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Langmuir 2007, 23, 7724-7729
Wetting of Nanogrooved Polymer Surfaces Janne T. Hirvi and Tapani A. Pakkanen* Department of Chemistry, UniVersity of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland ReceiVed February 26, 2007. In Final Form: April 17, 2007 Molecular dynamics simulations were used to study the wetting of nanogrooved PE and PVC polymer surfaces. The contact angles, equilibrium states, and equilibrium shapes of two nanosized water droplets were analyzed on surfaces with 1D-arranged periodic roughness of various dimensions. The composite solid-liquid contact, which is preferred in practical applications and in which a droplet rests on top of the surface asperities, was observed on the roughest PE surfaces, whereas water filled the similar but slightly deeper grooves on PVC surfaces. The transition from the wetted to composite contact regime occurred when the contact angle with a flat surface reached the value at which the apparent Wenzel and Cassie contact angles are equal. Droplets on grooved PE surfaces with the composite contact exhibited contact angles in agreement with Cassie’s equation, but the increase in hydrophobicity on smoother surfaces with the wetted contact was less than expected from Wenzel’s equation. The difference between the simulated and theoretical values decreased as the dimensions of the surface grooves increased. Only a slight increase or even a slight decrease in the contact angles was observed on the grooved PVC surfaces, owing to the less hydrophobic nature of the flat PVC surface. On both polymers, the nanodroplet assumed a spherical shape in the composite contact. Only minor anisotropy was observed in the wetted contact on PE surfaces, whereas even a highly anisotropic shape was seen on the grooved PVC surfaces. The contact angle in the direction of the grooves was smaller than that in the perpendicular direction, and the difference between the two angles decreased with the increasing size of the water droplet.
Introduction Topographic structure and chemical composition together determine the wettability of a surface. Hierarchical micro- and nanostructures are responsible for the superhydrophobicity frequently observed in nature.1 The self-cleaning effect of lotus plant leaves characterized by a large contact angle and a small sliding angle is a well-known example in which freely rolling rainwater droplets remove contaminating particles.2,3 A similar hierarchical structure on rice leaves exhibits an arrangement of the microstructures in 1D order, which hinders the motion of the water droplet perpendicular to the grooves.4 Special wetting properties can be achieved on artificial surfaces by mimicking nature. Surface roughness affects adhesion, and 1D ordering has an effect on anisotropy, which is important for microfluidic applications. A droplet on a surface with isotropic roughness is almost spherical, and the contact angle is determined by the Wenzel5 or Cassie6 equation depending on the equilibrium state. Wenzel’s equation describes a wetted contact in which liquid wets the grooves of the surface and homogeneous contact is observed. The apparent contact angle θW r is described by eq 1
cos θW r ) r cos θe
(1)
where the roughness parameter r is the ratio of the rough to the projected surface area and θe is the intrinsic contact angle on the flat surface. A heterogeneous composite contact with air trapped in the grooves of the surface is, however, energetically more * Corresponding author. E-mail:
[email protected]. Phone: +358 13 2513345. Fax: +358 13 2513344. (1) Sun, T.; Feng, L.; Gao, X.; Jiang, L. Acc. Chem. Res. 2005, 38, 644-652. (2) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1-8. (3) Neinhuis, C.; Barthlott, W. Ann. Bot. (London, U.K.) 1997, 79, 667-677. (4) Feng, L.; Li, S.; Li, Y.; Li, H.; Zhang, L.; Zhai, J.; Song, Y.; Liu, B.; Jiang, L.; Zhu, D. AdV. Mater. 2002, 14, 1857-1860. (5) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988-994. (6) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546-551.
