaning Homogenerous Wettability Surfaces via Contact Printing Wettability Gradient Surfaces via Contact Printing Wetability Evaluation via Contact Angle Measurements Water droplet motion on inclined solid surfaces Experimental Setup Data Collections and Analysis Water Droplet Movements on Wettability Gradient Surfaces Experimental Setup Data Collection and Analysis...63 vii

8 IV. RESULTS AND DISCUSSION Effects of Contact Time on Wettability of Organosilane Modified Surfaces Introduction Reactivity of Organosilanes Determination of Suitable Temperatures for Octadecylmethyldichlorosilane (OMDS) Contact Printing Octadecyltrichlorosilane (OTS) Modified Surfaces Octadecylmethyldichlorosilane (OMDS) Modified Surfaces Summary Wettability Gradient Surfaces of Organosilanes Introduction Gradient Surfaces of Octadecyltrichlorosilanes (OTS) Gradient Surfaces of Octadecylmethyldichlorosilanes (OMDS) Step-wise Gradients Summary Water Droplet Movements on Wettability Gradient Surfaces Experimental Observatios and Analysis Effects of Gradient Size Effects of Contact Angle Hysteresis (CAH) Effects of Interfacial Friction Summary Water Droplet Movements on inclined solid surfaces Introduction Non-Wettable OTS Surfaces (90 < θ w < 60 ) Partially Non-Wettable OTS Surfaces (60 < θ w < 30 ) viii

9 4.4.4 DDS Surface (θ w = 98 ) Summary Summary of Results and Discussion V. CONCLUDING REMARKS AND FUTURE STUDIES Concluding Remarks Future Studies REFERENCES APPENDIX. ADDITIONAL RESULTS AND DISCUSSION ix

10 LIST OF TABLES Table Page 3.1 Physical properties of organosilanes used in this study Physical properties of organic and inorganic reagents used in this study...46 x

11 LIST OF FIGURES Figure Page 1-1 Schematics of possible motions of a water droplet on a wettability gradient surface A sessile drop of a probe liquid with a finite contact angle (θ) on a solidsurface Schematic of formation of the organosilane self-assembled monolayer0(sam) on Si/SiO 2 substrate Schematic of organosilane deposition techniques: (a) solution deposition, (b) vapor phase deposition, and (c) CP (generation of homogeneous or heterogeneous surfaces) Schematic illustration of various types of PDMS stamp fabrications (a) Schematic illustration of the generation of a continuous gradient surface by CP of an inked hemispherical elastomeric PDMS stamp. (b) Schematic illustration of the dimensions used in the text to describe the droplet movements on a radial gradient surface (the largest circle) Schematic illustration of the experimental setup to observe the water droplet movement on an inclined homogeneous organosilane surface Schematic illustration of a water droplet moving on an inclined surface Schematic illustration of the experimental setup to observe the droplet movement on a continuous organosilane gradient surface The advancing (filled symbols) and receding (unfilled symbols) contact angles of deionized water on the organosilane modified surfaces Water contact angles of OMDS modified surface (filled for advancing contact angle, and unfilled for the receding contact angle) as a function of temperature at different contact times...70 xi

12 4-3 The advancing ( ) and receding ( ) contact angles of deionized water on the OTS modified silicon surfaces DI water CAH of OTS modified surfaces as a function of the contact time DI water CAH of OMDS modified surfaces as a function of the contact time cosθ d of an OTS gradient surface as a function of the dimensionless relative location, L/S cosθ d of an OMDS gradient surface as a function of the dimensionless relative location, L/S Estimated advancing (solid line) and receding (dashed line) contact angles of water on the radial gradient surfaces generated step-wisely with five steps Relative radius of a droplet (R/S 0 ) on various sizes of gradient surfaces as a function of relative location of the droplet (L/S 0 ) Velocity of a water droplet on various sizes of gradient surfaces as a function of relative radius of the droplet (R/S 0 ) under water mist condition on gradient surfaces Droplet velocities, in terms of Ca, as a function of R* (R*=R dcosθ d /dl) on OTS and OMDS gradient surfaces Comparison of relative velocities (Ca=vη/γ) of water droplets on various sizes of gradient surfaces as a function of R* (R*=R dcosθ d /dl) in a short range of relative position (L/S 0 : 0.32 ~ 0.45), in which the steepness of gradient could be treated as a constant value for each case Illustration of water droplet movement on a one-dimensional organosilane wettability gradient surface with the coalescence occurring during its moving process Comparison of the droplet velocities in term of Ca (Ca=vη/γ) on various sizes of gradient surfaces as a function of R* (R*=R dcosθ d /dl) in a short range of relative position (L/S 0 : 0.32 ~ 0.45), in which the steepness of gradient could be treated as a constant value for each case Sequential images of a water droplet moving down on an inclined OTS surface with a water contact angle of 88± Motion behaviors and internal fluidity of a water drop during its downfall along the OTS modified surface with a water contact angle of 88± xii

13 4-17 Motion behaviors and internal fluidity of a water droplet during its downfall on the OTS surface with a water contact angle of 88± Sequential images of a water droplet moving on the inclined OTS surface with a water contact angle of 75± Motion behaviors and internal fluidity of a water droplet during its downfall along the OTS surface with a water contact angle of 75± Sequential images of a water droplet moving on the inclined OTS surface with a water contact angle of 68± a Motion behaviors and internal fluidity of a water droplet during its downfall on the OTS surface with a water contact angle of 68± b Motion behaviors and internal fluidity of a water droplet during its downfall on the OTS surface with a water contact angle of 68± A motion behavior of a water drop during its downfall on the OTS modified surface with a water contact angle of 44± A motion behavior of a water droplet during its downfall on the OTS surface with a water contact angle of 44± Motion behaviors of a water droplet during its downfall on the DDS surface are summarized Experimental estimation of static frictional force as a function of the contact area of a water drop Capillary number of a pure water drop as a function of Re Schematic illustration of movement of a water drop on an inclined DDS surface, on which the mass center of the drop changes from M 1 to M Torque Index (K T ) of a water drop moving on inclined sample surface as a function of IA Torque Index (K T ) effect on the rolling mode of a water drop Torque Index (K T ) effect on the slipping mode of a water drop Torque Index (K T ) effect on the sliding mode of a water drop K H effect on the slipping and rolling of a water drop xiii

14 NOTATION Roman Letters A A d Hydrophobic side of a wettability gradient surface Contact area of a water droplet with a solid surface a Defined in equation 4-1 a 1 The area fraction of component 1, defined in equation 2-18 a 2 The area fraction of component 2, defined in equation 2-18 B Hydrophilic side of a wettability gradient surface b Defined in equation 4-1 c Defined in equation 4-2 Ca F c F D f d F f F g F H F min F v Capillary number, Ca = vη/γ Critical resistance force Driving force Driving force per unit length Frictional force Gravitational force Contact angle hysteresis (CAH) force Minimum force needed to overcome the CAH Hydrodynamic viscous force xiv

15 f v g H v h k Viscous force per unit length Gravitational acceleration Heat of vaporization Thickness of the droplet Contact printing speed K 1 Constant, defined in v=k 1 (θ d -θ s ) K 2 Constant, defined in equation 2-11 K H Torque index defined in equation 4-16 K T Torque index defined in equation 4-15 k w L Ls R Thermal conductivity The distance from the center of the droplet to the edge of the contact area The slip length The droplet base radius R* R* = R(dcosθ/dx) R 0 R c R cmin R e The curvature of the droplet on a solid surface The critical droplet radius The minimum critical droplet radius Reynolds number S 0 The gradient size, defined in Figure 4-5 T Temperature T S Torque resulted from the sliding motion defined in equation 4-13 T R Torque resulted by the rolling motion defined in equation 4-12 xv

16 T t U d U max U p U rmax U r U ra U sld U slp V x min Degree of subcooling Time Average velocity of the droplet Maximum velocity of the drop The particle velocity at the air/liquid interface Maximum rolling velocity of the drop Rolling velocity of the drop Average rolling velocity of the drop Sliding velocity of the droplet Slipping velocity of the droplet The droplet volume Cutoff length in a molecular scale Greek Letters α α c β The inclined angle The critical inclined angle The angle describing the shift of drop mass center κ 1 The Laplace length, defined in equation 2-19 μ γ γ LV γ SL The frictional coefficient Surface energy or surface tension surface tension atthe liquid/vapor interface surface tension at the liquid/solid interface xvi

17 γ SV γ D γ p γ S η surface tension at the solid/vapor interface Dispersion component of surface energy Polar component of surface energy Substrate surface energy Viscosity of liquid λ The gradient steepness, defined in equation 2-1 θ θ a θ d θ e θ r θ s θ w ρ Contact angle Advancing contact angle Dynamic contact angle Equilibrium contact angle Receding contact angle Static contact angle Water contact angle Density of the liquid xvii

18 CHAPTER I 1INTRODUCTION 1.1 Issues on Droplet Movements When a liquid condenses or deposits on a non-wettable solid surface, it forms drops on the surface. These drops are problematic in some applications, while they are advantageous in other applications. In the case of automobile windshields, water drops from rain or dew diffract the light and reduce the visibility. For glass or plastic shower doors, the drops lead to dirty stains or mildew build-ups. On the other hand, as compared to a continuous liquid film condensed on a heat-exchanging surface, condensed liquid drops can result in orders of magnitude enhancement in heat transfer efficiency. 1;2 In the area of micro/nano fluids, 3-10 discrete droplets moving on a surface are more practical in mixing, scaling and reconfiguring over the continuous flow in microchannels. 11 In both heat exchanging and microfluidics applications, transporting drops on a surface is important. Quick drainage of condensed liquid drops can further improve heat transfer for heat exchangers, 1;2 and mixing or reconfiguration can only be achieved when the droplets are made to move towards each other. 11 Droplets on a solid surface can be 1

19 driven to move by various external forces, 7;8;12-50 such as gravitational force, surface tension gradient, magnetic force, and electric potential. In order to properly select the driving force for moving a drop for a particular application, the basic modes of drop motion and the contribution of each mode should be determined. General speaking, a deformable object, such as a liquid drop, moves on a solid surface experiences a variety of motions including rolling, sliding, and slipping (see Figure 1-1). 32 Rolling is defined as a combination of the rotation of an object around its center of curvature and the translation of the object along the direction parallel to the solid surface. Although most of the rolling phenomena are observed with rigid solid bodies, rolling of a soft deformable body (i.e. liquid drop) in this study is assumed to follow the rolling behaviors of a solid body. Particularly, the maximum velocity is resulted at the air/liquid interface, while the velocity of the soft body at the liquid/solid interface is zero. For a solid object, the object moves with a constant velocity throughout the entire body when it is only under sliding motion. Sliding (or sliding velocity) is equivalent to slipping (or slipping velocity), which is defined as the motion (or velocity) at the solid/solid interface. However, when a fluid moves over a solid surface, the velocities at different locations of the fluid body are normally different due to the different shear stress experienced by the fluid at each location. In most cases, a parabola velocity profile is resulted (Fig. 1-1 (b)), and the velocity at the fluid/solid interface equals to zero (or the non-slip boundary condition). When the fluid slips at the fluid/solid interface (the slip boundary condition), the fluid/solid interfacial velocity is no longer zero, and the fluid movement will be termed sliding with slipping. 2

20 (a) (b) (c) Figure 1-1 Schematics of possible motions of a water droplet on a solid surface. (a) The rolling behavior of a spherical capped drop as proposed by Sakai et al 51. (b) Sliding without slipping, in which the velocity profile (U sld (x)) matches that of the classical fluid flow on a solid surface with a zero velocity at the liquid/solid interface. (c) Sliding with slipping, in which the interfacial velocity (U s1p ) is not zero and the velocity profile (U sld (x)) has shifted to the right as compared to the non-slip case, where L s is the slip length. 3

21 It is believed that the motion of a liquid drop depends on the contact area between the liquid and the solid, the interfacial roughness, and the size of the drop. When a drop makes a large contact with the solid surface, it would likely slide down the surface, while a drop has a minimum contact with the solid surface would likely roll on the surface. Apart from the interfacial contact, the interfacial roughness, which is the main source of the two resisting forces caused by contact angle hysteresis (CAH) and interfacial friction, also affects the mode(s) of liquid motion. A higher interfacial friction makes it harder for the liquid to slide on the solid surface, while a greater contact angle hysteresis leads to the pinning of the liquid at the three-phase contact line and the pinning can be more easily overcome by rolling rather than sliding and/or slipping. 52 However, the exact motion mode(s) of a liquid drop on a solid surface, especially under the surface energy gradient, has not been systematically verified. Furthermore, as the drop size decreases, the interplay between the two resisting forces and the drop movement could become more complex. Therefore, extensive studies are needed to evaluate the drop movement behaviors, essentially the motion mode(s), on a solid surface. The insights of such studies will provide basic guides for designing surfaces, particularly wettability gradient surfaces, for transporting liquid drops on solid surfaces. In addition to the applications in heat exchanging and micro-fluidics, transporting discrete drops on a surface also has potential applications in the field of Micro-Electro-Mechanical Systems (MEMS), chemical and biochemical analyzing systems for the liquid transport/mixing, and the material recovery/removal process in the microgravity environment of space. 4

22 1.2 Issues on Droplet Movements on Wettability Gradient Surfaces One approach to move liquid drops on a surface is by minimizing the total system free energy using a wettability gradient surface, 15;19-21;26;33;38;45 where the drops are induced to move toward the higher wettability region. This approach was first theoretically identified by Greenspan 26 and later experimentally demonstrated by Chaudhury and Whitesides. 19 A wettability gradient in wettability leads to imbalanced Young s forces acting on a liquid droplet at the three-phase contact line, which drive the drop to move in the direction of increasing wettability. In theoretical studies, 15;21;45 the sliding mode of the droplet is assumed and the droplet velocity and the forces acting on the droplet are derived based on either the lubrication approximation 15;21 or the wedge approximation, 45 both with the assumption that the contact angle of the droplet with the solid surfaceis small (generally < 30 ). According to Brochard 15 and later Daniel et al, 21 the forces acting on the droplet on a wettability gradient surface include the driving force (F D, the imbalanced Young s forces) and the two resistance forces: the CAH (F H ) and the interfacial friction (F f ). Usually the CAH is believed to be the main obstacle for the drop movement and the driving force must first compensate the CAH force acting on the advancing and receding edges of the droplet. This results in a critical droplet size (R c ), below which the droplet can not move. However, the effect of CAH on droplet movements has not been methodically studied, and in this project, we intend to systematically study such effect by using different wettability gradient surfaces. On the other hand, in some studies 38 the interfacial friction has been considered to be more important. To the best of our 5

23 knowledge, there are even fewer reports on the investigation of the effect of the interfacial friction on droplet movements on wettability gradient surfaces. Therefore, we will also address the effect of the interfacial friction on water droplet movements in this project. Even though some studies on droplet movements on wettability gradients surfaces have been conducted, the movement process and associated phenomena have not been completely understood. In practical situations, when a droplet moves on a wettability gradient surface with a typical contact angle of water from ~ 100 down to ~ 20, 33 most of the contact angles are greater than that assumed in the theoretical analysis (< 30 ). 15;21 In addition, many researchers 53-74, who studied the fluid flow on a solid surface, have found that a strong slip at the liquid/solid interface surface occurs. Besides slipping, the rolling behavior of a drop moving down along an inclined solid surface has been reported. 12;32 Therefore, a combination of rolling, sliding, and slipping is possible during the movement of a liquid drop, and if so, all of these modes should be included in mathematical analysis that predicts the drop motion behaviors, particularly the velocity on a wettability gradient surface. 1.3 Issues on Generating Wettability Gradient Surfaces Apart from the issues associated with droplet movements on a solid surface, generating a desired wettability gradient surface to move liquid droplets on a surface could be challenging. A common approach in generating wettability gradient surfaces is using organosilane 19-21;33;38;50;75-77 with either a diffusion-based technique 19-21;33;38;50;77 or 6

24 a contact printing (CP) based method. 75;76;78 The diffusion-based technique normally requires well-controlled deposition conditions, generates large amounts of organic waste, and results in a random gradient steepness and a large gradient scale. In comparison, the CP technique is more adequate for our studies, in which various scales and steepness of the wettability gradients are needed. In most cases, the CP technique yields various surface coverage self-assembled monolayers (SAMs) depending on the contact time (within a few seconds to a few minutes; 75;78 thus a wettability gradient surface can be achieved by simply varying the contact time continuously or in stepwise manner over the contacted area. The approach is fast, convenient, reproducible, and inexpensive. In addition, the gradient steepness could be easily varied, which allows us a possibility to study the effect of gradient steepness (i.e. gradient size) on the droplet movements. According to the theoretical prediction, 21 the critical droplet size is inversely proportional to the gradient steepness, thus steeper gradient surfaces will provide the possibility of transporting pico/nano-liter water droplets, which has shown to be challenging with other approaches. 1.4 Objectives and Organization of the Dissertation The overall objective of this project is to experimentally determine the motion mode(s) of liquid drops and the relationships between the droplet velocity and the properties of liquid, solid surface, and the liquid/solid interface. First, the effects of gradient steepness on droplet movements will be investigated by using four different sizes of continuous OTS wettability gradient surfaces, ranging from 700 μm to 65 μm. Then, the two main resistance forces caused by water CAH and the interfacial friction on 7

25 the droplet movements will be investigated. To achieve this, we will systematically vary the CAH by using different organosilanes to generate the comparable wettability gradient surfaces and in the meantime maintain the wettability difference acting on the droplet. Also, we will create wettability gradient surfaces by using the same organosilane, to maintain the CAH while varying the interfacial friction. Further, water droplet movements on inclined uniform OTS covered surfaces, having various wettability, will be conducted to determine the droplet motion modes and the degrees of each motion mode. Because of the large water CAH of OTS modified surface, the water drop size used in the study cannot be reduced. In order to evaluate the drop size effect on the drop motion mode, dimethyldichlorosilane (DDS) modified surfaces, which have much smaller CAH (~ 5 ) as compared to OTS modified surfaces (about 20 ), will be utilized to allow relatively smaller water drops to move on the inclined surfaces. As a result, the factor(s) affecting the degree of rolling or sliding of the drop can be determined and certain relationships between them might be obtained. In this chapter, the issues of the droplet movements on both wettability gradient surfaces and inclined surfaces and the objectives of this work are briefly presented. Literature reviews of droplet movements on a solid surface and the related background will be summarized in Chapter II. The preparation of the organosilane surfaces and the conduction of water droplet movements on both wettability gradient surfaces and inclined organosilane modified surfaces will described in Chapter III. The experimental results on droplet movements will be reported and discussed in Chapter IV. Finally, the conclusion and suggestions for the future work will be presented in Chapter V. 8

26 CHAPTER II 2BACKGROUND Water droplet movements on wettability gradient surfaces and inclined surfaces are reviewed in this chapter as well as other relevant information on droplet movements. Experimental and theoretical studies of droplet movements on both a wettability gradient surface and an inclined solid surface will be first summarized, followed by the contact angle and the contact angle hysteresis (CAH), the friction at the liquid/solid interface, the non-slip and slip boundary condition of a fluid flowing on a solid surface, and the modification of surfaces using organosilanes. 2.1 Water Droplet Motion Behavior on Wettability Gradient Surfaces As mentioned in Chapter I, the movement of a liquid droplet on a wettability gradient surface has many practical and potential applications. As a result, the movements induced by wettability gradients have recently attracted substantial research attentions Experimental Studies Chaudhury and Whitesides 19 first reported liquid droplet movement on a wettability gradient surface in Science in In their studies, a one-dimensional 9

27 organosilane gradient surface was generated by using a vapor phase diffusion method over a Si-wafer substrate. The resulting surface displayed a gradient of wettability (with water contact angle changing from 97 to 25 ) over a distance of 1 cm. When a water drop (with a volume of 1 μl) was placed at the less wettable end of the gradient surface, the drop moved toward the more wettable end with an average velocity of 1~2 mm/s. The imbalance Young s forces resulting from the surface tension acting on the liquid-solid contact line on the two opposite sides of the drop caused the drop to move on such a surface. The contact angle on the receding side (low surface energy) of the drop should be larger than that on the advancing side (high surface energy) of the drop in order for the drop to move. The effect of gravity on the drop shape was insignificant in their case because the drop radius (1 to 1.5 mm) was smaller than the Laplace length (2.7 mm). They proposed that the speeds of the liquid drops depended on the CAH, the surface tension and the viscosity of the drops, the drop size (i.e. the drop radius), and the steepness of the gradient. But the details on the effects of these factors were not reported in this seminal paper. Chaudhury and co-workers later investigated how various factors affect the movement of liquid droplets on wettability gradient surfaces. In 2002, 21 they used ethylene glycol as the test liquid to investigate drop movement on a surface with a onedimension gradient. The surface for the study was generated by the same diffusioncontrolled silanization technique reported in It was found that the velocity of the droplet linearly increased with the increase of drop radius when the steepness of the gradient remained the same, and the droplet needed to be greater than a critical drop size 10

28 (0.055 cm for ethyl glycol for the gradient steepness of 0.6 /cm) in order to move. The existence of this critical drop size was attributed to the CAH. They attempted to qualify the CAH effect on the droplet motion in another paper published in 2004, 7 in which a variety of probe liquids were used. They found that effects of the CAH on drop movements only changed the intercept values on the R* axis in the plot of Ca vs. R*, where Ca (Ca=Uη/γ, U, η, and γ are the velocity, viscosity, and the surface tension of the drop, respectively) is the capillary number and R* is the product of R, the radius of the drop, and dcosθ/dx, the gradient steepness. The intercept on the R* axis corresponds to the critical drop radius. The majority of the intercept values obtained in their studies seemed to match well with theoretical predictions, which were derived by Brochard. The only exception is for di-propylene glycerol, but no explanation was provided for this special case. The slope of Ca vs. R*, proposed by Daniel and Chaudhury, was to be dependent on the mode of the relaxation of stress singularity at the three-phase contact line, or the properties and interactions of the liquid and the substrate surface. Moumen et al 33 applied the same organosilane deposition technique to generate the organosilane gradient surfaces. The probe liquid used in their study was tetraethylene glycol and droplet volume was varied from 50 nl to 2500 nl, all are small enough to neglect the gravitational effect. They found that the velocity of the drops is a strong function of position along the gradient and at a particular position, the velocity of the droplet increases linearly with the increase of droplet size. A quasi-steady state model that balances the local hydrodynamic resistance and the local driving force generally was used to interpret their experimental results. Only on the region of the gradient surface 11

29 with a contact angle less than 60, the experimental results match well with their predictions, which are based on the wedge approximation with the driving force corrected by hysteresis. The results, on the other hand, differ from the predictions of the analysis derived by Brochard 15 and later Daniel et al 21 (The assumptions made for the predictions of Moumen et al 33 will be discussed later). Daniel et al 20 have also prepared a radial wettability gradient surface with the contact angle of water about 100 at the center and with near-zero water contact angle towards the edges to study water droplet movements. They found that under ambient conditions, the water droplet (1 to 2 mm in diameter) moved radially outward with typical speeds of 2 to 3 mm/s. But when the saturated steam passed over a this gradient surface, the speeds of even smaller water droplets (0.1 to 0.3 mm in diameter) were two orders of magnitude higher than those observed under ambient conditions. They proposed the reasons for such high droplet speeds are: (1) a loss of interfacial resistance by a hydrodynamic lubricating water film on the surface could speed up the droplet motion, (2) wetting hysteresis is bypassed under rapid condensation and/or additional energy from condensation is supplied to the droplet to surmount hysteresis, and (3) in the presence of fast condensation, droplet movement can be aided by the direct condensation of steam and by coalescence with other droplets. The above studies mainly focused on d the effects of the CAH, interfacial friction, and droplet displacement on droplet movements by using an organosilane wettability gradient surface. But the estimation of the driving force acting on a liquid droplet is also 12

30 essential in understanding droplet movement. Suda and Yamada 77 first directly measured the driving force, or the unbalanced Young s forces minus the force arisen from the CAH, acting on the water drop by using a glass microneedle as the drop moved on the organosilane wettability gradient surface prepared by using the same technique as that used by Chaudhury and Daniel et al. 7;19-21 They found that a slight change in force caused a big change in the drop velocity, which implied that the adhesion force is essentially dominant against the velocity of the drop movement, and the hydrodynamic viscous force is relatively small. All the above studies were carried out on a wettability gradient surface with the hydrocarbon organosilanes. Petrie and coworker 38 chose heptadecafluoro-1,1,2,2- tetrahydrodecyl trichlorosilane instead of the hydrocarbon organosilane to produce gradients both on smooth and porous Si-wafer surfaces. Petrie et al. attributed the higher speed of a water droplet with volumes of 4 to 12 μl moving on such surfaces to the low friction of the fluorinated surfaces. Even higher speeds were observed on a porous surface. This increase in speed in comparison with the speeds on the smooth surface was attributed to the air trapped in the holes beneath the droplet on the porous surface, which cannot be wetted by the moving droplet, and thus the friction between the droplet and the substrate surface was significantly reduced. As reported in the paper, the CAH of fluorosilane modified surfaces was much higher than that of the hydrocarbon organosilane modified surfaces. They only discussed the frictional effect on droplet movement based on their experimental results while neglected the effect of the CAH. 13

