Supporting Information

Supporting Information On the Minimal Size of Coffee Ring Structure Xiaoying Shen, Chih-Ming Ho and Tak-Sing Wong * Mechanical and Aerospace Engineering Department, University of California, Los Angeles, California 90095. Institute of Microelectronics Engineering, Peking University, Beijing, P. R. China *Corresponding author. E-mail: tswong@ucla.edu Experimental Section Materials. Polystyrene latex beads (SIGMA, LB-1) surfactant-stabilized suspension with a particle diameter of 113 ± 11 nm (m = 20, where m is the number of the independent measurements from scanning electron microscope, SEM), was used as received, where the particle density was 1.828 10 14 particles/ml. In some of the experiments, the suspension was further diluted by 10 or 100 times, with the addition of trace amount of anionic surfactant sodium dodecyl sulphate (SDS) (Fluka, Switzerland, diluted to < 0.01%) to stabilize the particle suspension. In addition, carboxyl latex beads (Molecular Probes ) charge-stabilized suspension was used as received. Three different particle sizes were used in the experiments: 28 ± 5 nm, 3.3 x 10 15 particles/ml; 62 ± 6 nm, 3.1 x 10 14 particles/ml; 140 ± 13 nm, 2.7 x 10 13 particles/ml. Purified deionized water with a resistivity of ~18.3 MΩ/cm was used for the dilution. S1

Fabrication of Chemically Heterogeneous Surfaces. Following the published experimental protocol (Wong T.S. et al., Langmuir 2009, 25, 12, 6599-6603), standard photolithography procedures were used to create engineered surfaces with patterned platinum (Pt) hydrophilic cylindrical structures on a relatively nonwetting surface coated with hexamthyldisilazane (HMDS). These surfaces were utilized to control the size of liquid droplets. The diameters of the hydrophilic cylindrical structures ranged from 3 µm to 1 mm, and the height of the structures measured ~20 nm, as confirmed by atomic force microscopy (AFM, Veeco Dimension 3100; AFM tip used: RTESP Veeco, NY, with specified tip radius of curvature < 10 nm) measurement. Based on the patterned heterogeneous surfaces, a colloidal solution, with known particle size and particle concentration, receded from a relatively nonwetting substrate onto the hydrophilic structures. Liquid droplets were retained on the structures as a result of pinning to the solid edge. Nanoparticle deposits were formed on the hydrophilic surfaces upon solvent evaporation under a humidity-controlled environment at room temperature. Surface Characterization. Contact angle measurements were carried out for all the particle suspensions on both Pt and HMDS surfaces by a drop shape analysis system (FTA 4000) at ambient temperature (24 26 o C) with ~50% relative humidity under an enclosed environment. The droplet volume for the measurement was ~0.5 µl (for static contact angle), and the droplet profile was captured through a camera equipped with an optical system for the amplification of the captured images. All the contact angle measurements were performed within 30 seconds; otherwise the data point will be discarded due to excessive evaporation of the droplet. The droplet profile was fitted into a spherical cap profile by an in-built computer program provided by the system, in order to determine the contact angle. In addition, dynamic receding and advancing contact angle measurements were achieved by withdrawal and addition of tested colloidal solutions through an automated syringe system, and the droplet profiles were captured subsequently for the measurements. The droplet evaporation history was also studied using the FTA 4000 system. The contact angle and the base diameter of a droplet in each frame were measured separately using the in-built program. S2