favorable for very rough hydrophobic materials. The base of the liquid droplet then consists of solid-liquid and liquid-air interfaces, and the apparent contact angle θCr is given by the modified Cassie equation
cos θCr ) φs cos θe - (1 - φs)
(2)
in which the roughness parameter φs is the fraction of the solidliquid interface at the base of the droplet. These two equilibrium states have different contact angles if they differ in energy, and the one with a smaller contact angle has lower energy and is favorable.7 The apparent contact angle on a surface with anisotropic roughness, created by parallel grooves, for example, may vary along the contact line, so deviating from Wenzel’s and Cassie’s predictions. The contact angle perpendicular (θ⊥r ) to the grooves is larger than that in the parallel direction (θ|r), as has been observed experimentally on the macroscale in agreement with theory.8-10 The projected contact angles for a composite contact with a hydrophobic surface are larger than those for a flat surface (θe), and the theoretical value of Cassie’s equation (θCr ) lies between the perpendicular and parallel contact angles. The trapping of droplets on grooved structures nevertheless allows multiple equilibrium droplet shapes depending on how the droplet formed, and experimentally observed droplet geometry does not necessarily correspond to the lowest energy state.10 Impact velocity and position have been demonstrated to affect the final equilibrium shape on chemically striped surfaces.11 Numerical simulations on such surfaces have shown that an almost spherical (7) Patankar, N. A. Langmuir 2003, 19, 1249-1253. (8) Bico, J.; Marzolin, C.; Que´re´, D. Europhys. Lett. 1999, 47, 220-226. (9) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818-5822. (10) Chen, Y.; He, B.; Lee, J.; Patankar, N. J. Colloid Interface Sci. 2005, 281, 458-464. (11) Le´opolde`s, J.; Dupuis, A.; Bucknall, D. G.; Yeomans, J. M. Langmuir 2003, 19, 9818-9822.
10.1021/la700558v CCC: $37.00 © 2007 American Chemical Society Published on Web 06/09/2007
Wetting of NanogrooVed Polymer Surfaces
contact line is energetically the most favorable, especially for larger droplets.12 The similarity of droplet spreading on chemically13 and topographically10 patterned surfaces is also emphasized by the apparent corrugated conformation of the three-phase contact line. Chemical and topographical effects can be combined by constructing hydrophobic stripes on a background with hydrophilic wetting properties and vice versa.14 Molecular dynamics simulations on the nanoscale have contributed to our understanding of roughness-induced superhydrophobicity. The reduced wettability of rough surfaces has been observed in contact with the bulk liquid phase15-17 and also with single nanodroplets where exact contact angles on pillar surfaces were determined.18 However, all of the studied topographical structures studied thus far have been 2D, and the spreading of a liquid droplet19 or cylinder20 has been simulated only on chemically striped surfaces. In the present work, we study the wetting of topographically grooved polyethylene (PE) and poly(vinyl chloride) (PVC) polymer surfaces by molecular dynamics simulations. The controlled 1D surface roughness, even on the nanoscale, is expected to introduce some anisotropy, unlike the 2D roughness studied earlier.18 The effect of the relation between the droplet radius and the dimensions of the surface roughness is studied by simulating two nanosized water droplets on frozen crystal surfaces with periodically arranged grooves of five different dimensions. Visually observed equilibrium states and equilibrium shapes are quantified through cylindrically averaged contact angles and projected contact angles perpendicular to and parallel to the grooves. The simulated nanoscale results are compared with Wenzel’s and Cassie’s theoretical predictions. Methods Molecular dynamics simulations were used to study the wetting of polymer surfaces with 1D groove structures. Grooved surfaces were constructed from the experimental crystal structures, and a separately equilibrated water droplet was transferred on top of the frozen surface for the spreading simulation. Averaged contact angles were extracted from the simulations for comparison with the corresponding angles of the smooth crystalline surfaces. Models. Smooth crystalline (100) surfaces were duplicated from the orthorhombic unit cells of experimental PE21 and PVC22 crystal structures, and periodically roughened surfaces were constructed from the smooth surfaces by cutting grooves in the direction of polymer chains. The crystalline structure of the surfaces remained otherwise undisturbed because only whole polymer chains were removed. The lateral dimensions of the PE surface planes were approximately 160 Å. A much larger space parallel to the grooves was needed for some syndiotactic PVC surfaces to avoid the interactions of periodic images of the water droplet. The largest striped PVC surface was approximately 260 × 190 Å2 in the lateral dimensions. Underneath the partial polymer layers were either two (2C) or three (3C) complete layers of the corresponding polymer. Two complete layers were used in our earlier studies of pillar structures,18 (12) Brandon, S; Haimovich, N; Yeger, E.; Marmur, A J. Colloid Interface Sci. 2003, 263, 237-243. (13) Le´opolde`s, J.; Bucknall, D. G. J. Phys. Chem. B 2005, 109, 8973-8977. (14) Gleiche, M.; Chi, L. F.; Fuchs, H. Nature 2000, 403, 173-175. (15) Tang, J. Z.; Harris, J. G. J. Chem. Phys. 1995, 103, 8201-8208. (16) Pal, S.; Weiss, H.; Keller, H., Mu¨ller-Plathe, F. Langmuir 2005, 21, 36993709. (17) Pal, S.; Mu¨ller-Plathe, F. J. Phys. Chem. B 2005, 109, 6405-6415. (18) Hirvi, J. T.; Pakkanen, T. A. J. Phys. Chem. B 2007, 111, 3336-3341. (19) Yaneva, J.; Milchev, A.; Binder, K. J. Phys.: Condens. Matter 2005, 17, S4199-S4211. (20) Grest, G. S.; Heine, D. R.; Webb, E. B., III. Langmuir 2006, 22, 47454749. (21) Kavesh, S.; Schultz, J. M. J. Polym. Sci., Part A-2 1970, 8, 243-276. (22) Wilkes, C. E.; Folt, V. L.; Krimm, S. Macromolecules 1973, 6, 235-237.