31 2.1.2 Analysis In practical conditions, the liquid droplet moves on the gradient surface either induced by thermal gradient or wettability gradient, and both the Reynolds number (the ratio of inertial to viscous force) and the capillary number (the ration of surface tension to viscous force) are very small (<< 1). Therefore, its motion can be treated as a Newtonian flow. Motivated by cell spreading and motion on a solid surface, Greenspan 26 analyzed the movement of a small viscous droplet on a gradient surface using a lubrication approximation, which assumed the gravity effect on the deformation of the droplet shape is negligible and the contact angle is small. Greenspan further assumed that the velocity of the fluid (U) at the contact line is directly proportional to the difference between the dynamic contact angle θ d and the static contact angle θ s, or U = K ( θ θ ), under a 1 d s condition that θ θ is much smaller than θ s, where K 1 is a constant. d s In the case of a droplet creeping on a coated wettability gradient surface, Greenspan assumed that the equilibrium contact angle, θ e, has a linear relationship with the position, x, θ ( x) = θ (1 λx) 2-1 e s and that the gradient steepness ( λ << 1) is assumed to be very gradual. The final expression of the droplet velocity, assumingθ θ, could be given as: d θ θ = λθ R 2-2 e s s 14 e

32 and U = K1λθ s R 2-3 where R is the base radius of the droplet. The above expression clearly suggests that increasing the droplet size or the gradient steepness will facilitate the droplet movement. In a real condition, θ e does not vary linearly with the position, and also the CAH is nonzero and must be taken into account. Brochard 15 is the first to theoretically and systematically study droplet motion induced by thermal or chemical gradients on a solid surface. The thickness of a droplet in the study is less than the Laplace length so that deformation due to gravity is negligible. For a droplet moving on a chemical (wettability) gradient surface with a small gradient steepness, the total force acting on the droplet is balanced by two forces at the liquid/solid interface. One of them (called driving force) is directly related to the gradients of the liquid/solid interfacial energies, the other (called hydrodynamic drag force or viscous force) is the integral of the viscous stress over the base area of the droplet. The former is expressed, as shown in equation 2-4, based upon the variation of the interfacial free energy change, while the later can be written in equation 2-5 based on the lubrication theory (when the contact angle is lower than 30, under which the droplet can be treated like a thin liquid film, the velocity profile is the same as that derived from the classic hydrodynamics with no-slip boundary condition) at the liquid/solid interface with the noslip boundary condition: f d 2 dθ e = ( γ SL γ SV ) B ( γ SL γ SV ) A = 2γ LVθ e R( ) 2-4 dx 15

33 f v B dx U R = 3η U = 6η ln( ) 2-5 A h( x) θ e x min Where f d : the driving force per unit length f v : the viscous force per unit length U: the average velocity of the droplet γ: the surface tension (here, S designated as solid, L as liquid, and V as vapor) η: the viscosity of the liquid h: the thickness of the droplet, h = x / tanθ Thus, in the absence of the CAH, the velocity of droplet (U) can be derived by setting f d (equation 2-4) equal to f v (equation 2-5), and the expression (equation 2-6) clearly shows that U increases linearly with both droplet radius (R) and gradient steepness (dθ e /dx). Brochard 15 also found that the velocity of the droplet increased with the increase of the base radius of the droplet and the gradient steepness. In addition, the droplet velocity at the advancing edge is a function of liquid properties such as viscosity and surface tension. U 2 γ LVθ e R dθ e = ( ) 2-6 R dx 3η ln( ) x min Where θ e : the equilibrium contact angle R: the base radius of the droplet dθ e : the gradient steepness dx 16

34 R : the ratio of the length scale of the droplet to the cut-off (slip) distance from x min the contact line The velocity (U) of the droplet used in the equation is the velocity of the flow patterns advancing in the ridge with small contact angles or of nearly flat films. She ignored to report the expression of droplet velocity in the receding edge, and omitted the discussion on how the possible expression of the droplet velocity could be when the contact angle is relatively large. Daniel and Chaudhury 7;21 expanded Brochard s 15 analysis on droplet motion on a wettability gradient surface by taking into account the effect of the CAH on the droplet movements. Following Brochard, 15 they assumed the cosine values of the advancing and receding contact angles vary linearly with the position within the range of the base diameter of the droplet. The total force (F D F H, here, F H is the force resulted from the CAH) acting on the droplet can be integrated over the entire periphery of the droplet to give equation 2-7: F D 2 d cosθd FH = πr γ 2γR(cosθr 0 cosθa0) 2-7 dx 1 where cosθ d = (cosθ a + cosθ r ), and θ r0 and θ a0 denote the receding and advancing 2 contact angles at the center of the droplet, respectively. At a steady state, the viscous force, under the lubrication approximation, is ln( R / x ) F 3ηπ min v = RU 2-8 sinθ 17

35 Equating ( F F D H ) to F v yields an expression for the steady-state velocity of the drop as: U γ sinθr d cosθ d 2γ sinθ (cosθ r0 cosθ a0 ) = 2-9 3η ln( R / x ) dx 3πη ln( R / x ) min min When the driving force due to the free energy gradient is balanced by the CAH force, the critical droplet radius can be estimated by equation Below this value, the droplet does not move. πr 2 c d cosθ dx d = cosθ r0 cosθ a Since the driving force increases with the contact area while the drag force increases with the perimeter of the contact, they proposed that the steady-state velocity of the drop, in d cosθ d terms of capillary number ( Ca = Uη / γ ), increases linearly with R* ( R* = R ) as dx d cosθ Ca = K R d = K dx 2 2R * 2-11 The coefficient K 2 is a constant and depends on the mode of the relaxation of stress singularity at the three-phase contact line. But in their experimental study, the contact angle values (within range of 45 to 65 ) were larger than the required value (θ < 30 radian) of the lubrication approximation. Subramanian et al 45 derived the hydrodynamic force experienced by a sphericalcap droplet moving on a solid surface by using two approximate analytical solutions and predicted the speed of the droplet on a wettability surface under the quasi-steady state condition. One solution is to rely on the wedge approximation for a two-dimensional 18

36 Stokes flow in the cylindrical coordinates. Based on the simplifications (small capillary, negligible Reynolds and Bond numbers, and air as the displacement fluid) from the equation given by Cox (1986), 79 who studied the displacement of one fluid by another immiscible fluid on a solid surface, the final expression of the hydrodynamic force and the speed of the droplet can be obtained in equations 2-12 and 2-13 when the wedge angle is small. Apparently, the hydrodynamic viscous force is closely twice of that predicted by Brochard 15 while the velocity is half of that predicted by Brochard. 15 F v U 6πηUR 2R = ln( ) 2-12 θ x min 2 γ LVθ e R dθ e = ( ) R dx 6η ln( ) x min Another solution is based on the lubrication approximation. 45 The results of expressions of the hydrodynamic viscous force and the droplet velocity are slightly different from those predicted by using the wedge approximation. Both experimental and theoretical studies of droplet movements on a wettability gradient surface showed that droplet velocity increases with the droplet base radius. A critical droplet size exists in all cases and can be estimated from the CAH. When Ca is plotted against R*, the CAH only affects the intercept value on the R* axis while the interfacial friction affects the slope of the plot, which is dependent on the mode of the relaxation of stress singularity at the three-phase contact line. 19

37 A completely different view of the droplet motion behavior was proposed by Gao and McCarthy. 52 They suggested that droplets can move (1) by sliding, in which water molecules near the solid surface are exchanged with the interfacial ones and the bulk of the droplet remains stationary with respect to itself as a reference, (2) by rolling, in which water molecules at liquid/solid interface exchange with the interfacial ones and all other water molecules in the droplet rotate with movement, or (3) by the combination of these two extremes. The degree of contribution to droplet movement by each of these two extreme modes depends on the surface chemistry and topography. Also, they suggested that a water droplet needs to either advance or recede along the entire three-phase contact line before it starts to move. This means that when the CAH is not zero, a change in the shape of the droplet from a spherical cap is required, which would likely result in the increase of the liquid/solid and the liquid/vapor interface areas. Although several researchers, 7;15;19-21;33;38 as mentioned above, have studied droplet movements on organosilane wettability gradient surfaces, no direct observations on how a droplet moves on a wettability gradient surface have been reported. Droplet movements on an inclined surface could provide some insights to the understanding of the droplet motion behavior on a wettability gradient surface, since the only difference of the droplet movements on these two types of the surfaces is the source of the driving force acting on the droplet. On a wettability gradient surface, the driving force arises from the energy gradient while on the inclined surface it comes from the gravitational force. On the other hand, many researchers, 53-56;58;60-62;65;66;70;71;74;80-93 who studied the fluid flow on a solid surface, have found that a strong slip at the liquid/solid interface 20

38 does occur at micro- and nano-scales. In the following subsections, droplet movements on an inclined solid surface are discussed followed by the slip phenomena of the fluid flow on a solid surface. 2.2 Water Droplet Movements on Inclined Solid Surfaces The motion behavior of a droplet on an inclined solid surface 12;24;31;34;37;39;94-96 is similar to that on a wettability gradient surface; the only difference is the source of the driving force acting on a droplet as mentioned above. It has been proposed that a droplet moving down a tilted surface could have just one of the three motion modes: rolling, sliding, slipping, or could be the combination of all three Experimental Studies Allen and Benson 12 in 1975 studied water drop movement on an inclined glass plane. In their experiments, a water drop less than 1 cm in diameter was placed on a horizontal glass plate, which was then inclined until the drop started to move down the plate. Their observations were mainly made by naked eyes and showed that the drop initially accelerated rapidly as it traveled approximately one-drop diameter, and then attained a dynamic equilibrium by moving smoothly down the plane. The surface streamline pattern in a moving drop and the vortex motion in a moving drop head were interpreted by Allen and Benson as the drop may slide at the liquid/solid interface while the fluid inside rolls. They also stated that whether the drop at the advancing side rolls or slides may well depend on the advancing contact angle being greater or less than

39 The motion of a water droplet on an inclined hydrophilic surface, with both the advancing and the receding water contact angles less than 25, was also investigated by Huethorst et al. 94 The experimental observations showed that the advancing perimeter became slightly narrower than the receding perimeter at very low moving speeds. At high speeds, an extensive elongation in the direction of the movement took place with a contracting receding perimeter and an expanding advancing perimeter. They found that for low speeds, the droplet speed increased linearly with sine values of the tilted angle, regardless of the droplet volume, and the CAH increased with the drop speed. Several researchers studied droplet movements on an inclined surface with the surface wettability from partially wettable to non-wettable. Sakai et al 96 is first to apply polystyrene indicator particles to directly observe the internal fluidity of a water droplet during its motion. Their experimental observations clearly showed that the droplet fell at high velocities by slipping on the superhydrophobic surface with a contact angle of 150, while both slipping and rolling occurred during motion down along a normal hydrophobic surface with a contact angle from 100 to Also, the distance traveled by the advancing edge of the water droplet was quite close to that traveled by the receding edge of the water droplet. This suggested that the droplet retained its shape during movement. In fact, they did not observe rolling of the indicator particles within the droplet, but only the movement of particles at the liquid/solid interface. Indicator particles inside the droplet remained still with respect to the droplet during movement. 22

40 Kim et al 30 performed experiments to measure the steady velocity of partially wetted viscous drops moving down an inclined solid surface. In their experiments, ethylene glycol, glycerin, and a mixture of glycerin with water (80/20 wt% ratio) were used, and polycarbonate was used as the solid surface. The equilibrium contact angles of ethylene glycol, glycerin, and the mixture of glycerin/water on the surface were 70.2, 78.1, and 73.6, respectively. In the plot of the traveling distance of glycerin droplet versus time, linear relationships were obtained for both the advancing and the receding contact lines, which moved with the same pace. Also, the velocity of the drop increased with the inclined angle when the volume of the drop was held constant. They did not specifically point out the motion mode of the drop, but the surface wettability and their experimental observations were quite similar to ours. On the inclined non-wettable solid surface, Nakajima et al 34 investigated water droplet movements by using a solid surface treated with octadecyltrichlorosilane. The experimental results showed that, with the same inclined angle of 15.1, the sliding acceleration of a water droplet increased with the droplet weight or droplet volume. As the driving force (F D ) (part of the gravitational force) increased linearly with the droplet weight (i.e. volume), the resistant force (F H, due to the CAH) only increased with the increase of the contact line or droplet volume to a 1/3 power. The increase of the droplet weight resulted in the increase of the acceleration force (F D F H ) at the initial condition. The motion acceleration of water droplets was also investigated by Suzuki et al 97 as the droplets moved on an inclined surface coated with fluoroalkylsilane and octadecyltrimethoxysilane following Nakajima et al. 34 They found that after a short time 23

41 the droplet motion reached a steady state with a constant velocity and apparent droplet length was slightly increased (less than 8%) as the velocity of the droplet was increased Theoretical Analysis In addition, except the above experimental studies, theoretical studies of the droplet movements were also investigated by many researchers. Huethorst et al 94 theoretically investigated the motion of a water droplet on an inclined hydrophilic surface. They found that the minimum force needed to overcome the CAH is: F min = γ (cosθ cosθ ) 2-14 LV w r a Where, w is the maximum width of the deformed droplet perpendicular to the direction of the applied force F min. In this analysis, the viscous force resulting from the flow resistance within the droplet due to the liquid viscosity can be split into two parts: the viscous stress near the droplet perimeter and the viscous stress in the bulk of the droplet. Based on the lubrication approximation, they integrated both parts separately and stated that the former part gave the dominant contribution as long as half of the length of the droplet in the moving direction was smaller than the Laplace length. The final expression of the viscous force is given in equation 2-15, where the dynamic contact angles of the droplet change with the droplet speed. F v 2R 1 1 = 3η U ln( )( + ) 2-15 x θ ( U ) θ ( U ) min r a Dimitrakopoulos and co-workers 98;99 had published two papers on the analysis of liquid droplets moving down an inclined surface. In their first paper, 98 Dimitrakopoulos 24

42 studied a two-dimensional droplet on a solid surface with low-reynolds-numbers through a series of numerical computations. The gravitational force normal to the solid boundary has a significant effect on the displacement process; the forces reduce the critical shear rate for a viscous drop and increase the rate for a low viscosity droplet. In their second paper, 99 Dimitrakopoulos et al used the numerical computation method to study threedimensional droplet movement on an inclined solid surface. The relevant parameters included the Bond number (the ratio of the gravitational force to the interfacial force), the inclination angle, the advancing and the receding contact angles. They found that the critical conditions for drop displacement are sensitive to the values of the contact angles. Elsherbini 22 conducted experiments with two liquids and eight surfaces to investigate the geometric change of a droplet during movement on an inclined solid surface. The results showed that the contact-angle variation along the circumference of a droplet was best fitted by a third-degree polynomial with respect to the azimuthal angle. The droplet contour can be described by an ellipse with the aspect ratio increasing with Bond number. In their next paper 100 modeling droplet shape, it was found that simplifying the droplet shape to a spherical cap can lead to up to 75% error in dropletvolume prediction. In their third paper, 101 retention force for a droplet is found to be insignificantly affected by the aspect ratio of its contour. The Bond number is found to be constant for a given surface and liquid. When a droplet moves on an inclined superhydrophobic surface with a contact angle over 150, the general understanding is that the droplet moves by rolling instead of 25

43 sliding (slipping is also found by some researchers), which is verified both by experimental observations and theoretical analysis. But this is different from observations by Sakai et al, 96 which showed that a droplet slips down a superhydrophobic surface. In their paper, the sample surface has already been tilted and a rapid increase in the droplet velocity resulted when a droplet was placed on the surface. In their earlier paper, 34 they proposed that the rolling mode was the plausible one for the droplet movement if the surface is gradually tilted and the droplet gradually moves from a stationary state. In another example, Gogte et al 102 found that on textured inclined surfaces drops roll faster than on a coated un-textured surface at the same tilted angle and a reduction of drag force of 10% or more resulted. Richard et al 40 and Mathadevan et al 32 found that viscous droplets roll on a tilted non-wettable solid surface. Many researchers studied droplet movements or droplet spreading on a solid surface in terms of the movement of the three phase contact line. 14;15;17;25;28;30;31;35;36;39;45;47;59;79;98; They suggested that the contact line motion obeys the slipping mode in order to avoid the singularity. In the case of a drop spreading on a horizontal plane, Reznik et al 39 proposed that the drop spreading was almost fully governed by the effect of gravity and rolling motion occurred at the contact line. On the other hand, in the case of drop spreading on an inclined surface, the rolling motion near the leading contact line sets in when the slope angle exceeds a certain threshold value and the drop develops a bump near the leading contact line while a long tail emerges. 26

44 Droplet motion on an inclined surface is significantly influenced by the surface properties, but so far, no common understanding of the droplet motion mode is accepted. For a small contact angle, both sliding mode and rolling mode were proposed (some suggested rolling only occurs at the contact line); while for a large contact angle the mode of rolling and/or slipping was generally accepted. Since in our cases the contact angle ranges from 90 to 30, the analysis based on the lubrication approximation may not be suitable to our cases. 2.3 Boundary Slip of Fluid Flow on Solid Surfaces The classic fluid-dynamics assumption of no-slip boundary condition (the velocity of a viscous flow vanishes near the stationary solid surface) is generally satisfactory in dealing with most viscous flow of continuum fluids. This assumption remains questionable at the nano/microscopic scale. It has received new attention recently as engineering applications (e.g., micro-fluidic device) reach down to the micrometer and nanometer scale, and as the diagnostic technique improves our ability to probe the physics of fluid-surface interactions at the molecular scale. At the nano/microscopic scale, surface effects on fluid flow are inherently more important and the surface slip is no longer negligible. Recent experimental results 53-58;62;65;86;102; have shown that a strong slip at the wall at the microscopic scale was observed and the degree of the slip depends on several fluid/solid interfacial parameters (e.g. wettability and the roughness of the solid surface). These observations were also reinforced by the molecular dynamics simulations. 59;60;66;87;106 27

45 Boundary slip 60 is usually described in terms of a slip length, which is defined as the linearly extrapolated distance into a solid surface at which a no-slip condition would hold true. The influence of the slip boundary condition leads to a bulk effect (e.g. plug flow). Therefore, it is unnecessary to directly measure the flow at/near the boundary; instead, one can use the bulk measurement to verify that the flow is parabolic and extrapolate to the boundary to obtain the correct slip condition. Although there is considerable disagreement regarding the existence of slip over a hydrophilic surface, it is generally believed that surface hydrophobicity aides slip (a large slip resulting from superhydrophobic surfaces have been experimentally and theoretically verified), while the exact mode is yet to be completely understood. Many studies have reported that hydrophobic surfaces allow a noticeable slip ranging from nanometers to a micrometer in slip length. Several modes for fluid slips over hydrophobic surfaces have been proposed, including a decrease in viscosity at the boundary layer and a gas gap or nano-bubbles at the liquid/solid interface Experimental Studies Recently, surface force apparatus (SFA) has been used by several researchers to study slip phenomena on both a smooth surface and a rough surface. Baudry et al 80 applied SFA technique to experimentally study the hydrodynamic force between a sphere and a plane immersed in glycerol. They found that the hydrophobic surface showed a slip length around 38 nm while for the hydrophilic surfaces the slip is zero. Similar studies by Zhu and Granick 92;116;117 were carried out for water against a methyl-terminated surface. The experimental results showed that slip length (in tens of nm) depends strongly on the 28

46 approach rate and the surface wettability. The study by Bonaccurso et al 82 showed clearly an enhanced slip length at the wall as roughness increased, and a very large slip length was reported on the order of hundreds of nanometers. Another technique, particle image velocimetry (PIV), is frequently applied to study slip phenomena on a solid surface at nano/micro scales. Fluorescent spheres, having a density similar to water and a diameter of around 200 nm were used. In this technique, the velocity profile is determined from the motion of a collection of the fluorescent particles in an interrogation area. Tretheway et al 70;71 applied this technique to measure the velocity profile of water flowing through micrometer-scaled and hydrophobic channels, they found that the slip velocity was approximately 10% of the free-stream velocity and yielded a slip length of approximately 1 μm. For a clean and hydrophilic channel, the measured velocities were consistent with the no-slip boundary condition. They proposed that their experimental results indicated that the assumption of no-slip boundary condition at the micro-scale may not be accurate, and may depend upon the interaction between the fluid and the wall surface. In a separate study by Joseph and coworkers 63;64, their noticed that the slip length was below 100 nm, and was independent of the shear rate. Huang et al 85 applied three-dimensional total internal reflection velocimetry to directly measure the slip velocity of the fluid over a hydrophilic surface and a hydrophobic surface (octadecyltrichlorosilane coated glass). Their experimental results indicated that slip is minimal at low shear rates but increases slightly as the shear rate 29

47 increases for water flowing over a hydrophilic surface, while the surface hydrophobicity is observed to induce a small slip velocity with the slip length reaching close to 100 nm. Choi et al 55;56 examined the slip effect of water flow in hydrophilic (SiOx) and hydrophobic (OTS treated) microchannels of 1 to 2 μm depth. They found that slip length varied around approximately 30 nm for the flow of water over hydrophobic surfaces at a shear rate of 10 5 s -1, while over the hydrophilic surfaces the existence of slip remains uncertain. When they 55 applied a conventional microfabrication technique to modify the solid surface to maximize the slip under practical conditions. They found a large slip of the fluid (a slip length around 20 μm for water flow) resulted on nanostructural hydrophobic surfaces and two-third of drag reduction was expected for water Theoretical Analysis Nearly two hundred years ago, Navier proposed a general boundary condition that incorporates the possibility of fluid slip at a solid boundary. The description widely accepted by many researchers of the slip velocity of fluid at a liquid/solid interface is assumed to be proportional to the shear stress at the surface v σ ( r, z) η dv x s2 = Ls = Ls ( ) z= 0 dz 2-16 Where v s2 is the interfacial velocity, σ is the shear stress at the solid surface, L s is the slip length, η is the liquid viscosity, and dv/dz is the shear rate. This equation receives its most fundamental justification when applied to slip at a gas-solid boundary. It is one of the slip modes based on the assumption of the existence of a very thin gas gap between 30

48 the liquid and the solid surface. Near a stationary solid surface, randomly moving gas molecules collide with the surface and lose any directional bias they may have had. However, during the time between collisions, an imposed shear stress can transmit a mean momentum to the gas adjacent to the surface, and in a rarefied gas this can result in an appreciable slip velocity. In the description of the hydrodynamic viscous force 59;67;71;114 at the liquid/solid interface, many researchers presented the following equations when a spherical solid with a radius of R approaches a molecularly flat surface. F v 2 6πUηR = f * 2-17 h D D 6L f * = [(1 + )ln(1 + ) 1] 3L 6L D s 2-18 This condition is valid for small separation distances, h<<r s, where U=dD/dt is the approach velocity, η is the liquid viscosity, f* is a correction factor due to the slip (for no-slip boundary conditions f* = 1, otherwise f* < 1), and L s is the slip length. The above equations show that if the slip occurs at the interface, then the hydrodynamic viscous force is less and the liquid can move more easily. At the nano/micro scale, surface effects on fluid flow are inherently more important and the surface slip can no longer be negligible. Although the real mode of slip is not fully understood, it is generally believed that the surface hydrophobicity aids slip. The slip phenomenon not only helps avoid the singularity at the three-phase contact line 31

49 in the study of the contact line motion of a droplet (many researchers assumed that slip is present at the contact line even if on the rest of the contact area no-slip boundary condition is applicable), but also reduces the liquid/solid interfacial friction force. Regardless the droplet moves on a wettability gradient surface and on an inclined surface with or without slip at the interface of liquid/solid, the contact angle hysteresis (CAH) and the interfacial friction are the two main factors to affect the droplet movements. In the following sections, both the CAH and the interfacial friction are discussed. 2.4 Contact Angle and Contact Angle Hysteresis (CAH) Both contact angle and CAH are the surface properties of a solid surface, and can be estimated by using the contact angle measurements. More discussion on these two is presented below Contact Angle When a small amount (e.g. microliter) of liquid is placed on a solid surface, it forms a droplet (if the droplet does not completely spread), whose shape is determined by the liquid volume and the properties (e.g. surface tension and viscosity) of the liquid and the solid surface (e.g. surface free energy and roughness) at the equilibrium condition. If 1 the base radius of a droplet is smaller than the capillary length κ (Laplace length, for water is about 2.7 mm), 15 the gravitational effect on the droplet shape is negligible, otherwise the droplet would be flattened. 32

50 1 κ = γ ρg 2-19 where κ -1 : the Laplace length γ: the liquid surface tension, ρ: the liquid density g: the gravitational acceleration. The contact angle (Figure 2-1) at a given point on the three-phase contact line is the angle between the tangent plane to the liquid and the liquid/solid interface. Values of Probe liquid γ LV γ SV θ γ SL Substrate Figure 2-1. A sessile drop of a probe liquid with a finite contact angle (θ) on a solid surface. the contact angles are directly related to the system free energy. As the apparent contact angle approaches the equilibrium contact angle, θ e, the free energy of the system reaches a local minimum. If the surface is ideal (smooth, planar, rigid, insoluble, and chemically homogeneous), the equilibrium contact angle is equal to the Young s angle, which can be estimated from the Young s equation (equation 2-20). This equation is based on the 33

51 force balance between the interfacial tensions at the three-phase contact line formed by solid, liquid, and vapor (Figure 2-1). γ LV cos θ = γ γ 2-20 e SV SL where θ e : the equilibrium contact angle, γ LV : the surface tension of liquid, γ SV : the surface tension of the solid, γ SL : the surface tension of liquid/solid interface. As clearly shown in equation 2-20, the Young s contact angle depends only on the physical-chemical natural of the three phases (solid, liquid, and vapor) and is independent of gravity. The contact angle value of a solid surface directly represents the surface wettability, so that a surface with a contact angle of greater than 90 is generally considered as a highly non-wettable surface, ranging from 90 to 60 is non-wettable surface, ranging from 45 to 30 is a partially wettable surface, and less than 10 is considered as a wettable surface. On a heterogeneous surface with two chemical components, Cassie 118 proposed the following equation to describe the contact angle: cosθ = f + f θ cosθ1 2 cos 2 where f 1 and f 2 are the area fraction of each component, f + f 1, with equilibrium 1 2 = contact angles θ 1 and θ 2. If the chemical heterogeneity is not in the form of discrete patches but rather is of atomic or molecular dimensions, then van der Waals and 34