Formation of Particle Deposits. A chip with patterned surfaces was transferred to a humidity-controlled chamber (Electro-Tech Systems Inc, PA) for the particle deposits formation process. The relative humidity of the chamber can be controlled from 10% to 90% (with accuracy of ±2%) at room temperature of 22 o C 25 o C. The humidity chamber was adjusted to the targeted relative humidity (e.g., 50%) for ~1 hour prior to the experiments. In all of the experiments, ~80 µl of the colloidal solution was placed on the chip, where it was tilted to remove the excess solution. The chip was left in the humidity chamber for ~30 min until the solvent was fully evaporated. The pinning of the liquid to the hydrophilic surfaces and the subsequent formation of liquid droplets were further confirmed through the use of a digital video camera connected to an optical microscope. Observation and Measurement. A combination of scanning electron microscope (SEM, Hitachi S4700) and AFM were utilized to obtain the quantitative measurements of the particle deposits. SEM was utilized to obtain two-dimensional information of the deposits (i.e. particle density distribution and the distance between the edge of the ring structure and the initial contact line) and AFM was used to obtain the third dimensional information (i.e. height). Besides, SEM was also utilized to measure the diameter of the hydrophilic surfaces and particle diameters. Data Analysis. The diameters of the hydrophilic sites used for the experiments are listed as follow: 3 µm, 5 µm, 10 µm, 25 µm, 50 µm, 100 µm, 250 µm, 500 µm, and 1 mm. The captured SEM images were processed and analyzed using an image processing software ImageJ (developed at National Institute of Health, USA). The SEM images (1280 960 pixels) were processed to obtain the dimension of each pixel, which will be used for the quantitative measurements of the nanoparticle deposits. A minimum of 10 independent measurements were carried out for each hydrophilic site to obtain L p for all of the experiments. S3

Engineered Heterogeneous Surfaces and the Liquid Receding Experiment Figure S1. (a) SEM image showing the engineered heterogeneous surfaces. The diameter of the hydrophilic sites ranged from 1 mm down to 3 µm. (b) Time sequence optical images showing the droplet formation process on the hydrophilic sites (droplet size: 100 µm and 250 µm). A macroscopic colloidal solution was first applied onto the surface, where the solution was withdrew from the surface, leaving part of the liquid being trapped onto the hydrophilic structures due to pinning. Upon the solvent evaporation, nanoparticles deposit form on the hydrophilic sites. S4

Summary of macroscopic contact angle measurements Table S1. Contact angle measurements of water and colloidal solutions used in the experiments. Measurement Type Water 100 nm Surfactantstablized 100 nm Chargestablized 60 nm Chargestablized 20 nm Chargestablized Pt θ adv 47.0 ±0.4 59.8 ±0.6 55.0 ±2.4 58.3 ±6.7 48.1 ±4.1 θ static 22.8 ±1.4 25.2 ±0.5 35.0 ±0.1 33.0 ±0.1 26.4 ±0.3 θ rec 11.3 ±2.9 - - - - HMDS θ adv 78.4 ± 3.0 68.4 ±0.2 84.1 ±3.8 72.1 ±4.7 65.1 ±5.8 θ rec 63.9 ±5.2 - - - - Note: The receding angles of the colloidal droplets cannot be measured accurately due to the strong CL pinning by the coffee ring structures. S5

Droplet Evaporation History of Various Colloidal Solutions on Pt surfaces. Figure S2. Evaporation history of different particle suspensions on Pt surfaces Table S2. Evaporation history of different particle suspensions on Pt surfaces Water 100 nm Surfactantstabilized 100 nm Chargestabilized 60 nm Chargestabilized 20 nm Chargestabilized Slope -0.19-0.18-0.22-0.21-0.27 θ initial 21.9 ±0.0 18.4 ±0.2 21.2 ±0.1 18.4 ±0.1 21.8 ±0.6 The initial stage of the evaporation dynamics for both 100 nm (b) surfactant-stabilized solution and (c) charged-stabilized solution are similar to that of the (a) pure water, where they kept a constant area mode of evaporation, indicating strong pinning of the CL to the edge of the hydrophilic sites. For colloidal particles with smaller particle sizes, the droplet first followed a constant area mode of evaporation, and then transited to a constant contact angle mode of evaporation. The observation was more pronounced for the colloidal solution with 20 nm particles, indicating that the CL pinning ability is S6

weaker compared to that of 100 nm particles. Table S1 shows the slope (i.e., evaporation rate) and initial contact angle obtained from the evaporation history plots. S7

