J. Phys. Chem. B 2005, 109, 8973-8977
8973
Droplet Spreading on Microstriped Surfaces J. Le´ opolde` s* and D. G. Bucknall Department of Materials, Oxford UniVersity, Oxford OX1 3PH, U.K. ReceiVed: February 16, 2005; In Final Form: March 16, 2005
When a droplet of fluid is deposited on a surface with chemical and/or topological patterns, its static shape is highly dependent on the 2D distribution of the patterns. In the case of chemical stripes, three distinct spreading regimes have been observed as a function of wettability contrast between the two kind of stripes. For low wettability contrast, the droplet spreads with different velocities and both types of surface energy and the macroscopic contact angle is close to Cassie’s contact angle. When the wettability contrast is intermediate/high, the resulting shape of the droplets is elongated. In the intermediate wettability contrast regime, an ideal situation shows stick and slip behavior of the contact line, during which the contact line jumps from one stripe to another. For a high wettability contrast, the confinement of the fluid between two chemical stripes leads to a 2D spreading.
I. Introduction Surface chemical heterogeneities are known to have important effects on the static wetting behavior of a fluid droplet. When these heterogeneities are very small compared to the size of the droplet, the effect of surface chemistry heterogeneities on the equilibrium contact angle can be predicted using Cassie’s equation.1,2 When the size of the heterogeneities is of the same order as the size of the droplet, its static shape is distorted. The wettability contrast and size and shape of the heterogeneities are the main parameters governing the profile of the triple line,3,4 and the equilibrium states of a droplet adsorbed on a few defects have been determined recently.5,6 These states correspond to the global minima of the free energy. The dynamic behavior of a fluid droplet on such surfaces is not known but plays a significant role in many areas such as coating, printing, or microfluidics because understanding the relationships between spreading kinetics and surface chemical structure would allow accurate control of the deposition of a liquid film on a surface. It has been shown that when the solid surface is composed of two dispersed chemical components the spreading dynamics are linked to the friction coefficient at the contact line.7 Introduction of well-defined surface “defects” provides a way to modify spreading dynamics by provoking additional heat losses at the edge of the spreading droplet. The development of microcontact printing provides an ideal tool to tackle such a problem. Here we focus on the experimental study of spontaneous spreading of a droplet on substrates with controlled chemical heterogeneities. These heterogeneities are micrometer-size chemical stripes, whose widths vary between 2 and 80 µm. The actual shape of the droplets deposited on those stripes corresponds only to local minima and is determined by spreading dynamics. The system is therefore in a metastable state, dictated by the amount of energy dissipation on the solid surface during the spreading. II. Experiments Different fluids are used in this study: squalane (viscosity η ) 35.0 mPa, surface tension γ ) 30.1 mN m-1), diethylene glycol (η ) 38.5 mPa, γ ) 44.8 mN m-1), and silicon oil (η ) * Corresponding author. E-mail:
[email protected].
1000 mPa, γ ) 20 mN m-1) at 21°. The surfaces used are goldcoated (001) silicon wafers. A Park Scientific atomic force microscope in contact mode was used with silicon nitride tips to determine an average RMS roughness of the Au surface of the substrates equal to 1-2 nm measured over 10 µm2 areas on three different samples. The surface chemistry of the reference samples is adjusted by grafting homogeneous monolayers of mercaptoundecanoic acid (MUA, denoted subsequently as surface C1) or octadecanethiol (ODT, surface C2). The thiols were obtained from Aldrich and used as supplied. Reference samples are prepared by immersion of the substrates in alkanethiol solutions (1 mmol in ethanol) for 18 h at room temperature, leading to a wellordered self-assembled monolayer (SAM). Heterogeneous samples are achieved by microcontact printing3,8 of chemical lyophobic (C2) parallel stripes and completing the pattern with lyophilic ones (C1) of the same dimensions (d). Six different sizes were used in the study: d ) 2, 5, 10, 20, 40, and 80 µm. All of the samples were analyzed by scanning electron microscopy, and the size of the stripes did not vary by more than 10% of the desired values. The spreading rates were measured at 20.8 °C. The droplet (volume, Ω ≈ 3.5 mm3) was deposited by a syringe on the substrate using an autodispenser. The spreading was then recorded with a CCD black and white camera (640 × 512 pixels) collecting 25 images per second and connected to a computer. The contact angles were determined by fitting of the droplet profile by the Laplace-Young equation. The patterned substrates were analyzed by recording the spreading dynamics parallel and normal to the direction of the stripes. Each measurement was repeated on three different samples, and then averaged. The standard deviation of each series of three measurements was around 1° for contact angles and 0.15 mm for diameter. III. Different Spreading Regimes Here we present an overview of different spreading regimes obtained on patterned substrates. As the contact angle difference (∆θ) observed on the surface (C1 and C2) stripes increases, three different types of spreading on striped surfaces can be observed (see examples Figure 1: ∆θa ) 25°, ∆θb ) 40°, and ∆θc ) 51°). In case a, which is obtained with silicon oil, there is no
10.1021/jp0508094 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/08/2005
8974 J. Phys. Chem. B, Vol. 109, No. 18, 2005
Le´opolde`s and Bucknall
Figure 1. Different droplet-spreading data on striped surfaces, where three distinct spreading regimes can be observed. (a) ∆θa ) 25°, (b) ∆θb ) 40°, and (c) ∆θc ) 51°. The dotted lines indicate spreading normal to the stripes, and the solid lines are the spreading along the stripes. ∆θ is the difference of the contact angles obtained on homogeneous surfaces of MUA and ODT in separate experiments.