52 electrostatic forces theories indicate that it is not the cohesion energy that should be averaged but the polarizabilities, dipole moments, or surface charges of the surface. Thus, a new equation was proposed by Israelachvili et al 119 to replace the Cassie equation for the two-component and chemically heterogeneous surfaces with atomic or molecular scale patches: ( 1+ cosθ ) = f 1(1 + cosθ1) + f 2 (1 + cosθ 2 ) Contact Angle Hysteresis (CAH) In a real situation, the exact equilibrium contact angle is neither the Young s contact angle nor the measured static contact angle, but varies slightly from these angles. If the liquid is carefully withdrawn from the liquid drop with a micro-syringe, the drop decreases in volume while maintaining the same contact area until the drop begins to recede with a constant contact angle, θ r, this is called the receding contact angle. The receding contact angle illustrates the characteristic of the surface chemistry and topography. On the other hand, if the liquid is carefully and gradually added to the liquid drop with a micro-syringe, the drop increases in volume while maintaining the same contact area until it begins to advance with a constant contact angle, θ a, which is the advancing contact angle. The advancing contact angle is normally greater than the receding contact angle, and the difference between the two angles is defined as the contact angle hysteresis (CAH). Pease 120 first suggested in 1945 that the CAH is a 1-D issue, affected only by the contact line structure. According to de Gennes, 107 the CAH is related to non-idealities 35

53 such as surface roughness, surface contamination or heterogeneity, and film formation caused by solute deposited from the liquids, which may either enhance or reduce the hysteresis. But the origin of this phenomenon has not yet been fully understood. This has stimulated extensive research to understand the cause and the meaning of the CAH. Gao and McCarthy 52 viewed the CAH from the perspectives of the three-phase contact line and of the kinetics of contact line motion. If one droplet is placed on a horizontal surface and moves by some reason from one location to another with the same contact area, the droplet must change its shape from a sphere cap. As a result, the liquid/vapor interfacial area increases and the drop moves with advancing in the front side of the droplet and receding in the rear side, unless the hysteresis is zero. During this process, the entire three-phase contact line is involved in motion, and the necessary shape change can be regarded as an activation barrier to motion. The advancing and the receding contact angles are formed through the shape change of the droplet. Therefore, the CAH is the reflection of the activation energy required for the movement of a droplet from one metastable state to another on a surface. Fadeev et al 121 investigated the CAH on surfaces chemically grafted with various trialkylsilanes, and they found that the CAH is a function of alkyl group structure and bonding density related to flexibility and rotational mobility of alkyl chains. Well-packed rigid surfaces exhibit low hysteresis while those surfaces with flexible alkyl chains exhibit high hysteresis. Water contact angles on these surfaces (θ a /θ r ~ 105 /94 ) are found to be independent of chain length, which indicate that methyl groups on these surfaces are projected toward the probe fluid and prevent water (polar) from penetrating 36

54 the monolayers and interacting with residual silanols. For the non-polar probe liquid, the phenomenon is just reversible. The surface roughness and the packing density of organosilane molecules at the molecular level on these surfaces are responsible for the observed hysteresis. In their next paper, 122 they investigated the effects of trichloroalkylsilane and dichloroalkylsilane on the CAH. They found that a full surface coverage of dichloro-alkylsilane resulted in less hysteresis than those of trichloroalkylsilane. This result was attributed to the rigid cross-linked structure formed by trichloroalkylsilane at the molecular level. In summary, the property (roughness and structural heterogeneity) of surfaces modified with organosilanes influences the CAH. The existence of the CAH leads to the shape change of a droplet during its motion process. As described in 2.1and 2.2, the CAH plays a significant role in a droplet movement (major resistance force). Another resistance force for droplet to move is the friction at the liquid/solid interface. 2.5 Friction at Liquid/Solid Interfaces Friction is one of the oldest problems in physics and has tremendous practical significance. Generally, there are three types of frictions: normal friction, boundary friction, and interfacial friction. Normal friction 87;88; is described by Amonton s law: F f = μf load, where F f is the friction force, F load is the normal load, and μ is the friction coefficient. Boundary friction usually occurs when a thin boundary layer with a thickness of about a few nanometers exists between shear surfaces. Such friction is determined by the contact area, interfacial rheology, mechanical and structural properties 37

55 of the surfaces. Interfacial friction was introduced by Homola et al 129 to describe the situation when sliding occurs between undamaged, molecularly smooth surfaces with well-defined surface area. In the case of a liquid flowing on a solid surface, only interfacial friction occurs at the liquid/solid interface. Yoshizawa et al 126;127 stated that interfacial friction for a liquid flowing on a liquid-like monolayer increases with increasing sliding velocity. At a steady state, for liquid films confined between two planar surfaces with an area of A d and a separation distance of D, the hydrodynamic drag force (F v ) for a Couette flow during sliding at a velocity of U is given by 126;127;130 F = A ηu D 2-23 v d / Studies of friction, wear, and lubrication have always been motivated by the need to reduce energy losses and material degradation in moving mechanical devices. All complex phenomena that occur between interacting surfaces include the formation of interfacial bonds, adhesion, structural rearrangement in solid and liquid during shear, and hydrodynamics of a liquid film. In the case of a liquid flowing on a solid surface, the reduction of the interfacial friction can be carried out by changing the solid surface properties (e.g. roughness, wettability). As described earlier in 2.3, the expression of the hydrodynamic viscous force shown in equation 2-17 was derived by many researchers and the correction factor f* is related to the degree of slip. For a clean and smooth hydrophilic surface (f* = 1), slip 38

56 phenomenon usually does not occur; while on the hydrophobic surface (f* < 1), the slip occurs at the micrometer or nanometer scale. The degree of the interfacial friction reduction depends on the degree of slip. Ou et al 118;131 experimentally observed a significant drag reduction for laminar flows of water through the micro-channels having hydrophobic surfaces and well-defined micro-sized surface roughness. When the fluid contacts only a very small fraction of the solid surface due to the micro-structure, an almost shear-free interface was resulted. The liquid/solid interfacial friction depends on the properties of the liquid and the solid surface, and is proportional to the contact area and the fluid velocity as indicated in equation Decreasing the surface wettability will not only decrease the contact area of a droplet and a solid surface, but will also increase the slip velocity at the interface of liquid/solid, which results in the reduction of the interfacial friction. The CAH and interfacial friction are both related to the properties of the solid surface. Organosilanes are widely applied for modifying hydroxylated substrate surfaces, such as silicon wafer and glass. In the following section, organosilane modified surfaces will be reviewed. 2.6 Organosilane Modified Surfaces Organosilanes are widely applied for modifying hydroxylated surfaces such as SiO x, Al 2 O 3, glass, and mica, due to their chemical, mechanical, and thermal stability. 39

57 Such modification does not alter the bulk properties of the substrate. Therefore, organosilane modified surfaces have tremendous applications in many fields Formation of Organosilane Self-Assembled Monolayers Organosilane couple agents generally have a common formula of R-(CH 2 ) n -SiX 3, where R is a organofunctional group (-CH 3, -NH 2, -SH, -CF 3, etc.) at the end, and X is a hydrolysable group (e.g. -Cl, -OCH 3, and -OC 2 H 5 ). The general formation mode of organosilane self-assembled monolayer (SAM) 7;8;19-21;33;34;38;55-58;65;66;75-77;83;95;96;102;114;121;122; is shown in Figure 2-2. The organosilane molecules first are hydrolyzed to generate hydroxyl groups through the reaction with water, which is present either in an organic solution, in air (moisture), or in a thin layer of water on the substrate OH OH OH OH Cl Si Cl Cl H 2 O Hydrolysis HO Si OH OH Silicon Wafer Adsorption H H H HO Si O O Si O O Si O O Si OH O H O H OH H O H H H O O OH O Silicon Wafer -H 2 O Condensation O O O HO Si Si Si Si O O OH OH O Silicon Wafer Figure 2-2. Schematic of formation of the organosilane self-assembled monolayer (SAM) on Si/SiO 2 substrate. The organosilane molecules are first hydrolyzed, and then chemically adsorbed on the hydroxylated solid surface through condensation reaction with release of water molecules. It is possible that the condensation reaction might take place between organosilane molecules at the same time. 40

58 surface. Next, hydrogen bonds are formed between the hydroxyl groups in organosilane molecules and those on the substrate surface and/or possibly among the organosilane molecules. The further condensation reaction occur to release a water molecule and form a Si-O-Si bond with the long tail (carbon chain) pointing to air. The formation of different organosilane SAMs has been extensively studied, as well as the factors affecting their formation,such as moisture, 132 solvent, 158 temperature, 139;159 and substrate Deposition Techniques The most commonly used techniques (Figure 2-3) to deposit organosilanes onto a solid surface are solution deposition, 136;139 vapor phase deposition, 7;19-21;33;38;160 and contact printing (CP). 75;76;78 In solution deposition, a certain concentration of silane solution substrate silane or mixture substrate (a) (b) PDMS stamp ink substrate (c) Figure 2-3. Schematic of organosilane deposition techniques: (a) solution deposition, (b) vapor phase deposition, and (c) and contact printing (CP) 41

59 organosilanes is prepared using a suitable organic solvent, and the clean substrate is immersed in the solution for a certain amount of time. In vapor phase deposition, pure organosilane or its mixture with mineral oil is used and the deposition is carried out in a closed chamber under a heating or vacuum condition. For CP, a silicone stamp is wetted by an organosilane solution, upon drying of the solvent; the stamp is brought down into contact with the cleaned substrate for a period of time, allowing organosilane molecules to transfer from the stamp onto the substrate surface to react with the silanol groups on the surface through the condensation reaction mentioned above. The modification can be carried out either at room temperature or at an elevated temperature while the deposition times may vary to achieve the desired surface coverage of organosilane. The SAM of an organosilane exhibiting remarkable stability can be achieved through reactions occurring between the substrate silanol groups and the organosilane molecules and/or among the organosilane molecules. Therefore, the wettability of organosilane-modified surfaces can be easily changed by choosing a proper organosilane as well as the deposition time. As reported, the vapor deposition method gave a relatively lower CAH compared to solution deposition. In comparison with the solution and the vapor phase deposition methods, a closely packed organosilane SAM generated by the CP technique can be achieved within a few minutes and this technique is convenient, reproducible, inexpensive, and more importantly, less waster generation. 42

60 2.6.3 Generation of Wettability Gradient Surfaces One approach of generating wettability gradient surface is to deposit a monolayer of organosilane onto the substrate. A diffusion-based method from either a solution or a vapor phase is commonly used. The scale of the gradient surface using the diffusionbased approach normally ranges from millimeters to centimeters. For the vapor phase deposition, organosilanes that have high vapor pressure and well-controlled deposition conditions are needed. For the solution-based deposition, a large amount of organic waste is generated. As a result, the contact printing (CP) based technique is desired. CP has been successfully applied to generate OTS gradient surfaces. 75;78 In particular, a curved elastomeric silicone (i.e. PDMS) stamp is inked with OTS/hexane solution, and then brought into contact with a substrate. After the initial contact, the curved stamp (Figure 2-3 (c)) can be slowly pressed down further to make more contact with the substrate, and the contact area increases as the corresponding contact time decreases. The area with a longer contact time has more OTS molecules transferred and grafted to the surface, while the area with a shorter contact has less OTS molecules. As a result, a gradient coverage of OTS, whose molecule contains a hydrophobic CH 3 terminal group, consequently a wettability gradient surface, is created. By changing the stamp size, the speed of pressing the stamp during contacting, and using different curved surfaces, various wettability gradient sizes, gradient steepness, and gradient geometries can be generated by the contact printing based approach, 43

61 2.6.4 Characterization of Organosilane Modified Surfaces Some common techniques used for characterization of the organosilane modified surfaces, include contact angle measurement, scanning probe microscopy (SPM) or atomic force microscopy (AFM), and XPS. Both contact angle measure and AFM can verify the OTS surface coverage; AFM images of organosilane-modified surfaces also provide the formation mode of the organosilane film. For the contact angle measurement, three types of liquid contact angles are used to describe the surface properties: the equilibrium contact angle, static contact angle, and dynamic contact angle. The dynamic contact angle, which includes the advancing and the receding contact angles, is more important than the other two when studying liquid droplet motion on a solid substrate surface. Therefore, this technique is frequently used to characterize the organosilane-modified surfaces used in our study. To summarize this sub-section, organosilane molecules can be readily hydrolyzed and then react with the silanols groups on an oxidized substrate (e.g. SiO x ) surface to form a closed-pack self-assembled monolayer. Compared to the solution and vapor deposition techniques, the CP technique is a more convenient to modify substrate surfaces. By carefully choosing the proper organosilane, stamp size and contact printing speed, wettability gradient surfaces with variable gradient sizes can be generated by CP technique. The quality of the organosilane-modified surfaces is normally assessed by contact angle measurements and AFM, and sometimes complemented by XPS. 44

62 CHAPTER III EXPERIMENTAL In the study of water droplet movement on organosilane modified surfaces, several organosilanes and related organic chemicals used will be described in 3.1. The procedures to modify silicon wafer surfaces and surface characterization techniques will be introduced in 3.2. The experimental procedures to conduct water droplet movements (3.3 on an inclined surface and 3.4 on wettability gradient surface) on a substrate surface and the approaches for data analysis will also be provided in this chapter. 3.1 Materials and Equipment In this section, all materials used in the study are presented below in detail and followed by the relevant equipment Materials n-octadecyltrichlorosilane (OTS) (95%), n-octadecylmethyldichlorosilane (OMDS) (95%), n-octadecyldimethylchlorosilane (ODCS) (95%), dimethyldichlorosilane (DDS), and (heptadecylfluoro-1,1,2,2-tetrahydrodecyl) trichlorosilane (FTS) (details about the compounds are summarized in Table 3.1) were purchased from Gelest, Inc. and used as received. The solvents (detailed information is provided in Table 3.2) used for the 45

63 Table 3.1. Physical properties of organosilanes used in this study Name Abbreviation MW a 20b D 4 perfluorodecyl-1h,1h,2h,2h-trichlorosilane (CF 3 (CF 2 ) 7 (CH 2 ) 2 SiCl 3 ) FTS n-octadecyltrichlorosilane (CH 3 (CH 2 ) 16 CH 2 SiCl 3 ) OTS n-octadecylmethyldichlorosilane (CH 3 (CH 2 ) 16 CH 2 SiCl 2 (CH)) OMDS n-octadecyldimethylchlorosilane (CH 3 (CH 2 ) 16 CH 2 SiCl(CH) 2 ) ODCS N/A dimethyldichlorosilane (DDS) (CH 3 ) 2 SiCl 2 DDS a Molecular weight (g/mol) b Specific gravity measured at 20 C or otherwise indicated in the table (g/cm 3 ) Table 3.2. Physical properties of organic and inorganic reagents used in this study Sample cleaning Sample generation Contact angle measurements a Molecular weight (g/mol) b Density (g/cm 3 ) Name MW a ρ b Water content Company Concentrated H 2 SO 4 (98.5%) N/A N/A Fisher H 2 O 2 (30%) (ACS Grade) N/A 70% VWR Hexane (ACS Grade) 98.5% min N/A EMD Chemicals Inc. Toluene- ACS Grade, 99.5% min N/A DI water in house purified (conductivity less than 0.1 omh) Hexane-HPLC Grade DI water in house purified (conductivity less than 0.1 omh) methylene iodide (99%) % % % N/A EMD Chemicals Inc. in house purified Fisher Scientifics in house purified Sigma- Aldrich 46

64 study were HPLC-grade hexane for preparing organosilane solutions, and ACS-grade hexane and ACS-grade toluene for cleaning samples. Other chemicals, also summarized in Table 3.2, used in our study included concentrated (98.5%) H 2 SO 4, 30% H 2 O 2, demonized (DI) water, and methylene iodide. The silicone elastomer, used for fabricating stamps, was a two-component (a base elastomer and a curing agent) Sylgard 184 from Dow Corning Corp. The silicon wafer (SW) used in the studies was P (100) test wafers obtained from Silicon Quest International Equipment A micromanipulator (model 3926M with x-y axis transducing, from Parker Automation) incorporated with an in-house modified electric motor was used for CP. The cleaning equipment included a UV/ozone cleaner (model 42 from Jelight) and an ultrasonic cleaner (model 50HT from VWR). The micro-syringes used for contact angle measurements were from Gilmont Instruments, and the measurements were carried out with a Rame-Hart goniometer (model ) equipped with a digital CCD camera that connected directly to a desktop computer. An infinite tube microscope and a JAI microscope were used to observe the contact printed areas during the CP process and also used for following water droplet movements. Holmes HM485-U2 Ultrasonic Humidifier was used to generate cool water mist for droplet movement studies. Droplet motion was recorded on a videotape using a Sony VCR (model SLV-N80), which is capable of recording up to 30 frames/s. Both real time images and images played back from the VCR tape were captured using a Dazzle digital video creator and its software. 47

65 3.2 Preparation of Organosilane Surfaces As reviewed in Chapter 2, organosilanes are suitable for modifying oxidized and subsequently hydroxylated surfaces of solid substrates (SiO 2 on Si, Al 2 O 3 on Al, glass, mica, etc.). As mentioned in 2.6.2, the CP technique (Figure 2-3), with the use of an elastomeric stamp, can be used to generate organosilane modified surfaces; the detailed procedure to generate the homogenous and gradient organosilane surfaces by using this technique is described below Poly(dimethylsiloxane) (PDMS) Stamp Fabrication First, the elastomeric stamps were fabricated from silicone (polydimethylsiloxane, PDMS) elastomer by mixing Sylgard 184 elastomer base and its curing agent with the normal ratio of base/curing agent of 10/1 by mass. For softer stamps, a slightly less curing agent ratio was used. Several types of masters (their preparation is detailed later), as shown in Figure 3-1, were used to generate stamps with a curved surface. For planar stamps and stamps with a spherical cap having the radius of curvature of less than 5 mm, the master was a large piece of silicon wafer treated with FTS. For semi-cylindrical stamps, masters bearing a radius of curvature in millimeters to centimeters were cut from a glass tube and then its ends were closed by flat glass slides. The mixture of Sylgard 184 base and the curing agent was thoroughly mixed and degassed and then poured into a plastic weighing dish containing masters and/or molds placed on the bottom of the dish. For relatively small hemispherical PDMS stamps with 48

66 (a) (b) (c) Figure 3-1. Schematic illustration of various types of PDMS stamp fabrications. (a) Fabrication of a planar PDMS stamp in a plastic Petri dish, in which a FTS modified SW was placed face up on the bottom. (b) Fabrication of a cylindrical shape of PDMS stamp. The inner surface of the cylindrical mold was modified with FTS prior to the fabrication of PDMS stamps. (c) Fabrication of small sizes of the hemispherical PDMS stamps. A drop of PDMS solution with a certain volume was placed on a FTS modified flat SW surface by a micro-syringe, a hemispherical cap was resulted. All the PDMS stamps were cured for 48 hours at room temperature or 2 hours at 160 C following by extraction in toluene at the reflux condition in Soxhlet extractor for 3 hours and drying at ambient conditions. 49

67 a radius of curvature less than 5 mm, drops of the silicone mixture were individually placed on a FTS modified SW surface. Due to the low surface energy of FTS, the PDMS drop forms a spherical cap on the FTS surface. After the mixture was cured at ambient condition for 48 hours or 160 C for 2 hours, the stamps were peeled off from the masters or the FTS surface. All the fabricated stamps were extracted in ACS-grade toluene in a Soxhlet extractor for 3 hours to remove the un-crosslinked PDMS chains, and allowed to naturally dry inside a loosely capped glass petri-dish inside a fume hood for at least 48 hours to completely remove toluene prior to use. As mentioned above, the masters are critical for the preparation of various shapes of the PDMS stamps. In order to easily remove the cured PDMS stamps from these master surfaces, the surfaces of these masters were modified with a low surface energy organosilane, i.e. FTS, in a solution or a vapor. For the solution deposition, the freshly cleaned masters were immersed into 2 ~ 5 mm FTS/HPLC-grade hexane solution for 1 hour. The solution was decanted, and the FTS modified surfaces were thoroughly rinsed by ACS-grade hexane. Then, each individual sample was sonicated in ACS-grade hexane for 2 minutes to further remove the unreacted organosilane molecules from the surface, and dried with a stream of N 2 gas. While for the vapor phase deposition, 200 mg of FTS was added to 3 g of mineral oil in a glass vial and then thoroughly mixed. The mixture was poured into a plastic weighing dish and placed inside an empty glass desiccator. The desiccator was evacuated to a pressure of ca. 10 mtorr and maintained at that pressure for 30 minutes to completely remove air bubbles trapped in solution. Then, a cleaned and oxidized master was suspended (by attaching to a glass slide using double-side scotch 50

68 tape) face down across the plastic weighing dish approximately 1 cm above the degassed solution. The assembly was evacuated again to the same pressure and maintained for 1 hour. After the organosilane-treated silicon wafer was removed from the desiccator, it was rinsed with ACS-grade toluene and sonicated in ACS-grade toluene for 2 min. The sample was then dried with a stream of N 2 gas Substrate Cleaning Silicon wafers (SW) were cut into 1 cm 1 cm pieces and immersed in a freshly prepared Piranha solution, which consists of seven parts of the concentrated H 2 SO 4 and three parts of 30% H 2 O 2, both by volume. A half hour later, the solution was poured out, and the SW substrates were rinsed thoroughly with deionized water. The cleaned SW substrates were dried under a stream of N 2 gas and then exposed to ultraviolet/ozone (UV/O cleaner model 42, Jelight) oxidization for 6 min immediately prior to the deposition of organosilanes. The entire cleaning process provided silicon wafers with clean and oxidized surfaces containing mainly Si-OH groups on the surface Homogeneous Wettability Surfaces via Contact Printing To generate a uniform surface coverage of OTS via CP, one or two drops of 2 mm OTS/HPLC-hexane solution were added, using a glass pipette, onto a 1 1 cm planar PDMS stamp so that the OTS solution completely covered the stamp surface. After a few seconds, the solution was drawn out by a Kimwipe, and the inked stamp was dried with a stream of N 2. Then the stamp was brought into complete contact with a cleaned and oxidized silicon wafer for a particular duration (1, 10, 30, 60, 80, or 120 s) under slight 51

69 finger pressure. After a specific contact duration, the stamp was removed and thoroughly rinsed with ACS hexane, dried with a N 2 stream, and cleaned with a piece of Scotch tape to remove loose organosilane and possible dust prior to next use. Each stamped SW wafer was stored, individually, inside a polystyrene Petri dish and kept under ambient condition for 1 hour to provide sufficient time for the organosilane molecules to reactto the wafer surface. Then, each individual sample was sonicated in ACS-grade hexane for 2 minutes to remove unreacted organosilane molecules, and dried with a stream of N 2. OTS CP was carried out under ambient conditions in all cases in our study (~24 C, and 40 60% relative humidity). For OMDS and ODCS CP, the CP process and conditions were similar as OTS CP except the CP temperature, which ranges from room temperature to 60 C. The CP was conducted on a hot plate, the surface temperature of which was well-controlled at each required temperature. In order to ensure that the temperature of the hot plate maintained constant during the CP process, the hot plate surface was heated slowly to a required temperature and maintained at that temperature for about a hour prior to placing cleaned and oxidized SW substrates onto the hot plate, and the SW substrates were kept on the hot plate for about 10 minutes prior to CP. Each SW substrate was removed from the hot plate right after CP and stored in a plastic Petri dish for 1 hour. In addition, a hemispherical PMDS stamp was also used to produce homogeneous organosilane modified surfaces. The hemispherical PMDS stamp was brought into contact with the SW surface with a certain contact area (e.g., 100 μm in radius) for a 52

70 certain amount of time (i.e. 30 s). These homogeneous organosilane surfaces were used as comparisons to the gradient organozilane surfaces as well as to evaluate the organosilane diffusion effect on the quality of the organosilane modified surface Wettability Gradient Surfaces via Contact Printing To generate a radially continuous gradient surface of organosilane, an in-housebuilt setup, as shown in Figure 3-2, was used. The inked hemispherical PDMS stamp with organosilane was adhered, with its flat surface, onto a glass cantilever, which was attached to a micromanipulator. The stamp was gradually brought down towards a cleaned SW substrate by an electric motor, which also was attached to the micromanipulator, and eventually made contact with the substrate. The contact area was increased as the stamp continued to move down. The various scales and steepness of the organosilane gradient surfaces can be generated by changing the motor speed (dz/dt) and/or the size of the hemispherical stamp (related to its curvature). The entire contactprinting process, primarily the variation of the contact area as a function of contact time, was monitored through an optical microscope video system coupled with a CCD camera, and videotaped using a Sony VCR for data analysis later. As a result, the contact area can be monitored and precisely controlled. The treatments of the stamped samples are the same as those with uniform organosilane coverage generated with planar stamps. Radially stepwise gradient surfaces of organosilanes were also generated using the same setup, but the inked hemispherical PDMS stamp was manually pressed down 53