Langmuir, Vol. 23, No. 14, 2007 7725 Table 1. Dimensional Parameters for the Periodic Striped Structures on PE and PVC Surfacesa ay (Å)
by (Å)
H (Å)
4.80 9.73 9.73 4.80 9.73
3.69 3.69 7.39 22.16 22.16
5.10 10.34 8.94 3.70 8.94
5.12 5.12 10.24 30.72 30.72
PEa 3C1P11 3C1P22 2C2P22 2C6P31 2C6P22
5.06 9.99 9.99 14.92 9.99
3C1P11 3C1P22 2C2P22 2C6P31 2C6P22
5.38 10.62 12.02 17.26 12.02
PVCb
a See Figure 1 for an explanations of the parameters. b C and P combined with the preceding values refer, respectively, to the number of complete and partial polymer layers, and the last two values refer to the number of remaining and removed polymer chains in the period of the topmost partial layer.
Figure 1. Largest grooves (2C6P22) of the PE surfaces viewed from (a) the side and (b) the top. but here we also studied the effect of smaller-scale 1D roughness on anisotropy by cutting parts of only one layer from a smooth surface with four complete polymer layers.23 Dimensional parameters of the grooved PE and PVC surfaces are summarized in Table 1, and side and top views of the PE surface with the largest grooves (2C6P22) are shown in Figure 1. The van der Waals radii of the atoms were taken into account in determining the width of the grooves. The values (Table 1) were used to calculate the surface roughness parameters for the grooves as a rectangle. At the initial configuration of the wetting simulation, a freely relaxed water droplet consisting of 4000 or 13 500 molecules was centered on top of the grooved surface. A rigid version of the simple point-charge model (SPC)24 was used, in which bond distances and bond angles were fixed with the SETTLE algorithm.25 Relatively good agreement between the simulated and both experimental and theoretical water contact angles has been obtained with the SPC model.18,23 The surface was kept fixed at the bottom of a high simulation box whose lateral dimensions were equal to the dimensions of the surface. The simulation box was 3 times as large in the dimension perpendicular to the surface plane as in the maximal lateral dimension. Constant volume and temperature (NVT) simulations were performed with periodic boundary conditions at 300 K using the GROMACS molecular dynamics package26 with singleprecision compilation. Temperature coupling employed the Berendsen27 algorithm with a coupling time constant τT of 0.1 ps. The models consist of frozen surfaces and rigid water molecules, which eliminate all intramolecular interactions. Intermolecular (23) Hirvi, J. T.; Pakkanen, T. A. J. Chem. Phys. 2006, 125, 144712. (24) Bederdsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. In Intermolecular Forces; Pullman, B., Ed.; Reidel: Dordrecht, The Netherlands, 1981; pp 331-342. (25) Miyamoto, S.; Kollman, P. A. J. Comput. Chem. 1992, 13, 952-962. (26) van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. J. Comput. Chem. 2005, 26, 1701-1718. (27) Berendsen, H. J. C.; Postma, J. P. M.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3864-3690.
