HYDRODYNAMIC FORCE MICROSCOPY

Transcription

1 HYDRODYNAMIC FORCE MICROSCOPY by Elaine Schmid Ulrich Copyright Elaine Schmid Ulrich 2008 A Dissertation Submitted to the Faculty of the DEPARTMENT OF OPTICAL SCIENCES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2008

2 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Elaine Schmid Ulrich entitled Hydrodynamic Force Microscopy and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy Date: August 4, 2008 Srinivas Manne Date: August 4, 2008 Thomas Milster Date: August 4, 2008 Ewan Wright Final approval and acceptance of this dissertation is contingent upon the candidate s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: August 4, 2008 Dissertation Director: Srinivas Manne

3 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder. SIGNED: Elaine Ulrich

4 4 ACKNOWLEDGEMENTS I would like to first thank my dissertation research advisor, Srinivas Manne. I really enjoyed working on this project, and I feel privileged to have had the opportunity to do this work. He gave me the freedom and resources to make this all possible. I had considerable help from Chris Limbach and Alex Fay in setting up equipment for the experiments undertaken, and their thoughtful discussions and great attitudes made working in the lab enjoyable. Anne Murdaugh, my faithful labmate, saw me through good times and bad. She is a great scientist and friend, to whom I will be forever grateful. Ian Jones has been a wonderful partner and companion throughout this process. His thoughtful comments and help in editing were outstanding. My family: Dad, Mom, Ali, Taylor, and all my grandparents have supported me all along this journey and I could not have done this without their love and support. Russ Frye and Mirto Stone have treated me like family, and helped me to keep looking forward. Robin Richards, Steve ONeil and everyone at the OTT kept me smiling and helped to remind me each week, of all the reasons I love what I am doing. Mike Nofziger and Jim Palmer have been great friends, mentors and examples of the best that the University of Arizona has to offer. They reminded me not to take myself too seriously, and gave me an appreciation for the irreverence that is necessary to really enjoy the scientific endeavors we undertake. Alex Cronin, Chris Dombrowski, and Burle Corp. all provided experimental equipment to me free of charge. Eric Lauga s initial conversations sparked the beginnings of this work, thanks to him for asking and answering questions. Finally, thanks to my committee members, Ewan Wright and Thomas Milster. I hope this work has been as fun and interesting for them to explore as it was for me.

5 5 For the women in my family: Clara, Jean, Betty, Danette, Alexandra, Lonna, Mary, Kathy, A m y, Cristina, Kirsten, Anna, Chelsea, Rosa and Jeannie

6 6 TABLE OF CONTENTS LIST OF FIGURES... 8 LIST OF TABLES ABSTRACT INTRODUCTION TO ATOMIC FORCE MICROSCOPY HI S T O R Y : TRADITIONAL ATO M I C FORCE MICROSCOPY: BASIC PRINCIPLES: CONTACT MODE FORCE VS. DISTANCE CURVES CONTACT MODE CONSTANT FO R C E V S. CONSTANT HEIGHT IMAGING OTHER AFM MEASUREMENT TECHNIQUES INTRODUCTION TO FLUID FLOW THE REYNOLDS NUMBER: THE KNUDSEN NUMBER: POISEUILLE FLOW: EN T R Y LENGTH: DRAG: FLUID JETS AND ENTRAINMENT THE COANDA EFFECT KNUDSEN AND MOLECULAR FLOW CONSIDERATIONS CU R R E N T FLOW MEASUREMENT METHODS CONTACT HYDRODYNAMIC FORCE MICROSCOPY INTRODUCTION TO HYDRODYNAMIC FORCE MICROSCOPY HFM THEORY AND LIMITS POROUS SAMPLES PR I M A R Y CONTACT HFM TECHNIQUES CONTACT HFM EXPERIMENTAL RESULTS HFM CALIBRATION FLOW THROUGH A 20 MICRON DIAMETER HOLE: CANTILEVER CONVOLUTION FLOW THROUGH MICROCHANNEL PLATES: DETECTING LOCAL FLOW VARIATIONS AND SUBSURFACE FOULING TRACK ETCH MEMBRANES: POISEUILLE FLOW DETECTION LA C E Y CARBON FILM: UNIFORM FLOW THROUGH A SCREEN TEM GRID: SCREEN OR CHANNELS? VACUUM STUDIES OTHER FLOW CONFIGURATIONS USING CONTACT MODE HFM... 79

7 7 TABLE OF CONTENTS CONTINUED 5. TAPPING HFM, HFM IN FLUIDS AND FUTURE DIRECTIONS TAPPING MODE LIQUID FLOWS ENGINEERED FLOWS AND PROBES CONCLUSIONS REFERENCES... 94

8 8 LIST OF FIGURES Figure 1-1AFM measures surface topography. A laser beam is reflecteded off the back of a springy cantilever with a sharp tip. As the tip scans across the surface, the vertical deflection of the cantilever is measured by monitoring changes in the position of the laser beam on a quadrant photodetector. The scanner and photodetector send and receive signals from a computer which processes the deflection data to produce a topographic map of the surface with nanometer vertical and lateral resolution Figure 1-2: AFM operation Figure 1-3 Typical AFM images of some fabricated quantum dots. The Height image (left) shows the topography of the surface, deflection (center) can be used for edge detection and friction (right) indicates variations in the surface roughness and chemical makeup Figure 1-4 Quadrant Photodiode. The laser spot is reflected off the back of the cantilever and moves around the quadrant photodetector. By mapping the photodiode signal, a topographic and lateral force images are created Figure 1-5 AFM contact mode cantilevers Figure 1-6 Typical Height, Deflection, and Friction images of a calcite crystal with monolayer growth of calcium sulfite, the friction image indicates the square pits are filled with the calcium sulfite Figure 1-7 A Typical AFM Force Curve Figure 1-8 Deflection setpoint on photodiode Figure 1-9 The Flow cell and the AFM Scanner Figure 2-1 Limits of approximations in modeling gas micro flows. L (vertical axis) corresponds to the characteristic length and n/n o is the number density normalized with corresponding atmospheric conditions. The lines that define the various Knudsen numbers regimes are based on air at isothermal conditions at T= 273 K. (Redrawn from Karniadakis 11 ) Figure 2-2 Poiseuille flow through a pipe develops a parabolic velocity profile, with a maximum

9 9 velocity in the center of the pipe and zero velocity at the fluid/pipe wall interface Figure 2-3A parabolic Poiseuille flow profile develops as the fluid moves through the pipe Figure 2-4 Flow near a sphere. Viscous drag acts to create a layer with zero velocity around the sphere. Behind the sphere, along the flow axis, the flow velocity is lower than the bulk velocity, and increases with distance from the sphere Figure 2-5 As a fluid jet moves away from the orifice it expands and entrains surrounding fluid. The maximum velocity also decreases Figure 2-6 The Coanda Effect leads to the attachment of a jet flow to a nearby wall Figure 3-1 Various Hydrodynamic Force Microscopy (HFM) techniques Figure 3-2 Hydrodynamic Force Microscopy (HFM) applied to porous samples. Drag forces on the cantilever are used to image local flow profiles, map the substrate pore structure, and pinpoint subsurface fouling undetectable by conventional topography scans Figure 4-1 A 10 µm radius hole without (left) and with (right) a jet of nitrogen. Flow velocity is ~1m/s Figure 4-2 A series of 100 µm square HFM scans. All images are taken slightly above the surface while a constant pressure of nitrogen gas is applied to a 10 µm radius hole. The highest pressure is applied in the upper left corner; the lowest pressure is in the lower right corner. As the flow is decreased, the probe interaction area becomes increasingly isolated to the region near the pyramid probe tip and less on the entire cantilever. The wavy character of the images is due to optical interference Figure 4-3 Data taken while scanning the cantilever over a jet from a 20 µm hole is a convolution of the jet and the cantilever. A simulation (right) of the cantilever convolved with the force due to a uniform jet of air is consistent with our experimental results (left) Figure 4-4 A height image of the nitrogen jet on the left indicates upward deflection of the cantilever due to the flow. A friction image of the jet on the right indicates that the cantilever twists in opposite directions as it passes over the nitrogen jet

10 10 Figure 4-5 A typical 30 µm square contact AFM topography image of a microchannel plate Figure 4-6 An image of the flow above a microchannel plate indicates that the jets of air are not centered above the center of the channels. This is because the channels are not perpendicular to the surface, so the nitrogen jets exiting each channel have a lateral as well as vertical velocity component Figure 4-7 Height image and a profile of the flow above the surface show parabolic shape due to Poiseuille flow Figure 4-8 Contact mode image of the 2 µm microchannel plate with flow. The holes of the channels no longer appear black (as in the previous figures) as the tip is lifted by the flow in each channel. Each flow profile has a slight parabolic shape due to Poiseuille flow. This parabolic flow is visible as the lumps in the bottom of each hole in the line section Figure µm square scan of a glass microchannel plate comprising 2 µm diameter, 120 µm deep cylindrical pores. (a) Height image of plate surface without flow. (b) Deflection image taken 4 with tip positioned ~500 nm above surface with flow ( P 10 P a, v ~ 5 m/s). Circles and arrows indicate the same areas and locate four fouled pores. The dark features in 2(b) were reproduced over several successive images. The horizontal structure that appears to link some of the jets in the deflection image is likely due to optical interference Figure 4-10 Top row: 10 µm square images of a polycarbonate track etch membrane. White box indicates the same region in each image. Bottom row: 6 µm long sections along the lines indicated in yellow in images. Features i, ii and iii are the same in all images and sections Figure Cantilever force profiles taken from 13 pores in figure 4-10, + s indicate the data is taken from 3(b) where the tip was in contact with surface. Dots indicate data from the same 13 pores in image 3(c) where the tip was 500 nm above surface. Each profile indicates the force on the cantilever as the tip scans across each pore and is displayed along with its best parabolic fit line. Maximum force set at r = 0 and arbitrary offset applied for clarity Figure 4-12 Flow interactions localized to the tip region can give excellent resolution (left). Flow

11 1 1 interactions that involve the cantilever give a background deflection, but local fluctuations are still detectable as the local flow-tip interaction is greater than the flow-cantilever interaction.. 69 Figure 4-13, Simulation of flow mapping with varying tip sizes. A convolution of a uniform circular plate with radius r and a cylindrical parabolic flow with 500 nm radius. For an effective probe size < 1 µm the parabolic shape is reproduced near the center, though broadened Figure 4-14 Lacey Carbon Film (LCF) with and without flow. Web-like screen created by nm diameter carbon-coated threads. (a) AFM topography image of an LCF without flow (b) HFM image of the same area of the LCF with flow appears to have a noisy flat bottom below threads. (c) Comparison of scaled sections from (a) and (b) show a flat profile created by uniform flow Figure 4-15 Partial contact images of LCF with flow. Even very close to the surface, the location of the LCF threads is not distinguishable on the left side of these images Figure 4-16a line section from the TEM grid indicates non-uniform flow (the short wide humps in the bottom of each well) indicating the flow is being altered by its interaction with the sample. In addition, the tip may be experiencing some drafting as it passes over the grid Figure µm square images of the same area of a TEM Grid. Each row is made up of the Height, Deflection and Friction images from a single scan. The first row is a contact image taken with no flow. Rows 2-4 are all taken with the same flow velocity, but with decreasing amounts of contact with the surface. The friction images in particular show significant optical interference due to light being reflected from the shiny copper sample interfering with light from the cantilever. The optical interference appears as horizontal waves or stripes as see in Figs. 4-2, 4-4 and Figure µm square images taken on/above the TEM grid. The first image is a contact image taken with no flow. The second is taken just above the surface (~50 nm) with flow. The third image shows the first two images overlaid, the flow maxima correspond to the apertures in the TEM grid