71 To the electric manipulator Z S 0 R L (a) (b) Figure 3-2. (a) Schematic illustration of the generation of a continuous gradient surface by CP of an inked hemispherical elastomeric PDMS stamp. The stamp was secured onto a rigid support (i.e. glass slide), which was attached to an electric driven micromanipulator. As the micromanipulator traveled down, the stamp first made contact with a cleaned and oxidized silicon wafer, and then gradually increased the contact area while the contact time from the center outward decreased. The longer the contact the more molecules were transferred and deposited on the surface. By using OTS or OMDS as the ink, an energy gradient with least wettability at the center and most wettability near the edge was achieved. (b) Schematic illustration of the dimensions used in the text to describe the droplet movements on a radial gradient surface (the largest circle). A water droplet (white circle) with a radius of R is located at a distance L away from the edge of the gradient. S 0 represents the distance of the CP region produced by gradually decreasing the contact time from the inside out by a constant speed of the manipulator traveled down, while the inner dotted circle represents the CP region produced by jump-to-contact and unsteady-state speed. stepwisely to increase the contact area. For each step of CP, the contact time and the step size were precisely controlled through the microscope video monitoring system. For the laterally continuous or stepwise gradient surface, a semi-cylindrical PDMS stamp, instead of a hemispherical PDMS stamp, was used. The other conditions were the same as using the hemispherical stamp. For all the samples prepared by CP, the total contact time was 47 s. OTS CP was carried out at ambient condition while OMDS CP was conducted at 50 C. 54

72 3.2.5 Wettability Evaluation via Contact Angle Measurements The modified SW surfaces with uniform coverage of organosilanes were first examined with contact angle measurements via the sessile drop method. Both the D advancing and the receding contact angles of DI water ( γ = 22.0 mj/m 2 P, γ = 50.2 mj/m 2, γ L = 72.2 mj/m 2 D ) and methylene iodide ( γ = 48.5 mj/m 2 P, γ = 2.3 mj/m 2, L L L L γ L = 50.8 mj/m 2 ) on the uniform organosilane covered surfaces were measured. Four images of advancing (θ a ) and receding (θ r ) angles on two randomly chosen spots of each sample were taken using image capturing equipment (Dazzle DVC, Dazzle media) and contact angles on both sides of the drop were measured using the Scion Image software. For the organosilane-modified surface via CP, a calibration curve, which described the relationship between water contact angle and contact time, was first obtained from the homogenous samples generated by CP using planar stamps. In order to more precisely determine the gradient surface wettability, a modified gradient surface of OTS, with a gradient size of about 4 mm was also used for contact angle measurement via the sessile drop method (Experimental results were shown in B-2 in Appendix). The water drop was slowly dragged in stepwise from the hydrophobic side to the hydrophilic side along the gradient, and at each particular position the advancing and receding angles of the water drop were measured. All the measurements were performed under ambient conditions (1 atm, ~24 C). 55

73 3.3 Water Droplet Movement on an Inclined Solid Surface In the study, water droplet movement on an inclined organosilane modified surface was conducted. The experimental setup, and data collection and analysis are described in detail in the following Experimental Setup OTS surfaces with different wettability (contact time of 1, 5, 10, and 30s) were chosen to investigate the water droplet movement on inclined OTS surfaces, where the gravitational force is the driving force to overcome the resistance force arisen from the CAH and the viscous force. In order to visualize how the water droplet moves on solid surfaces with different wettability, polystyrene tracer particles with density of 1.05 g/cm 3 were suspended in the water drop. The experimental setup (Figure 3-3) of drop movements on an inclined surface mainly included two OM (one for the top and the other for the side to view the droplet movement), two video recording systems, two monitors for visualization, and a manipulator. The manipulator was connected to one end of the supporter plate while the other end was fixed. The manipulator lifts the unfixed end of the supporter plate to tilt the sample surface, which was fixed face up on the supporter plate. Therefore, the lifting speed of the supporter plate could be controlled. Various sizes of water droplets (volume ranging from 35 μl to 70 μl) were carefully placed on one end of a horizontal surface using a micropipette and remained on the surface for a short period of time (few seconds) until random movements of all PS particles inside the water droplet ceased. Then as one 56

74 end of the sample surface remained fixed, the other end, with the water droplet on it, was gradually lifted using the manipulator until the water droplet just started to move down along the inclined surface. Under this condition, the inclined angle is defined as the sliding angle or critical incline angle. The surface was lifted gently so that the PS particles remained relatively still inside the droplet and the external force caused by connected to manipulator and 2: OM 3 and 4: video recorder 5 and 6: monitor 7: a water droplet 8: sample surface 9: supporter plate Figure 3-3. Schematic illustration of the experimental setup to observe water droplet movement on an inclined homogeneous organosilane surface. The organosilane sample surface was placed face up on a glass slide using the double-side Scotch tape. A water droplet with PS particle (40 μm) inside was first carefully placed on the horizontal sample surface using a micropipette and then the sample surface was gradually tilted using a micro-manipulator until the water droplet started to move down along the inclined surface. There were two OM for the simultaneous observation of the water droplet movement on an inclined surface from the top view and the side view separately. Each OM was connected to one monitor with a video recording system which was used to record the droplet movement. Side view of the droplet also showed the tilted angle and the cross-section shape of the droplet while the top view provided the shape of the threephase contact line. 57

75 lifting on the droplet could be minimized. Under this condition, the inclined angle was slightly higher than the critical inclined angle so that the droplet could achieve a certain speed (e.g., mm/s) Data Collection and Analysis Every sample surface was characterized by water contact angle. The average value of the advancing and the receding contact angles was used as the dynamic contact angle (θ d ) and the difference between the advancing and the receding contact angles was assigned as the CAH for this specific surface. By playing back the videotape, the motion of PS particles either inside the droplet or at the interface of liquid/solid can be obtained. The pictures of the water droplet motion were taken frame by frame from the playback video. The travel distances (x ad and x re ) with respect to the advancing and receding edges of the water droplet (Figure 3-4) could be directly measured along the x-direction as well as the distance traveled by the particle at the liquid/solid interface. The traveling distances (X, and Z in Figure 3-4) of the PS particle inside the water droplet were also estimated. The absolute distances traveled by the droplet (advancing and receding edges) and the PS particles at the liquid/solid interface with respect to the substrate surface against the traveling time were analyzed separately while in the meantime the relative distance traveled by the PS particle inside the droplet with respect to the droplet against the traveling time were also analyzed. The PS particle movement inside a droplet would reflect the internal flow behavior, while the PS particle movement at the liquid/solid interface reflected the fluid flow behavior at the interface. Through a series of 58

76 experiments, the effects of the surface wettability, inclined angle, and the droplet size on the droplet movements and the motion mode of the droplet would be obtained. When a drop moves on an inclined solid surface, at a steady state, the sliding velocity (U sld ) profile no longer changes with time, and the slipping velocity (U slp ) is a constant, thus the relative movement of the particle with respect to the drop is contributed by rolling. In the experiments, the velocities of rolling and slipping are estimated by deducing the particle velocity at the air/liquid interface and liquid/solid interface, respectively. On the other hand, the average sliding velocity of the water drop can not be directly obtained, thus the sliding velocity is estimated by subtracting the velocities of rolling and slipping from the average drop velocity. Based on the model of the internal fluidity of a spherical capped drop as proposed by Sakai et al 51 by using the average rolling velocity (U ra ) as half of the maximum rolling velocity (U rmax ), the following equations are resulted. U = U + U + U 3-1 d ra sld slp U = U max + U + U 3-2 p r sld slp U r max = 2U ra 3-3 Where U d and U p are the average drop velocity and the particle velocity at the air/liquid interface, respectively. Then, the average rolling velocity (U ra ) of the drop can be obtained and is shown in Eq Therefore, the degree of each component (rolling, sliding, and slipping) can be estimated in term of the velocity fraction of each component. In the practical estimation of rolling velocity, if a particle appears beneath the air/liquid 59

77 interface with a certain distance, the rolling velocity of the particle is converted to the rolling velocity (U rmax ) at the air/liquid interface. U U = U 3-4 p d ra X Z y x z x re x ad Figure 3-4. Schematic illustration of a water droplet moving on an inclined surface. The pictures of the water droplet motion were taken frame by frame from the video. For each picture like this shown here, the distances (x ad and x re ) of the advancing and the receding edges of a droplet referred to one side of the frame in the x-direction were directly measured. The distances (X and Z) of the PS particle referred to the left edge and the top edge of the frame were also directly measured and can be easily converted into these in the x-direction and the z-direction based on the value of the inclined angle. 3.4 Water Droplet Movements on Wettability Gradient Surfaces In the study, water droplet movement on organosilane gradient surfaces were conducted. The experimental setup, and data collection and analysis are described in detail in the following. 60

78 3.4.1 Experimental Setup Water droplets in our study were formed by two methods. One was from the condensation of cold water mist, which was continuously generated by an ultrasonic humidifier. The droplet grew larger by adopting the condensed water from water mist and/or the coalescence of two or more neighboring droplets (usually smaller droplets). In this case, a wide size range of water droplets was produced and distributed randomly on the wettability gradient surface. Another method was to manually place a certain volume of water on the wettability gradient surface from a glass micropipette. This method could precisely control the droplet volume, but it was only suitable for a relatively larger size of a gradient surface (larger than 2 mm). Experimental setup in Figure 3-5 shows that the cold water mist was continually generated by the ultrasonic humidifier at a controlled flow rate, and distributed onto the substrate by an air current, flow in parallel to the substrate surface. The air current was also produced by the humidifier. As the cold mist was condensed on the surface, tiny droplets, in the shape of spherical caps with a base diameter of less than 5 μm, were formed. On the highly hydrophilic, noncontact-printed region, tiny droplets quickly spread out to wet the surface and merged with each other to form a thin continuous water layer. On the other hand, the droplets on the contact-printed area stayed beading up, and as more mist was deposited on the surface, the droplets grew in size and occasionally merged with neighboring droplets. During this process, various radii of droplets were found to move along the direction of the wettability gradient (i.e. from the less wettable region moves towards to the more wettable region). In the study, no water mist gradient 61

79 would need to be considered because the gradient size (< 1 mm in diameter) is much smaller than the area covered by the water mist (> 100 mm in diameter). The entire process of water droplet movements was monitored and recorded by an optical microscope video system. Plastic tubing 7.5 cm To the humidifier Optical microscopy Substrate with a gradient surface Supporter 3.5 cm Figure 3-5. Schematic illustration of the experimental setup to observe the droplet movement on a continuous organosilane gradient surface. The photograph of the actual experimental setup is shown in B-8 in Appendix as comparison. Cold water mist continually produced by the ultrasonic humidifier was perpendicularly directed to the supporter surface using plastic tubing with an inner diameter of ½ inch, and then radially flowed in parallel to the supporter surface after it hit the supporter surface. The solid arrows showed the directions of water mist. The outlet of the tubing was located ~ 7 cm above the supporter surface and ~ 3.5 cm to the left from the gradient surface. Under such constrains, only small amount of water mist from the humidifier can pass through the gradient surface, and the effect of airflow can be minimized. The behaviors (growth and movement) of water droplets on the gradient surface were monitored using an optical microscopy and video taped. Due to the limitation of the video format in our video recording system (allows only 30 fps), a high speed camera (Redlake PCI 2000, the frame rate: 60 to 4000 fps) was also applied to record the droplet movements on a wettability gradient surface and used as a comparison. The duration of the recording time, however, of this high speed camera 62

80 only lasted 2 seconds (the frame rate used in our study: 250 fps). In order to collect more data (up to a few minutes), the process became quite challenging, and only a limit amount of runs were conducted using the high-speed camera. The experimental results were shown in B-9 in Appendix. In order to evaluate whether the cold water mist has an effect on the water droplet movements on the wettability gradient surfaces, various sizes of water droplets (volume ranging from 200 nl to 750 nl) were carefully placed on a OTS gradient surface using a glass micro-needle with a inside diameter of 22 μm to observe their movement behaviors. The entire process of water droplet movements was again recorded using the optical microscope video system Data Collections and Analysis The recorded videotape was played back and the distance traveled by the droplet along the direction of the gradient was tracked frame by frame, and the velocity of droplet was estimated from the distance vs. time data. The drop size and drop location, on the gradient surface, were also determined from the still images of the moving droplet taken by using the Dazzle digital video creator and its software (Dazzle media). For the data recorded using the high-speed camera, the images of droplet movement on the gradient surface was also checked frame by frame. The traveling distance by a water droplet as well as the drop size (i.e. diameter) were measured, and the droplet velocity was estimated. 63

81 CHAPTER IV 3RESULTS AND DISCUSSION This chapter consists of four main sections. Section 4.1 discusses the effects of contact time on the surface wettability of organosilane modified surfaces. Section 4.2 describes various wettability gradient surfaces of organosilanes generated for the study. Section 4.3 discusses water droplet movements on wettability gradient surfaces, and section 4.4 investigates water droplet movements on inclined organosilane modified surfaces. 4.1 Effects of Contact Time on Wettability of Organosilane Modified Surfaces In this section, three different organosilanes (OTS, OMDS and ODCS) were chosen to investigate the effects of the CP time on the surface wettability of organosilanemodified surfaces. The experimental results are presented one by one Introduction Surface wettability is important for a solid substrate regarding to its applications in coating, adhesion, biomaterials adsorption, cell motion, and fluid flow. Tuning surface wettability can be achieved by many methods. One of the common methods is to modify 64

82 solid substrates (mainly hydroxylated surfaces such as SiO 2 on Si, Al 2 O 3 on Al, glass, mica, etc.) with a self-assembled monolayer (SAM) of organosilanes. One major advantage of using organosilane SAMs is their strong chemical, mechanical, and thermal stability, and the modification does not alter the bulk properties of the substrate. Therefore, organosilanes have been widely applied in fundamental research and practical applications. Organosilanes can be deposited onto a solid surface by solution deposition, vapor phase deposition, or contact printing (CP). The reactions between the organosilane molecules and the solid surface, for all the methods, usually occur at room temperature while the deposition times may vary to ensure the expected surface coverage of the organosilane can be achieved. In some cases, higher reaction temperature may be necessary, especially for organosilanes with a low reactivity at room temperature. The reactivity of organosilanes is affected by the ease of hydrolysis of the head groups and steric hindrance of organosilane molecules. In comparison with other two techniques, a closely packed organosilane SAM can be generated by CP within a few minutes, and this technique is convenient and inexpensive with reproducible results and minimum waste generation (a few milliliters per batch). The quality of the CP organosilane SAMs, however, is affected by many factors, 146 including the humidity of the reaction environment, the temperature at which the printing is carried out, the type and cleanliness of the substrate, the solvent used to prepare the ink, the vapor pressure of ink molecules, and the ink concentration. When the other parameters are remained, the surface coverage 65

83 of some organosilanes was found to be contact time dependent. 75;78 This provides us a means to tune the wettability of an organosilane-modified surface by varying the contact time. Three nonpolar organosilanes, octadecyltrichlorosilane (OTS), octadecylmethyldichlorosilane (OMDS), and octadecyldimethylchlorosilane (ODCS), were chosen to generate suitable wettability surfaces for the study. The three organosilanes are all terminated with methyl group and have 17 methylene units in their backbone; the only difference is the number of reactive head groups attached to Si. The reactivity of organosilane molecules, which is directly related to the number of the reactive groups, plays an important role in the organosilane SAM formation, especially the time it takes to achieve a specific surface coverage. In order to achieve a high coverage in less reaction time, it may be necessary to carry out the CP at elevated temperatures. The suitable experimental conditions to achieve a comparable surface wettability of these three organosilanes with a same CP time are first to be determined Reactivity of Organosilanes The molecules of monofunctional organosilanes (e.g. ODCS), having only one reactive group, the molecules can only graft to the surface via covalent bonding (Si-O- Si), and the grafting reaction is very slow. As a result, a long reaction time (several days) is necessary to achieve maximum bonding density. On the other hand, trifunctional organosilanes (e.g. OTS) are more reactive, and can be grafted to a surface with a relatively high surface coverage within tens of seconds to few minutes, 66

84 Most studies 121;122;140;146;147;149;150;159;161 investigating the formation of monolayers of mono-, di-, and trifunctional organosilanes were conducted in either solution or vapor, but not with the CP approach. As reviewed in Chapter 2, a closely packed organosilane SAM can be achieved by CP within a few minutes. However, the details of the contact time dependent layer formation, thus the wettability, for the three organosilanes, OTS, OMDS, ODCS, have not been investigated. Therefore, the CP results of the three organosilanes, as a function of contact time, were first reported. Both the advancing and the receding contact angles of water on the surfaces modified under ambient condition were measured and shown in Figure 4-1. It is found that both the advancing and the receding contact angles increase with the increase of contact time for each organosilane, while OMDS and ODCS gives a very slow pace of increase. With 120 s of contact, the advancing angle of OTS (103 ± 3 ) is very close to the documented value of the full coverage OTS from solution (103 ) or from vapor (104 ). 121;122 With the same contact time (120 s), the advancing angle of OMDS (72 ± 3 ) and ODCS (52 ± 3 ), on the other hand, are much lower than that of a fully covered layer ( ) generated from solution, which takes about 3 days at C. In addition, it is found that, with a same contact time, ODCS modified surfaces result in the smallest water contact angles amongst the three organosilanes. Therefore, in this study, we only evaluate the formation of OMDS layers generated using CP at higher temperatures, since the reactivity of ODCS is too low to achieve the desired surface coverage within our desired time frames of contact printing (a few minutes). 67

85 contact angle, θ ( ) contact time, t (s) Figure 4-1. The advancing (filled symbols) and receding (unfilled symbols) contact angles of deionized water on the organosilane modified surfaces. All the surfaces were generated by the CP technique at ambient conditions. The symbols of circular (, ), triangle (, ), and square (, ) denote OTS, OMDS, and ODCS, respectively. Both of the advancing (filled symbols) and the receding (open symbols) contact angles increase with the increase of contact time for each organosilane. ODCS modified surfaces show the smallest contact angle values followed by OMDS and then OTS at each contact time. 68

86 4.1.3 Determination of the Suitable Temperature for OMDS Contact Printing The self-assembled OMDS layer has shown to exhibit a low water CAH 121;122 with a full coverage. It is a good candidate, in addition to OTS, to be used for investigating CAH effects on water droplet movements. Since the OMDS molecules grafted slowly to a substrate under ambient conditions, a higher temperature that allows the contact printed OMDS surface, with the same amount of contact time, to have similar wettability as the OTS contact printed surface generated under ambient conditions is then determined. The CP of OMDS was carried out on a well-controlled hot plate at various temperatures, ranging from 25 C to 60 C. At each temperature (25 C, 40 C, 50 C, 55 C, and 60 C), six samples were prepared with different contact times (1 s, 10 s, 30 s, 60 s, 80 s, and 120 s). Each sample was removed from the hot plate immediately after the CP and stored inside a plastic Petri dish for 1 h under ambient conditions. After removing the unreacted OMDS molecules by sonication in ACS-grade toluene and properly drying with a N 2 stream, the surface wettability of all the samples was characterized using water contact angle measurement. The advancing and the receding contact angles of water of all samples are shown in Figure 4-2, which illustrates that the temperature has a substantial effect on the wettability of the OMDS modified surface. Both the advancing and the receding contact angles increase more rapidly with contact time at a higher temperature ( 50 C) and reach around 90 (θ a ) in less than 30s. This faster increase in water contact angle at a 69

87 water contact angle, θ ( ) contact time, t (s) Figure 4-2. Water contact angles of OMDS modified surface (filled for advancing contact angle, and unfilled for the receding contact angle) as a function of temperature at different contact times. The CP was carried out at 25 C (, ), 40 C (, ), 50 C (, ), 55 C (, ), and 60 C (, ). At each contact time, with a lower temperature, less OMDS molecules are transferred and less transferred OMDS molecules were grafted to the surface. Therefore, a lower water contact angle is resulted. However, with the highest temperature of 60 C, the water contact angle reaches about 97 C in about 10 s due to the fast reaction of OMDS molecules to the surface. 50 C is found to be the most suitable temperature for generating OMDS gradient surface with a reasonable increase of water contact angle as the contact time increases using the contact-printing method. 70

88 higher CP temperature is the results of the faster binding of OMDS molecules to the surface. Experiments conducted by Harada et al 146 show that CP of OTS at higher temperatures accelerates the deposition process and facilitates the diffusive transport and reactions with a substrate surface. The experimental results show that water contact angles of OMDS modified surfaces are higher for samples prepared at elevated temperatures. However, when the temperature is too high, such as at 60 C, there is little difference of the water contact angle when the contact time is longer than 10 s; even with an 1 s of contact, a relatively low wettability (advancing contact angle of water about 73 ) has already resulted at a temperature of 60 C. Comparing all of the water contact angles at each temperature, 50 C is considered as suitable to generate OMDS surfaces to have comparable wettability as those of OTS surfaces generated at room temperature via CP within the same CP time scale (0 to 120 s). The temperature effect on the formation of OMDS on a surface is consistent with the general kinetic reaction principal, in which the reaction rate increases with the increase of reaction temperature Octadecyltrichlorosilane (OTS) Modified Surfaces Previous studies 75;78 have clearly shown, from SPM scanning, that the surface coverage of OTS is CP time-dependent when the OTS surface is generated via the CP approach. Jeon and coworkers 148 used reflection absorption infrared spectroscopy (RAIRS) and atomic force microscopy (AFM) to investigate the effects of reaction times on OTS film structure by using CP. They found that the OTS layer growth follows island 71

89 formation, island growth, island coalescent, and finally the standing up of the OTS chains due to the sufficient lateral interactions between the chains. Choi and Newby 75 have confirmed the above results via AFM studies, as a result the surface wettability decreases with the increase of contact time. In our studies, OTS samples were prepared at 25 C as the contact time varied from 1 s to 120 s. Both the advancing and the receding contact angles of OTS modified surfaces, shown in Figure 4-3, increase with the increase of contact times. For the advancing contact angle, the relationship is found to be θ = 10.4ln( t) , and for the receding contact angles, it is θ = 10.0ln( t) These correlations between the r corresponding water contact angles and the contact times are used later to estimate the contact angles on OTS gradient surfaces. a The water CAH, or the difference between the advancing and the receding contact angles, of samples with different contact times is summarized in Figure 4-4. It is found that the water CAH of the OTS modified surface changes slightly with the CP time except for 1 s of contact when using the difference of between cosine values of the advancing and the receding contact angles to describe CAH. Fadeev and coworkers 121;122 proposed that the disordered structure of the methyl groups (the molecular topography roughness and rigidity) are responsible for the higher hysteresis. Figure 4-4 shows that the CAH increases to the maximum value at 60 s of contact, and then decreases slightly with the increase of contact time. AFM study 75 confirms that the most heterogeneous 72

90 contact angle, θ ( ) contact time, t (s) Figure 4-3. The advancing ( ) and receding ( ) contact angles of deionized water on the OTS modified silicon surfaces. The surfaces were modified by CP with inked planar PDMS stamps on the cleaned and oxidized Si-wafer under various contact times. The ink used for CP was 2 mm OTS in HPLC-grade hexane. The water advancing and receding contact angles on OTS modified surfaces increase with the increase of contact times with logarithmic relationships. The expressions are θ = 10.4ln( t) and θr = 10.0ln( t) for the advancing contact angle and the receding contact angle respectively. The error bars are the standard derivations of at least eight measurements on each type of surfaces, and three different samples of each type of surfaces are used. These empirical relationships between the water contact angles and the contact times are later used for estimating water contact angle values of various regions of gradient surfaces (from micrometer-scale to the millimeter-scale) based on the contact time for each region. 73 a

91 θ a -θ r ( ) cosθ r -cosθ a contact time, t (s) Figure 4-4. DI water CAH of OTS modified surfaces as a function of the contact time. Here, the CAH is expressed both in terms of the difference ( ) between the advancing and the receding contact angles, and in terms of the difference ( ) of the cosine value between the advancing and the receding contact angles. Both of these definitions are frequently used in literature under different situations. The CAH seems to be slightly affected as the contact time varied except for 1 s of the contact. 74

92 surface (with OTS islands grown to the size to be coalescent with each other) with the highest surface roughness is resulted at 60 s of CP Octadecylmethyldichlorosilane (OMDS) Modified Surfaces A fully covered OMDS layer has been shown to exhibit a low water CAH 122 as compared to that of OTS. For the OMDS samples prepared at ~ 50 C, the advancing and the receding contact angles (Figure 4-2) increase with contact time as θ = 8.5ln( t) and θ = 10.0ln( t) , respectively. These correlations between the corresponding r water contact angles and the contact times are also used later to estimate the contact angles on OMDS gradient surfaces. a The water CAH of OMDS of samples is summarized in Figure 4-5. It is found that the CAH of the OMDS modified surfaces decreases with the increase of CP time. The water CAH of the sample generated with 120 s of contact is comparable to the value reported of a fully covered OMDS surface. In addition, OMDS modified surfaces have smaller water CAH than OTS modified surfaces with the same contact times. Fadeev and McCarthy 121;122 proposed possible layer structures of alkylchlorosilanes grafted to SW surfaces. For the monofunctional silane, the molecule covalent attaches to the surface by chemical bonds because it has just one hydrolysable group. However, for the di- and trifunctional silanes, at least two hydrolysable groups are present; the Si-O-Si bonds are formed not only between organosilane molecules and the SW surface but also between organosilane molecules. As a result, the possible resulting 75

93 θ a -θ r ( ) cosθ r -cosθ a contact time, t (s) Figure 4-5. DI water CAH of OMDS modified surfaces as a function of the contact time. Here, the CAH is expressed both in term of the difference ( ) between the advancing and the receding contact angles, and in term of the difference ( ) of the cosine value between the advancing and the receding contact angles. The experimental results show that the CAH using both expressions decreases with the increase of the contact time except that of 1 s of the contact. 76