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Table 2. Partial Charges for Water Molecules and Polymer Surface Atoms PE water qO (e) qH (e) qC (e) qCl (e)
-0.820 0.410
PVC
CH2
CHCl
CH2
0.053 -0.106
0.1486 0.0313 -0.1987
0.0990 -0.1792
Results and Discussion
interactions were modeled with Coulombic and Lennard-Jones 12-6 interactions (eq 3) among water molecules and between water molecules and surface atoms. Water hydrogens of the SPC model are interacting only through partial charges. Parameters of the polymer consistent force field (PCFF) of the Cerius2 program28 were employed for PE, whereas parameters for PVC were taken from a specific force field29,30 derived from ab initio calculations. van der Waals interactions between water oxygens and PE surface atoms were also modeled with the Lennard-Jones 12-6 potential, although the PE force field itself has the 9-6 form of the corresponding potential. Combinations were performed by taking the geometric means of the collision diameters (σij) and the well depths (ij). Partial charges and nonbonded parameters for the systems are presented in Tables 2 and 3. VLJ(rij) ) ij
(( ) ( ) ) Rij rij
12
-2
Rij rij
interface was defined from this profile as the location where the density falls below 0.5 g/cm3. Finally, a circle was fitted to the liquid-vapor profile, excluding data points that were less than 8 Å above the surface to avoid the influence of water density fluctuations on the contact angle. The contact angle was determined at the intersection of the fitted circle and the surface reference level, which was defined as the topmost atomic layer.23
6
(3)
The contribution of electrostatic interactions was calculated by using the particle mesh Ewald method (PME)31,32 with slab correction (3dc).33 The direct space cutoff radius was 12 Å, and in reciprocal space, a maximum grid spacing of 1.2 Å was employed with cubic interpolation. With the tolerance dir ) 10-5, the Ewald parameter β was 0.26 Å-1. van der Waals interactions beyond 12 Å were truncated. An integration time step of 2 fs was used, and neighbor lists were updated every 10th time step. The total simulation time varied from 1.0 to 6.0 ns depending on the stabilization of the height of the center of mass of the water droplet. Contact Angles. Three contact angles were extracted from each simulation. A cylindrically averaged contact angle (θSIM r ) was calculated assuming a circular shape of the water droplet around a line perpendicular to the surface and passing through the center of mass of the droplet.34,35 Because this contact angle is inappropriate , if the water droplet is anisotropically spread, contact angles (θSIM(|) r θSIM(⊥) ) were also calculated for the planes that were parallel (xz r plane) and perpendicular (yz plane) to the grooves and passed through the center of mass of the water droplet. A three-step procedure was used to calculate the contact angles. A water density profile was first defined from the momentary coordinate datum of the water droplet stored at intervals of 0.25 ps after the stabilization of the height of the center of mass of the droplet. Cylindrical binning with respect to the center of mass of the water droplet34,35 and rectangular binning parallel and perpendicular to the stripes, through the center of mass of the water droplet, were used to obtain the profile for the cylindrically averaged and projected contact angles, respectively. The density profile was plotted as a function of the radial distance from the center of mass of the water droplet and the height from the surface, and the liquid-vapor (28) Cerius2, version 4.8; Accelrys: Cambridge, U.K., 2002. (29) Smith, G. D.; Jaffe, R. L.; Yoon, D. Y. Macromolecules 1993, 26, 298304. (30) Smith, G. D.; Ludovice, P. J.; Jaffe, R. L.; Yoon, D. Y. J. Phys. Chem. 1995, 99, 164-172. (31) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 1008910092. (32) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577-8593. (33) Yeh, I.-C.; Berkowitz, M. L. J. Chem. Phys. 1999, 111, 3155-3162. (34) Lundgren, M.; Allan, N. L.; Cosgrove, T.; George, N. Langmuir 2002, 18, 10462-10466. (35) Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. J. Phys. Chem. B 2003, 107, 1345-1352.