12 12 Figure µm scans of the 20 µm aperture with suction. The first is a contact image with no flow through the aperture (the dark area near the top of the image). The second image shows the tip being brought into contact with the surface due to the suction through the hole. The third demonstrates non-contact imaging as the cantilever is drawn downwards due to the suction, but does not make contact with the surface. The last image is from Chapter 4 and depicts flow out of the hole. Note the inverted contrast from the 2 vacuum images, which also demonstrate cantilever convolution effects similar to the images of the outward jet from this same aperture Figure 5-1 Tapping mode cantilevers, Note that these have not only a different geometry, but also a higher spring constant and resonance frequency Figure 5-2Basic HFM tapping mode technique Figure µm square Tapping mode image taken above the surface of the 20 mm hole aperture with flow. The image displays a convolution of the tapping mode tip shape due to the same convolution effects seen in Chapter 5 with a contact mode tip Figure 5-4 Tapping HFM method (not to scale ). Helium streams through the track etch membrane while Nitrogen is used as a sweep gas. The nitrogen source was much larger than the cantilever or membrane channels Figure 5-5 Helium flow through a track etch membrane. Above the white line nitrogen sweep gas was applied and contrast is good, below the white line, the helium flow is allowed to build up a layer of gas near the surface which appears to decrease the contrast Figure 5-6 A line section taken along the black line from a track etch membrane with He gas flow. Above the white line nitrogen gas is used to sweep away excess He from the surface, below the white line the nitrogen gas is turned off while the He continues to flow, the apparent pore depth is much smaller without the sweep gas, resulting in a loss of contrast Figure 5-7 LCF with water flow. The images are very noisy, and not crisp

13 13 LIST OF TABLES Table 1 Interaction length as a function of flow rate. The interaction length should remain constant for all flow rates... 53

14 14 ABSTRACT Microfluidic networks and microporous materials have long been of interest in areas such as hydrology, petroleum engineering, chemical and electrochemical engineering, medicine and biochemical engineering. With the emergence of new processes in gas separation, cell sorting, ultrafiltration, and advanced materials synthesis, the importance of building a better qualitative and quantitative understanding of these key technologies has become apparent. However, microfluidic measurement and theory is still relatively underdeveloped, presenting a significant obstacle to the systematic design of microfluidic devices and materials. Theoretical challenges arise from the breakdown of classical viscous flow models as the flow dimensions approach the mean free path of individual molecules. Experimental challenges arise from the lack of flow profilometry techniques at sub-micron length scales. Here we present an extension of scanning probe microscopy techniques, which we have termed Hydrodynamic Force Microscopy (HFM). HFM exploits fluid drag to profile microflows and to map the permeability of microporous materials. In this technique, an atomic force microscope (AFM) cantilever is scanned close to a microporous sample surface. The hydrodynamic interactions arising from a pressure-driven flow through the sample are then detected by mapping the deflection of an AFM cantilever. For gas flows at atmospheric pressure, HFM has been shown to achieve a velocity sensitivity of 1 cm/s with a spatial resolution of ~ 10 nm. This compares very favorably to established techniques such as hot-wire and laser Doppler anemometry, whose spatial resolutions typically exceed 1 µm and which may rely on the use of tracer particles or flow markers 1.

15 15 We demonstrate that HFM can successfully profile Poiseuille flows inside pores as small as 100 nm and can distinguish Poiseuille flow from uniform flow for short entry lengths. HFM detection of fluid jets escaping from porous samples can also reveal a permeability map of a sample s pore structure, allowing us to distinguish between clear and blocked pores, even in cases where the subsurface fouling is undetectable by conventional AFM. The experimental data is discussed in context with theoretical aspects of HFM microflow measurement and practical limits of this technique. Finally, we conclude with variations of standard HFM techniques that show some promise for investigation of smaller nanometer-scale flows of gases and liquids.

16 16 1. INTRODUCTION TO ATOMIC FORCE MICROSCOPY 1.1. HI S T O R Y : The Atomic Force Microscope (AFM) relies on the simple technique of mapping the deflection of a sharp probe or stylus that is raster-scanned across a surface. By recording the changes in the height of the probe, surface topography can be effectively mapped. Modern AFMs use microfabricated probes with tip radii ~10 nm along with a computer system that reconstructs the digital signal of the probe height data into topographic maps. This technique of mapping a scanned probe s deflection in order to image surface topology has been used for nearly 80 years. In 1929, Schmalz 2 first used an optical lever arm to magnify the motion of a sharp probe and then recorded that motion on photographic paper. He was able to generate profile images with magnification greater than 1000x. In the 1980s, the first scanning tunneling microscope (STM) was developed by Binning and Rohrer 3. STM monitors the variations in the electron tunneling current between a conducting sample and probe tip as the probe passes over a surface. Finally in 1986, Binning and Quate 4 demonstrated the first Atomic Force Microscope. These first AFMs operated by scanning an ultra-small and sharp probe tip that remained in contact with a surface during measurements. So-called contact mode AFM has since been refined to achieve atomic scale resolution and is used to profile surfaces in gas, liquid, and vacuum environments.

17 17 Figure 1-1AFM measures surface topography. A laser beam is reflecteded off the back of a springy cantilever with a sharp tip. As the tip scans across the surface, the vertical deflection of the cantilever is measured by monitoring changes in the position of the laser beam on a quadrant photodetector. The scanner and photodetector send and receive signals from a computer which processes the deflection data to produce a topographic map of the surface with nanometer vertical and lateral resolution. Contact mode AFM (Fig. 1-1) has faced challenges in imaging soft and weakly bound samples as these are easily damaged by the sharp tips. In response to this challenge, non-contact, or tapping mode was developed in In tapping mode, the AFM is oscillated near its resonance frequency as it passes over a sample surface. Long-range attractive forces result in measurable changes in the amplitude, frequency, and phase of the cantilever. Because there is an absence of lateral forces in tapping mode, a wider array of soft samples and loosely bound adsorbates can be imaged without damage. AFM technology has continued to improve in the following 20 years with a wide range of specialized microfabricated probes becoming commercially available. New probe techniques now regularly include the use of conducting or magnetically coated tips, and the use of light collecting micro-pipettes and optical fibers to probe local optical properties beyond the optical diffraction limit.

18 TRADITIONAL ATO M I C FORCE MICROSCOPY: BASIC PRINCIPLES: AFM is a non-optical microscopy technique that falls into the classification of Scanning Probe Microscopy (SPM). SPM techniques typically raster scan some kind of interacting probe tip over a sample surface and then record the variations in the tip-sample interaction. SPM techniques can be used to measure surface topography as well as other characteristics such as conductivity, chemical composition, and charge density. In the simplest case, an AFM in contact mode uses a spring-like cantilever probe to measure surface topography by recording the varying deflection of the cantilever as it is scanned across a surface. The restoring force of the cantilever probe that allows it to maintain a constant force or height while scanning is estimated using Hooke's Law: F = kz 1.1 Where F = force, k = spring constant, and z = cantilever deflection AFM interaction forces As the tip of the cantilever approaches a sample surface, it typically encounters the four following external forces in both contact and tapping mode: capillary forces, electrostatic forces, Van der Waals forces, and Born repulsion 6. The capillary or fluid surface tension force arises due to the condensation of water vapor on a surface and the cantilever in the area nm above the surface. When water wicks around the tip a strong attractive force develops and helps to hold the tip in contact with the surface (along with the other forces). The magnitude of the force depends on the tip-to-sample separation. For a relatively uniform layer of water, the capillary force is

19 19 constant as long as the tip maintains contact with the sample. When imaging a surface that is immersed in liquid, in vacuum, or very dry conditions, the thin water film is not present, so the capillary force no longer applies. For this reason, imaging in liquids is used as a tool to minimize the force on samples and can prevent surface damage. Electrostatic forces act on any charged bodies and are attractive for charges of opposite sign and repulsive for like charges. The end of a typical cantilever probe has a radius of order 10 nm. Electrostatic forces between the finite number of atoms on the tip of the probe and the surface interact via electrostatic forces as the tip approaches surface contact. Charge buildup on the tip or sample can occur due to contact electrification in dry air; but this effect can be mitigated in humid air, or virtually eliminated by imaging in polar liquids. As the tip-sample separation approaches a few nanometers, Van der Waals forces arise due to the dipole-dipole and induced dipole interactions between the molecules in the tip and surface. The Van der Waals force is attractive and proportional to 1/R 6 (where R is the distance between the tip and surface) and can lead the tip to suddenly jump into contact with the surface. The tip and sample are in contact when their atoms experience Born repulsion. Born repulsion prevents the intrusion of one material into the other (largely due to the Pauli Exclusion Principle). This combination of forces makes up the common contact force between macroscopic solid objects. When the tip is in contact, any additional applied pressure results in bending and deflection of the cantilever. Excessive pressure however, can distort or damage the sample material or the tip. Very close to the surface,

20 20 these forces all interact together with the AFM probe to attract the tip and keep it in contact with the surface while the AFM scans across a sample surface CONTACT MODE The AFM has a highly adjustable control panel that allows users to carefully control tipsurface interactions. For most of the HFM experiments presented, contact mode was used; though tapping mode was also tested and employed. The AFM functions by reflecting a laser beam off the back of a flexible cantilever. The position of the cantilever is then detected by measuring the changing signal on a position-sensitive photodetector, in this case a quadrant photodiode. The system can detect sub-angstrom vertical movement of the cantilever tip because the ratio of the path length between the cantilever and the detector to the length of the cantilever itself produces a mechanical amplification (Fig 1-2). Figure 1-2: AFM operation

21 21 A computer and feedback electronics store the distance the scanner moves vertically at each (x,y) data point. These data points form a topographic image of the sample surface. Figure 1-3 Typical AFM images of some fabricated quantum dots. The Height image (left) shows the topography of the surface, deflection (center) can be used for edge detection and friction (right) indicates variations in the surface roughness and chemical makeup. 7 While scanning, three images are displayed. The images are titled height, deflection and friction (Fig 1-3). The height image displays the height of the cantilever. The height data is recorded from the AFM feedback circuit that functions to maintain a constant photodetector voltage value by adjusting the height of the cantilever via a piezoelectric transducer. The distance the piezo moves is calibrated, so the height image displays the changes in the cantilever height created by the feedback mechanism.