94 structures could be covalent attachment on SW surface with polymerization between the organosilane molecules in the horizontal and/or the vertical directions. The polymerization between the organosilane molecules would result in disordered structures (surface roughness, orientation of molecules). In addition, some hydroxyl groups in the organosilane molecules might remain free from forming any bonds with others. From the molecular structure of OTS and OMDS, an OTS molecule has one more reactive group (- Cl) than an OMDS molecule. The consequence of having more reactive groups in a molecule is more disordered structures of the resulting layer, rougher surface and less mobility, and may even be more hydroxyl groups remain intact. As a result, the CAH of OMDS is smaller than that of OTS. The longer contact time not only results in a higher surface density (reduction of silanol groups on the surface) but also leads to less exposure of the residual silanol groups to air. Increasing the surface density would also prevent the penetration of water molecules into OMDS thin film. That may be the main reason why the CAH of water of OMDS decreased with increasing contact time. Both the advancing and the receding contact angles depend on both the density of the non-polar and the polar components, but the density of the polar component influence more on the receding contact angle. For OTS surfaces generated by CP, the density of the non-polar component increases with the increase of contact time, while the density of the polar component may vary at a different pace due to more intact hydroxyl groups on the OTS surface at a longer contact time. As a result, it is possible that the CAH of OTS surface first increases rapidly and then at a slower pace as the contact time increases. 77

95 4.1.6 Summary Three different organosilanes (OTS, OMDS and ODCS) were chosen to investigate the effects of the CP time on the surface wettability of organosilane-modified surfaces. The experimental results indicate that the reactivity of the organosilane depends on the number of functional head groups and the reactivity of organosilane, after groups and the reactivity of organosilane molecules with a SW surface followed ODCS < OMDS < OTS, in agreement with expectations. ODCS is excluded for additional experiments due to its lower reactivity. Increasing the contact-printing temperature of OMDS allows the generation of comparable gradient surfaces as those of OTS with the same range of contact time. A suitable temperature for OMDS CP is found to be around 50 C. The water contact angles of OTS and OMDS modified surfaces increase with the increase of contact time. While the CAH varies slightly with the contact time for OTS, the CAH decreases with the increase of contact time for OMDS. Also, all OMDS modified surfaces have lower CAH of water than OTS modified surfaces. Therefore, both OTS and OMDS can be used to generate comparable wettability gradient surfaces to investigate the effect of the water CAH on the water droplet movements. 4.2 Wettability Gradient Surfaces of Organosilanes In this section, two comparable continuous as well as stepwise wettability gradient surfaces of OTS and OMDS were prepared by using contact printing technique described in Chapter III. 78

96 4.2.1 Introduction In the CP of organosilnae, an elastomeric PDMS stamp is first inked with organosilane, and then is brought into contact with a substrate surface for a certain contact time. The ink molecules transfer from the stamp to the substrate and graft to the substrate, and the longer of contact, the more molecules are expected to be transferred and grafted to the surface. When the increase of contact area, correspondingly the decrease of contact time, is controlled either continuously or step-wisely, gradient surfaces can be generated using the CP approach Gradient Surfaces of Octadecyltrichlorosilanes (OTS) Various sizes (65 μm, 131 μm, 400 μm, and 700 μm) of OTS continuous gradient surfaces were obtained. The total contact time of OTS gradient surface was 47 s while the later ~ 35 s allowed the gradual variation of the contact area or the contact size, S 0, during which the contact speed was a constant. The local wettability of OTS gradient surfaces is characterized by the cosine of the dynamic contact angle of water (θ d ) and shown in Figure 4-6. The cosθ d value decreases sharply in the range of 0 to 0.2 of L/S 0 (where L is the distance from the edge of the contact), and then decreases at a slower pace at greater L/S 0. The steep gradient (- dcosθ d /d(l/s 0 )) near the edge of the gradient surface will result in a significant difference 79

97 d(cosθ d )/d(l/s 0 ) cosθ d L/S L/S 0 Figure 4-6. cosθ d of an OTS gradient surface as a function of the dimensionless relative location, L/S 0. The inset plot shows the corresponding dimensionless steepness (- dcosθ d /d(l/s 0 )) of the gradient generated by the CP technique, the steepness initially decreases significantly with the increase of L/S 0 and then decreases with a lower pace as L/S 0 >

98 in the unbalanced Young s force, acting on a water droplet, in comparison with that of the same size droplet located closer to the center of the gradient surface Gradient Surfaces of Octadecylmethyldichlorosilanes (OMDS) The continuous OMDS gradient surface, with the gradient size (S 0 ) of 131 μmwas generated with the contact time increased from 0 s to about 35 s. The wettability variation (cosθ d vs. L/S 0 ) of the OMDS gradient surface is shown in Figure 4-7. The wettability variation of OMDS is similar to that of OTS. The OMDS gradient surface does give a slight greater gradient steepness (-dcosθ d /d(l/s 0 )) at a particular location (L/S 0 ), as a result, the droplet motion on the OMDS gradient surface might behave differently from that on the OTS gradient surface Step-wise Gradients Comparable, in terms of step width and gradient steepness, gradient surfaces of OTS and OMDS were generated. A representing stepwise OTS gradient surface with five steps is shown in Figure 4-8a in which the contact time from the center to the edge is 55s, 25 s, 15 s, 5 s, and 1 s and each step size is around 30 μm. The wettability gradient steepness (-dcosθ/dl) is ~ μm -1. A five-step stepwise gradient of OMDS (Figure 4-8b) is illustrated, the contact time from center to the edge was 80 s, 25 s, 10 s, 3 s, and 1 s and each step size is around 30 μm. The steepness (-dcosθ/dl) of the OMDS wettability gradients is ~ μm -1. These comparable stepwise gradients of OTS and OMDS are used later in the water droplet movement study to determine the effects of CAH. 81

99 d(cosθ d )/d(l/s 0 ) cosθ d L/S L/S 0 Figure 4-7. cosθ d of an OMDS gradient surface as a function of the dimensionless relative location, L/S 0. The inset plot shows the corresponding dimensionless steepness (- dcosθ d /d(l/s 0 )) of the gradient generated by the CP technique, the steepness initially decreases significantly with the increase of L/S 0 and then decreases with a lower pace as L/S 0 >

100 1.0 (a) cosθ L (μm) 1.0 (b) cosθ L (μm) Figure 4-8. Estimated advancing (solid line) and receding (dashed line) contact angles of water on the radial gradient surfaces generated step-wisely with five steps. (a) for OTS gradient surface, the contact time from center to the edge was 55 s, 25 s, 15 s, 5 s, and 1 s while (b) for OMDS gradient surface, the contact time from center to the edge was 80 s, 25 s, 10 s, 3 s, and 1 s. 83

101 4.2.5 Summary Comparable continuous as well as stepwise wettability gradient surfaces of OTS and OMDS were generated. The gradient steepness is much greater for both OTS and OMDS gradient surfaces, generated via the contact printing approach, at regions closer to the edge of the contact. This steeper gradient would lead to a greater driving force for the movement of a water droplet in comparison with that of the same size droplet located farther in on the gradient surface. 4.3 Water Droplet Movements on Wettability Gradient Surfaces Normally, liquid droplets exhibit two-dimensional random motions on a hydrophobic and homogeneous surface as they merge or coalesce. When a surface wettability gradient is created, the droplets will move along the gradient toward the region with higher wettability (higher surface energy) to minimize the system free energy. Droplet movements are influenced by many factors associated with liquid properties (viscosity and surface tension), solid surface properties (wettability, gradient steepness, and CAH), and liquid/solid interfacial properties (interfacial friction). Daniel et al 7;21 demonstrated that the main obstacle in drop movement on a solid surface arises from the CAH, which must be first overcome by the driving force resulted from the wettability gradient in order for the drop to move. Researchers 7;21;38 investigated droplet movements on an organosilane wettability gradient surface have found that droplet velocity is proportional to droplet size. The effect of the CAH is reflected to a critical droplet size, only above which the droplet can move. The effect of interfacial friction is 84

102 reflected to the slope of the Ca vs. R* plot. In our cases, other factors, such as the water droplet placement, or gradient steepness, may also influence droplet movement. In order to investigate water droplet motion behaviors on a variety of organosilane modified gradient surfaces, the properties of a particular location (due to the challenges in direct characterization of the small area) on the gradient surface are assumed to be the same as those generated using the same CP time via planar PDMS stamps. Also, no defect or disorder of organosilane SAMs at the molecular level is assumed. The velocity, radius, and location of each water droplet on a gradient surface are carefully measured from photo prints taken from the recorded video. Several factors (e.g. gradient steepness, CAH, interfacial friction, and placement of a water droplet) affecting the droplet movements are addressed Experimental Observations and Analysis As a cold-water mist is deposited to the gradient surface, tiny droplets are first formed everywhere on the surface and continue to grow through adsorption of water mist and/or coalescence of neighboring droplets. During each coalescence process, droplets quickly merge into a drop located on the higher wettability region, regardless the droplet size. This process would continue until the size of the newly formed droplet is large enough at the specific location to overcome the CAH force, and then the droplet starts to move toward the higher wettability region. For a droplet to move, the droplet located closer to the center of the contact area needs to be larger in comparison with one located near the edge of the contact area. 85

103 In the appendix, we reported that a diffusion zone is formed during and/or after CP, and the size of the diffusion zone decreases as the contact time decreases. For the gradient surface, the diffusion zone is anticipated to be much smaller than the contact area since the contact time decreases from the center (47 s) to the edge (0 s) of the contact. Experimental observations of droplet movements show that the diffusion zone is less than 10% of the contact area in each case, and after the cold-water mist continues to deposit onto the gradient surface for 10 minutes, the diffusion zone can no longer keep water from spreading. As a result, all the droplets collected in the study are located within the original contact printed area. As indicated in section 4.1.4, both the advancing (θ a ) and the receding (θ r ) contact angles of water were experimentally estimated and had the general relationship of: θ = a ln( t) b 4-1 a + θ = a ln( t) c 4-2 r + The gradient steepness, d cosθd, can be easily estimated as dl d cosθ dl = a(sinθ a + sinθ r ) 4-3 L d 1 where, L = kt ( k is the contact printing speed and t is the contact printing time) and cosθ d = (cosθ a + cosθ r )/2. In order to move a droplet on a solid surface, the driving force acting on a droplet must first overcome the resistance force due to CAH, which results in the critical droplet size. Below this value at a particular position on the gradient surface, the droplet cannot move. According to Daniel et al, 21 the critical droplet size can be roughly 86

104 estimated using equation 4-4, where the driving force due to wettability gradient is balanced by the CAH. R c d cosθ = d 2(cosθ r 0 cosθ ao ) / π 4-4 dl Substituting equation 4-3 into equation 4-4 leads to R c 2(cosθ r 0 cosθ a0 ) = L 4-5 aπ (sinθ + sinθ ) a0 r 0 Equation 4-5 indicates that the critical droplet size is position-dependent, as θ values are position dependent, and proportional to L Effects of Gradient Sizes For all different sizes of continuous gradient surfaces, the contact time varies from 0 s, at the edge of the gradient surface, to ~ 35 s, at the most inner region of the gradient to be considered for droplet movement studies. Thus, the gradient steepness d cosθd ( ) decreases as the gradient size (S 0 ) increases, and bigger droplets are needed to dl move on the larger gradient surfaces. Also, as R c is position-dependent, the radius (R) of a droplet moving on the wettability gradient surface is likely also depend on its location (i.e. L). Experimental observations (Figure 4-9) agree well with the above expectations. Experimental data of droplet movement on various gradient surfaces basically fall on the same curve with a positive intercept (around 0.04) on the R/S 0 axis, which is directly related to the minimum critical droplet radius (R cmin. ) of a water droplet on a wettability 87

105 R/S L/S 0 Figure 4-9. Relative radius of a droplet (R/S 0 ) on various sizes of gradient surfaces as a function of relative location of the droplet (L/S 0 ). The sizes of the OTS gradient (S 0 ) were 700 μm ( ), 400 μm ( ), 131 μm ( ), and 65 μm ( ). The experimental data obtained on all cases of OTS gradient surfaces fall on a same straight line, which has positive intercept values on R/S 0 axis. It suggests that the size of the droplet moving on gradient surface is position-dependant. 88

106 gradient surface. For each of our gradient surfaces, the gradient steepness is greater at regions located closer to curve with a positive intercept (around 0.04) on the R/S 0 axis, which is directly related to the R cmin of a water droplet on a wettability gradient surface. For each of our gradient surfaces, the gradient steepness is greater at regions located closer to the edge (see Figure 4-6), thus the R cmin, on a particular gradient surface, decreases as the droplet locates closer to the edge. The R cmin corresponds to the greatest gradient steepness on each gradient surface, and it increases proportionally with the gradient size. The velocity (Figure 4-10) of a water droplet is found to increase with droplet radius. Previous studies have found that the velocity of a droplet moving on a wettability gradient surface increased linearly with droplet base radius (R). When a linear correlation of the velocity vs. R/S 0 for each gradient size is drawn, a similar positive intercept (~ 0.04) on the R/S 0 axis is noticed,while the slopes are 32.3 s -1, 20.0 s -1, 3.2 s -1, and 1.9 s -1 for the gradient size (S 0 ) of 700 μm, 400 μm, 131 μm, and 65 μm, respectively. In previous theoretical studies, 7;15;19;21;33;45 droplet velocity was mainly derived based on the lubrication approximation, in which, the common no-slip hydrodynamic boundary condition was applied. Recent studies have found that the no-slip boundary condition might not be applicable for fluid flow on a solid surface at a micro- and/or nano-scale, especially on a hydrophobic surface. Even on a completely wetting surface, the slipping phenomena are still observed under high shear rate at the micrometer scale. The degree of slipping is likely dependent on the viscosity of the liquid, the roughness of a solid, and the interaction between the liquid and the solid. When excluding the slipping 89

107 15 velocity (mm/s) R/S 0 Figure Velocity of a water droplet on various sizes of gradient surfaces as a function of relative radius of the droplet (R/S 0 ) under water mist condition on gradient surfaces. The sizes of the OTS gradient (S 0 ) were 700 μm ( ), 400 μm ( ), 131 μm ( ), and 65 μm ( ). Total contact time was 47 s while about 35 s is needed for the length of S 0 for all different cases. The experimental data obtained show rough linear relationships of the drop velocity against R/S 0 with the same intercept values, but different slopes that increase with the increase of the gradient size. 90

108 velocity at the liquid/solid interface, the velocity of a droplet is proportional to the droplet base radius Effects of Contact Angle Hysteresis (CAH) Daniel et al 21 found that even small differences in CAH could have significant effects on the liquid droplet velocity. Experimental force measurements by Suda et al 77 also verify that the CAH plays one of the major roles in droplet movement. Since the OMDS modified surface has lower water CAH than the OTS modified surface, using comparable gradient surfaces of OMDS and OTS allows us to evaluate the CAH effect on droplet movement. When plotting the dimensionless droplet velocity, or the capillary number (Ca), against the normalized droplet radius (R*), the intercept on the R* axis represents the CAH effect while the slope reflects the interfacial friction effects. 21,38 In most previous studies, 7,21,38 the gradient steepness is basically constant in the studied range of gradient size. However, in our cases, the gradient steepness is positiondependant (Figures 4-6 and 4-8). To achieve a better comparison, only droplets located within a small range of L, where the gradient steepness is basically a constant, are used and the L range having very close values of dcosθ/dl of the two types of gradient are selected. Figure 4-11(a) shows droplet movements on the continuous gradient surfaces of OTS and OMDS having an S 0 of about 130 μm. By treating Ca vs. R* with a linear relationship, the linear lines (slope 1.0E-04) for the two gradient surfaces seems to be 91

109 2.0e-4 (a) 1.5e-4 Ca 1.0e-4 5.0e R* 2.0e-4 (b) 1.5e-4 Ca 1.0e-4 5.0e R* Figure Droplet velocity, in terms of Ca, as a function of R* (R*=R dcosθ d /dl) on OTS and OMDS gradient surfaces. (a) is for the continuous gradient surfaces ( and denote the OTS surface and OMDS surface, respectively), while (b) for the stepwise gradient surfaces ( and represent the OTS surface and OMDS surface, respectively). 92

110 parallel, but the intercept values on the R* axis are and 0.003, respectively, for the OTS and OMDS gradient surfaces. The lower intercept for the OMDS gradient surface is the result of the lower CAH of OMDS. This suggests that the same sized water droplet likely moves more easily on the OMDS gradient surface than that on the comparable OTS gradient surface. Also, due to the similar molecular structure of OTS and OMDS, the interfacial friction between water and these two surfaces is likely comparable, leading to the similar slopes of the Ca vs. R* curves. Figure 4-11(b) shows droplet movements on the stepwise gradient surfaces of OTS and OMDS with a S 0 of about 125 μm. Again by treating Ca vs. R* with the linear relationship, the similar results are obtained. Thus, regardless of the gradient type, a lower CAH of the gradient surface facilitates droplet movements on the surface. However, the intercept values on the R* axis for both the OTS and OMDS gradient surfaces seems to be un-reasonable as compared to the values reported by others. One possibility for smaller intercept values obtained in our systems is the slipping at the liquid/solid interface. If the slipping phenomenon does occur in our cases, then the Ca values are overestimated, as a result the smaller or even negative intercept on the R* axis can be obtained. Since slipping at the liquid/solid interface has been reported, especially on a hydrophobic surface at the micro- and nano-scales and the slip velocity is likely independent of droplet radius, the actual values of Ca would exclude the contribution of the slip velocity. Another possibility may be caused by rolling, which also results in relatively larger droplet velocity. 93

111 The third possibility is the way that water was deposited to the gradient surface. Since all the above experiments were carried out under the cold-water mist condition. The water mist might carry with it some additional kinetic energy when deposited to the surface, contributing to a faster droplet velocity. In order to evaluate the effects of the cold-water mist on the droplet movements, two similar continuous OTS gradient surfaces were used. One was used for water droplets formed from the condensation of the coldwater mist while in the other was used for droplets to be placed on the gradient surface by a glass micro- pipette. As shown in Figure 4-12, the slope of the droplet velocity vs. R/S 0 for droplets condensed from the cold water mist is 35.5 s -1, while it is 20.0 s -1 for the droplets dispensed to the gradient surface by using a micro-pipette. This indicates that the condensation of water droplets from a flowing cold-water mist likely enhances, to some extent, the movements of the water droplets on the gradient surface. The enhancement of droplet movement by condensing steam on a wettability gradient surface has been reported. 20 The primarily reason for such an enhancement is the large temperature difference between steam and the wettability gradient surface, and the incorporation of the thermal energy of the steam into the kinetic energy of the droplet. The characteristic velocity (U c ) 20 of the droplet at the advancing side by condensation can be written as U c 2k wδt ~ 4-6 ρh R v where k w is the thermal conductivity of water, ρ is the density of water, H v is the heat of vaporization of water, R is the base radius of the droplet, and ΔT is the degree of 94

112 25 20 velocity (mm/s) R/S 0 Figure Comparison of velocities of water droplets as a function of relative radii of the droplets (R/S 0 ) under different conditions ( denotes the formation of a droplet from the cold-water mist and from the micro-syringe). The S 0 was about 1000 μm. It is found that the slope in the plots under the water mist condition gives larger value. This suggests that the cold-water mist did enhance, to some extent, the droplet motion. 95

113 subcooling of the substrate surface from that of depositing stream. In our case, ΔT is basically zero, since the temperature of the cold-water mist is basically the same as the temperature of the wettability gradient surface. Thus, the contribution from the condensation to the droplet velocity is negligible. The water droplets grow much slowly in our case as compared to using high temperature steam. In addition, the frequency of coalescence is also much lower. Therefore, from the deposition perspective, the cold-water mist has little or no effect on the droplet movement in our study. However, it is possible the tiny water droplets deposited, from the water mist, along the path where the droplet travels can coalescent with the traveling droplet, and leading to a slight enhancement of the droplet velocity (see Figure 4-13). To be cautious, only those droplets, which start to move toward the higher wettability region with no obvious coalescence, are collected and analyzed. When the moving droplet coalesces with tiny droplets, the mass center of the new droplet moves toward the higher wettability region and this new droplet would need time to recover its contact angles at A and B (Figure 4-13) to what it should be. But, when the coalescence occurs as the droplet moves towards the higher wettability region, it will not have enough time to adjust its contact angle. As a result, the contact angle at B would be smaller than the value it should be, while the projected length perpendicular to the gradient direction would remain the same. Consequently, the total force acting on the droplet, which is proportional to (cosθ B cosθ A ), will be greater, leading to an enhanced droplet velocity. 96

114 Water contact angle, θ ( ) θ a θ r A θ ra B θ ab Position on a gradient surface Figure Illustration of water droplet movement on a one-dimensional organosilane wettability gradient surface with the coalescence occurring during its moving process. θ a and θ r represent the advancing and receding contact angles, respectively. The upper inset shows the contact angle change at A and B when the droplet coalesces with the tiny droplet ahead of its traveling path. Previous studies 7;38 using two different wettability gradients generated via the diffusion based approach showed that similar intercept values (~0.18) on the R* axis were obtained. 7;21;38 One of the gradients is created from patadecafluoro-1,1,2,2,- tetrahydrodecyltrichlorosilane 38 with a CAH (in term of cosine contact angle) of ~ 0.44, while another is from 7-octenyltrichlorosilane 7;21 with a CAH of ~ One would expect to obtain different intercept values on the R* axis, but the observations were not explained. Hence, the current accepted interpretation of Ca vs. R* curves might only qualitatively predict the effects of the CAH, and other factors that influence droplet movements might need to be sought and included in the interpretation. For example, AFM studies have revealed that organosilane SAMs generated by contact printing 97

115 involves the formation and growth of organosilane islands, if a substrate surface is not fully covered, it is possible that any disordered chain or defects on such organosilane SAMs could affect the actual CAH and subsequently influence the droplet movement Effects of Interfacial Friction As mentioned before, the hydrodynamic viscous force (or interfacial friction) exerted on a droplet is a function of droplet size, droplet velocity, liquid viscosity, surface tension of the liquid, and the properties of the solid surface. To understand the interfacial friction effects on water droplet movement, droplets located within the range of L/S 0 of 0.32~0.45 were chosen. In this short range of the wettability gradient surface, the steepness of the gradient (dcosθ d /d(l/s 0 )) can be treated as a constant of ~ Due to this limitation, only a few droplets on each surface were found to match the requirements. As mention above, the slope in the Ca vs. R* curve reflects the interfacial friction effects on droplet movements. It is shown in Figure 4-14 that a linear correlation can be roughly applied for each gradient size to have a similar positive intercept (around 0.018) on the R* axis but different slopes. The slopes are ~ 1.0E-03, 6.5E-04, 1.83E-04, and 5.3E-05 for the gradient sizes of 700 μm, 400 μm, 131 μm, and 65 μm, respectively. These data suggests that for various sized OTS gradient surfaces, the CAH has similar effects on water droplet movement, but the interfacial friction becomes more important in resisting water droplet movement when the gradient size scales down. 98

116 1.5e-4 1.0e-4 Ca 5.0e R* Figure Comparison of the droplet velocities in term of Ca (Ca=vη/γ) on various sizes of gradient surfaces as a function of R* (R*=R dcosθ d /dl) in a short range of relative position (L/S 0 : 0.32 ~ 0.45), in which the steepness of gradient could be treated as a constant value for each case. The sizes of the OTS gradient (S 0 ) were 700 μm ( ), 400 μm ( ), 131 μm ( ), and 65 μm ( ). It is shown that if a linear relationship of Ca against R* is applied in all cases the same intercept on the R* axis is obtained while the slope increases as the gradient size increases. This suggests that the interfacial friction plays a crucial role in the droplet movement as the gradient size scales down while the water CAH has a similar effect on the droplet movements. 99

117 4.3.5 Summary Various sizes of OTS continuous gradient surfaces and comparable OMDS gradient surfaces were generated by using the CP technique. The droplet movements on these surfaces show that droplet velocity increases with droplet radius for all cases. The effect of CAH is studied by using the comparable OTS and OMDS continuous and stepwise gradient surfaces, and the results are expected. In particular, the water droplets can be moved more easily on the OMDS gradient surfaces. The interfacial friction effects on the droplet movements are found to become more important as the wettability gradient size scales down. Since in our study, the water droplet size was too small (few micrometers to less 300 micrometers) and the traveling time of the water droplet was too short (less than 1/10 s), we could not observe how the water droplet moved on a gradient surface. In order to understand the contribution of the water CAH and the interfacial friction in the resisting the droplet motion on wettability gradient surface, the droplet motion mode(s) should be first determined. However, under current experimental conditions, it is too challenging to obtain the droplet motion modes on wettability gradient surface. Alternatively, we designed another experiment, which was to study the movement of a large water drop and the trace particles (premixed with water) on inclined homogeneous organosilane modified surfaces (OTS and DDS surfaces), to directly observe the internal fluidity of a water droplet through deducing movements of trace particles. If the surface wettability of such OTS surface is controlled to be the same as that at a particular position of the OTS wettability gradient surface, droplet motion on the inclined OTS surface reflects, to some 100

118 extent, droplet motion on the comparable wettability gradient surface. In the next section, the movements of a water droplet containing tracer PS particles inside on several inclined OTS and DDS surfaces with different surface wettability were investigated. 4.4 Water Droplet Movements on Inclined Solid Surfaces Water droplet movement on inclined DDS surfaces were also investigated. Varieties of drops with different volumes were involved at six different inclined angles. The experimental results suggest that both drop size and incline angle play an important role in the drop motion modes Introduction Motion and stability of a droplet on an inclined surface with homogeneous wettability have also attracted interest in both fundamental and applied research. Motion behavior of a droplet on an inclined solid surface is anticipated to be similar to that on a wettability gradient surface. The only difference is the source of the driving force; for an inclined surface it is the gravitational force while for a wettability gradient surface, it is the unbalanced Young s force. In order to determine which of the above droplet movement mode (rolling, sliding, slipping, or their combination) accurately accounts water droplet motion on an organosilane-modified surface, four different inclined OTS modified surfaces, each with a particular homogenous coverage, were studied. These OTS surfaces were also generated by CP using a planar PDMS stamp. CP times of the four different types of OTS 101