Nanoparticle Deposits at Different Length Scales Figure S3. SEM images for nanoparticle deposits on hydrophilic Pt structures with diameters ranging from 3 µm to 500 µm. Representative SEM images showing the deposit patterns at different droplet diameters: (a) 3 µm, (b) 5 µm, (c) 10 µm, (d) 25 µm, (e) 50 µm, (f) 100 µm, (g) 250 µm, (h) 500µm. Two different regimes of the deposit patterns are clearly distinguishable. SEM images show that for the droplet smaller than 10µm, the nanoparticles are dispersed homogeneously on the surface. For the droplet large enough, nanoparticles form coffee ring structure after droplet evaporation. It is important to note that the image contrast of the SEM images is dependent on the local thickness of the coffee ring structure. Therefore the perimeters of the coffee ring structures appear to be darker as the number of the nanoparticles layers increase. S8

Effect of Surfactants to the Coffee Ring Formation. Figure S4. Comparison of the evaporation rate and L p between the surfactant-stabilized particle suspension and surfactant-free charge-stabilized colloidal solutions. The plots indicate that the presence of surfactants does not severely impact the evaporation rate of the colloidal solution, as well as L p for the coffee ring structures. S9

Nanoparticle Deposits for Small Droplets Figure S5. (a) SEM image of 100 nm particles deposited in a 3 µm droplet. (particle concentration: 1.828 10 14 particles/ml, relative humidity = 50% at room temperature). (b) SEM image of 100 nm particles deposit in a 5 µm droplet (particle concentration: 1.828 10 14 particles/ml, relative humidity = 50% at room temperature). In these SEM images, it is clear that there were sufficient nanoparticles to form at least one concentric coffee ring structure at the edge of the droplet, yet no coffee rings were formed due to the fast evaporation of small droplets. This further highlights that the evaporation time of the droplets plays an important role in the coffee ring formation process. S10

Monolayer Layer Formation near the Contact Line Figure S6. (a) An AFM image showing the surface topography of a coffee ring section (A A ) formed by surfactant-stabilized 100 nm particles. The monolayer formation at the boundary of the coffee ring structure is confirmed by the particle height measurement, where the average particle height (i.e., the difference between the red dotted lines) matches to the diameter of a single particle (i.e., ~100 nm). This indicates that the formation of the coffee ring structure is first initiated from the formation of monolayer, which plays an important role for the CL pinning. (b) SEM images showing a coffee ring structure formed for a 25 µm droplet. From the magnified image at the corner of coffee ring structures, we can see that a small number of concentric rings of nanoparticles are sufficient for the CL pinning. S11

Nanoparticle Deposit Patterns for 20 nm and 60 nm particles Figure S7. Representative SEM images showing the nanoparticle deposit patterns for (a) 20 nm and (b) 60 nm particle suspension. For the 20 nm particles, all of the nanoparticles were distributed uniformly on the surface; whereas for the 60 nm particles, concentric circular patterns were formed on the hydrophilic sites instead of a single coffee ring structure, indicating repeated CL pinning and depinning. S12

Derivation of Eq. 1 in the Main Text Figure S8. (a) SEM image showing the monolayer formation of nanoparticles close to the contact line, where a finite distance is observed between the edge of the particle monolayer and the initial contact line of droplet. By simple geometry, we derived a relationship which relates L p and the particle sizes of the colloidal suspension, L p = r θ tan( local 2) (S-e1) where r is the radius of the nanoparticles, and θ local is the local contact angle between the three phase CL at the particle surface and the horizontal Pt surface. Notice that this equation is derived under the conditions where D >> D c and r << D, where D is the diameter of the hydrophilic site. S13