Figure 2. (a) Optical micrographs (top view) of the edge of a squalane droplet (black part) adsorbed on each type of patterned substrate used in the study. The size of the stripes is, from left to right and top to bottom, 2, 5, 10, 20, 40, and 80 µm. (b) Confocal microscopy image of the edge of a squalane droplet on 80-µm stripes.
influence of the surface heterogeneities until the very late stages of spreading. Then the contact line slows down on a low-energy stripe and accelerates on the hydrophilic part. The overall spreading dynamics nevertheless remain largely unchanged normal and parallel to the stripes. Case b corresponds to a regime where the contact line parallel to the stripes jumps from one metastable state to another, thus spreading slightly more slowly than the contact line normal to the stripes. In case c, the wettability contrast between the stripes is so high that only 2D spreading occurs parallel to the stripes. In regimes b (ethylene glycol) and c (squalane), the orientation of the substrate patterning influences the amount of spreading such that elongated droplets are obtained. Examples of edge patterns formed by the squalane droplets are shown in Figure 2a and b. The contact line is highly distorted because of the wettability contrast between the C1 and C2 stripes and adopts a corrugated conformation.9,10 Because of the completely wetting properties of the C1 stripes, some liquid is able to spread out of the droplet on the completely wetting microstripes (Figure 2b: we estimate a film thickness of ∼200 nm on the C1 stripes, ahead of the droplet.). Note that the completely wetting stripes are fully covered by fluid on the whole sample. Because the stripes are of finite dimensions and the vapor tension of squalane is very low, we observe long-lived metastable states that differ from the configurations corresponding to the global minima in ref 6. IV. High Wettability Contrast The fluid used here is squalane, which completely wets surface C1 and has a contact angle (θ2) equal to 51° on surface C2. Independent of the size of the stripes, spreading normal to the stripes was completed before the detection limit of the camera (e40 ms). This effect occurs because of contact line pinning occurring normal to the stripes. The very limited wetting normal to the stripes occurs during the inertial wetting regime, and no effect of surface chemistry on spreading rate is expected,
Figure 3. (a) Sketch of a squalane droplet spreading on a microstriped surface. (b) Typical equilibrium profiles on patterned substrates for two different sizes of stripe. Upper row, 2-µm stripes; lower row, 80-µm stripes; left-hand column, images taken parallel to the direction of the stripes; right-hand column, images taken normal to the direction of the stripes.