22 22 Figure 1-4 Quadrant Photodiode. The laser spot is reflected off the back of the cantilever and moves around the quadrant photodetector. By mapping the photodiode signal, a topographic and lateral force images are created. The deflection image shows the deviations that the feedback loop does not properly correct. This displays the difference signal between the photodetector s two upper quadrants and two lower quadrants [(A+B) (C+D)]. This signal is typically generated because the circuit has a finite bandwidth and is therefore too slow to adequately compensate for sharp height changes. This makes the deflection mode helpful in edge detection. It is also useful because it can be used to display the photodiode signal if the feedback loop is disabled. This function will become very important later, as this feature allowed us to map the raw cantilever deflection during fluid flow. Finally, the friction signal maps the side to side twisting [(B+D)-(A+C)] caused by torque on the cantilever as it is scanned. A positive friction signal indicates that the tip drags a little as it moves along the fast scan direction. This method also becomes important, because for noncontact imaging, this signal indicates whether the cantilever is just deflecting upward, or if it is also experiences torque via a non-uniform force across the cantilever. Even in the

23 23 absence of a contact friction force, the lateral friction signal will vary between positive and negative values in response to non-uniform forces, and the sign of the signal simply indicates the direction of the twist. Figure 1-5 AFM contact mode cantilevers 8 In contact mode, the tip raster-scans along a fast and slow scan direction. We used standard silicon nitride contact mode tips that are on the end of cantilevers shaped like an open triangle (Fig 1-5). The pyramid tips are about 3-4 µm high and the cantilever legs are ~ µm long. The cantilever mounting chip is slightly beveled in order to ensure that the tip is closest to the surface and is the first object to come into contact with the surface. The cantilever can be raster-scanned with the fast scan axis at any angle parallel to the surface. A 90 degree scan angle was typically used, because this allows one to measure the twisting or friction force simultaneously while acquiring topographic data.

24 24 Figure 1-6 Typical Height, Deflection, and Friction images of a calcite crystal with monolayer growth of calcium sulfite, the friction image indicates the square pits are filled with the calcium sulfite 7. The simultaneous capture of height, deflection and friction data produces three correlated images (Figure 1-6). In the height image, bright and dark areas correspond to high and low features respectively. The Z range indicates the maximum range of height values displayed, in the height image in Figure 1-6. The difference in height between a black feature and white feature is at least 5 nm; the shades of brown in between indicate intermediate heights. If improperly scaled, high features in an image can saturate and appear white, with no variation to indicate height differences above the maximum height value set. Z range values are user-defined parameters. In the central image, a deflection scan is displayed. The edges of the monolayer steps in the crystal on the surface are accentuated more than in the height image. The right image is the friction data. Friction images help to identify variations in surface roughness and chemical composition. For a uniform surface, friction images do not display any contrast. In Figure 1-6 the friction image indicates light areas with calcium sulfite, on the darker calcite substrate surface. In some cases, the topography of a sample may be completely uniform, but by measuring friction data, variations in the makeup of the surface molecules can still be detected and

25 25 mapped FORCE VS. DISTANCE CU R V E S The AFM has a built-in feature that allows for the calibration of the real-time forces the tip experiences as it interacts with a surface. The tip is repeatedly brought into and then taken out of contact with a surface and the tip movement vs. force is plotted (Fig 1-7). As the tip approaches the surface, initially there is no interaction, then as the tip gets closer, there is a sudden attraction due to surface tension or Van der Waals forces. Thich can be seen in the small dip on the left side of the red plot. The tip jumps into contact with the surface, and then the sloped region on the right indicates the contact region. If the cantilever mounting chip is brought closer to the surface when the tip is already in contact, the cantilever bends and deflects upwards to accommodate the decreased distance between the cantilever mounting chip and the sample. By measuring the slope of this force curve in this region, the detector sensitivity can be obtained. The blue curve indicates the forces on the tip as it is withdrawn from the surface. As the tip is pulled away, it remains adhered to the surface, and then suddenly snaps free and jumps out of contact, before returning to free deflection. Force curves can be taken very rapidly, and the attractive and repulsive forces can be modified in various manners to give other dif- ferent profiles in the region approaching contact. This diagnostic tool allows us to calibrate the forces on the cantilever and to monitor any changes in those forces as we explore a variety of samples.

26 26 Figure 1-7 A Typical AFM Force Curve 1.5. CONTACT MODE CONSTANT FORCE VS. CONSTANT HEIGHT IMAGING In order to bring the AFM probe s tip into contact with a surface, and to keep it in contact while scanning, a deflection setpoint must be selected. Far above a surface, the cantilever sits at some relatively stable free deflection position. The photodetector signal is usually set such that free cantilever deflection returns a zero signal, and then a deflection setpoint is determined. This setpoint is a voltage value that must be achieved in order for the feedback loop to turn on and function. Typically this value is set to 1-2 V. When engaging the tip with the surface, the photodetector value is monitored as the tip nears the surface. Once the tip comes into contact with the surface, the cantilever bends and the laser beam is deflected upwards. The photodetector voltage then increases and reaches the set-

27 27 point value, signaling the feedback loop to turn on and the AFM to begin to scanning. 10 V A C B D 1 V 0 V -10 V Figure 1-8 Deflection setpoint on photodiode The feedback loop uses the deflection setpoint as the reference value for the cantilever deflection level and the computer adjusts the scanner height to maintain this constant setpoint value. When a large setpoint value is chosen, the cantilever must be deflected a large amount to engage the feedback loop, and the tip therefore applies a large force to the sample. In general, a low positive setpoint value is maintained in order to keep the tip in contact, but not to apply a large force, which might scratch, or otherwise damage a sample surface. While scanning, we can do a maneuver referred to as a soft disengage, where the tip is removed from contact, but continues to scan right above the surface. This is done by setting the deflection setpoint to a low or negative value. This is because lower photodetector voltages are achieved by moving away from the surface. With a zero or negative deflection setpoint, the feedback loop will move the tip away from the surface in an attempt to lower the voltage to the negative value. There is actually a slight attractive force between most surfaces and the tip that keeps them in contact as the AFM scans.

28 28 Because the free deflection value is zero, the voltage will usually dip slightly below zero as the tip moves away and must pull off and out of the attractive area. The feedback loop then will become ineffective as the height is now typically constant because the tip is not in contact and there are no forces on the tip. We can re-engage with the surface by slowly increasing the deflection setpoint to a positive value. The integral and proportional gain values for the feedback loop are also user-adjustable, so the feedback loop can be disabled by setting the gain values to zero. If the gains are at positive values, the feedback loop is on and the AFM operates in a constant force mode, as it attempts to maintain a constant photodetector voltage by changing height, but maintaining constant force. If the feedback loop is turned off by setting the gain values to zero, then the AFM operates in a constant height mode. In this mode, the tip continues to scan, but the feedback loop no longer compensates for changes in height caused by varying forces on the tip. The operations of performing a soft disengage and re-engage by changing the deflection setpoint are used to change or minimize the force applied to the surface and to switch between contact and non-contact imaging of surfaces and flows. The operation of turning the feedback loop on and off allows us to switch between constant force and constant height modes. In order to be in the non-contact regime, the tip must be far enough away from the surface to no longer be significantly affected by electrostatic, capillary, and Van der Waals forces.

29 29 Figure 1-9 The Flow cell and the AFM Scanner OTHER AFM MEASUREMENT TECHNIQUES In addition to constant force and constant height contact modes, AFM has increasingly become a tool for characterizing surface and material properties at the nanoscale. Utilizing forces other than those present in standard contact mode to create contrast for material characterization has become a means for expanding AFM and SPM related techniques beyond basic topographic and lateral force characterization. Electric Force Microscopy and Magnetic Force Microscopy (EFM and MFM) use conducting, charged, or magnetic tips to measure variations in electric and magnetic forces as the AFM scans a surface 9. These methods allow the study of microelectronics, recording and data storage media. Measuring electric double layer 10 and other long range forces has enabled the imaging of

30 30 soft surfaces and materials and has extended t h e A F M s use into a range of biological and chemical applications, including the study of proteins, cellular membranes, and micelles. These new techniques however face significant challenges. Calibrating the forces associated with a particular contrast can be complex. For example, when measuring soft samples, large cantilever forces can cause deformation and sample damage. In addition, if the force gradient (effective spring constant) of a sample is very weak, then the deflection measured by the cantilever will be suppressed or attenuated as the sample and the cantilever both deflect while interacting. This can lead to false topographic information. The AFM can still successfully locate various surface features and maintains good lateral resolution, but may yield convoluted height results that depend on variations both in local sample stiffness as well as topography changes. Analyzing force curves can help to illuminate details about the forces and interactions between tips and samples in these other modes and when dealing with soft samples.

31 31 2. INTRODUCTION T O FLUID FLOW Fluid dynamics constitutes a field of study that is beyond the scope of this document; however, there are a few general concepts and terms that will be used in following chapters. Most available fluid dynamics theory is used to describe the two extremes of flow behavior: those which can be accurately described using continuum dynamics and those described by molecular dynamics. Continuum dynamics theories of both incompressible and compressible flow rely on solutions derived from the Navier-Stokes equations 11. While these equations can be used to describe a range of phenomena from fluid flow to global weather systems, they are a set of non-linear partial differential equations that continue to elude full mathematical understanding. For example, in three dimensions, mathematical existence and smoothness have still not been proven for the Navier-Stokes equations. Molecular dynamics theories are less well developed, and a number of competing models have arisen over the past century 12. Both continuum and molecular theories include terms that describe variations in pressure, temperature, fluid velocity, and assume conservation of mass, momentum, and energy. Continuum theories often assume constant density and viscosity, and a no-slip boundary condition which sets flow velocity equal to zero at solid-fluid interfaces. The Reynolds number (Sec. 2.1) is used to determine whether laminar or turbulent models are used. The choice of continuum, transitional or free-molecular flow theories are determined by the Knudsen number (Sec 2.2), which relates the flow dimensions to the mean

32 32 free path. The Navier-Stokes equations are no longer valid when the no-slip boundary condition breaks down or fails at Knudsen numbers above 1. In addition, the kinetic viscosity and mean free path may vary, and effects such as rarefaction and thermal creep must be accounted for in order to construct effective models. As is the case in much of nanotechnology, transitional flow theory has been difficult to develop as certain effects from both the continuum and free molecular flow regimes often come together and must be reconciled THE REYNOLDS NUMBER: The Reynolds number (Re) is a non-dimensional number used to distinguish whether flow in a system is laminar or turbulent and can help determine which theoretical models should be used to describe various flow phenomena. For flow in channels, the Reynolds number depends on the following parameters: the pipe or channel diameter d, the average flow speed v av, the fluid density ρ, and the viscosity µ. The Reynolds number for channel flow is defined as 1 1 : More generally it is defined as: dv av ρ Re = 2.1 µ LVρ = µ where L and V are characteristic length and velocity values for a system. Re 2.2 The experimental results presented here, assume the following values: the density of air = 1.2 kg/m 3 = 1.2 mg/cm 3, the viscosity of air = 1.8x10-5 N s/m 2. We assume that the nitrogen gas flowing into air is essentially equivalent to a pure-air system. Our expe-

33 33 riments are always in the laminar flow regime with Reynolds numbers < THE KNUDSEN NUMBER: The Knudsen number (Kn) is another measure based on the geometric properties of gas microflows, which is used to determine applicable models. It classifies flows as continuum, slip, transitional, or free molecular flows. The Knudsen number is defined as 13 : λ Kn = 2.3 L Where λ is the mean free path, m / Pa λ = πd par n P L i s a characteristic size-scale of the system and d par is the effective diameter of the particle or molecule. The mean free path indicates the average distance a gas molecule travels before colliding with another molecule. A typical mean free path of an air molecule in ambient conditions is 68 nm (~100 nm). In vacuum, or for cases where the scattering cross-section of the gas molecules increase, the mean free path increases to larger values. Figure 2-1 indicates the limiting Knudsen numbers when applying various models to microflows. In some cases the samples investigated contain apertures and obstructions that are ~100 nm in size. The resulting Knudsen numbers are close to 1, indicating that we are examining the slip and transition flow regimes, where little experimental data or theory exists. Obtaining experimental data for flows in this regime has remained a constant challenge in developing micro and nanoflow theory.