Derivation of Eqs. 2 to 7 in the Main Text Time of Evaporation ( τ evap ): We consider the evaporation process of a sessile droplet of particle suspension on a horizontal surface. In our experiments, the droplet diameter is sufficiently small (D < 1 mm) so that surface tension is dominant, and the gravitational effect can be neglected. Therefore the droplet can be modeled as a spherical-cap shape. As supported by our experimental measurements on the evaporation dynamics of colloidal liquid droplets, the initial phase of the evaporation process is predominately in constant contact base diameter mode. Therefore we employed the constant contact base diameter evaporation model for our calculation. The contact angle is small enough (θ << 57.2 ) and the maximum height of droplet is much smaller than its radius. We assume that the droplet profile is not affected by either the particle transport or the capillary flow developed within droplet. Based on our assumptions and experimental conditions, we applied the theoretical model by Popov et al. (Popov et al. Physical Review E 71, 036313 2005) to deduce τ evap, which is described as follow. Figure S9. A schematic showing a droplet sitting on a solid surface. Considering in Figures S6 where a liquid droplet sits on a horizontal solid surface with base diameter, D, radius, R = 2 D and a contact angle of θ (i.e., the angle between the liquid-vapor interface and the horizontal plane of the substrate). The volume of the liquid droplet, V d (t), can be calculated as, 3 R( t) 1 R ( t) 2 Vd ( t) = h( r, t)2π rdr= π (1 cosθ ( t)) (2+ cosθ ( t)) (S-e2) 0 3 3 sin θ ( t) where R( t) sinθ ( t) is the curvature radius of the droplet surface, and the height of droplet surface at r can be expressed as S14

2 R ( t) 2 h( r, t) = r R( t) cotθ ( t) 2 sin θ ( t) (S-e3) For small contact angle, θ << 57.2, Eq. S-e3 can be simplified as 2 2 R ( t) r 3 h ( r, t) = θ ( t) + O( θ ) 2R( t) (S-e4) 3 πr dv d = dθ 4 (S-e5) Based on our experimental observations, the contact base diameter of the liquid droplet stayed constant for the majority of the evaporation process, therefore we have D(t)=D i, where D i is the initial base diameter. In addition, we further assume that the evaporation process is not influenced by of the presence of solute inside the droplet (see for example, Drisdell et al., Proc. Natl. Acad. Sci. USA 2009, 106, 18897 18901). The evaporation rate can be expressed as 2 Dv ( c J ( r) = π R 0 c ) 2 i r 2 (S-e6) where D v is the molecular diffusion constant of the vapor in air, c 0 is the density of the saturated vapor immediate above the liquid-vapor interface, c is the ambient vapor density. M wpvs c0 c = ( )(1 RH ) (S-e7) R T g where M w is the molar mass of water, Pvs is the saturation water vapor pressure, R g is the ideal gas constant, and T is temperature in Kelvin. From Eq. (S-e4) to (S-e7), the time derivative of droplet volume can be expressed as dv dt d = 0 R i J ( r) ρ 1+ ( h) r 2 4 v ( 0 ) 2πrdr = D c c ρ L R i (S-e8) By integrating Eq. (S-e5) and Eq. (S-e8), we can obtain the relation of θ with time. 3 i π R dθ 4D ( c c ) 4 dt v 0 = Ri (S-e9) ρl S15

4 θ ( t) = θ Kt (S-e10) initial πr 2 where K is a characteristic parameter represents droplet evaporation rate in the following form, i K 4Dv ( c0 c ) = (S-e11) ρ L It is important to correctly define the characteristic time scale, τ evap. Based on our experiments, we found that under the conditions where the coffee rings were well formed, there always existed a finite distance, L p, between the initial pinning point and the boundary of the coffee ring. This distance can be estimated by the following simple geometrical relationship as shown earlier, L p r = (S-e12) θ / 2) tan( local where θ local is the local contact angle at the time when the particles start to form ring-like deposit. By using experimentally measured L p and the size of the particles, r, one can determine the θ local during the coffee ring formation process. Specifically, the evaporation time from θ initial to θ local represents the time required to initiate the coffee ring formation. Based on the measured L p, we found that θ local is consistently between θ initial and θ receding. Based on our experimental observations together with (S-e10) and (S-e11), the time for a droplet contact angle changes from the initial contact angle θ initial to receding contact angle θ receding can be expressed as, τ evap θinitial θ receding 2 = πri (S-e13) 4K Time of Particle Movement ( τ particle ): To determine τ particle, we consider the diffusion time required for two adjacent nanoparticles near the CL to meet each others. The mean distance between two particles within the liquid suspension, L m, can be estimated as 3 V d / n, where V d is the volume of the droplet and n is the number of nanoparticles within the droplet. The induced capillary flow velocity is very small S16