taking the time scale into account. The maximum lateral dimension reached by the droplet normal to the stripes, ω (see Figure 3a and b), is constant and approximately equal to 3.7 mm for all of the experiments (stripes from 2 to 80 µm). In Figure 4, the spreading curves for the smallest stripes can be compared to the behavior obtained during the spreading on a homogeneous surface (prepared by immersion for 18 h in a 1 mM solution of 66% MUA and 33% ODT) of the same contact angle (see Figure 4). Because of the confinement of the same volume of liquid between two lyophobic stripes, the spreading on patterned substrates is faster than that on a homogeneous one. A power law for the spreading dynamics of a droplet on a chemical stripe has been reported recently.11 At late stages of spreading, the dominant influence of the transverse radius of curvature would lead to a scaling law such that L(t) ≈ t1/5. Now, let us consider the spreading of a droplet confined between two low surface energy stripes. The pressure inside the droplet varies according to the Laplace equation
∆P ) γ ×
(
)
1 1 + R1 R2
(1)
where R1 and R2 are the radii of curvature of the liquid-air interface. We have performed a detailed experimental analysis of the evolution of the radii of curvature and found that during the spreading the variation of the transverse curvature is small as compared to the longitudinal one. As a first approximation, we consider that the capillary pressure that drives the spreading is due to the longitudinal curvature of the interface so that
∆P ≈ γ ×
() h L2
(2)
Droplet Spreading on Microstriped Surfaces
J. Phys. Chem. B, Vol. 109, No. 18, 2005 8975
Figure 4. Spreading along the stripes measured as the evolution of the contact angle and diameter as a function of time. Circles, inverted triangles, squares, diamonds, triangles, and hexagons correspond to 2, 5, 10, 20, 40, and 80-µm stripes, respectively. Only one-fifth of the total number of points are represented for clarity. Black points, spreading on a homogeneous surface; insets, evolution of quasiequilibrium contact angle and final length, Lf (mm), as a function of the width of the stripes, d (µm). The solid line is a fit θa ≈ (θ2e + 2EA/γ(1 + Bd))1/2, as derived in the text.
where h is the height of the droplet and L is the dimension of the droplet along the stripes. Within the lubrication approximation, we consider that the velocity profile follows a Poiseuille law:
∂L h2 ∆P ≈ ∂t L η
(3)
The volume of liquid Ω ≈ hωL is constant during the spreading. By inserting the volume conservation law and by substituting eq 1 into eq 3, we obtain the following:
∂L γΩ3 1 ≈ ∂t ηω3 L6
(4)
This results in the relation
L ≈ Ct1/7
(5)
where C ) (7γΩ3/ηω3)1/7. Therefore, a droplet spreading on a homogeneous, completely wetting stripe should spread initially like L ≈ t1/7 and crossover to L ≈ t1/5 at a time t* ≈ ω10η/γΩ3, when the effect of the transverse curvature becomes dominant. The extremely high dependence of t* with ω suggests that this phenomenon could be of importance in microfluidics applications in which the size of the ribbon would be critical in controlling the spreading velocity of the volume of fluid confined on it. By using the same approach, we can now consider the spreading of a droplet on a ribbon composed of a network of parallel stripes, which is the case we address experimentally (because ω is constant, see Figure 3a). Let R be the separation between widely spaced lyophilic stripes (the dissipation occurs mainly on the wetting stripes and not between them), and suppose that they impose the spreading kinetics. The situation remains exactly the same as before, but the volume conservation law changes: Ω ≈ L2hω/R. This leads to L ≈ Dt1/10 where D ) (10γΩ3R3/ηω3)1/10. On a striped surface, an increase of R should enhance the amount of spreading at a given time, which is indeed observed experimentally (see Figure 4). However none of the cases studied here seem to correspond to a scaling law, and only partial wetting is observed. When R is too small, a great amount of heat dissipation between lyophilic stripes occurs and the assumption of “sparse stripes” breaks down. This tends to slow the spreading and leads to a behavior different from what is