34 34 Figure 2-1 Limits of approximations in modeling gas micro flows. L (vertical axis) corresponds to the characteristic length and n/n o is the number density normalized with corresponding atmospheric conditions. The lines that define the various Knudsen numbers regimes are based on air at isothermal conditions at T= 273 K. (Redrawn from Karniadakis 12 ) 2.3. POISEUILLE FLOW: For low Reynolds numbers (Re < 30), viscous incompressible flows through pipes and channels have a well defined, closed-form solution in the laminar flow regime 1 1. Flow through a long, straight cylindrical pipe or tube of uniform cross-section can be generated by maintaining a constant pressure difference between the two ends of the pipe. Fluid flow then moves from the high pressure end of the pipe to the low pressure end of the

35 35 pipe. It is assumed that gravitational effects on the flow are negligible, either due to geometry, or because the pressure forces involved are much greater than gravitational forces (Fig 2-2). Figure 2-2 Poiseuille flow through a pipe develops a parabolic velocity profile, with a maximum velocity in the center of the pipe and zero velocity at the fluid/pipe wall interface. This type of pipe flow is known as Poiseuille flow. After taking into account the pressure differences at each end of the pipe and the boundary conditions requiring the flow to have zero velocity at the pipe walls, it can be shown that the velocity distribution in a cylindrical pipe is: 1 P 2 2 v( r) = ( R r ) µ z Where P is the pressure difference, z is the length of the pipe, R is the pipe radius, µ is the viscosity of the fluid and r is the distance from the center of the pipe. The maximum velocity occurs in the center of the pipe and is: v 1 4 P z 2 max = R 2.6 µ

36 36 The average velocity, defined as the mass flux divided by the density and the crosssectional area is half of the maximum velocity. v av 1 8 P z 2 = R 2.7 µ 2.4. EN T R Y LENGTH: For low Reynolds numbers (Re < 30) and long pipes, Poiseuille theory provides an accurate description of fluid velocity flow profiles. For higher Reynolds numbers though, Poiseuille flow takes a finite distance to develop as indicated in Figure 2-3. For very shallow samples, the expected flow profile may be something between uniform and parabolic flow due to the finite entry length, and the lack of necessary bounding by a long channel wall length. Uniform Flow enters the pipe Boundary Layer Edge Entrance Region Fully Developed Flow Figure 2-3A parabolic Poiseuille flow profile develops as the fluid moves through the pipe (Redrawn from Tritton) DRAG: For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), the drag force F on the object is: F drag = bv 2.8

37 37 Where the drag constant b is: b = 6πµa 2.9 where a is the radius of the particle, and µ is the fluid viscosity. By changing reference frame, the drag on a stationary object in a constant flow field is the same. For low Reynolds numbers, the drag force on any blunt object is approximately 6πµav, where a is a characteristic length associated with an object. In the case of a sphere or disc, a is the simply the radius. Figure 2-4 Flow near a sphere. Viscous drag acts to create a layer with zero velocity around the sphere. Behind the sphere, along the flow axis, the flow velocity is lower than the bulk velocity, and increases with distance from the sphere. Flows through screens and past smaller obstructions modify flow, usually by setting up an area of decreased velocity directly behind the obstructions FLUID JETS AND ENTRAINMENT As fluid emerges from an orifice, it forms a jet. The simplest jet configurations involve the case of the fluid emerging into the same fluid as the jet itself. In 1937, Andrade and Tsein 14 expanded and added corrections to initial jet theory 15 by photographing the paths of tracer particles near the exit of a pipette. At low Reynolds numbers, as the jet exits an

38 38 orifice, the fluid spreads out in all directions and entrains the surrounding fluid. Figure 2-5 As a fluid jet moves away from the orifice it expands and entrains surrounding fluid. The maximum velocity also decreases. While there is no closed form expression for the shape of a fluid jet right at the mouth of an orifice, the fluid profile within a pipe (Poiseuille flow), and a few diameters away from the pipe (jet flow) are well known. This expression for the jet profile assumes that the ambient fluid is at rest, the jet is cylindrically symmetric, and that the velocity profile maintains a similar shape at varying distances downstream. By also incorporating conservation of momentum, and assuming that the maximum velocity is at the center of the jet, the following solution can be found for a jet emerging with an initially uniform velocity profile: 3 J 1 v r, z) = 8π µ z * 2 r 1 + C 2 z * 3 J C = 64π ρµ ( 2 z* = z * Re* R 2.10

39 39 Here, J is the momentum crossing a plane normal to the axis of the jet, z is the distance from the orifice, and r is the radial distance from the axis of the jet. This solution is not applicable right at the exit of the orifice. The jet starts out with a finite velocity, and with a different profile than that given by the above equation (inside a pipe, the velocity has a parabolic Poiseuille profile). The transition region just outside the orifice exhibits some instability due to the sharp solid-fluid boundary, but a few diameters away from the orifice Eq becomes valid. This solution indicates a velocity profile that has a decreasing maximum velocity (at the center of the jet), and increasing width with increasing distance from the orifice. The solution also has the property: d ρ vdr > dz indicating that the amount of fluid being transported by the jet also increases with distance from the orifice as the jet draws fluid into itself from the sides; a process known as entrainment of the surrounding fluid THE COANDA EFFECT The entrainment of fluid by a jet leads to the Coanda effect 16. If a jet emits into a region that is bounded by a side wall, entrainment of fluid is inhibited, as the jet can no longer draw in fluid from all sides. Since the jet cannot draw fluid into itself, the jet is drawn towards the wall and can attach to the wall, with a thin separating boundary layer. Two parallel jets will similarly be drawn together into a single jet due to the Coanda effect.

40 40 Figure 2-6 The Coanda Effect leads to the attachment of a jet flow to a nearby wall 2.8. KNUDSEN AND MOLECULAR FLOW CONSIDERATIONS When examining micro and nanoflows, continuum theory begins to break down as a variety of effects become relevant. On the opposite end of the spectrum from continuum theories are molecular flow models based on statistical mechanics principles. These models help to account for variations in the kinetic viscosity and mean free path, as well as rarefaction effects. There are well defined expressions for the Poiseuille mass flow rate in the continuum flow regime and the molecular flow regime. They are 12 : Molecular: dm molecular dt 4 P R 3 3 z 2π R T = 2.12 M Continuum: dm continuum dt π = R 8 4 P ρ z µ 2.13 These expressions both depend on the change in pressure and the length of the channel. The molecular flow rate goes as the pipe diameter to the third power, and relies on the specific gas constant (R M ) and temperature to determine mass flow rate. In contrast, the

41 41 continuum theory goes as the pipe diameter to the fourth power and uses the fluid density and viscosity to determine the mass flow rate. One important detail is that the kinetic viscosity, µ used in the continuum theory actually varies as a function of the Knudsen number and the mean free path, both of which vary at these scales: 1 µ = ρv av λ Kn The mean free path varies with pressure ( Eqn. 2.4). Given these values, we find that the continuum flow theory is valid for apertures with R > 500 nm, otherwise it underestimates the flow rate so that molecular or Knudsen theory must be used. Finding corresponding expressions in the intermediate, Knudsen regime has proved difficult, especially because there is little experimental data on which to base results. Computer models including Direct Simulation Monte Carlo (DSMC) methods attempt to bridge the solutions of the continuum and molecular theories. Fortunately, it can be shown that velocity profiles for pipe flows remain relatively parabolic in shape for a large range of Knudsen numbers (0.1-10). Good theoretical results have been achieved in modeling these flows as maintaining parabolic velocity profiles in the entire Knudsen regime by incorporating a consistent slip condition. Rarefaction develops as intermolecular collisions are reduced significantly and only the collisions with the walls are considered, however, by including the above corrections in the dynamic viscosity this increased rarefaction can be accounted for. The Poiseuille volume flow rate in the Knudsen regime has been modeled by Karniadakis and Beskok 12 and is given by: 4 πr P Q = 8µ z ( 1+ αkn) 1+ 4Kn 1 Kn 2.15

42 42 where α is a constant (~1) that has been experimentally determined and varies from 0.9 (Kn = 0.1) to 1.36 (Kn = 1000), R is the pipe radius, L the pipe length, and µ the continuum kinetic viscosity introduced in previous expressions. The velocity distribution in a pipe is now given by: v( r) = v av 2 r Kn R 1+ Kn 1 Kn Kn 2.16 Where v is the average velocity in the Knudsen regime, found by equating the volume av flow rate is the product of the pipe area by the average flow velocity ( Q 2 = πr v ave ). By combining this mass flow rate equation with equations 2.15 and 2.16 we find the Poiseuille velocity distribution in the Knudsen regime is: v( r) = 2 PR 1+ αkn 4µ z 1+ Kn ( 1+ 3Kn) ( 1+ Kn) r R T w o things to note: the first fraction in Eq is the continuum v max (Eqn. 2.6), and when Kn = 0 (continuum flow regime), v(r) = v max (1-(r/R) 2 )), which gives the continuum Poiseuille distribution. Another interesting result of Eq is that for Kn > 1, both the maximum and minimum velocities in the pipe can be much greater than the continuum velocity predictions. These results show that in general, as size scales shrink, continuum Poiseuille flow underestimates the velocity of fluid flows, even though the overall shape of the velocity profile remains parabolic.