119 surfaces were 30 s, 10 s, 5 s, and 1 s, and the corresponding water contact angles were 88±2, 75±3, 68±2, and 44±2, respectively. These contact times were chosen due to the fact that organosilane gradient surfaces were generated with less than 35 s of contact. When a drop moves on an inclined solid surface, at steady state, the sliding velocity (U sld ) profile no longer changes with time, and the slipping velocity (U slp ) is a constant, thus the relative movement of the particle with respect to the drop is contributed by rolling. Based on the model of the internal fluidity of a spherical capped drop as proposed by Sakai et al, 162 by using the average rolling velocity (U ra ) as half of the maximum rolling velocity (U rmax ), the following equations are resulted. U = U + U + U 4-7 d ra sld slp U = U max + U + U 4-8 p r sld slp U r max = 2U ra 4-9 Where U d and U p are the average drop velocity and the particle velocity at the air/liquid interface, respectively. Then, the average rolling velocity (U ra ) of the drop can be obtained and is shown in the following equation. U U = U 4-10 p d ra Non-Wettable OTS Surfaces (90 θ w > 60 ) The OTS surfaces with contact time of 30 s, 10 s, and 5 s are considered as nonwettable (with a water contact angle of 90 θ > 60 ) in this study. A water drop containing tracer PS particles with a volume of 35 μl (for a water contact angle of 88±2 ) 102

120 or 45 μl (for water contact angles of 68±2 and 75±3 ) was used for the study of drop movement on inclined OTS surfaces. Experimental observations from the top view of drop movement showed that the three-phase contact line of the drop is basically maintained circular for a sample with a contact angle of 88±2. For samples with water contact angles of 68±2 and 75±3, the three-phase contact line is slightly elongated along the motion direction. The typical video images of a moving water drop on an inclined surface (with an inclined angle of 33 ) modified with OTS having a contact angle of 88±2, taken from the side view, are shown in Figure One aggregate of PS particles is located just beneath the water/air interface and the fluid of a water drop rolls down with along the Inclined surface. The water drop retains its shape as it moves down; this suggests that the entire drop, from the macroscopic point of view, likely moves with the same speed. On the other hand, the movement of the PS tracers inside the drop suggests that the internal fluidity, at least to some extent, contains rolling mode. This observation is in agreement with those observed by Allen 12 as well as Sakai et al 96. Allen proposed, from his observations of water drops moving down a glass surface, that at least the internal fluid of a water drop roll down along the inclined surface. He further suggested that whether the surface of the water drop rolls or slides on an inclined surface depends on the advancing contact angle being, respectively, greater or less than 90. Sakai and coworkers 96 suggested, from their observations of water drops containing PS particles moving down along the inclined hydrophobic surfaces (water contact angle: 100 and 79.5 ), that the 103

121 drop movement is a combination of rolling and slipping even if the motion of the PS particle observed only occurs at the liquid/solid interface. 5 mm 0.00 s 0.20 s 0.40 s 0.60 s Figure Sequential images of the water drop moving down on an inclined OTS surface with a water contact angle of 88±2. The images were captured by playing back the recorded video tape (30 fps). A PS aggregate, circled, just beneath the surface of the water drop seems to roll with the water drop. Here, it should indicate that time 0 corresponds to when the PS particle is noticed to move with the water drop. Motion behaviors of the water drop are summarized in Figure At the beginning (unsteady state), the drop is being accelerated, and after a short of time (0.4 s), the drop reaches a steady velocity (U d ) of 8.94 mm/s at its advancing edge, while the particle inside the drop travels along the air/liquid interface 104

122 7 6 traveling distance (mm) f(t)=14.22t-2.38 R 2 =0.99 f(t)=8.94t-2.18 R 2 = time (s) Figure Motion behaviors and internal fluidity of a water drop during its downfall along the OTS modified surface with a water contact angle of 88±2. The results show that the distances traveled by the water drop of the advancing edge ( ) and the receding edge ( ) and by the aggregate of the PS particles ( ) inside the drop with respect to the substrate surface. The locations of the aggregate of the PS particle inside the water drop are shown in Figure After a short time (0.4 s), the drop motion reaches a steady state with a constant velocity (14.22 mm/s and 8.94 mm/s for the PS particle and the water drop, respectively). 105

123 (Figure 4-15) with a velocity (U p ) of mm/s. As seen in Figure 4-16, there is only a slight difference in motion behavior between the advancing edge and receding edge of the drop. The moving patterns of PS particles inside the water drop during drop motion can be obtained from the photo images as shown in Figure Those images indicate that the aggregate of the trace particles seems to roll from the back of the drop to the front of the drop as the drop travels down the surface. Since the particle is located at the air/water interface, this particle velocity (U p ) represents the maximum velocity of the drop at the air/water interface, contributed by rolling, slipping and sliding if all three modes are involved. As a result, its velocity (slope in Figure 4-16) is greater than the average drop velocity. Therefore, the average rolling velocity (5.28 mm/s) of the drop can be obtained (based on the equation 4-10) and the degree of the rolling is about 59.1%. The rest of the velocity of the water drop reflects the velocity contributed by the sliding and/or slipping. Unfortunately, for most cases, it was difficult to find PS particles moving both at the liquid/solid interface and just beneath the water/air interface at the same time. Therefore, the data for a PS aggregate to move at the liquid/solid interface is normally obtained in a separate study using the same OTS modified surface. Motion behaviors of a water drop and a PS aggregate at the liquid/solid interface are summarized in Figure The aggregate moves at ~ 0.47 mm/s and the total drop velocity is ~ 1.35 mm/s. Since the aggregate is located close/at the liquid/solid interface, its velocity roughly represents the slip velocity of the water drop at the interface, which is approximately 35 % of the total drop velocity. The drop velocities obtained from two separated drop movements could have large difference; one reason is the surface contamination caused by the PS particles left behind on the solid surface as the drop passed away (see Figure B-12 in 106

124 0.5 traveling distance (mm) f(t)=1.35t R 2 =0.99 f(t)=0.47t R 2 = time (s) Figure Motion behaviors and internal fluidity of a water drop during its downfall on the OTS surface with a water contact angle of 88±2. The distance traveled by the PS aggregate ( ) located at the liquid/solid interface is smaller than that of the drop. The distances traveled by the water drop of both the advancing edge ( ) and the receding edge ( ) are quite close. The drop motion seems to move at a steady state with a constant of speed (0.47 mm/s and 1.35 mm/s for the particle and the water drop, respectively) down the substrate surface. 107

125 Appendix). However, if the surface contamination is assumed to only affect the drop velocity but not the motion mode, then these data indicates that the motion behavior of the water drop on the OTS modified surface with a contact angle of ~ 90º is dominated by rolling and slipping. For the OTS modified surface with a water contact angle of 75±3, a water drop with a volume of 45 μl was used to study drop motion on the inclined surface with an inclined angle of 46. The typical video images taken from the side view are shown in Figure One aggregate of PS particles, located just beneath water/air interface, is followed to access the internal fluid flow, which, as indicated by PS particles, still contains rolling to some extent. Experimental data shown in Figures 4-19 indicates that there is only a very slight difference in the traveling distance between the advancing and receding edges of the drop. Therefore, the drop shape in this case also remains during the motion process. The traveling distances of both the drop and the PS aggregate in Figure 4-19 roughly vary linearly with the traveling time, and the traveling velocities of 7.38 mm/s for the drop and mm/s for the PS aggregate with respect to the substrate surface are obtained. The velocity difference (5.06 mm/s) between the PS aggregate and the drop is the average rolling velocity of the drop and the degree of rolling is about 68.6%. The slip velocity estimated from PS particles, both at the liquid/solid and the air/liquid interface, for various drops (with PS particles inside) moving down on this OTS surface is in the range 108

126 of 30 50%. Therefore, the motion of the water drop on the OTS surface with a water contact angle of 75±3 is also dominated by both rolling and slipping. 5 mm 5 mm 0.00 s 0.10 s 0.20 s 0.30 s Figure Sequential images of a water drop moving on the inclined OTS surface with a water contact angle of 75±3. The images were captured by playing back the video tape (recorded at 30 fps). The movement of water drops with a volume of 45 μl was also conducted on the inclined OTS modified surface with a water contact angle of 68±2. The inclined angle was 45. Typical video images taken from the side view are shown in Figure 4-20a, in which only one agglomerate of PS particles at the interface of water/solid is visible and found to move with the water drop along the interface. A slower velocity of the PS aggregate is observed at the interface in comparison with that of the water drop, this indicates that the slip phenomenon likely occurs at the water/ots interface. When a 109

127 4 traveling distance (mm) f(t)=12.44t R 2 =0.99 f(t)=7.38t R 2 = time (s) Figure Motion behaviors and internal fluidity of a water drop during its downfall along the OTS modified surface with a water contact angle of 75±3. The results show that the distances traveled by the water drop of the advancing edge ( ) and the receding ( ) edge and by the PS particle ( ) inside the drop with respect to the substrate surface. The locations of the aggregate of the PS particles inside the water drop are shown in Figure The drop motion seems to move at a steady state with a constant velocity (12.44 mm/s and 7.38 mm/s for the particle and the water drop, respectively) down the substrate surface. 110

128 a 5 mm 0.00 s 0.50 s 1.00 s 1.50 s b 5 mm 0.00 s 0.67 s 1.33 s 2.00 s Figure Sequential images of a water drop moving on the inclined OTS modified surface with a water contact angle of 68±2. The images were captured by playing back the video tape. (a) An aggregate of the PS particles at the liquid/solid interface moves slower than the water drop, and (b) A PS aggregate at the air/water interface seems to roll with the drop. 111

129 water drop with a volume of 70 μl (Figure 4-20b) was used at an inclined angle of 29.2, a visible PS aggregate inside the water drop is observed to roll down with the drop. The relative position of the PS aggregate with respect to the water drop seems to be maintained. This suggests that slipping and rolling still contribute substantially to the drop movement on such a surface. The distances traveled by the advancing and receding edges of the water drop are similar for both cases, and the experimental results, in terms of traveling distance vs.time, of both the drop and the PS aggregate are shown in Figures 4-21a and 4-21b. The curves in Figure 4-21a are basically linear, suggesting that the water drop moves with a constant velocity of ~ 1.32 mm/s, while the PS agglomerate also moves with a constant velocity of ~ 0.80 mm/s. The velocity of the PS aggregate at the liquid/solid interface roughly represents the slip velocity of the drop, which is about 60% of the total velocity of the drop in this case. Also, rolling still occurs (Figure 4-20b) and the rolling velocity composes as large as ~ 80% (Figure 4-21b) of the total drop velocity. This again evidences that both rolling and slipping are the main contributors in drop motion down an inclined surface. Since the experimental results of degrees of rolling and slipping were obtained from two separate experimental sets, even smaller surface property change could cause the big change of the drop velocity (as seen from the experimental results, the drop velocity changes significantly) and could further affect the degree of motion mode. As a result, a big experimental error could be possible (i.e. the sum of degree of rolling and slipping is larger than one on this surface). If the particles both at the liquid/solid interface and inside a drop are simultaneously observed to move with the 112

130 f(t)=0.80t f(t)=1.32t R 2 =1.00.0time (s)00traveling distance (mm)0r 2 = Figure 4-21a. Motion behaviors and internal fluidity of a water drop during its downfall on the OTS modified surface with a water contact angle of 68±2. A PS aggregate ( ) was located at the liquid/solid interface (as shown in Figure 4-21a). The results show that the distances traveled by the water drop of the advancing edge ( ) and the receding edge ( ) are almost identical. The drop seems to move at a steady state with a constant speed (0.80 mm/s and 1.32 mm/s for the particle and the water drop, respectively) down the substrate surface. 113

131 traveling distance (mm) f(t)=1.04t R 2 =0.99 f(t)=0.57t R 2 = time (s) Figure 4-21b. Motion behaviors and internal fluidity of a water drop during its downfall on OTS modified surface with a water contact angle of 68±2. The aggregate of the PS particles ( ) was located inside the drop as shown in Figure 4-20b. The results show that the water drop ( ) moves down faster than the PS aggregate. 114

132 drop, the experimental results should be more accurate. Unfortunately, we could not observe such phenomena at the same time. That is the main reason why we continue to study water drop movement on an inclined DDS surface (discussed later) Partially Wettable OTS Surfaces (60 θ w > 30 ) For an OTS modified surface with a water contact angle of 44±2, a water drop with a volume of 70 μl was used to study drop motion behavior on this surface with an inclined angle of 37. In Figure 4-22, a PS aggregate inside the water drop is observed to move with the same speed as the drop. The particle observed in Figure 4-21 is almost at 5 mm 0.00 s 0.40 s 0.80 s 1.20 s Figure Sequential images of a water drop moving on the OTS modified surface with a water contact angle of 44±2. The images were captured by playing back the video tape (recorded at 30 fps). 115

133 the middle of the z-scale, so its velocity is most likely close to the average velocity of the drop traveled, thus it is reasonable to have this particle move with a similar velocity as the drop (the velocity of the entire drop should be moved at its average velocity). The relative position of this PS aggregate with respect to the water drop seems to change only slightly. The traveling distances of the advancing and the receding edge of the drop as a function of the traveling time are shown in Figure A steady state velocity of 0.76 mm/s is found, from the linear fit, for both the particles and the drop. From the above experimental observations, several common findings are noted below. First, the drop remains its shape during the motion process and its advancing and receding edges move with a basically identical velocity. Second, some PS particles or the aggregates are left behind on the OTS surface after the drop has traveled pass, but no observable water, under the experimental magnifications, is left on the surface. Third, the OTS surface is contaminated by the PS particles left behind as the drop travels pass; as a result, the drop velocity is difficult to be reproduced. Fourth, it is hard to observe, at the same time, PS particles moving both inside and at the interface. As a result, larger experimental errors are possible, and it is hard to quantify, or even qualify, the factor(s) affecting motion mode of a water drop. Since the size of water drop used here is much larger than the water drop on the gradient surfaces and the drop size can not be reduced due to the large water CAH on the OTS surface. The experimental results on the drop motion modes obtained on inclined OTS surfaces cannot exactly applied to interpret the phenomenon of water drop motion on wettability gradient surface. In order to use the experimental results obtained on the inclined surfaces to interpret the drop motion 116

134 traveling distance (mm) f(t)=0.76t R 2 = time (s) Figure A motion behavior of a water drop during its downfall on the OTS modified surface with a water contact angle of 44±2. The distance traveled by the advancing edge ( ) of the water drop was identical to that by the receding edge ( ). The drop seems to move at a steady state with a constant speed of 0.76 mm/s. 117

135 behavior on a gradient surface, one attempt is to reduce the water drop size by using methyl terminated organosilane with a low CAH. Dimethyldichlorosilane (DDS), whose SAM has a water contact angle of 98 and a water CAH of 5, is the suitable choice. Therefore, the systematic study of water drop movement on the inclined DDS surface were also conducted to obtain effects of both the drop size and inclined angle on drop motion DDS Surface (θ w = 98 ) In the experiments of water drop moving on OTS modified surfaces, only a few particles were found to move both inside the drop and at the interface of liquid/solid. In reality, there were many particles mixed with water. The reason is that the PS particles were rarely observable due to the large drop size caused by the large water CAH on OTS surfaces. Therefore, reducing the size of a moving drop size is likely more effective in observing particle motion both inside the drop and at the interface at the same time, and a DDS modified surface, due to its low water CAH, makes it possible for such an attempt. In the study of water drop motion, first, pure water drops with different volumes ranging from 10 to 40 μl were used to study drop motion at six different inclined angles (αs). The traveling distances of drops with a volume of 20 μl as a function of the traveling time at six different αs as an example are reported in Figure The experimental results indicate that it takes very short time (less 1/100s) to reach a pseudo steady-state condition, and the drop velocity in each condition seems to be constant (the corresponded slope values in Figure 4-24). In addition, it is found that the drop velocity 118

136 traveling distance (mm) α=15 α=17 α=20 α=24 α=27 α= time (s) Figure Motion behaviors of a water droplet during its downfall on the DDS surface are summarized. A water drop with the volume of 20 μl was used in this study at six different inclined angles (αs) of 15, 17, 20, 24, 27, and 31. The results show that water drops, under each case, move at a pseudo steady state and the drop velocity (slope of each curve) increases with the increase of α. The acceleration of a water drop at the initial condition is large enough that the time needed to reach the maximum velocity of the drop is short (less than 1/100 s). 119

137 increases with the increase of α, because the driving force comes from the gravitational force (mg sinα), a larger α results in a greater driving force, consequently a greater drop velocity. When a water drop is placed on an inclined surface, it always has tendency to move down the surface. Once the driving force acting on the water drop overcomes the total resistance forces, including the CAH force and the critical resistance force, the drop starts to move down. Otherwise, it stays still on the inclined surface. Regardless of CAH, the critical frictional force (F c ) coming from the interactions between two surfaces will increase to prevent any relative motion up until the point when the drop motion occurs. Figure 4-25 shows that the experimentally estimated critical frictional force has a rough linear relationship with the contact area of a water drop with a positive intercept on the axis of contact area, at which the driving force (mgsinα) is just equal to the CAH force and the F c is zero. This intercept value also suggests that the driving force needs to first overcome the CAH force, and then followed by the frictional force. Once both of them are overcome, the drop starts to move and the hydrodynamic frictional force replaces the F c. Experimental results of capillary number (Ca) as a function of Reynolds number (Re) of water drops are shown in Figure All the experimental data seems to fall on the same straight line, which passes through the origin. It suggests that there is a linear relationship between Ca and Re. In addition, it is found that these low Re values correspond to the Laminar flow, in which the viscous force is dominant. When we look at 120

138 80 60 F c (μn) 40 F c =3.89A R 2 = contact area, A (mm 2 ) Figure Experimental estimation of critical frictional force (F c ) as a function of the contact area of a water drop. Water drops with the volume of 10, 15, 20, 30, and 40 μl were used in the study at six different inclined angles of 15, 17, 20, 24, 27, and 31. For each size of water drops, the critical frictional force was experimentally estimated. The experimental results show that the critical frictional force increases linearly with the increase of the contact area of the water drop. The intercept on the axis of the contact area is the result of the CAH. 121

139 1e-3 8e-4 Ca 6e-4 Ca=2.7e-06Re R 2 =0.99 4e-4 2e Re Figure Capillary (Ca) of a pure water drop as a function of Re. the velocity of the drop is found to have a linear relationship with Re. Here, the experimental data are included under various conditions (five different water drops at six different inclined angles). 122

140 the Ca values, it suggests that the surface tension is dominant instead of the viscous force since in fluidic mechanics, the Ca represents the relative effect of viscous force vs. surface tension. When we apply Bond number (Bo as shown in equation 4-11), which in fluidic mechanics is a dimensionless number expressing the ratio of body force (often gravitational) to surface tension force, to describe drop movement down an inclined surface, we find that in our experiments, Bo is always smaller than 1. Thus again it indicates that the surface tension dominates the drop movements. B O 2 ρgr = 4-11 γ LV where ρ: the density of the flowing fluid, g: the acceleration of the gravity, R: the radius of a drop, γ LV : the surface tension of the liquid. As we know that when a water drop is placed on an inclined hydrophobic plane (in our study the water contact angle of the substrate surface is about 98 ), the position of its mass center will change from M 1 to M 2 as shown in Figure 4-27, where O is the curvature center of the drop. The angle between OM 1 and OM 2, or β, represents the shift of mass center of the drop. Based on our experimental observation, M 2 is independent of the inclined angle (except at α=0 ). Once the surface is tilted, the drop forms an advancing angle at its front edge (A) and a receding angle at its back edge (B). The values of the advancing angle and the receding angle appear to be maintained as the 123

141 surface is further tilted, thus the shape of the drop, consequently its mass center and center of curvature, no longer changes. When the drop just starts to move down the sample surface at the initial condition, the following equation can be obtained. F S = mg sinα 4-12 Where F S is the sliding force, which will be balanced by the water CAH and the hydrodynamic friction force at pseudo steady state. With the shift of mass center, a possible rolling mode of drop movement could be resulted. In order to quantify the rolling of a drop, we introduce two torques, T f and T b. From Figure 4-27, the body force (mg) results in the torque (T f ), which has tendency to push the drop to roll while the Figure Schematic illustration of movement of a water drop on an inclined DDS surface, on which the mass center of the drop changes from M 1 to M 2. This displacement of the drop mass center causes a potential rolling in the direction pointing to the advancing side of the drop. sliding force (mgsinα) resulting in the torque (T b ), which is in the opposite direction of T f, has tendency to prevent the drop from rolling. T f and T b can be expressed as: T f = mg sin( α + β ) l

142 T b = F d = mg sinαd 4-14 S Where l is the distance from O to M 2 and d is the distance from O to the sample surface. In order to mathematically analyze the potential rolling or sliding of the drop, a new parameter, Torque index (K T ), is introduced and defined in equation 4-12 as the ratio of these two torques (T f and T b ). K T T f sin( α + β ) l = = 4-15 T sinα d b When K T is larger than one, it is obvious that the drop has a tendency to roll but that does not necessary mean the drop will roll and a higher K T would expect to result in more rolling while more sliding at a low K T. Since l, d, and β are fixed in the study for the same sample surface at any inclined angle (α), K T is only a function of α and decreases with increasing α. The estimated K T is shown in Figure It clearly indicates that more rolling of the water drop on the inclined surface at a low α (larger than the critical α or α c ) would be resulted. Figure 4-28 shows the general relationship between K T and α without considering CAH effect, which leads to the α c. Therefore, in the specific case, the valid K T is in a certain range and is determined by α ranging from α c (below α c the drop does not move due to the effect of the water CAH) to 90. The experimental evaluation of the degree of rolling of a water drop with the volume of 10, 15, 20, 30, and 40 μl as a function of K T is summarized in Figure It is found that as K T increases in a certain range for each drop size the degree of rolling of the drop increases. This suggests that the drop has a higher tendency to roll at larger K T. In 125

143 K T sinα Figure Torque Index (K T ) of a water drop moving on an inclined sample surface as a function of α. The estimated results indicate that at small αs there is more contribution from the rolling while less contribution from the sliding to the drop motion. 126

144 degree of rolling K T Figure Torque Index (K T ) effect on the rolling mode of a water drop. Five different volumes of water drops were used in the study, ranging from 10 μl to 40 μl. For the same drop, the degree of rolling of the water drop decreases as the K T increases. However, for a relatively smaller drop, there is total rolling behavior under certain condition. On the other hand, as a water drop becomes larger, no rolling behavior could occur. 127

145 degree of slipping K T Figure Torque Index (K T ) effect on the slipping mode of a water drop. Experimental error bars are overlapped by the large symbols due to smaller errors (around 1%) for each drop size. Five different volumes of water drops were used in the study, ranging from 10 μl to 40 μl. In most cases, the degree of slipping decreases as the K T increases. The exceptions appear to occur for larger drops moving down the surface at high inclined angles. 128

146 addition, it is found that a larger drop has a low tendency to roll down in comparison to a smaller drop when the inclined angle remains the same and under certain conditions (small or large K T ), no rolling or complete rolling could be possible. The experimental evaluation of the degree of slipping of a water drop as a function of K T is summarized in Figure The experimental results suggest that the degree of slipping of small drops decreases as K T increases, the same tendency applies for large water drops at low αs. As we discussed in Chapter 2, the slipping phenomenon can occur at the interface of liquid/solid, especially at the micro- and nano-scales, and the hydrophobicity of the substrate surface is usually considered to facilitate slipping. However, the exact causes and conditions of the slipping phenomenon are still not completely understood. The total velocity of the water drop is the combination of velocities of rolling, sliding, and slipping; the sliding velocity of the water drop can be easily obtained by subtracting the velocities of rolling and slipping from the total velocity. The experimental estimation of the degree of sliding of a water drop with volume of 10, 15, 20, 30, and 40 μl as a function of K T is summarized in Figure It is found that as K T increases in a certain range for each drop size the degree of sliding of the drop decreases, which suggests that the drop has a higher tendency of sliding when it moves down along the inclined surface at a larger α. In addition, it is found that a larger drop has a higher tendency to slide down in comparison to a smaller drop when these water drops move on the inclined surface at the same α. This finding can be easily interpreted by using Figure 129

147 degree of sliding K T Figure Torque Index (K T ) effect on the sliding mode of a water drop. For the same drop, the degree of sliding of the water drop decreases as K T increases. However, for a relatively smaller drop, under certain condition, there is no sliding behavior, which means that the water drop only rolls with possible slipping. On the other hand, as a water drop becomes larger, the total sliding behavior can occur or when K T is smaller than a certain value the total sliding behavior can happen if the linear tendency for each case can be applied. 130

148 4-28. On the other hand, no sliding or complete sliding of a water drop can be expected by knowing the K T value. Hodges and coworkers 163 theoretically studied the a viscous drop in liquid medium down a gently inclined plane under conditions of α << 1 (about 57 ) and the Bond number (B) << 1. The drop does not wet the wall but is supported by a thin lubrication film of liquid. They proposed that for a highly viscous drop, the distorted drop slides down the plane without rotating; while for a relatively non-viscous drop, it slips down the plane. For a liquid with an intermediate viscosity, the drop moves with a combination of rolling, sliding, and slipping, and the internal flow of the drop plays a dominant role in the overall motion. In their analysis, three different types of drop shapes (pancake, flat-spot, and circular) were investigated. Among them, a flat-spot drop is similar to a water drop used in our study, in which the water drop in air medium down an inclined surface with α, ranging from 15 to 30, is investigated. In addition, the bond number in our study is always smaller than 1 (i.e. for a drop with a volume of 15 μl moving at an inclined angle of 21, the bond number is about 0.1). Since there are some similarities to our case, especially for a drop with flat-spot shape, their findings from theoretical analysis can be used to interpret our experimental observations if we assume that our system is comparable to their system. They pointed out that for a drop with flat-spot shape, the rolling velocity, the sliding velocity, and the slipping velocity are proportional to α/r, α 3, and (αr) 3/2, respectively. When these relationships are applied in our case, for a drop with the same size at different inclined 131