expected in the ideal case. Those experiments raise the following questions: when increasing the amount of surface defects on a completely wetting surface (where the behavior is supposed to follow Tanner’s law), is there a transition to another (slower) scaling behavior due to surface heterogeneities? In that case, what would be the limit where the spreading becomes only partial? We will try to answer those questions in a forthcoming publication. In addition, we have observed a slight but significant enhancement of spreading parallel to the stripes with increasing microstripe width (see the insets in Figure 4). At the same time, the limiting (“equilibrium”) contact angles decrease with increasing microstripe width, thus confirming that the enhanced spreading is not due to a variation of ω but to the specific nature of the microstriped surfaces. The total volume of liquid adsorbed on the microstripes being V ≈ 10-4 mm 3 , Ω, a variation in droplet volume due to “stripe dragging”12,13 cannot be the origin of the variation of the contact angle with the microstripe width. We interpret this variation with a simple theory by taking into account the imperfections of the microstripes in which we assume that the borders between the C1 and C2 stripes are chemically “rough”. Indeed, the resolution of the pattern edges obtained via microcontact printing is governed by the diffusion of thiol molecules from the stamp to the surface and limited by the granularity of the gold substrate (∼15-30 nm). Therefore, the edges of the patterns obtained by microcontact printing are rough,14 and although a variation of microstripe size does not change the average surface chemical composition, it induces a fluctuation of disorder on the surface. The number of defects per unit surface area due to the stripe edges (n) varies with the dimension of the microstripes (d) according to n ≈ A/(1 + Bd). (A is the number of defects on a homogeneous surface of the same composition, and B is the number of defect-free sites per unit length of stripe.) The capillary force during spreading is balanced by the defect forces so that γ(cosθe - cosθa) ≈ nE4, where θa is the advancing contact angle, θe represents the equilibrium contact angle obtained on a surface patterned by ideal stripes (which would have perfectly smooth edges), and E is the energy dissipated while the contact line jumps through a surface defect. (This expression, found in ref 4, was derived for dilute defects on an ideal surface and corresponds to the present study, where the distance between two defects is at least 2 µm.) Assuming that the shape of microstripe edges do not vary with d in the limit of small angles we obtain θa ≈ (θ2e + 2EA/γ(1 + Bd))1/2. Taking E to be of the order of 1 × 10-16 N‚m, ref 15 fits experimental data satisfactorily (see inset Figure 4) and gives physically acceptable values: θe ≈ 25°; the size of the defects on the homogeneous surface would be ∼4 nm, and ∼300 µm separates the defects on the stripe edges. We show, therefore, that two surfaces of the same overall composition can lead to different contact angles because of variations in surface disorder. With the wettability contrast and defect surface fraction used in this case, we suspect that some chemical defects slightly smaller than a micrometer would not have any noticeable influence on the static shape of the elongated droplet. V. Intermediate Wettability Contrast Intermediate wettability contrast corresponds to case b, for which the fluid used is diethyleneglycol (θC1 ) 10 and θC2 ) 50°). In the example shown in Figure 5, the size of the stripes is w ) 10 µm. Here, the contact line normal to the stripes sticks and slips on low energy borders. This behavior can be expected in a rather small wettability contrast range corresponding to 30 < ∆θ < 50. Surprisingly, even if three well-defined pinning
8976 J. Phys. Chem. B, Vol. 109, No. 18, 2005
Figure 5. Spreading on stripes with intermediate wettability contrast. The contact line shows a typical stick and slip behavior. Dots, spreading normal to the stripes; solid lines, spreading along the stripes.
Figure 6. Case c: spreading on stripes with low wettability contrast. Solid lines, spreading along the stripes.
events are observed, the equilibrium length of the drop is only slightly larger along than parallel to the stripes. The distance corresponding to a jump (see Figure 5) matches the dimensions of the stripes and indicates that each jump occurs from one lyophobic stripe border to another. During a “plateau”, the contact angles as measured by fitting the liquid-air interface with a Young-Laplace law do not show any variation, therefore showing the very local scale of pinning/depinning dynamics. The example shown corresponds to an “ideal” situation where both sides of the droplet pins-depins exactly at the same time, as indicated by the variations of both left and right contact angles. For larger defects, we would expect the “impact” point to play a major role as discussed in ref 3. A more quantitative discussion is not possible at this stage because of the low resolution of the contact angle measurements, but it is worthwhile noting the similarities between the results shown here and the theory by Nikolayev et al.16 These authors showed that in the case of a 2D droplet the presence of defects does not strongly change the relaxation time and the time “lost” during pinning is recovered during slip motion. This is indeed very close to what we observe experimentally in a quiet similar situation. VI. Low Wettability Contrast The third behavior on a low