43 CURRENT FLOW MEASUREMENT METHODS Currently, few techniques for measuring micro and nanoflow phenomena exist and those available have resolution limited to ~1 µm 1. A common tool that has been miniaturized over the years for increased resolution are hot-wire anemometers which rely on changes in temperature (and therefore resistance), current, or voltage resulting from molecular collisions to determine local flow rates. This method is limited to ~1 µm resolution due to the physical size of the wires themselves and the accompanying circuitry. Any accumulation of particles can alter their performance, and small wires have poor mechanical stability. Laser Doppler Anemometry (LDA) and micro Particle Imaging Velocimetry (µpiv) are both techniques that rely on the use of tracer particles and optical detection to map and measure flow. Both of these techniques are size limited by the Rayleigh criterion, and they can only be used with transparent fluids, and with the addition of tracer particles, which does not allow for direct measurement of the fluid flow itself. Finally, techniques that measure the deflection of some kind of fiber , whisker, or cantilever have mapped fluid flow using tools such as optical fibers and AFMs. These techniques have successfully mapped one dimensional fluid flows, and have been used for rheological measurements of local viscosity , yielding spatial resolutions near 1 µm. The lack of data for flow rates in the Knudsen regime and the limited spatial resolution and performance of the above techniques led us to investigate the possibility of extending the use AFM as a tool for mapping micro and nanoflows. The intent of these studies was to determine first, if flows could be measured in two and three dimensions by a cantilever based device, and second to improve the spatial and velocity resolution beyond

44 that of previous techniques. 44

45 45 3. CONTACT HYDRODYNAMIC FORCE MICROSCOPY 3.1. INTRODUCTION TO HYDRODYNAMIC FORCE MICROSCOPY We propose that hydrodynamic forces can be used to provide a contrast mechanism in order to characterize surfaces and samples 25. Any AFM technique that utilizes hydrodynamic forces, whether they are simple pressure or viscous drag forces, attractive Coanda or Venturi Forces, drafting forces or even forces generated via spatial or time varying flows can be designated Hydrodynamic Force Microscopy (HFM) techniques. Possible contact mode HFM configurations include flow from above a sample, flow parallel to a surface, flow generated by the relative velocity between a probe and sample, flows that originate from the probe, flows that are the result of engineered tips and cantilevers, or other specially engineered flows (Fig 3-1). Figure 3-1 Various Hydrodynamic Force Microscopy (HFM) techniques.

46 HFM THEORY AND LIMITS While we will show that the HFM technique has already proven capable of imaging with higher spatial resolution than any other current flow measurement techniques, it is important to recognize that there are limits to its flow measurement capabilities. In the simplest model, the deflection of the cantilever is due to collisions with fluid molecules. By looking at simple energy and momentum conservation, the actual ener - gy transfer can be calculated. For inelastic collisions between two objects, with one object being much more massive than the other: m k2 f m1 ki m2 The kinetic energy transferred from a collision is approximately proportional to the ratio 2 >> m of the mass of the molecule to the mass of the cantilever, which is an extremely small value. For elastic collisions, a similar analysis shows that the kinetic energy transferred is: f 4m1 3.2 ki m2 These results indicate why single molecule detection is not possible with AFM. k For macroscopic collections of molecules, the thermal noise limit for detection in the vertical direction is estimated by setting the spring energy equal to the thermal ener - gy: 1 2 kz zmin = K BT k In actuality, because the deflection is measured via an optical lever, and also because the 2 = 1 2 K B T 3.3

47 47 cantilever has limited vibration modes, the noise limit for free oscillation and a supported tip (one in contact with a surface) actually differ slightly from this value and are 26 : z z free = contact = 4K K B B T T 3k 3k 3.4 By considering that in the simplest case, the primary force on a cantilever is the viscous drag force created by the flow: F = kz = bv 3.5 And then substituting bv/k = z we find that : kk BT vmin = 3.6 b The experiments used standard silicon nitride cantilevers, typically with spring constants near 0.1 N/m. There are however, commercially available cantilevers with spring constants as low as N/m. By incorporating these small spring constants, and assuming room temperature and a maximum interaction length ~100 µm (as found in calibration, see section 4.1) the minimum velocity resolution using a cantilever spring system is found to be approximately 150 µm/s in air and 3µm/s in water. We will show that we have achieved velocity resolution ~1cm/s. Thermal noise constitutes the most significant noise source in measuring flows. While AFM electronic systems all exhibit 1/f, shot, and thermal (Johnson) noise, the thermal noise of the cantilever dominates under ambient imaging conditions. If the HFM probe interaction size was isolated to a region smaller than the mean free path, statistical fluctuations associated with the Maxwell velocity distribution could become significant, but with appropriate time and/or size averaging these effects can be minimized.

48 48 Other sources of systematic error in the HFM system can be attributed to two ef - fects. The first is optical interference. Optical interference can appear in AFM images anytime a reflective sample is used. Because the laser diode used to measure the cantilever deflection is highly coherent, and the distance between the cantilever and the sample is small (< 5 µm) optical interference between light reflected from the sample surface and light reflected from the cantilever can occur. This effect is intensified when the cantilever is scanned in a free deflection mode above a surface. This is because as the cantilever scans, its distance from the sample varies, unlike contact mode, where the cantilever maintains contact with the surface. This change in distance between the sample and cantilever can result in an effect very similar to Newton s Rings in optical interferometers and typically manifests as stripes or waves in an image. The second source of systematic error in HFM is associated with fluid flow boundary instabilities. For flows with significant volume flow rates, or large apertures, interactions that occur at the edges of the cantilever become significant. The cantilever has a large perimeter edge that creates a region where wake behavior, like vortex shedding, can take place. This sharp solid-fluid interface region can result in significant random vibration in the cantilever for flows that are not well isolated to the tip region. The error caused by these boundary effects can cause deflection variations as large as 100 nm even for moderate Reynolds number systems. We can calculate the size of the smallest Poiseuille flow detectable via HFM by assuming that for very small apertures, the aperture radius limits the flow interaction area and is therefore equal to the interaction length. By again assuming the minimum canti-

49 49 lever spring constant of ~0.001 N/m, a sample of thickness ~5 µm, and an applied pressure of ~1 atm the smallest aperture size is found to be of order 10 nm when using either the continuum or Knudsen models for calculating flow velocity, we will present data profiling Poiseuille flows with aperture size < 500 nm POROUS SAMPLES One particularly promising application of HFM is the study of porous materials via measuring flow through thin porous membranes. Porous materials constitute a wide range of solids and semisolid materials. Porous materials are ubiquitous: in textiles, building materials, soil, rock, biological systems, active carbons, and silica gels. Because of the prevalence of porous materials, their study is of great interest and importance to the following technological areas: hydrology, petroleum engineering, chemical and electrochemical engineering, medicine and biochemical engineering. In order to effectively utilize HFM to study a sample, the porous material must be permeable to fluid flow at a rate higher than that of diffusion alone, and the flow rate must be great enough to satisfy the conditions laid out earlier in this chapter. In order to develop good quality models of porous systems a number of factors must be determined. Characteristics that might be illuminated via HFM include: the porosity of a sample (the % of the sample that is a void), the permeability, the homogeneity, and the connectivity of pores. Local permeability measurements are of particular interest, because often the permeability of a porous material is not the result of a uniform constant permeability

50 50 throughout the material. Porous media are often micro and macroscopically heterogeneous and may exhibit anisotropic permeability in various directions. These variations in permeability can be distributed over several orders of magnitude within a single sample. Mapping local permeability variations has important implications for understanding and distinguishing the bulk properties of various homogeneous and heterogeneous porous materials PR I M A R Y CONTACT HFM TECHNIQUES Data are presented for a series of samples including single apertures, aperture arrays, random porous samples, and screens. All samples presented in Chapter 4 were explored using the following HFM technique. Figure 3-2 Hydrodynamic Force Microscopy (HFM) applied to porous samples. Drag forces on the cantilever are used to image local flow profiles, map the substrate pore structure, and pinpoint subsurface fouling undetectable by conventional topography scans.

51 51 Results were obtained using a Veeco Dimension 3100 SPM system and Veeco DNP-S contact mode AFM tips with nominal spring constant 0.12 N/m and typical scan rates of 3-5 Hz. Porous substrates were glued to the circumference of a metal ring (~5 mm diameter), which in turn was attached to an airtight reservoir (~100 µl volume) containing a single fluid inlet. A constant pressure of nitrogen was applied through this inlet using a regulated gas (usually nitrogen) tank. All imaging was in contact mode, with the cantilever either in physical contact with the substrate or positioned at an approximately constant distance above the substrate plane (using the motor adjustment); both constant force and constant height modes were used.

52 52 4. CONTACT HFM EXPERIMENTAL RESULTS 4.1. HFM CALIBRATION Quantitative analysis of the magnitude of forces and effects measurable using the HFM technique were performed in order to provide a rough calibration of the expected results. First, the cantilever spring constant was obtained by measuring a force distance curve on a microscope slide (which serves as a generic hard surface). This hard surface measurement gave a cantilever deflection calibration constant of nm/v of deflection on the photodiode. A syringe pump was then used to provide a constant flow rate of air through a 20 gauge syringe needle with a 292 micron radius. The raw cantilever deflection measured when the cantilever was above the needle was measured, and we assume that the spring force on the cantilever is equal to the drag force: kz 6πrµ v = 4.1 The physical cantilever deflection (z) can then be calculated using the force curve calibration value. As the spring constant of the cantilever and viscosity of air are known, we can use these measurements to find the effective interaction length discussed in section 2.5. This calculation results in a value of r is 64.6 µm. By varying the fluid velocity and measuring the deflection multiple times, we obtained the following values (Table 1) for the effective interaction size of the tip-cantilever system:

53 53 Flow Rate Deflection Effective interaction length 7.5 ml/min 0.6 V 59.2 µm 10 ml/min 0.8 V 64.6 µm 15 ml/min 1.1 V 64.6 µm Table 1 Interaction length as a function of flow rate. The interaction length should remain constant for all flow rates The measured interaction length indicates that flows interacting with the entire tip and cantilever have an effective probe size of 65 (+/-7) µm. The length of a cantilever is about 200 µm and the width of the cantilever legs are about 40 µm, so 64.6 µm is a reasonable interaction length. This calibration provides us with an approximate upper limit for the interaction size when analyzing our experimental data FLOW THROUGH A 20 MICRON DIAMETER HOLE: CANTILEVER CONVOLUTION The first experiments conducted studied a jet of nitrogen created by applying uniform pressure to a single 10 µm radius laser ablated hole in an aluminum disk. These initial results were obtained in standard, constant force, contact mode. While scanning over the hole and jet, the tip largely maintained contact with the surface when scanning over areas outside the hole. In order to detect the jet, the force on the cantilever had to be sufficient to overcome the attractive forces that typically keep the tip in contact with a surface. The result was that the signal reached saturation as the tip suddenly jumped off the surface and then touched back down. The jet could be detected in these scans as the tip was lifted

54 54 off the surface and in the area over the hole. Initially, a round jet profile was expected to emerge from the hole. The asymmetry of the jet that was observed instead, is due to cantilever effects as discussed below. Figure 4-1 A 10 µm radius hole without (left) and with (right) a jet of nitrogen. Flow velocity is ~1m/s By lowering the deflection setpoint, the tip was scanned slightly above the surface, so that it was no longer subject to contact forces. In this mode, the tip became sensitive only to the hydrodynamic forces created by the flow of the jet and it was much easier to detect the location of the flow. The pressure was subsequently lowered until it was undetectable via our regulator or even by touch, yet a force was still detectable via HFM. Significant optical interference was evident during free deflection imaging, causing the wavy structure in images 4-2 through 4-4.