The wetting of frozen crystalline PE and PVC surfaces with five differently sized groove structures was studied by atomistic molecular dynamics simulations. The contact angles and equilibrium shapes of two nanosized water droplets were analyzed. The influence of the occasional evaporation of water molecules on the total volume of the droplet and thus on the contact angle is only minor during the analysis part of the simulation.18,23 The total number of evaporated molecules is affected by the free volume of the simulation box and also slightly by the simulation time, but the fluctuations during the contact angle determination are negligible, in part because of the occasional condensation of evaporated molecules. However, evaporation had to be taken into account in calculating the density profiles. Polyethylene. Simulated contact angles parallel (θSIM(|) ) and r perpendicular (θSIM(⊥) ) to the grooves for droplets consisting of r 4000 or 13 500 water molecules on structured PE surfaces are presented in Table 4. As can be seen, the results are practically independent of the droplet size. Most of the projected contact angles for the various combinations of droplet size and surface roughness are within 3°, which indicates a well-sustained spherical shape of the droplet in the error limits of the method. Cylindrically averaged contact angles are approximately equal to averages of the projected contact angles, but they enhance the reliability of the analysis through the greater number of statistics as compared with that for the projected contact angles, calculated only in lines parallel or perpendicular to the stripes. The maximal anisotropy effect is observed for the larger droplet on the 2C2P22 surface with the wetted contact, where the contact angle parallel to the stripes is 5° smaller than that in the perpendicular direction. Table 4 also presents the theoretical contact angles predicted by the Wenzel (eq 1) and Cassie (eq 2) equations for the wetted and composite contacts, respectively. The apparent contact angles are calculated using a rectangular approximation for the surface roughness. The global energy minimum corresponds to the equilibrium shape with the lower apparent contact angle, and the limiting value θW)C of the contact angle on a flat surface for e which the wetted and composite contacts are energetically identical defines the favored equilibrium state.7 An equilibrium contact angle on a flat surface (θe) smaller than θW)C stabilizes e the wetting contact with Wenzel’s contact angle, and a larger one stabilizes the composite contact with Cassie’s contact angle. Both equilibrium states were observed in the simulations, in good agreement with the predictions. For the 3C1P11 and 2C2P22 surfaces, the wetted and composite contacts were energetically very similar, and the simulated equilibrium state was a slightly unfavorable wetted contact. However, this result is partially due to the surface roughness height being less than the employed van der Waals interaction cutoff.18 When the height of the grooves was increased, the transition from the wetted contact to the composite contact was observed, as presented in Figure 2 for the 2C2P22 and 2C6P22 surfaces. Good agreement between the simulated and predicted equilibrium states is not fully achieved for the corresponding contact angles. For small-scale surface roughness, the theoretically predicted contact angles are much larger than the simulated contact
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Langmuir, Vol. 23, No. 14, 2007 7727
Table 3. Lennard-Jones Parameters for the Interactions among Water Molecules and between Water Molecules and Polymer Surface Atoms water-water Rij (Å) ij (kJ mol-1)
PE-water
PVC-water
O/O
C/O
H/O
C/O
H/O
Cl/O
3.5532322 0.6501940
3.7378448 0.3832783
3.2303345 0.2332557
3.6745935 0.5487710
3.3269082 0.2194340
3.6992652 0.9472021
Table 4. Simulated Contact Angles Parallel (θSIM(|) ) and r Perpendicular (θSIM(⊥) ) to the Stripes for Two Droplet Sizes on r Structured PE Surfacesa θSIM(|) r (deg)c
θSIM(⊥) r (deg)c
θW r (deg)
θCr (deg)
θW)C e (deg)d
3C1P11 3C1P22 2C2P22 2C6P31 2C6P22
120.5W 113.6W 126.3W 121.7C 131.1C
θ4000 ) 115.2°b e 118.8W 138.1 112.0W 125.8 128.6W 138.2 124.3C >180 134.3C >180
134.9 135.2 135.2 124.4 135.2
113.2W,C 124.7W 113.4W,C 95.6C 100.4C
3C1P11 3C1P22 2C2P22 2C6P31 2C6P22
118.4W 116.2W 127.5W 123.9C 133.9C
500 θ13 ) 114.4°b e 118.7W 136.2 119.0W 124.6 132.5W 136.3 123.0C >180 134.9C >180
134.3 134.6 134.6 123.8 134.6
113.2W,C 124.7W 113.4W,C 95.6C 100.4C
C a Theoretical Wenzel (θW r ) and Cassie (θr ) contact angles are also presented, along with the contact angle on the flat PE surface that corresponds to equal wetted and composite contact angles (θW)C ). e b Reference 23. c W refers to the observed wetted contact, and C refers to the observed composite contact. d W refers to the predicted wetted contact, and C refers to the predicted composite contact.