wettability contrast surface (w ) 80 µm, θC1 ) 0 and θC2 ) 25°) is shown in Figure 6 (here the fluid used is silicon oil). During approximatively half of the spreading time, the behavior parallel and normal to the stripes is identical. The contact line normal to the stripes is, however, slowed at the later stages of spreading. This slowing down is different from the jumps occurring in the case of intermediate wettability contrast. Indeed, for intermediate wettability contrast, the contact line stops on a lyophobic stripe, and when the local contact angle is higher than θC2, a sudden jump occurs. Here the spreading rate is slowed simply because the contact line is advancing on a lyophobic part. Once a lyophilic stripe has been reached, it accelerates until the next lyophobic stripe is reached. Note that, similar to the case of
Le´opolde`s and Bucknall intermediate wettability contrast, the spreading amount lost during the deceleration is recovered during the acceleration on the C1 stripes, leading to an equilibrium diameter equal to the one measured along the stripes. The similarity between the spreading normal and parallel to the stripes suggests that more than the structure, the average wettability of the surface is the most important parameter to consider in order to determine the extent of wetting. This is confirmed by the values of the limiting contact angles, which are very close to Cassie’s contact angle for both situations (θeq ≈ 17° for both situations). Therefore, this experiment suggests that Cassie’s law would hold even for large but weak and/or sparse heterogeneities, provided that very few or no significant contact line pinning occurs. This point would need to be verified in more systematic experiments. VII. Conclusions We have studied experimentally the spreading of droplets on microstriped surfaces achieved by microcontact printing. We show that a rich set of behaviors is obtained when varying the wettability contrast between the stripes. Three different spreading regimes can be obtained on striped surfaces when ∆θ is adjusted. In the case of a high wettability contrast, surface chemical structuring provokes contact line pinning normal to the stripes at the very early stages of spreading. This results in a spreading occurring mainly in one direction and therefore finally leads to an elongated droplet shape. The longitudinal equilibrium dimension of the droplets is altered by the disorder at the chemical edges, whereas the spreading dynamics do not follow scaling laws when half of the substrate is covered by the completely wetting monolayer. Further work is needed to determine whether scaling behaviors are observable on heterogeneous surfaces. For intermediate wettability contrast, a stick and slip behavior is observed, corresponding to jumps from one lyophobic border to an adjacent one. However, the “time lost” during pinning is essentially recovered after a jump. The same effect holds for a low wettability contrast. Nevertheless, for case a, the stick and slip is different and occurs via two different spreading velocities on the two different stripes and not by a jump. This study has been achieved by keeping the lyophobic and lyophilic areas equal. Then, it is now necessary to study systematically the effect of an increasing surface fraction of defects. Acknowledgment. We thank C.D. Bain and J.M. Yeomans for helpful suggestions and criticisms. This study forms part of the IMAGE-IN project which is funded by the European Community through a Framework 5 grant (contract no. GRD1CT-2002-00663). References and Notes (1) Cassie, A. B. D. Discuss. Faraday Soc. 1948, 3, 11. (2) Bain, C. D.; Evall, J.; Whitesides, G. M. J. Am. Chem. Soc. 1989, 111, 7155-7164. (3) Le´opolde`s, J.; Dupuis, A.; Bucknall, D. G.; Yeomans, J. M. Langmuir 2003, 19, 9818-9822. (4) Joanny, J. F.; deGennes, P. G. J. Chem. Phys. 1984, 81, 552-562. (5) Lenz, P.; Lipowski, R. Phys. ReV. Lett. 1998, 80, 1920-1923. (6) Gau, G.; Hermingaus, H.; Lenz, P.; Lipowsky, R. Science 1999, 283, 46-49. (7) Semal, S.; Bauthier, C.; Voue´, M.; VandenEynde, J. J.; Gouttebaron, R.; DeConinck, J. J. Phys. Chem. B 2000, 104, 6225-6232. (8) Kumar, A.; Biebuyck, H. A.; Whitesides, G. M. Langmuir 1994, 10. (9) Drelich, J.; Wilbur, J. L.; Miller, J. D.; Whitesides, G. M. Langmuir 1996, 12, 1913-1922. (10) Pompe, T.; Herminghaus, S. Phys. ReV. Lett. 2000, 85, 1930-1933. (11) Warren, P. B. Phys. ReV. E 2004, 69, 041601. (12) Darhuber, A. A.; Troian, S. M.; Reisner, W. W. Phys. ReV. E 2001, 64, 031603.
Droplet Spreading on Microstriped Surfaces (13) Li, D. Colloids Surf., A 1996, 116, 1-23. (14) Libioulle, L.; Bietsch, A.; Schmid, H.; Michel, B.; Delamarche, E. Langmuir 1999, 15, 300-304.
J. Phys. Chem. B, Vol. 109, No. 18, 2005 8977 (15) Ramos, S. M. M.; Charlaix, E.; Benyagoub, A.; Toulemonde, M. Phys. ReV. E 2003, 67, 031604. (16) Nikolayev, V. S.; Beysens, D. A. Phys. ReV. E 2002, 65, 046135.