55 55 Figure 4-2 A series of 100 µm square HFM scans. All images are taken slightly above the surface while a constant pressure of nitrogen gas is applied to a 10 µm radius hole. The highest pressure is applied in the upper left corner; the lowest pressure is in the lower right corner. As the flow is decreased, the probe interaction area becomes increasingly isolated to the region near the pyramid probe tip and less on the entire cantilever. The wavy character of the images is due to optical interference. The shape of the jet appears to be very similar to that of the scanning cantilever. A basic simulation was performed to verify the interaction between the cantilever and the jet. This model assumed a uniform jet interacting with a force proportional to the area of the

56 56 cantilever exposed to the flow. Examining the force on the tip at each location as it scans the surface is equivalent to performing a convolution of the tip and a hole of appropriate size. The result of this convolution model indicates the size and intensity of the force on the cantilever by a uniform fluid jet: Cantilever Figure 4-3 Data taken while scanning the cantilever over a jet from a 20 µm hole is a convolution of the jet and the cantilever. A simulation (right) of the cantilever convolved with the force due to a uniform jet of air is consistent with our experimental results (left). This also elucidates the underlying cause of the shape of the height image, and why the triangular tip shape is inverted from the tip s scanning orientation. The tip experiences the largest force as the increasingly large areas of the cantilever scan over the jet. In addition, as the flow velocity decreases the flow interaction transitions from primarily cantilever-based to primarily tip-based interaction. For large flow velocities, the slowly varying jet velocity results in a force that is nearly constant over the full range of the cantilever deflection resulting in a binary on-off type of interaction. The cantilever is either fully deflected, or not deflected at all as the entire probe interacts with the jet. There is a

57 57 relatively sharp transition from free deflection to saturated deflection areas; and therefore, the cantilever profile is traced out as it passes over the jet. As the velocity decreases there is a sharper gradient in the fall-off of the jet velocity above the sample plane. This acts to create a larger difference in the magnitude of the flow velocity at the tip vs. the cantilever, as the tip of the pyramid probe is ~4 µm closer to the orifice than the cantilever. This results in an interaction that is more limited to the tip region, so the jet-probe interaction profile shrinks to the area near the tip. Friction images also reveal a subtle detail. The jet interacts primarily with one side of the cantilever, then with the other as the cantilever crosses the center of the orifice. This causes an opposite twist force on each side of the probe resulting in a change of polarity of the friction signal (Fig 4-4). The friction image appears to trace out a dark region above the cantilever twisting axis, and a bright region below it. Figure 4-4 A height image of the nitrogen jet on the left indicates upward deflection of the cantilever due to the flow. A friction image of the jet on the right indicates that the cantilever twists in opposite directions as it passes over the nitrogen jet.

58 58 These initial experiments with a large single jet of nitrogen proved that flow is detectable with an AFM. These experiments are dominated by effects resulting from the interaction between the jet and the entire cantilever. These promising first results prompted us to explore the resolution limits and challenges that result when measuring flow from smaller apertures, multiple apertures, and porous samples FLOW THROUGH MICROCHANNEL PLATES: DETECTING LOCAL FLOW VARIATIONS AND SUBSURFACE FOULING Three microchannel plates with varying channel sizes of 25 µm, 10 µm, and 2 µm 28 were obtained to serve as samples with closely packed uniform apertures while varying size. A typical microchannel plate is fabricated by bundling together glass pipes, and then heating and drawing these pipes (much in the same way a glass optical fiber is fabricated) to form a hexagonal array of closely packed microscopic channels. This array of glass channels is then sliced into a plate and is coated with a conductive layer. The plate may be sliced with the channels perpendicular to the surface, or at a slight angle in order to increase the channel depth while maintaining a thin plate. These microchannel plates are typically used as an electron multiplier array behind a photoelectric device in order to amplify light signals. Each of the plates has a large depth to diameter aspect ratio ( >20) ensuring that many electron collisions occur, and in our case, helping to guarantee that flow profiles have fully developed and stabilized uniformly across the samples. A typical contact image of a microchannel plate is shown in Figure 4-5. The channels appear as dark circles on a relatively uniform surface, and the depth of the channels can not be de-

59 59 termined with standard contact mode AFM techniques. Figure 4-5 A typical 30 µm square contact AFM topography image of a microchannel plate As these microchannel plates have a large open fraction (~0.3) with closely packed channels, we can assume that the flow becomes relatively uniform at a few diameters above the plate 29. This is due to quick expansion and entrainment of each jet as the fluid exits each channel. This constant flow coming from the channel array creates a nearly constant background flow pressure on the cantilever. The contrast that is detectable via HFM above a surface is due primarily to the local tip-flow interactions. The interaction the tip experiences is relatively large because the tip is closer to the mouth of the channel than the rest of the cantilever. This effect is also magnified because the tip is at the end of the cantilever where the applied forces exert the greatest bending moment. In Figure 4-6, individual jets emerging from the 25 µm microchannel plate are displayed. The jets do not appear to be directly above the channels because the channels are not perpendicular to the surface. As the tip passes over each channel it is lifted above and out of contact with the surface, as in the case of the single aperture. The tip touches

60 60 back down onto the surface and even dips into the channels slightly (as indicated by the black circles in the image) near the edges. Figure 4-6 An image of the flow above a microchannel plate indicates that the jets of air are not centered above the center of the channels. This is because the channels are not perpendicular to the surface, so the nitrogen jets exiting each channel have a lateral as well as vertical velocity component It is clear that the jets are not uniform, but instead have a maximum velocity in the center that tapers off near their edges due to the parabolic Poiseuille flow that has developed in each channel.

61 61 Figure 4-7 Height image and a profile of the flow above the surface show parabolic shape due to Poiseuille flow In order to probe changes in flow behavior with size, two more microchannel plates with smaller hole sizes were examined. Knudsen flow theory predicts that the fluid flow velocity will vary with changing channel size (and therefore Knudsen number, see Eqn. 2.17) while maintaining a parabolic shape for poiseuille flows. This height image and profile from a 2 µm diameter microchannel plate section shows that the flow profiles inside these smaller channels also have a parabolic shape.

62 62 Parabolic profiles inside channels Figure 4-8 Contact mode image of the 2 µm microchannel plate with flow. The holes of the channels no longer appear black (as in the previous figures) as the tip is lifted by the flow in each channel. Each flow profile has a slight parabolic shape due to Poiseuille flow. This parabolic flow is visible as the lumps in the bottom of each hole in the line section. In addition to measuring the shape of the flow in and above the channels, Figure 4-9 shows images of the 2 µm diameter microchannel plate which indicate that HFM is capable of non-contact imaging, as well as detection of sub-surface characteristics unresolvable via conventional force microscopy. In Figure 4-9(a) (left image), a contact image of the plate is taken without flow. In 4-9(b) (right image), a constant height image is taken approximately 500 nm above the surface. Each hole location in the contact image corresponds to a jet in the HFM image with the exception of the four pores indicated in yellow. The fouled pore in the upper left area of the images is blocked on the surface and can be identified in the contact image and also in the non-contact image. However, the remaining 3 pores are fouled somewhere deep below the surface. This technique s ability to identify whether or not an apparent hole in a surface is actually a through pore, or just a surface depression with a depth exceeding the tip reach makes this an attractive new technology for the study a variety of porous materials.

63 63 a b 5um Figure µm square scan of a glass microchannel plate comprising 2 µm diameter, 120 µm deep cylindrical pores. (a) Height image of plate surface without flow. (b) Deflection image taken with tip positioned ~500 nm above surface with flow ( P 10 Pa, v ~ 5 m/s). Circles and arrows indicate the same 4 areas and locate four fouled pores. The dark features in 2(b) were reproduced over several successive images. The horizontal structure that appears to link some of the jets in the deflection image is likely due to optical interference. Attempts to alter the flow pattern by cementing two microchannel plates together with differing channel diameters, were also made. The intent of this was to restrict the flow in the smaller, upper plate to the areas above the channels in the larger plate below. We were unable to effectively seal the area between the plates, and therefore observed flow through the channels uniformly across the plate. Nevertheless, given the clear indication of individual fouled pores, we can only assume that it should be possible to effectively detect the masking of some pores, or the connectivity of pores in networks TRACK ETCH MEMBRANES: POISEUILLE FLOW DETECTION A 6 µm thick PCTE track-etch membrane 30 consisting of small (400 nm) irregular pores spaced far apart, acts as a sample with limited interaction between neighboring fluid jets. A track etch membrane is created by bombarding a thin membrane with alpha particles from a distant source, and then using a chemical etchant to etch channels in the areas where the alpha particles have broken molecular bonds. Because a distant alpha source is

64 64 used, the channels are approximately parallel, but the channels have a random, irregular spacing and can vary in size and shape, especially at the surface. The pores can be approximated as long channels, much like the microchannel plates, but the membranes are far less rigid, and can rupture under high applied pressures. The permeability is also relatively low compared to the microchannel plate (pore fraction ~0.1 vs. 0.3 for microchannel). HFM images of this membrane (Fig. 4-10) show successful noncontact mapping of the nanopore structure, the ability to distinguish between true cross-membrane pores and surface depressions, and flow profilometry through individual nanopores. Figure 4-10 Top row: 10 µm square images of a polycarbonate track etch membrane. White box indicates the same region in each image. Bottom row: 6 µm long sections along the lines indicated in yellow in images. Features i, ii and iii are the same in all images and sections.

65 65 An AFM topography image in the absence of flow (Fig. 4-10(a)) shows dark holes whose line sections reflect the characteristic V shape of the AFM tip, indicating that the probe width and size limits the tip s ability to image the depth of the pores. Figure 4-10 (a) Height image without flow. The section indicates the location of three depressions or pores. Pore shape and depth characterization is limited by tip convolution effects. An HFM deflection image taken during flow, with the tip and membrane surface in contact (Fig. 4-10(b)), reveal pores that now appear brighter and smoother in the center, though rimmed with a dark, low edge. Line sections show that the bottoms of the V s are now truncated by abrupt upward deflections, caused by flow within the pores. The drag force is insufficient to deflect the tip near the pore edges, where the no-slip condition keeps the flow velocity small.

66 66 P 10 Figure 4-10 (b) Deflection image in contact with surface (, v ~ 2.5 m/s) shows forces on cantilever due to flow. Feature (ii) and (iii) display parabolic profiles (indicated by red arrows), while (i) does not. As the fluid escapes into jets above the pores (Fig. 4-10(c)), HFM allows noncontact imaging of the pore structure by scanning the tip ~500 nm above the surface. Noncontact HFM reveals not only pore locations but also the relative permeabilities of individual pores; in Figure 4-10(c) the largest pores are also the brightest (show the largest 1 P 2 peak velocity), as predicted by viscous flow theory (Eqn. 2.6 vmax = R ). Features 4 µ z (ii) and (iii) display parabolic and jet profiles in both the images taken with flow, while feature (i) is identified as a surface depression without flow. 4 Pa Figure 4-10(c) Deflection image taken with tip 500 nm above surface. The bright areas indicating cantilever deflection clearly show the location of pores with flow and further supports evidence that feature (i) is a deep hole, not a through pore.