when it is close to the substrate surface due to the no-slip flow boundary condition, therefore it is reasonable to neglect the impact of flow velocity on the particle movement. To estimate the time for the nanoparticles to travel through L m, we use the Einstein diffusion equation to estimate τ particle, (Einstein, 1956, ISBN 0486603040) the particle motion can be described as x 2 = 2D t (S-e14) where the diffusion coefficient of a spherical object, D p, is given by the Stokes-Einstein equation, p D p k BT =, where η is the viscosity of the suspending fluid and r is the radius of the sphere. Since the 6πηr average diffusion distance can be approximately by L m, we get 2 m L τ particle = (S-e15) 2D p By equating (S-e13) and (S-e15), we can determine a critical length scale important to the coffee ring formation, which can be expressed as, D c 8K = 2R = Lm (S-e16) = D i τ evap τ particle π ( θinitial θ receding ) p Eq. (S-e16) conveys a number of critical information for an evaporating colloidal liquid droplet. For example, the parameter K indicates the evaporation rate, which is dictated by the liquid medium and the evaporating environment. L m and D p are parameters related to the properties of the particle suspensions, such as particle concentration and sizes. The contact angle (θ initial θ receding ) characterizes the surface property. All of these parameters collectively give rise to the compact form of Eq. (S-e16) that describes the minimal size of the coffee ring structure. S17

Table S3. Physical Constants Used in the Calculations Symbol Physical Parameter Value Unit & Specification Ref. R g Ideal gas constant 8.3144 J mol -1 K -1 η Viscosity of water 0.001 Pa s at 20 C [S1] *P Pressure 101.3 10 3 Pa *T Temperature 25 C M w Molar mass of water 18.0152 g mol -1 [S1] P vs Saturation water vapor pressure 3167.1 Pa for T = 0 80 C [S2] k B Boltzmann constant 1.380 10-23 J K -1 ρ L Density of water 997.14 kg m -3 [S3] D v Diffusion coefficient of water vapor in air for T= 0 50 C error <0.1 kg m -3 2.4963 10-5 m 2 s -1 for T = 0-45 C, error <0.1 10-6 m 2 s -1 [S4] Note: * Ambient conditions in our experiments. Saturated water vapor pressure in air, empirical relation: degree Celcius ( C); range of validity, T = 0 80 C. P vs = 7.5T / 237.3+ T 610.7 10 ; Temperature T in 2 7 4 Density of water, empirical relation: ρ L = 1000 0.0067 ( T 3.98) + 5.2 10 ( T 3.98) ; range of validity, T = 0 50 C, error <0.1 kg m -3 6 Diffusion coefficient of water vapor in air, empirical relation: D v = 21.6 10 (1+ 0.0071T ) ; T: temperature, degree Celcius( C); range of validity, T = 0 45 C, error <0.1 10-6 m 2 s -1 References (1) Aylward, G.; Findlay, T. Pyrodynamic 1967, 5. (2) Monteith, J. L.; Unsworth, M. H. Principles of environmental physics; Edward Arnold: London, 1990. (3) Weast, R. C. Handbook of Chemistry and Physics, 67th edition ed.; CRC Press Inc.: Boca Raton, Florida, USA, 1986. (4) Gates, D. M. Biophysical ecology Springer VerlagNew York Heidelberg Berlin, 1980. S18