Figure 2. Final configurations of the larger water droplet (a) on the 2C2P22 PE surface with the wetted contact and (b) on the rougher 2C6P22 PE surface with the composite contact.
angles of the nanoscale water droplets. The maximal increase of the observed contact angle on the surface with only one partial polymer layer (3C1P11 and 3C1P22) is about 5°, compared with an increase of approximately 10-20° in the predicted Wenzel and Cassie contact angles. For the rougher surface with two partial layers (2C2P22), the contact angle increases 10-15° compared with a flat surface, still not reaching the value of the macroscopic theories, however. An increase in the height of the grooves makes the surface rougher, and finally the transition from the wetted surface to the composite surface is observed. The apparent contact angles of the Wenzel equation for the surfaces with the deepest grooves (2C6P31 and 2C6P22) have unrealistic values of >180°. In these cases, an energetically favored composite contact is observed with a contact angle in a good agreement with Cassie’s equation. Poly(vinyl chloride). The wetting behavior of similarly grooved PVC and PE surfaces is very different, owing to the smaller equilibrium contact angle and thus the weaker hydrophobicity of a flat PVC surface compared to those of a flat PE surface. The simulated projected contact angles for the structured
Table 5. Simulated Contact Angles Parallel (θSIM(|) ) and r Perpendicular (θSIM(⊥) ) to the Stripes for Two Droplet Sizes on r Structured PVC Surfacesa θSIM(|) r (deg)c
θSIM(⊥) r (deg)c
θW r (deg)
θCr (deg)
θW)C e (deg)d
3C1P11 3C1P22 2C2P22 2C6P31 2C6P22
77.0W 76.7W 66.7W 84.1W 0W
θ4000 ) 95.6°b e 88.5W 101.1 91.9W 98.4 107.6W 101.1 92.7W 112.6 0W 112.6
122.5 122.9 118.8 104.9 118.8
109.4W 120.2W 107.7W 93.3W,C 97.3W
3C1P11 3C1P22 2C2P22 2C6P31 2C6P22
86.6W 81.4W 76.3W 95.9C 58.4W
500 θ13 ) 92.6°b e 88.7W 95.1 90.3W 93.9 99.7W 95.1 94.7C 100.3 88.0W 100.3
120.7 121.1 116.9 102.3 116.9
109.4W 120.2W 107.7W 93.3W,C 97.3W
C a Theoretical Wenzel (θW r ) and Cassie (θr ) contact angles are also presented, together with the contact angle on the flat PVC surface that corresponds to equal wetted and composite contact angles (θW)C ). e b Reference 23. c W refers to the observed wetted contact, and C refers to the observed composite contact. d W refers to the predicted wetted contact, and C refers to the predicted composite contact.
PVC surfaces are given in Table 5, together with the theoretical values of the Wenzel (eq 1) and Cassie (eq 2) equations and the ) that separates the limiting contact angle of a flat surface (θW)C e wetted and composite regimes. Most of the PVC surface geometries induce significant anisotropy in the droplet shape, and cylindrically averaged contact angles are not, therefore, informative. The difference between the projected contact angles parallel and perpendicular to the grooves varies from almost 0° to over 40° depending on the ratio of the radius of the free droplet to the period of the grooved surface. The longitudinal curvature is always larger than the transverse one, corresponding to a smaller contact angle in the direction of the grooves than in the perpendicular direction. A look at the results for surfaces with one and two partial polymer layers reveals that the difference in the parallel and perpendicular angles increases with the width and depth of the groove in the sequence 3C1P11, 3C1P22, and 2C2P22. The surface roughness is not directly responsible for the increased anisotropy because the roughness parameter r for the 3C1P11 surface is equal to that of the 2C2P22 surface and both are larger than the corresponding value for the 3C1P22 surface. Increasing the groove depth from two layers (2C2P22) to six layers (2C6P22) causes the difference in the contact angles for the larger water droplet to increase from 23° to 30°, whereas the smaller droplet vanishes into the grooves with a contact angle of 0°. An increase in the droplet size decreases the observed anisotropy, and for the smallest surface modification, the shape of the droplet is spherical. This finding is in agreement with numerical simulations on chemically striped surfaces, which have shown that for larger droplets the spherical shape is the most favorable.12 The largest anisotropy effect is observed for the smaller water droplet on the 2C2P22 surface, where the difference in the contact angles is 41°. The final equilibrium shape of the droplet is visualized in Figure 3. Snapshots from different directions reveal that the base radius of the droplet in the direction
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Figure 4. Final configurations of (a) the smaller water droplet on the 2C6P31 PVC surface with the wetted contact and (b) the larger water droplet on the same surface with the composite contact.