149 angles, all of these three velocities increase with the increase of the inclined angle. However, the rolling velocity increases the least, followed by the slipping velocity and then the sliding velocity. As a result, at a larger inclined angle, the contribution of rolling (lower degree of rolling) decreases, while the contribution of sliding increases. The slipping contribution may not vary much. On the other hand, with the same inclined angle, as the drop size increases, the rolling velocity decreases and the slipping velocity increases, while the sliding velocity remains the same. As a result, the rolling contribution decreases while the slipping contribution increases. These analyses are, to some extent, in agreement with both our experimental observations and analysis. From above experimental results, both the inclined angle and the drop size determine the degree of rolling and the degree of slipping as well as the degree of sliding. If we replace sinα in the bottom of equation 4-15 with sinα c (α c is the critical inclined angle below which the drop does not move), and define another new parameter, K H, which is functions of α and drop size. The new parameter, as shown in shown in equation 4-16 should increase with the increase of both inclined angle and drop size, and the. K H sin( α + β ) l = 4-16 sinα d c smallest drop moving at a possible smallest inclined angle. Therefore, as compared to K T, it may be more precisely to apply K H to describe the drop motion modes. Since α c comes from the effect of contact angle hysteresis on drop motion, a smaller drop has a larger α c. As a result, a smaller drop has larger K H than a larger drop when α remains the same. On the other hand, for the same drop K H increases with the increase of α. 132

150 1.0 degree of motion modes K H Figure K H effect on the degree of motion modes (rolling ( ), slipping ( ), and sliding ( )). By considering the effects of both inclined angle and drop size, the degree of rolling decreases as K H increases while the degree of sliding increase as K H increases and the degree of slipping increases first with the increase of K H and then slowly reaches a plateau. With high drop velocity (corresponding to large K H values), both the rolling velocity and the slipping velocity at the liquid/solid interface could not be measured using our current set up. 133

151 The degrees of motion modes (rolling, sliding, and slipping) of the water drops with volume of 10, 15, 20, 30, and 40 μl as a function of K H is summarized in Figure The experimental data for both rolling and sliding are collapsed into one single curve; as K H increases the degree of sliding increases while, conversely, the degree of rolling decreases. The experimental data for slipping gives a different trend, although they are also collapsed into one single curve. The curve increases first with the increase of K H and then slowly reaches a plateau. The experimental data for higher K H was unable to be obtained with our current experimental set up. Nevertheless, our experimental results have shown that a smaller drop or a drop placed on the inclined surface with a smaller α experiences more contribution of rolling while a bigger drop or a drop placed on the inclined surface with a larger inclined angle experiences more contribution of sliding, which are in agreement with the above analysis. For a water drop placed on an inclined surface, it always has a tendency to roll down because of its soft body and the shift of mass center, which results in a positive torque acting on the drop to promote rolling. Rolling and sliding are competent rivals in drop motion on an inclined surface while the slipping could occur under certain circumstances, but so far the slipping phenomenon is not yet completely understood. Gao and McCarthy 52 suggested that droplets can move by rolling, sliding or some combination of mechanism between these two extremes, assuming no slipping; and the degree of each extreme mechanism depends on surface chemistry and topography. They thought that the droplet might move by sliding at some points of the contact line and rolling at other points or may advance by rolling and recede by sliding. Moreover, from 134

152 the thermodynamic perspective of the interfacial water molecules, rolling and sliding are equivalent energetically. In one case, the rolling mode will result in the smallest friction in comparison with the sliding mode, especially for a small drop with less driving force acting on it. In another case, if a drop is larger enough, the drop motion could be treated like the fluid flow (liquid thin film) on an inclined solid surface 94, which indicates that the sliding dominates the motion mode. Therefore, it is possible that 100% rolling or sliding of the water drop could occur Summary Four OTS homogeneous surfaces with different wettability, generated by using the CP technique, were used in the study of drop movements on inclined surfaces. The tracer PS particles suspended in the water drop, which moved on inclined OTS surfaces, provide an effective method to directly observe the drop motion mode on the inclined surface. The experimental observations and analysis on OTS surfaces indicate that the drop motion mode is a possible combination of sliding, slipping, and rolling. Due to the large water CAH (~ 20 ) on OTS surfaces, the drop size used in the experiments can not be reduced. In order to directly observe the drop motion modes in a small water drop, which has a comparable size as those moving on the gradient surfaces, DDS was used to modify the substrate surface and the resulted surface has a water contact angle of 98 and a water CAH about 5. As a result, relatively small water drops can be used to allow for visual observation of the internal fluidity of the moving drop. Systematic studies of drop movements on the DDS surface support that the drop motion is a combination of rolling, sliding and slipping. Also, 100% of either rolling or sliding of a water drop is possible. 135

153 Both inclined angle and water drop size are found to determine the drop motion mode. To interpret the observed phenomena, two new parameters, K T and K H, are introduced and used to describe the drop movements on the inclined surface. As compared to K T, K H is more general for the interpretation of obtained data, because K H accounts for the combined effects of both drop size and inclined angle. 4.5 Summary of Results and Discussion Water droplet movements on the various wettability gradient surfaces generated by the CP technique with OTS or OMDS were conducted and investigated. The experimental results showed that the droplet velocity increases with the increase of the droplet radius and the droplet velocity increases as the gradient size scaled up. The effects of the CAH played a crucial role in the droplet movements when the droplet movements were conducted on two comparable gradient surfaces with different properties of CAH. On the other hand, interfacial friction effects were also investigated and found that less effect of the interfacial friction on the water droplet movements resulted as the gradient size scaled up when the same organosilane was used to generate the gradient surfaces to maintain the CAH. Because the water droplet size in our experiments was so small and the traveling time of the droplet was too short (less than 1/10 s), we could not observe how the droplet moves on the wettability gradient surface. Under the current experimental conditions, it was too challenging to obtain the drop motion mode on a wettability gradient surface. Alternatively, measurements of movement of water drops premixed with the tracer PS 136

154 particles (40 μm in diameter and density 1.05 g/cm 3 ) on several inclined homogeneous OTS surfaces were conducted, the surface wettability of these OTS surfaces are controlled within the wettability range on a OTS gradient surface. The direct observations of the movements of both the water droplet and the tracer PS particle clearly suggested that the droplet motion mode is a combination of sliding, rolling, and slipping. Because OTS modified surfaces have large water CAH, the drop size used in the study cannot be reduced. Further studies of water drop movements were conducted on the inclined DDS modified surface, which has much smaller water CAH as compared to OTS surface. A systematic study of water drop movements on an inclined DDS surface indicates that the drop motion is also a combination of rolling, sliding, and slipping. Experimental results show that a smaller drop exhibits a larger rolling contribution to the drop motion. Under a small ratio (< about 18) of the torques after by considering the effects of both inclined angle and drop size, a complete rolling becomes possible; conversely, a large enough ratio (> about 36) of the torques leads to no rolling with small or even no slipping. When the degree of rolling and the degree of the interfacial slipping sum up to a value less than unity; the sliding of the drop likely accounts for the remaining portion of the droplet velocity. 137

155 CHAPTER V CONCLUDING REMARKS AND FUTURE STUDIES 5.1 Concluding Remarks Water droplet movements on a variety of organosilane wettability gradient surfaces (continuous and stepwise) were experimentally investigated. These gradient surfaces were generated by the CP technique with octadecyltrichlorosilane (OTS) and octadecylmethyldichlorosilane (OMDS). The experimental results showed that a water droplet as small as a few micrometers in radius could move toward the higher wettability region and droplet velocity increased with the increase of the droplet radius. The effects of CAH played an important role in droplet movements when the droplet movements were conducted on a pair of the comparable gradient surfaces with different CAH. On the other hand, interfacial friction effects became more important as the gradient size scaled down when the same organosilane was used to generate the gradient surfaces to maintain the same CAH. In addition, the effect of droplet displacement on the droplet movements was also evaluated and it was found that the cold-water mist likely facilitates the droplet movement. 138

156 Under the current experimental conditions (small droplet, and less than 1/10 s of traveling time), we could not determine the mode of the droplet motion on the wettability gradient surface. Direct observations and experimental analysis of the internal fluidity of large water drops, containing the tracer PS particles, on inclined homogeneous OTS surfaces indicated that the motion of the water droplet is a combination of rolling, sliding and slipping. Since the water CAH of OTS surface generated via CP technique was about 20 in our experiments, as a result, the minimum radius of a water drop used in the study of the drop movements on such inclined surfaces is too large. Therefore, a DDS surface with water CAH of about 5 was used for the further study of drop movements. Water droplet movements on the inclined DDS surface clearly indicated that in a certain range of K T, the drop motion is a combination of rolling, sliding and slipping. Either 100% rolling or 100% of sliding of a water drop could be possible as K T becomes small enough or large enough, respectively. 5.2 Future Studies In section 4.2, the water contact angles of a wettability gradient surface were experimentally estimated, but it was found that there is some difference between these values and those obtained from the homogeneous surfaces generated by CP technique with a planar stamp. In most experiments, the wettability gradient surface was not characterized by using the water contact angle measurement due to the difficulties in applying this method to measure the contact angle values on such small gradient surfaces prior to use for the study of the droplet movements. Daniel and Chaudhury found that the small difference of the CAH could cause significant effects on the droplet movements

157 However, the real reasons behind CAH have not been fully understood in the literature. According to de Gennes (1985), 107 CAH is related to non-idealities such as surface roughness, surface contamination or heterogeneity, and film formation caused by solute deposited from the liquids, which may either enhance or reduce the hysteresis. Therefore, CAH is a very complicated phenomenon. As a result, the reproducibility of the gradient surface properties becomes very important as the organosilane gradient surface scales down. It is necessary to find a way to quantitatively characterize the wettability property (or surface energy) of the micro- and nano-scaled gradient surface in order to precisely investigate the effects of these parameters (e.g. CAH, interfacial friction, and gradient steepness). In the study of water drop motion on the inclined DDS surface, we only used the DDS surface with a water contact angle of 98 0, so further study of drop motion on DDS surfaces with different wettability should be conducted to investigate whether the surface wettability has any effect on the drop motion mode. In addition, effects of liquid properties (i.e. surface tension, viscosity) should also be conducted by using different probe liquids to evaluate the liquid property contribution on the drop motion mode. 140

158 REFERENCE (1) Das, A. K.; Kilty, H. P.; Marto, P. J.; Andeen, G. B.; Kumar, A. J.Heat Transfer 2000, 122, (2) Rose, J. W. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 2002, 216, (3) Belder, D. Angewandte Chemie, International Edition 2005, 44, (4) Caelen, I.; Bernard, A.; Juncker, D.; Michel, B.; Heinzelmann, H.; Delamarche, E. Langmuir 2000, 16, (5) Chau, S. W.; Hsu, K. L.; Chen, S. C.; Liou, T. M.; Shih, K. C. Biosensors & Bioelectronics 2004, 20, (6) Cheng, J. T.; Giordano, N. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2002, 65, /5. (7) Daniel, S.; Sircar, S.; Gliem, J.; Chaudhury, M. K. Langmuir 2004, 20, (8) Daniel, S.; Chaudhury, M. K.; de Gennes, P. G. Langmuir 2005, 21, (9) Darhuber, A. A.; Valentino, J. P.; Davis, J. M.; Troian, S. M.; Wagner, S. Appl.Phys.Lett. 2003, 82, (10) Yamada, M.; Seki, M. Anal.Chem. 2004, 76, (11) Lindsay, S.; Vazquez, T.; Egatz-Gomez, A.; Loyprasert, S.; Garcia, A. A.; Wang, J. Analyst (Cambridge, United Kingdom) 2007, 132, (12) Allen, R. F. J.Colloid Interface Sci. 1975, 50, (13) Anilkumar, A. V.; Lee, C. P.; Wang, T. G. Phys.Fluids A 1991, 3, (14) Bain, C. D. ChemPhysChem 2001, 2, (15) Brochard, F. Langmuir 1989, 5, (16) Brzoska, J. B.; Brochard-Wyart, F.; Rondelez, F. Langmuir 1993, 9,

159 (17) Burton, J. C.; Taborek, P.; Rutledge, J. E. J.Low Temp.Phys. 2004, 134, (18) Carnero, C.; Aguiar, J.; Hierrezuelo, J. Neurologia 2001, 28, (19) Chaudhury, M. K.; Whitesides, G. M. Science (Washington, DC, United States) 1992, 256, (20) Daniel, S.; Chaudhury, M. K.; Chen, J. C. Science (Washington, DC, United States) 2001, 291, (21) Daniel, S.; Chaudhury, M. K. Langmuir 2002, 18, (22) ElSherbini, A. I.; Jacobi, A. M. J.Colloid Interface Sci. 2004, 273, (23) ElSherbini, A. I.; Jacobi, A. M. J.Colloid Interface Sci. 2004, 273, (24) Extrand, C. W.; Kumagai, Y. J.Colloid Interface Sci. 1995, 170, (25) Fan, H. J.Phys.: Condens.Matter 2006, 18, (26) Greenspan, H. P. J.Fluid Mech. 1978, 84, (27) Jeelani, S. A. K.; Hartland, S. J.Colloid Interface Sci. 1998, 206, (28) Katz, J. I. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 1994, 49, (29) Khattari, Z.; Steffen, P.; Fischer, T. M. J.Phys.: Condens.Matter 2002, 14, (30) Kim, H. Y.; Lee, H. J.; Kang, B. H. J.Colloid Interface Sci. 2002, 247, (31) Krasovitski, B.; Marmur, A. Langmuir 2005, 21, (32) Mahadevan, L.; Pomeau, Y. Physics of Fluids 1999, 11, (33) Moumen, N.; Subramanian, R. S.; McLaughlin, J. B. Langmuir 2006, 22, (34) Nakajima, A.; Suzuki, S.; Kameshima, Y.; Yoshida, N.; Watanabe, T.; Okada, K. Chem.Lett. 2003, 32, (35) Narhe, R.; Beysens, D.; Nikolayev, V. S. Langmuir 2004, 20, (36) Narhe, R.; Beysens, D.; Nikolayev, V. S. International Journal of Thermophysics 2005, 26, (37) Olsen, D. A.; Joyner, P. A.; Olson, M. D. J.Phys.Chem. 1962, 66,

160 (38) Petrie, R. J.; Bailey, T.; Gorman, C. B.; Genzer, J. Langmuir 2004, 20, (39) Reznik, S. N.; Yarin, A. L. Physics of Fluids 2002, 14, (40) Richard, D.; Quere, D. Europhys.Lett. 1999, 48, (41) Rio, E.; Daerr, A.; Andreotti, B.; Limat, L. Phys.Rev.Lett. 2005, 94, /4. (42) Savino, R.; Paterna, D.; Lappa, M. J.Fluid Mech. 2003, 479, (43) Seaver, A. E.; Berg, J. C. J.Appl.Polym.Sci. 1994, 52, (44) Steyer, A.; Guenoun, P.; Beysens, D. Phys.Rev.Lett. 1992, 68, (45) Subramanian, R. S.; Moumen, N.; McLaughlin, J. B. Langmuir 2005, 21, (46) Thiele, U.; Velarde, M. G.; Neuffer, K.; Bestehorn, M.; Pomeau, Y. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2001, 64, /12. (47) Velarde, M. G.; Redinkov, A. Y.; Ryazantsev, Y. S. J.Phys.: Condens.Matter 1996, 8, (48) Wasan, D. T.; Nikolov, A. D.; Brenner, H. Science (Washington, DC, United States) 2001, 291, (49) Yang, J. T.; Chen, J. C.; Huang, K. J.; Yeh, J. A. Journal of Microelectromechanical Systems 2006, 15, (50) Zhao, H.; Beysens, D. Langmuir 1995, 11, (51) Sakai, M.; Hashimoto, A.; Yoshida, N.; Suzuki, S.; Kameshima, Y.; Nakajima, A. Rev.Sci.Instrum. 2007, 78, (52) Gao, L.; McCarthy, T. J. Langmuir 2006, 22, (53) Andrienko, D.; Dunweg, B.; Vinogradova, O. I. J.Chem.Phys. 2003, 119, (54) Barrat, J. L.; Bocquet, L. Phys.Rev.Lett. 1999, 82, (55) Choi, C.-H.; Kim, C. Phys.Rev.Lett. 2006, 96, (56) Choi, C. H.; Westin, K. J.; Breuer, K. S. Physics of Fluids 2003, 15,

161 (57) Choi, C. H.; Kim, C. J. Phys.Rev.Lett. 2006, 97, (58) Choi, C. H.; Ulmanella, U.; Kim, J.; Ho, C. M.; Kim, C. J. Physics of Fluids 2006, 18, /8. (59) Cottin-Bizonne, C.; Cross, B.; Steinberger, A.; Charlaix, E. Phys.Rev.Lett. 2005, 94, /4. (60) de Gennes, P. G. Langmuir 2002, 18, (61) Granick, S.; Zhu, Y.; Lee, H. Nature Materials 2003, 2, (62) Hervet, H.; Leger, L. Comptes Rendus Physique 2003, 4, (63) Joseph, P.; Cottin-Bizonne, C.; Benoit, J. M.; Ybert, C.; Journet, C.; Tabeling, P.; Bocquet, L. Phys.Rev.Lett. 2006, 97, /4. (64) Joseph, P.; Tabeling, P. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2005, 71, /4. (65) Lauga, E. Langmuir 2004, 20, (66) Lauga, E.; Squires, T. M. Physics of Fluids 2005, 17, /16. (67) Spikes, H.; Granick, S. Langmuir 2003, 19, (68) Thompson, P. A.; Robbins, M. O. Phys.Rev.Lett. 1989, 63, (69) Thompson, P. A.; Troian, S. M. Nature (London) 1997, 389, (70) Tretheway, D. C.; Meinhart, C. D. Physics of Fluids 2002, 14, L9-L12. (71) Tretheway, D. C.; Meinhart, C. D. Physics of Fluids 2004, 16, (72) Vinogradova, O. I. J.Phys.: Condens.Matter 1996, 8, (73) Vinogradova, O. I. Langmuir 1996, 12, (74) Vinogradova, O. I. International Journal of Mineral Processing 1999, 56, (75) Choi, S. H.; Newby, B. Z. Langmuir 2003, 19, (76) Choi, S. H.; Newby, B. m. Z. Proceedings of the Annual Meeting of the Adhesion Society 2003, 26th, (77) Suda, H.; Yamada, S. Langmuir 2003, 19, (78) Song, F.; Cai, Y.; Zhang Newby, B. m. Appl.Surf.Sci. 2006, 253,

162 (79) Cox, R. G. J.Fluid Mech. 1986, 168, (80) Baudry, J.; Charlaix, E.; Tonck, A.; Mazuyer, D. Langmuir 2001, 17, (81) Bonaccurso, E.; Kappl, M.; Butt, H. J. Phys.Rev.Lett. 2002, 88, /4. (82) Bonaccurso, E.; Butt, H. J.; Craig, V. S. J. Phys.Rev.Lett. 2003, 90, /4. (83) Cho, J. H.; Law, B. M.; Rieutord, F. Phys.Rev.Lett. 2004, 92, /4. (84) Ellis, J. S.; Thompson, M. Physical Chemistry Chemical Physics 2004, 6, (85) Huang, P.; Guasto, J. S.; Breuer, K. S. J.Fluid Mech. 2006, 566, (86) Lauga, E.; Cossu, C. Physics of Fluids 2005, 17, /4. (87) Persson, B. N. J. Phys.Rev.Lett. 1993, 71, (88) Persson, B. N. J. Surface Science Reports 1999, 33, (89) Ponomarev, I. V.; Meyerovich, A. E. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2003, 67, /12. (90) Vinogradova, O. I.; Yakubov, G. E. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2006, 73, /4. (91) Voronov, R. S.; Papavassiliou, D. V.; Lee, L. L. J.Chem.Phys. 2006, 124, /10. (92) Zhu, Y.; Granick, S. Phys.Rev.Lett. 2001, 87, /4. (93) Zhu, Y.; Granick, S. Langmuir 2002, 18, (94) Huethorst, J. A. M.; Marra, J. Langmuir 1991, 7, (95) Sakai, M.; Song, J. H.; Yoshida, N.; Suzuki, S.; Kameshima, Y.; Nakajima, A. Surf.Sci. 2006, 600, L204-L208. (96) Sakai, M.; Song, J. H.; Yoshida, N.; Suzuki, S.; Kameshima, Y.; Nakajima, A. Langmuir 2006, 22, (97) Suzuki, S.; Nakajima, A.; Sakai, M.; Song, J. H.; Yoshida, N.; Kameshima, Y.; Okada, K. Surf.Sci. 2006, 600, (98) Dimitrakopoulos, P.; Higdon, J. J. L. J.Fluid Mech. 1997, 336,

163 (99) Dimitrakopoulos, P.; Higdon, J. J. L. J.Fluid Mech. 1999, 395, (100) ElSherbini, A. I.; Jacobi, A. M. J.Colloid Interface Sci. 2006, 299, (101) Elwing, H.; Welin-Klintstroem, S. Bioprocess Technology 1996, 23, (102) Gogte, S.; Vorobieff, P.; Truesdell, R.; Mammoli, A.; van Swol, F.; Shah, P.; Brinker, C. J. Physics of Fluids 2005, 17, /4. (103) Basu, S.; Nandakumar, K.; Masliyah, J. H. J.Colloid Interface Sci. 1997, 190, (104) Ben Amar, M.; Cummings, L. J.; Pomeau, Y. Physics of Fluids 2003, 15, (105) Checco, A.; Guenoun, P.; Daillant, J. Phys.Rev.Lett. 2003, 91, /4. (106) Cottin-Bizonne, C.; Barentin, C.; Charlaix, E.; Bocquet, L.; Barrat, J. L. European Physical Journal E: Soft Matter 2004, 15, (107) de Gennes, P. G. Reviews of Modern Physics 1985, 57, (108) de Ruijter, M. J.; De Coninck, J.; Oshanin, G. Langmuir 1999, 15, (109) Dorrer, C.; Ruehe, J. Langmuir 2006, 22, (110) Eggers, J. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2005, 72, /6. (111) Pismen, L. M.; Nir, A. Physics of Fluids 1982, 25, 3-7. (112) Zheng, L.; Wang, Y. X.; Plawsky, J. L.; Wayner, P. C., Jr. Langmuir 2002, 18, (113) Cheikh, C.; Koper, G. Phys.Rev.Lett. 2003, 91, /4. (114) Lauga, E.; Brenner, M. P. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2004, 70, /7. (115) Pit, R.; Hervet, H.; Leger, L. Tribology Letters 2000, 7, (116) Zhu, Y.; Granick, S. Materials Research Society Symposium Proceedings 2001, 651, T4. (117) Zhu, Y.; Granick, S. Phys.Rev.Lett. 2002, 88, /4. (118) Cassie, A. B. D. Discussion Faraday SOCiety 1952, 75,

164 (119) Israelachvili, J. N.; Gee, M. L. Langmuir 1989, 5, (120) Pease, D. C. J.Phys.Chem. 1945, 49, (121) Fadeev, A. Y.; McCarthy, T. J. Langmuir 1999, 15, (122) Fadeev, A. Y.; McCarthy, T. J. Langmuir 2000, 16, (123) Ren, S.; Yang, S.; Zhao, Y.; Zhou, J.; Xu, T.; Liu, W. Tribology Letters 2002, 13, (124) Leger, L. J.Phys.: Condens.Matter 2003, 15, S19-S29. (125) Choo, J. H.; Spikes, H. A.; Ratoi, M.; Glovnea, R.; Forrest, A. Tribology International 2006, 40, (126) Yoshizawa, H.; Israelachvili, J. J.Phys.Chem. 1993, 97, (127) Yoshizawa, H.; Chen, Y. L.; Israelachvili, J. J.Phys.Chem. 1993, 97, (128) Persson, B. Physical Review B: Condensed Matter and Materials Physics 1993, 48, (129) Homola, A. M.; Israelachvili, J. N.; Gee, M. L.; McGuiggan, P. M. Journal of Tribology 1989, 111, (130) Kumacheva, E. Prog.Surf.Sci. 1998, 58, (131) Ou, J.; Rothstein, J. P. Physics of Fluids 2005, 17, /10. (132) Angst, D. L.; Simmons, G. W. Langmuir 1991, 7, (133) Balgar, T.; Bautista, R.; Hartmann, N.; Hasselbrink, E. Surf.Sci. 2003, , (134) Bhat, R. R.; Fischer, D. A.; Genzer, J. Langmuir 2002, 18, (135) Bhat, R. R.; Genzer, J.; Chaney, B. N.; Sugg, H. W.; Liebmann-Vinson, A. Nanotechnology 2003, 14, (136) Bierbaum, K.; Grunze, M.; Baski, A. A.; Chi, L. F.; Schrepp, W.; Fuchs, H. Langmuir 1995, 11, (137) Bos, R.; De Jonge, J. H.; Van de Belt-Gritter, B.; De Vries, J.; Busscher, H. J. Langmuir 2000, 16, (138) Brunner, H.; Vallant, T.; Mayer, U.; Hoffmann, H.; Basnar, B.; Vallant, M.; Friedbacher, G. Langmuir 1999, 15,