67 67 Both the contact and non-contact HFM images (Figs. 4-10(b) and 4-10(c)) allow us to distinguish through pores (e.g., pores ii and iii in the figures) from local depressions or blocked pores (e.g., pore i). Quantitative flow profiles can be extracted from line sections across pores and compared to theoretical predictions. Assuming that viscous continuum theory holds, laminar flow along a cylindrical pore should exhibit a parabolic profile governed by the Poiseuille relation 11 : 1 P 2 2 v( r) = ( R r ) µ z Here v(r) is the axial flow velocity at a radius r from the center, R is the pore radius, η the fluid viscosity, and P/ z the axial pressure gradient. These assumptions predict that the tip drag force (F = bv) also exhibits a parabolic profile with a curvature, independent of pore size. Curvature: 2 d F 2 dr b P = 2µ z 4.3 Figure 4-11 shows force profiles extracted from within thirteen separate pores of Figure 4-10(b), confirming excellent parabolic fits for each profile. The measured curvatures taken from the contact HFM data fall in a broad range of 5 to 20 nn/µm 2, which is roughly consistent with the theoretically calculated value of order 10 nn/µm 2 for our experimental conditions. Deviations from parabolic profiles and variations in curvature may be due to a number of effects including tip convolution, tip and cantilever shape effects, irregular pore width and shape, and transition to the Knudsen flow regime 12. For

68 68 comparison with profiles from within the pores, Figure 4-11 also shows corresponding force profiles extracted from Figure 4-10(c), as the flow exits the pore and becomes a free jet. Here the radial curvature is expected to decrease due to fluid entrainment effects as is consistent with our results. Figure Cantilever force profiles taken from 13 pores in figure 4-10, + s indicate the data is taken from 3(b) where the tip was in contact with surface. Dots indicate data from the same 13 pores in image 3(c) where the tip was 500 nm above surface. Each profile indicates the force on the cantilever as the tip scans across each pore and is displayed along with its best parabolic fit line. Maximum force set at r = 0 and arbitrary offset applied for clarity In Section 4.1, the calibrated effective interaction size for the tip and cantilever found was ~65 µm, yet the parabolic flows measured from this membrane display a resolution of 15 nm or smaller. Because the flow comes from a restricted source and its interaction is limited to the tip region, the force on the tip is proportional to the local flow

69 69 speed. This holds for cases where the effective tip size and pore fraction are both very small. F _ drag = Fspring = kz = 6πa tip v 4.4 tip µ v average velocity v Figure 4-12 Flow interactions localized to the tip region can give excellent resolution (left). Flow interactions that involve the cantilever give a background deflection, but local fluctuations are still detectable as the local flow-tip interaction is greater than the flow-cantilever interaction When the flow is distributed over a large area of the tip and cantilever, (large pores or, large open fraction samples) the cantilever experiences an approximately uniform background force that acts on the whole tip-cantilever system F = 6πr v 4.5 lever drag lever µ The local tip interaction force, F tip drag, continues to probe the local variations in the flow, allowing HFM to resolve local flow structure as has been shown with both the microchannel plate and these track etch membranes. In order to better understand the resolution capabilities, a basic simulation of a parabolic flow mapping was executed. The tip crosssection was modeled as a disk with varying radii, and the flow was modeled as a cylindrically symmetric parabolic flow in a 1 µm diameter hole; and the two were convolved.

70 70 By plotting a central line section of this convolution the interaction size of the tip-flow system can be probed. Figure 4-13, Simulation of flow mapping with varying tip sizes. A convolution of a uniform circular plate with radius r and a cylindrical parabolic flow with 500 nm radius. For an effective probe size < 1 µm the parabolic shape is reproduced near the center, though broadened. This model system shows that for an effective tip size less than 1 µm (1 hole diameter,) the parabolic flow profile can be detected, but it is broadened. For an effective tip size of 100 nm or smaller the flow profile is very accurately recreated especially in the center of the flow. At the edges of the flow, the drag force on the tip approaches zero so the standard contact mode tip-sample interactions dominate. Experiments measuring Poiseuille and jet flows as shown in Sections 4.3 and 4.4 may be extended to illuminate Knudsen flow regime effects. Continuum theory predicts that the curvature of a Poiseuille flow should remain constant for systems with the same

71 71 pressure, viscosity and probe size (Eqn. 4.3). In the Knudsen regime however, the Poiseuille flow curvature becomes: 2 d F b P = ( 1+ αkn) dr 2µ z This indicates that varying pipe diameters, the resulting Knudsen number, and the curvature should also change. Another experiment of interest at this size scale is the measurement of jet expansion above an aperture. By profiling the same jet at varying heights above an aperture, Knudsen effects on jet flows could be investigated. In order to collect meaningful data, a single, isolated aperture should be used. This is because multiple holes can lead to entrainment and Coanda effects that distort jet profiles. In addition, there may also be ef - fects from neighboring jets acting on the cantilever in a manner that could be difficult to deconvolve. A sample with regularly spaced apertures could be used (like a microchannel plate), but it has been shown that evenly spaced arrays of jets (with jet spacing ~jet diameter) expand and merge to form a nearly uniform flow at a distance of ~5-50 aperture diameters above a surface 31. The reduced curvature of Poiseuille flow profiles in the Knudsen regime might shorten this merging distance further. Further experiments and quantitative analysis of flow profiles are anticipated LA C E Y CARBON FILM: UNIFORM FLOW THROUGH A SCREEN Flow through a lacey carbon film (LCF) provides an interesting contrast to the jet and parabolic profiles observed in the three previous samples. The LCF is a web of carboncoated Formvar threads 32 (100 to 500 nm in diameter) which act like a screen. Figure 4-

72 72 14(a) shows the LCF topography without flow and section 4-14(c-i) shows the usual V- shaped dips characteristic of tip convolution. Figure 4-14(b) shows the film with a high flow. The tip is buoyed up by the force of the air flow, causing the holes to appear filled as in Figure 4-10(b). Figure 4-14(c) shows corresponding line sections with and without flow. In contrast to Figure 4-10(b), the flow profile section 4-14(c-ii) is flat, indicating a spatially uniform flow. The negligible pore depth of the LCF prevents Poiseuille flow from developing, and instead reveals only the uniform background flow from the reservoir. This can be regarded as an effective control experiment for the track-etch membranes, showing that the parabolic profiles of are not primarily due to tip convolution ef - fects. The uniform flow region exhibits 5-20 times greater noise than the contact areas of the scan. The LCF threads have < 10 nm rms fluctuation, while the flow regions (where the tip is freely deflecting) exhibit height variations as large as 200 nm for large volume flow rates. The noise enhancement experienced by the cantilever in this sample vs. the noise in the track-etch membrane is likely due to cantilever boundary effects (Sec 3.2) resulting from the large aperture size and the significant volume flow rates through this screened system. The absence of a contact restoring force undoubtedly allows for greater noise to enter the system in the open region.

73 73 1um a b i ii ii c i Figure 4-14 Lacey Carbon Film (LCF) with and without flow. Web-like screen created by nm diameter carbon-coated threads. (a) AFM topography image of an LCF without flow (b) HFM image of the same area of the LCF with flow appears to have a noisy flat bottom below threads. (c) Comparison of scaled sections from (a) and (b) show a flat profile created by uniform flow. Another indicator that the flow through the LCF is uniform comes from images that are in partial contact with the surface. In Figure 8-2, a constant height image is taken. Due to some small tilt in the sample, the left side of the film sits slightly lower than the right side. When the tip leaves contact with the surface, there are no indications that the flow is altered in the area above the LCF threads. The tip deflection remains relatively constant and does not allow non-contact imaging of this sample.

74 74 Figure 4-15 Partial contact images of LCF with flow. Even very close to the surface, the location of the LCF threads is not distinguishable on the left side of these images. Initially, we speculated that drafting phenomena might act as a contrast mechanism in screen-like samples such as this one. As discussed in section 4.1: Flow Calibration, the effective size of the tip and cantilever when exposed to uniform flow is approximately 65 µm. The threads in the LCF are ~ nm in size, or ~10 3 times smaller. Any drafting effects between the tip and sample are therefore very small, especially at these low Reynolds numbers. While flow past cylindrical obstructions can result in attached eddies that create a buffer zone of low fluid velocity behind the obstruction, it is unlikely that this kind of phenomena has developed at this size and fluid velocity scale. The overall interaction of the tip-cantilever combination with the uniform flow was clearly much larger than any local modifications to the flow by the LCF TEM GRID: SCREEN OR CHANNELS? The final sample used to explore upward flow is a TEM (Transmission Electron Microscopy) grid 33. A TEM grid is a square copper grid with 5 µm thick bars, and 11.5 µm

75 75 open sections. These are often used as mounting substrates for TEM, but in this case they provide us with another gas-permeable sample with small feature size. In looking at the TEM grid, initially we expected to get similar results to those seen with the LCF. This sample has an open fraction of 0.49 and is 20.3 µm thick. Because of the large aperture size we assumed that this sample would also act like a screen, but the data clearly shows that the flow has a local maximum in the center of each aperture.. Non-uniform flow profile Figure 4-16a line section from the TEM grid indicates non-uniform flow (the short wide humps in the bottom of each well) indicating the flow is being altered by its interaction with the sample. In addition, the tip may be experiencing some drafting as it passes over the grid.

76 76 Figure µm square images of the same area of a TEM Grid. Each row is made up of the Height, Deflection and Friction images from a single scan. The first row is a contact image taken with no flow. Rows 2-4 are all taken with the same flow velocity, but with decreasing amounts of contact with the surface. The friction images in particular show significant optical interference due to light being reflected from the shiny copper sample interfering with light from the cantilever. The optical interference appears as horizontal waves or stripes as see in Figs. 4-2, 4-4 and 4-9. The two likely primary effects involved in shaping the measured flow profiles in the TEM grid are duct flow considerations, and drafting. First, the depth of the grid is

77 77 only twice as long as the aperture diameter, and is therefore considered a duct flow which must be treated as a finite length pipe. The flow will be slowed near the edges of the aperture in order to meet boundary conditions of flow velocity = 0 at the bars, but the entry length may not be sufficient to allow a full parabolic profile to develop. Second, the TEM grid bars are 5 µm wide which could potentially create a region above the surface where the tip experiences significantly lower flow velocities than in the areas above the grid bars. In the case of the LCF, the carbon threads were only a few hundred nanometers in diameter, and therefore 10 3 times smaller than the cantilever pyramid tip (which is about 4 µm wide and high), but the TEM grid bars and the cantilever probe pyramid are of comparable size (~5 µm). Because the entire cantilever is still experiencing a uniform flow from the rest of the sample, there are some convolution effects. In the non-contact image, the flow maxima appear to be in the center of the apertures, but there is evidence of flow forces along each bar, and the flow forces are minimized at the junctions where the grid bars cross one another. Figure µm square images taken on/above the TEM grid. The first image is a contact image taken with no flow. The second is taken just above the surface (~50 nm) with flow. The third image shows the first two images overlaid, the flow maxima correspond to the apertures in the TEM grid.

78 VACUUM STUDIES Various samples were also observed while suction from a vacuum pump was applied in order to reverse the pressure across the sample. In the case of applying vacuum to the single 20 µm diameter aperture (the first sample examined in Section 4.2), it was possible to map the suction force. The results were similar (though not identical) to those obtained for jets created by applying positive pressure. These observed differences result because as positive pressure is applied to the bottom of the aperture, the flow develops a steady profile that originates from a restricted source near the exit of the orifice. This constrains the source or the jet flow that disperses with increasing distance from the aperture. In the vacuum case, negative pressure created by suction from below the hole draws air in from all directions above the sample plane. This results in a much more diffuse flow profile near the aperture. The difference is illustrated by blowing on one s hand held a few inches in front of the mouth. The air flow on the hand is readily detected while blowing, but it is very difficult to detect air flow created by suction of air into the mouth, even if the hand is moved very close to the mouth. The high velocity gradient near the surface in the case of suction could, however, prove useful in maximizing the contrast in samples with varying permeability. T w o images with suction applied to the 20 µm hole are shown in Figure The shape of the flow takes on the same cantilever convolution shape that was apparent in the images taken of the jet coming from this same aperture in Chapter 4.2. The contrast is inverted because in the case of an upward jet the cantilever was deflected away from the aperture, whereas in this case, the cantilever is drawn downwards towards the

79 79 sample, and even drawn into contact with the surface despite a free deflection well above the surface. Figure µm scans of the 20 µm aperture with suction. The first is a contact image with no flow through the aperture (the dark area near the top of the image). The second image shows the tip being brought into contact with the surface due to the suction through the hole. The third demonstrates noncontact imaging as the cantilever is drawn downwards due to the suction, but does not make contact with the surface. The last image is from Chapter 4 and depicts flow out of the hole. Note the inverted contrast from the 2 vacuum images, which also demonstrate cantilever convolution effects similar to the images of the outward jet from this same aperture OTHER FLOW CONFIGURATIONS USING CONTACT MODE HFM Flow parallel to a surface There are many examples of attraction between objects when flow is applied in the gap between them: simple demonstrations of this hydrodynamic attraction often involve two spheres, two sheets of paper or foil, or a sphere and a hard wall. This attraction is due to differential pressure and drag forces at the boundaries of these objects. It is therefore conceivable that by applying flow parallel to a surface it may be possible to see differential attraction between the AFM tip and surface features of varying heights. It may even be possible to achieve this kind of effect due to flow generated by the motion of the cantilever itself. Unfortunately, our attempts to observe such effects were unsuccessful. Two experiments were carried out using the weakest of the standard (Veeco DNP-

80 80 S) silicon-nitride contact mode cantilevers. The first experiment consisted of simply scanning the cantilever at very high rates near the surface of a microchannel plate (this acts as a sample with large height variations). These experiments were carried out both in air and in water, and at varying scan rates from a few Hz up to the fastest scan rate achievable with the current AFM system 60 Hz over a 100 µm area. This translates into an actual surface velocity of 12 cm/sec, which is rather slow. Attempts were made to bring the cantilever as close to the surface as possible without actually making contact in order to maximize the likelihood that parallel flow induced attraction between the cantilever and surface would be detected. No deflection variations were detectable as the tip passed over these topologically varying surface features. In the second experiment, flows of varying speed were applied parallel to a rough surface via a syringe needle and the cantilever was scanned above the surface at various rates and directions with respect to the flow. Here also no deflection variations were detected Downward flow After successfully imaging porous surfaces with downward flow due to negative pressure, (section 4.7) an experiment in applying flow perpendicular to the sample, and originating above the cantilever and sample, was performed. The intent of this experiment was to vary and possibly control the force on the cantilever in a method similar to that of the vacuum experiments, but in a manner that could be applicable to impermeable solid surfaces. A syringe needle was installed above the cantilever and a downward flow was ap-

81 81 plied while the cantilever scanned across the surface. Unfortunately, the addition of downward flow to a solid surface system resulted in a large increase in noise. As the flow passes over and around the cantilever, there is typically a region with a depth of less than 10 µm before the flow reaches the surface and then must find another path to exit the area near the surface and cantilever. It seems that a large portion of the flow is scattered off of the surface. Due to the simplicity of the system used, the flow was not directed in a manner that limited its interaction to the cantilever in order to minimize the flow-surface interactions. For even very low flows, this technique made even normal contact mode imaging of a surface very difficult. This technique appears to need significant engineering to have any prospects for success. One unexplored configuration that might have a higher probability of success is to use a downward flow with suction in a nearby region to assist in better directing the flow in the tip-surface region.

82 82 5. TAPPING HFM, HFM IN FLUIDS AND FUTURE DIRECTIONS While the majority of experiments carried out in this work focus on effects involving steady flows through porous samples, other hydrodynamic forces, phenomena, and measurement techniques are still of interest for future exploration. One major challenge faced in this work was our inability to accurately measure flow velocity or pressure gradients across the samples. Without the use of vacuum quality components, pipe and fitting losses in the flow generating system could easily induce significant pressure changes in this primarily gas based system due to the very small size and low permeability of the apertures used. Generating and measuring very low flow velocities with any accuracy was not possible without investing in a significant amount of flow control and measurement equipment. This made quantitative analysis very difficult. In addition to calibration, there are several improvements and areas of study that could potentially advance this technology. We have begun to pursue some of these directions, and hope to continue to expand on the following techniques TAPPING MODE Traditional AFM Tapping Mode: Basic Principles In tapping mode, a small piezoelectric element mounted in the AFM tip holder drives the cantilever to oscillate up and down at a frequency near resonance. The amplitude of this oscillation is greater than 10 nm, and is typically 100 to 200 nm. Due to the interaction of forces acting on the cantilever when the tip comes close to the surface, Van der Waals force, electrostatic forces, and the forces discussed in this Chapter 1 cause the amplitude

83 83 of this oscillation to decrease as the tip gets closer to the sample. Using a mechanism similar to that in contact mode, a feedback loop controls the height of the cantilever above the sample. In tapping mode however, the feedback attempts to maintain a constant cantilever oscillation amplitude as it scans across a sample. Tapping mode AFM images are very similar to contact mode images for rigid samples, but for soft samples, or those with weakly bound adsorbates on a sample surface, tapping mode can be used to avoid surface modification or damage. Figure 5-1 Tapping mode cantilevers, Note that these have not only a different geometry, but also a higher spring constant and resonance frequency Tapping images of apertures The most basic method for examining fluid flow in the direction of the cantilever oscillation is to consider the effects that arise in the presence of an upward flow. The oscillating cantilever will experience an upward drag force that results in a measurable offset in the cantilever free deflection position. In addition, the drag force also causes a reduction in the oscillation amplitude, which the feedback loop interprets as a topographic

84 84 projection at the location of the jet. Oscillation Flow Figure 5-2Basic HFM tapping mode technique This tapping mode flow detection method was performed using the same 20 µm diameter aperture used in Sections 4-2 and 4-7. The tapping mode cantilevers are much stiffer and have higher resonance frequencies than contact mode tips (~300 khz for tapping vs. ~20 khz for contact) and they are extremely high Q (quality factor) systems (Q~ ). In addition they are also shaped like a diving board with a pointed end, rather than an open triangle. Images taken of flow through the 20 µm aperture were very similar to the noncontact images taken with the contact mode levers. The tapping cantilever was scanned about 500 nm above the aperture surface, and the deflection and amplitude of the tapping cantilever were recorded. These images reproduce the shape of the tapping cantilever, indicating a convolution effect that is nearly identical to that in the contact mode case. The amplitude signal shows surprisingly high resolution with variations corresponding to the location of the pyramidal tip on the diving board cantilever.

85 85 Figure µm square Tapping mode image taken above the surface of the 20 mm hole aperture with flow. The image displays a convolution of the tapping mode tip shape due to the same convolution effects seen in Chapter 5 with a contact mode tip Tapping HFM Frequency Sensing In tapping mode, the resonance frequency of the oscillating cantilever system is dependent not only on the size and spring constant of the cantilever itself, but also on the viscosity of the medium in which the cantilever is oscillating. By monitoring the shift in resonance frequency due to the presence of different fluids, it may be possible to use tapping mode to measure fluid flow in micro and nanofluidic systems. Using one gas species as a sweep or ambient gas, and a different gas species to supply fluid flow through the membrane may be used to extend the HFM technique into tapping mode by utilizing variations in resonance frequency as a contrast mechanism. Because of the high Q of this system, a small shift in the resonance frequency results in a large change in amplitude.

86 86 Experiments were preformed to investigate changes in the cantilever resonance frequency in the presence of various gases. The AFM has an integrated routine that ramps the applied driving frequency of a piezoelectric transducer in the cantilever holder and then maps the amplitude of the cantilever oscillation as a function of frequency and finds the peak to determine the resonance frequency of the cantilever. The resonance frequency of a single cantilever in the presence of different gases was measured. The resonance frequency in air was khz, in Nitrogen it was khz and in Helium it was khz all with peak full width (half maximum) of ~1 khz. With this data in hand, experiments measuring the flow of varied gases through a track-etch membrane were carried out. The tapping mode cantilever was tuned while nitrogen gas was flowing through a track-etch membrane with a nominal hole size of 200 nm. A helium gas flow was then applied through the pores. A large tube was installed in the AFM chamber that provided a steady flow of nitrogen to the area above the sample to help sweep away helium gas from above the surface in an effort to ensure that any effects observed would be due to local concentrations of helium very near the surface, rather than due to a buildup of a helium enriched environment.

87 87 Figure 5-4 Tapping HFM method (not to scale ). Helium streams through the track etch membrane while Nitrogen is used as a sweep gas. The nitrogen source was much larger than the cantilever or membrane channels. Scans of the sample taken with a cantilever oscillating at the nitrogen resonance frequency and measuring helium flow resulted in a decreased contrast between the pores and the rest of the surface. In particular, one image stood out. Figure 5-5 shows a scan of the membrane surface while helium gas is flowing though the membrane pores. In the upper third of the image (above the white line) Nitrogen gas is applied as a sweep gas to remove helium form the tip-sample region. Below the white line, the sweep gas is turned off. Without the nitrogen sweep gas, the contrast in both the height and amplitude images decreases significantly.

88 88 Figure 5-5 Helium flow through a track etch membrane. Above the white line nitrogen sweep gas was applied and contrast is good, below the white line, the helium flow is allowed to build up a layer of gas near the surface which appears to decrease the contrast. A line section of the membrane with helium flow with and without the nitrogen sweep gas indicates that with the sweep gas, the pores appear to be about 200 nm deep, and without it they only appear to be 50 nm deep. Figure 5-6 A line section taken along the black line from a track etch membrane with He gas flow. Above the white line nitrogen gas is used to sweep away excess He from the surface, below the white line the nitrogen gas is turned off while the He continues to flow, the apparent pore depth is much smaller without the sweep gas, resulting in a loss of contrast.