165 (139) Brzoska, J. B.; Azouz, I. B.; Rondelez, F. Langmuir 1994, 10, (140) Clear, S. C.; Nealey, P. F. Langmuir 2001, 17, (141) Delamarche, E.; Donzel, C.; Kamounah, F. S.; Wolf, H.; Geissler, M.; Stutz, R.; Schmidt-Winkel, P.; Michel, B.; Mathieu, H. J.; Schaumburg, K. Langmuir 2003, 19, (142) Doshi, D. A.; Shah, P. B.; Singh, S.; Branson, E. D.; Malanoski, A. P.; Watkins, E. B.; Majewski, J.; van Swol, F.; Brinker, C. J. Langmuir 2005, 21, (143) Fendler, J. H. Chem.Mater. 2001, 13, (144) Goldmann, M.; Davidovits, J. V.; Silberzan, P. Thin Solid Films 1998, , (145) Harada, Y.; Girolami, G. S.; Nuzzo, R. G. Langmuir 2003, 19, (146) Harada, Y.; Girolami, G. S.; Nuzzo, R. G. Langmuir 2004, 20, (147) Hild, R.; David, C.; Mueller, H. U.; Voelkel, B.; Kayser, D. R.; Grunze, M. Langmuir 1998, 14, (148) Jeon, N. L.; Finnie, K.; Branshaw, K.; Nuzzo, R. G. Langmuir 1997, 13, (149) Kim, S.; Christenson, H. K.; Curry, J. E. Langmuir 2002, 18, (150) Kluth, G. J.; Sung, M. M.; Maboudian, R. Langmuir 1997, 13, (151) Krasnoslobodtsev, A. V.; Smirnov, S. N. Langmuir 2002, 18, (152) Le Grange, J. D.; Markham, J. L.; Kurkjian, C. R. Langmuir 1993, 9, (153) Nagayama, G.; Cheng, P. Int.J.Heat Mass Transfer 2003, 47, (154) Rozlosnik, N.; Gerstenberg, M. C.; Larsen, N. B. Langmuir 2003, 19, (155) Rye, R. R.; Nelson, G. C.; Dugger, M. T. Langmuir 1997, 13, (156) Shastry, A.; Case, M. J.; Boehringer, K. F. Langmuir 2006, 22, (157) Stevens, M. J. Langmuir 1999, 15, (158) McGovern, M. E.; Kallury, K. M. R.; Thompson, M. Langmuir 1994, 10,

166 (159) Parikh, A. N.; Allara, D. L.; Azouz, I. B.; Rondelez, F. J.Phys.Chem. 1994, 98, (160) Yu, X.; Wang, Z.; Jiang, Y.; Zhang, X. Langmuir 2006, 22, (161) Finnie, K. R.; Haasch, R.; Nuzzo, R. G. Langmuir 2000, 16, (162) Sakai, M.; Hashimoto, A.; Yoshida, N.; Suzuki, S.; Kameshima, Y.; Nakajima, A. Rev.Sci.Instrum. 2007, 78, (163) Hodges, S. R.; Jensen, O. E.; Rallison, J. M. J.Fluid Mech. 2004, 512, (164) Pit, R.; Hervet, H.; Leger, L. Phys.Rev.Lett. 2000, 85, (165) Schmatko, T.; Hervet, H.; Leger, L. Langmuir 2006, 22, (166) Schwartz, L.; Eley, R. R. J.Colloid Interface Sci. 1998, 202,

167 APPENDIX 4ADDITIONAL RESULTS AND DISCUSSION A-1. Surface Energies of OMDS Modified Surfaces Temperatures had a significant effect on the ability and amount of OMDS to react to the surface as clearly shown in Figure A-1. It is consistent with the general kinetic reaction principal, in which the reaction rate increases with the increase of reaction temperature. The more OMDS molecules reacted with the substrate surface, the higher the surface hydrophobicity or the lower the surface wettability. It is known that the surface hydrophobicity of a smooth surface is related to the surface energy. The lowest surface energy corresponds to the highest surface hydrophobicity or the lowest wettability. The values of surface energies (Figure A-1) decreased slowly at a temperature lower than 40 C as the contact time increased, but they decreased more rapidly at a higher temperature (e.g. 55 C) and reached the saturated value of ~ 30 mj/m 2 in about 30s. The surface energies indicated again that 50 C was a suitable temperature for generating OMDS gradient surfaces to be comparable to OTS gradient surfaces generated at room temperature. 150

168 60 50 Surface energy, γ (mj/m 2 ) contact time, t (s) Figure A-1. OMDS surface energies as a function of temperature at different contact times. CP was carried out at room temperature ( ), 40 C ( ), 50 C ( ), and 55 C ( ). At each contact time, with a lower temperature, less transferred OMDS molecules grafted to the surface, and a higher surface energy resulted. However, with the higher temperature of 55 C, the surface energy reached the saturated value of ~ 30 mj/m 2 in about 30s due to the fast reaction of OMDS molecules to the surface. 50 C was again found to be most suitable to generate OMDS with a reasonable increase of water contact angle as the contact time increases using the contact-printing method. 151

169 A.2. Surface Properties of Organosilane Modified Surfaces via Solution Method In our study, the solution method was also applied, using 2 mm hexane solution under ambient conditions, to produce the organosilane-modified surfaces of OTS, OMDS, and ODCS. The experimental results of both the advancing and the receding angles of water on each organosilane modified surface are shown in Table A-1. The ODCS modified surface gave the lowest contact angle and the lowest CAH, followed by the OMDS modified surface. All of the experimental results obtained from the CP technique and the solution deposition technique clearly indicated that the reactivity of organosilane molecules with silicon wafer followed the order: ODCS < OMDS < OTS. Therefore, a higher CP temperature was necessary to achieve a higher surface coverage with the contact time for OMDS and ODCS generated via CP. In this study, we only evaluate the formation of OMDS layers generated using CP at higher temperatures, since the reactivity of ODCS was found to be too low to achieve the desired surface coverage with the contact time period of our interests. Table A-1. Deposition time effects on the surface wettability of OTS, OMDS, and ODCS generated using the solution deposition technique 3 hours 24 hours θ a ( ) θ r ( ) θ a - θ r ( ) θ a ( ) θ r ( ) θ a - θ r ( ) OTS 105 ± 2 81 ± ± 4 83 ± 1 23 OMDS 84 ± 2 65 ± ± 2 73 ± 5 18 ODCS 78 ± 3 60 ± ± 2 63 ±

170 A.3. Surface Properties of Continuous OTS Gradient Surfaces The calibration curve of the dynamic contact angle vs. the position on the gradient surface in the dissertation text was obtained from the experimental results using a planar stamp. In a practical condition, this curve may not match well with the actual dynamic contact angle of a gradient surface. In order to verify whether the above calibration curve could be used to represent the actual wettability of the gradient surface, a large size (3.8 mm) of OTS continuous gradient surface was generated via CP. The wettability of the OTS gradient surface was directly measured via the sessile drop method. A water drop was dragged stepwisely, each with a small increment, from the hydrophobic side to the hydrophilic side along the gradient surface; at each particular position the advancing and the receding of the water drop were made. All the measurements were performed under ambient conditions (1 atm, ~24 C). The experimental measurements of apparent advancing and apparent receding contact angles of water on an OTS gradient surface are shown in Figure A-2. The solid line and the dashed line represented, respectively, the estimated advancing and receding contact angles of water formed on OTS based on the calibration curves. The measured receding water contact angle for the gradient surface was close to (at a longer contact time) or slight lower than (at a shorter contact time) the estimated receding contact angle while the measured advancing contact angle was lower than the estimated advancing contact angle from a few degrees to around 20. One of the reasons to cause such relatively lower contact angles on a gradient surface compared to the estimated values by using a planar stamp is the effect of the geographical shape of the stamp used. As shown 153

171 contact angle, θ ( ) contact time, t (s) Figure A-2. The advancing ( ) and receding ( ) contact angles of deionized water on the OTS gradient surface generated by using the CP technique. The solid line and the dashed line represented the estimated advancing and receding contact angles based on the experimental results obtained by using the planar stamp. The gradient size (S 0 ) was ~ 2.2 mm, corresponding to 43 s of contact. The advancing and the receding water contact angles were measured at each position using the sessile water drop. 154

172 in Table A-2, when using a hemispherical stamp to generate the homogeneous surface (one-time contact), both the advancing and the receding contact angles of water were from a few degree to ~ 20 lower than those obtained by using a planar stamp with the same contact time. Table A-2. Surface wettability of modified OTS homogeneous surfaces Contact Planar stamp Hemispherical stamp time (s) θ a ( ) θ r ( ) θ ( ) θ a ( ) θ r ( ) θ ( ) 1 53±4 35±1 44±2 47±3 28±2 38±2 5 81±4 55±3 68±3 61±2 39±1 50± ±3 67±2 75±3 80±2 55±3 68± ±2 79±2 88±2 91±2 68±3 80±3 The increase in surface coverage of organosilane and subsequently the water contact angle is the result of organosilane molecules transferred to a substrate surface from the PDMS stamp during CP. When we prepared the inked stamp, the organosilane molecules not only stay on the PDMS surface but also may penetrate into the PDMS stamp. More organosilane molecules are expected to be left on the stamp surface and to penetrate into the planar stamp than the hemispherical stamp because of the longer retention time of the ink solution on the planar stamp, which could be caused by the experimental procedure. During CP, both the molecules on the stamp surface and inside the stamp could be transferred to the substrate surface, but the organosilane molecules 155

173 inside the stamp must first diffuse to the stamp surface. It is possible that fewer organosilane molecules are transferred to the substrate surface when using the curved PDMS stamp in the CP and result in the relatively lower contact angle of water. Another reason may be the experimental measurement. It is well known that when a water droplet is placed on a gradient surface (Figure A-3), it has a tendency to advance to the hydrophilic end and to recede from the hydrophobic end until it reaches equilibrium. As a result, the static contact angle of the droplet in Figure A-2 under equilibrium condition reflects the actual receding contact angle at point A of the droplet and the actual advancing contact angle at point B of the droplet. When performing the contact angle measurements by using a sessile drop method, the whole droplet is either Figure A-3. A water droplet on a wettability gradient surface generated by CP technique with OTS. At a steady state, the receding contact angle is formed at the point A of the droplet while the advancing contact angle at the point B of the droplet. advanced or receded at the same time as described before in Chapter III. Since the droplet at point A tends to recede due to the wettability gradient, the apparent advancing contact angle of the droplet is smaller than the actual advancing contact angle at this particular position. On the other hand, the apparent advancing contact angle at point B of the 156

174 droplet is quite close to the actual advancing contact angle, because at point B the droplet tends to advance. When the whole droplet is receding, the apparent receding contact angle at point A of the droplet is quite close to the actual receding contact angle at this particular position, because at this side the droplet tends to recede to reach the minimum contact angle value. However, the apparent receding contact angle at point B of the droplet is larger than the actual receding contact angle at this particular position, because at point B the droplet tends to advance to reach the maximum contact angle value. As a result, the apparent advancing contact angle would be expected to be slightly smaller than the actual advancing contact angle while the apparent receding contact angle would be expected to be slightly greater than the actual receding contact angle. The results shown in Figure A-3 suggested the combined effects of these two factors. A.4. Effect of Diffusion The CP technique is a convenient method for generating gradient surfaces; however, some issues associated with CP could have undesired impacts on the resulting gradient surfaces. One of the major issues is the diffusion of organosilane molecules during and after CP. Past studies indicated that the diffusion of organosilane molecules occurred, e.g. organosilane domains formed outside of the contact area, during and after CP. The molecular weight of organosilane as well as the CP conditions (i.e. temperature, contact time, and the humidity) greatly influences the kinetic competency of the transport mode of organosilane molecules through the vapor phase. Among them, the chain molecular weight and the molecular structure of organosilane are directly related to the vapor pressure of organosilane, which is Pa for OTS and Pa for OMDS at

175 C, and 0.33 Pa for OMDS at 50 C. Diffusion has a negligible effect on CP using a planar stamp, since the substrate surface is in complete contact with the stamp. However, when a curve stamp is used to generate the gradient surface, the diffusion effect needs to be addressed. Therefore, the systematic study to investigate the degree of the diffusion effect on the contact area was experimentally conducted for both OTS and OMDS under various conditions. To investigate the effect of organosilane molecules diffusion, a homogeneous organosilane surface with a certain contact area (e.g. having a radius of a = 100 μm in Figure A-4) was generated by bringing a hemispherical PMDS stamp into contact with 2a 2b 2a 2b (a) (b) Figure A-4. Illustration of diffusion of organosilane molecules during (a) and after (b) the CP. Red arrows show the possible diffusion pathways during and after the CP, 2a is the actual contact diameter and 2b is the apparent contact diameter with the diffusion effect. the SW surface for a certain time at ambient pressure. The CP temperature was room temperature for OTS and 50 C for OMDS. After proper post treatments, the apparent contact area (measured in term of the radius of b) was experimentally visualized by 158

176 depositing a water mist on the modified surface, since the area modified by OTS or OMDS is more hydrophobic than its oxidized surrounding. The diffusion zone was estimated as (b-a). A.4.1 CP of OTS While the contact time is a primarily factor for the resulting surface coverage of the contact-printed OTS samples, the length of the annealing time also influences the amount and the quality of OTS deposited to the surface. We defined the annealing time as the time used for the contact printed sample to be stored inside a Petri dish for the reaction to complete. The annealing time effect on the diffusion of OTS was investigated by using samples having the CP time of 30 s, and the results are shown in Figure A-5. In Figure A-5, the diffusion zone increased with annealing time up to 30 minutes and then approached a plateau value (about 30% of increase) in about 60 minutes of annealing. Based on this result, 60 minutes of annealing time was chosen for all contact printed samples. The effect of contact time on diffusion of contact printed OTS was also investigated by maintaining annealing time of 60 minutes and the results are summarized in Figure A-6. The diffusion, in terms of (b-a) or (b-a)/a, increases almost linearly with the increase of contact time. The experimental observations from the deposition of water mist showed that the apparent radius of the OTS modified area became smaller as the water mist continued to be deposited on the sample surface. This indicated that the diffusion region was only slightly modified by the OTS molecules diffused to the region. 159

177 (b-a), (μm) (b-a)/a annealing time, t (min) Figure A-5. Diffusion of OTS modified surfaces using the CP technique with a contact time of 30 s and the annealing time (the time that the sample was stored inside a plastic Petri dish after CP but prior to being sonicated) varied from 5 minutes to 60 minutes. Both the absolute diffusion zone (b-a, ) and the relative diffusion zone ((b-a)/a, ) showed that the diffusion zone increases within the first 30 minutes of annealing and then plateaus at ~ 30 minutes of annealing. 160

178 (b-a), (μm) (b-a)/a contact time, t (s) Figure A-6. Diffusion of OTS modified surfaces using the CP technique with the annealing time of 60 minutes and the contact time varied from 1 second to 120 seconds. Both the absolute diffusion zone (b-a, ) and the relative diffusion zone ((b-a)/a, ) showed that the diffusion zone increases with the increase of the contact time with a roughly linear relationship. 161

179 The diffusion effects on an OTS modified surface consist of two pathways. As shown in Figure A-4, one is that OTS molecules diffuse either laterally or vertically from the non-contact area of the curve stamp to the substrate surface during the CP process; the degree of the diffusion depends on the contact time and the vapor pressure of OTS as well as the distance between the stamp surface and the substrate surface. The longer the contact time, the more OTS molecules could diffuse to the substrate surface. The vicinity of the contact area receives more OTS molecules diffused from the stamp due to the shorter distance between the stamp surface and the substrate surface. Another pathway is that after CP, OTS molecules, which did not react with the substrate surface, may evaporate and diffuse as shown in Figure A-4. Figure A-5 shows that the diffusion zone increased sharply in the first 10 minutes of annealing. This indicates that some of OTS molecules transferred onto the substrate surface do not react with the silanol groups on the substrate surface and after a short time, most of OTS molecules are consumed by the reaction. As a result, the diffusion zone increases less as the annealing time increase. A.4.2 CP of OMDS As seen from OTS results, the contact time did affect the degree of diffusion. However, some other factors, such as temperature, also play important roles in the diffusion of organosilane molecules. The diffusion rate would be expected to increase as the temperature increases. In our experiments, OMDS CP was conducted at 50 C, so the temperature effect on diffusion cannot be ignored. 162

180 The homogeneous OMDS surfaces were generated at both room temperature and 50 C. The actual contact radius of each sample was kept almost the same (a ~ 110 μm). The apparent radius (b) of the OMDS modified surface was also experimentally estimated as that of the OTS modified surface. As shown in Figure A-7, the diffusion zone (b-a), at each temperature, increased with the increase of contact time and the temperature had a significant effect on the degree of diffusion. For the OMDS samples prepared at 50 C, even when the deposition time of the water mist was sufficiently long, there was a distinct difference between the final apparent radius (b) and the actual contact radius (a). This indicated that a higher CP temperature resulted in more OMDS molecules diffusing to the vicinity of the contact area and grafting to the surface. The diffusion region also had a relatively lower surface wettability in comparison with the samples prepared at room temperature. As discussed above, the diffusion zone is caused by two pathways: vertical diffusion of OMDS molecules and lateral diffusion of OMDS molecules. When other parameters affecting the diffusion zone are fixed (e.g. humidity, contact area, concentration of OMDS), the vapor pressure of OMDS at different temperatures dominates the diffusion, which is estimated about Pa at room temperature and 0.33 Pa at 50 C. The higher temperature not only increases the diffusion rate of OMDS molecules but also rapidly increases the reaction rate. As seen in Figure A-7, the diffusion zone at 50 C increases over 3 times the area than that at room temperature. 163

181 (b-a), (μm) (b-a)/a contact time, (s) Figure A-7. Diffusion of OMDS modified surfaces using the CP technique with annealing time of 60 minutes and the contact time varied from 1 second to 120 seconds. The experiments were carried out at both ambient condition (unfilled symbols) and 50 C (filled symbols) by using a hemispherical stamp. Both the absolute diffusion zone (b-a, and ) and the relative diffusion zone ((b-a)/a, and ) showed that the diffusion zone increases with contact time and the temperature has a significant effect on the diffusion zone. 164

182 Both OTS and OMDS have a similar molecular structure and the vapor pressures of these two organosilanes at 25 C are slightly different, which are Pa and Pa for OTS and OMDS, respectively. Similar effects of diffusion would be expected. Experimental results in Figure A-5 for OTS and Figure A-6 for OMDS (open symbols) at room temperature clearly indicated that OTS gave a slightly larger effect of diffusion for each timeframe of contact. A.5. Actual Experimental Setup of Droplet Movements on a Gradient Surface Figure 3-5 in the dissertation text shows the schematic illustration of the experimental setup to observe the droplet movement on a continuous organosilane gradient surface. However, in the experiments to carry out the droplet movements, the actual experimental setup used is showed in the following (Figure A-8). A.6. Comparison of Droplet Movements under Two Different Video Recording Systems A frame by frame analysis of droplet motion from the video-recorded images allow us easily to measure the droplet sizes, droplet locations, and the velocity of droplet migration on a gradient surface. The resolution of the video camera for capturing the droplet motion has a larger effect on the accuracy of the experimental measurement. The regular video recording system in our lab has just a frame rate of 30 fps. In order to verify whether our recording system can be used to capture droplet movements without significant error, a pair of experiments on water droplet movements was conducted on the same OTS wettability gradient surfaces prepared by using the CP technique with S 0 of about 75 μm. Cold water mist was used as a source of water droplets and droplet 165

183 OM humidifier substrate Figure A-8. Actual experimental setup of water droplet movements on a gradient surface. The substrate used was about 1 cm 0.5 cm and the gradient size in diameter was less than 1 mm. 166

184 movements were recorded by using both the high speed camera (Redlake PCI 2000) and our recording system. The Redlake PCI-2000 high-speed camera in Dr. Reneker s lab can capture 60 to 4000 fps, but the shutter speed of 1/250 s in our experiment is chosen because the video images are blurred beyond this shutter speed. The droplet velocities obtained from both video recording systems are summarized in Figure A-9. The droplet velocity was estimated from the video prints, based on at least three frames for the highspeed camera and one or two frames of the water droplet movement in our recording system. The experimental results indicate that there is no great difference between these two recording systems while using the high-speed camera leaded to more scattered data. The possible reason for scattered data could be that the droplets were collected from only total 10s of video of the water droplet movements with less droplets found to move on the gradient surface while the experimental data on droplet movements gathered using the regular recording system were obtained from 10 minutes of video. Anyway, the trend of the relationship between the droplet velocity and the droplet radius is quite close, therefore, the rest of the our experiments were only recorded by using regular video system, which can continue to record video up to several hours while the Redlake PCI 2000 can only record up to 2 s of video duration (500 images) each time. A.7 Effects of Gradient Constitution (continuous vs. step-wise) In a stepwise gradient surface, if each step size is sufficiently small the stepwise gradient surface is supposed to be quite close to a continuous gradient surface. In order to evaluate the gradient constitution effect on the droplet movement, water droplet movements were carried out on both continuous and stepwise gradient surfaces with the 167

185 1500 velocity (μm/s) droplet radius, R (μm) Figure A-9. Droplet motion behavior on two similar OTS continuous gradient surfaces under two different video recording systems. S 0 of the gradient surface was about 75 μm. and denote the high speed camera (250 fps) and the regular video recording system (30 fps) in our lab, respectively. 168

186 similar gradient size. On the stepwise gradient surfaces, when a water droplet starts to move toward the higher wettability region, the droplet must occupy at least two adjacent steps so that there is enough driving force acting on the droplet to overcome the resistant forces caused by the CAH. The diameter of droplets should be larger than the gradient step size to ensure that the droplet can continue to move. Experimental observations showed that the base radius of a water droplet ranged randomly from 26 μm to 52 μm on the OTS stepwise gradient surface and 24 μm to 48 μm on the OMDS stepwise gradient surface, which were all larger than the half of each gradient step (less than 40 μm). The velocities of water droplets on both the continuous and stepwise gradient surfaces were plotted together in Figure A-10. Figure A-10(a) shows that similar slopes for the OTS gradient surfaces were obtained. According to Chaudhury and Whitesides 19, in order for a water droplet to spontaneously move on a gradient surface, the contact angle at the receding edge of the water droplet should be larger than that at the advancing edge of the droplet. As shown in the Table A-3, for the stepwise gradient surface, the water droplet must occupy at least three adjourning steps to satisfy the requirement of the droplet movements, and a droplet size of larger than 40 μm was resulted. For the continuous gradient surface, the surface wettability gradually changed from the edge to the center of the contact-printed area, so the same size of droplets moved easier on the continuous gradient surface than on the stepwise gradient surface. Similar results were obtained on the OMDS gradients shown in Figure A-10 (b), much smaller droplet could move toward the higher wettability region. For the stepwise gradient surface, if the step size become smaller and smaller, then it will be quietly close to the continuous gradient 169

187 1500 (a) velocity (μm/s) R/S (b) velocity (μm/s) R/S 0 Figure A-10. Droplet movements on the continuous and the stepwise wettability gradient surfaces with a similar gradient size (S 0 around 130 μm). (a) OTS continuous ( ) and stepwise ( ) gradient surfaces, and (b) OMDS continuous ( ) and stepwise ( ) gradient surfaces. The data showed that smaller water droplets can move on continuous gradient surfaces and resulted in a smaller minimum critical droplet size. 170

188 surface. Therefore, the similar results would be expected. Figure A-9 showed that the droplet velocity on the stepwise gradient surfaces for both OTS and OMDS seemed to be no big difference. Table A-3. Surface properties (water contact angles and surface energy) of the stepwise gradient surfaces of OTS and OMDS. Each stepwise gradient surface consisted accordingly of five steps of contact with different particular contact time. OTS OMDS CP time θ a ( ) θ r ( ) γ (mj/m 2 ) CP time θ a ( ) θ r ( ) γ (mj/m 2 ) (s) (s) A.8. Effects of Water Droplet Placement All the above experiments were carried out under the cold-water mist condition. In order to better understand the effects of the cold-water mist on the droplet movements, two similar continuous OTS gradient surfaces were used for the comparison study; one used water droplets formed from the condensation of the cold-water mist while in the other droplets were placed on the gradient surface by a glass micro- pipette. R/S 0 was plotted against L/ S 0 (Figure A-11), and the data from both conditions basically fell on the same straight line with a positive intercept (ca ) on the R/S 0 axis, which corresponded to R cmin of 23.6 μm. This indicated that the water droplet displacement does not change the critical conditions of droplet movements on gradient surfaces. 171

189 R/S L/S 0 Figure A-11. Comparison of relative radius of a droplet (R/S 0 ) as a function of relative location of the droplet (L/S 0 ) on two gradient surfaces with same surface property under different conditions of water droplet placement. and represent the water droplet formed from the cold water mist and from a micro-needle, respectively. All the experimental data fall on the same straight line with a positive intercept on the R/S 0 axis. This suggested that this relationship is fixed for the same organosilane as using the CP technique to generate a continuous gradient surface. 172

190 A.9. Topography of organosilane modified surface after a drop moves away When a water drop with PS particles inside passes away, there always some particles left behind on the sample surface. The surface topography before and after the drop motion are shown in Figure A μm 500 μm 200 μm Figure A-12. OTS modified surface images before and after a water drop with PS particles pass through the surface. The top-left image showed the water drop on the OTS modified surface while the other images showed the morphology of the surface after the water drop traveled pass. The single PS particle is spherical and is about 40 μm in diameter. A.10 Drop movements on a DDS inclined surface In experiments of water drop movements with tracer PS particles suspended inside the water drop, the particles move along with the water drop. The movements of tracer particles inside the drop reflect the internal fluidity of the drop while the movements of trace particles at the interface of liquid/solid represent the drop motion at the interface. As a result, velocities of rolling, sliding, and possible slipping of the drop 173