Figure 3. Elongated final configuration of the smaller water droplet on the 2C2P22 PVC surface viewed (a) perpendicular and (b) parallel to the grooves and (c) from the top.
of the grooves is twice the radius in the perpendicular direction. This is due to the initial spherical shape of the droplet, which was confined to the boundaries of three stripes. Also visible is a “corrugated” three-phase contact line in which water molecules are spread further from the main body in the grooved areas. The grooves on the PVC surfaces are deeper than those on the PE surfaces because of the larger z dimension of the crystal structure, but the wetted contact is observed in most of the cases because of the weaker hydrophobicity of the flat surface. This is in agreement with the predictions because Wenzel contact angles on the surfaces are smaller than Cassie contact angles, with one partial exception for the 2C6P31 surface. For this surface, the apparent contact angles of the Wenzel (eq 1) and Cassie (eq 2) equations are so close to each other that the slight difference in the contact angle of the differently sized water droplets on the flat surface determines whether the Wenzel or Cassie contact is favored. On strictly theoretical grounds, the smaller droplet should equilibrate to the composite contact and the larger one should equilibrate to the wetted contact, but the opposite was observed, as presented in Figure 4. The complete wetting of the grooves of the 2C6P31 PVC surface by the smaller droplet was a slow process, taking about 5 ns, which indicates even competition between the two equilibrium states. A comparison of Figures 2b and 4b also reveals that the larger droplet has a tendency to penetrate deeper into the grooves on the 2C6P31 surface than in general in composite contact with PE. However, the larger droplet,
with its greater number of water-water interactions, resists the penetration as compared with the smaller droplet, and the composite contact is observed when gravity is not considered. The larger water droplet with composite contact on the rough 2C6P31 PVC surface is spherical in shape. Besides the larger water droplet on the PVC surface with the smallest grooves (3C1P11), it is the only isotropic droplet shape that was observed on the structured PVC surfaces. Nanoscale water droplets with the wetted contact on PVC surfaces adopt a pronounced anisotropical shape, whereas on the corresponding PE surfaces, anisotropy is nonexistent or minor as a result of the greater hydrophobicity of the flat surface. For droplets with the composite contact, an almost spherical shape is observed for both structured PE and structured PVC surfaces. The theoretically predicted increase in the apparent contact angle on grooved PVC surfaces ranges from a few degrees up to 15°, which is mostly less than on the striped PE surfaces. Regardless of the observed equilibrium state of the droplet, however, the simulated contact angles are still smaller than the Wenzel or Cassie contact angles. An increase in the apparent contact angle was observed for the droplet with composite contact, but it was only 2 to 3° as compared with about 10° increase in the Cassie contact angle. For the droplets exhibiting anisotropic wetted contact with the grooved PVC surfaces, contact angles, both parallel and perpendicular to the stripes, are mostly smaller than those predicted by Wenzel’s equation. The 2C2P22 surface, for which the apparent Wenzel contact angle lies between the projected contact angles, is an exception. These differences are tailor-made for emphasizing the multiplicity of the equilibrium shapes of liquid droplets, particularly nanoscale droplets.
Conclusions The wetting of 1D-structured PE and PVC surfaces was studied by molecular dynamics simulations. Nanosized water droplets consisting of either 4000 or 13 500 molecules were allowed to equilibrate on surfaces with 5 different groove dimensions. Observed equilibrium states and extracted contact angles were compared with values derived from the macroscopic theories of Wenzel and Cassie. Nanoscale anisotropy effects were evaluated through projected contact angles that reveal the exact shape of the equilibrium droplet. Both the wetted and composite contacts were observed on the simulated rough surfaces, in good agreement with Wenzel’s and Cassie’s equations. The transition from the Wenzel to the Cassie regime occurred when the contact angle with the flat surface reached the limiting value of θW)C , for which the equilibrium e states are energetically identical. The technically preferred composite contact is more easily achieved on grooved PE surfaces than on the corresponding PVC surfaces. Liquid may fill up the grooves of the more deeply structured PVC surface as a result of the weaker hydrophobicity of the PVC surface.
Wetting of NanogrooVed Polymer Surfaces
Contact angles of water droplets on grooved PE surfaces with the composite contact were very similar to the predicted Cassie contact angles, but the droplets with the wetted contact on smoother PE surfaces exhibited contact angles smaller than the Wenzel contact angles. With one partial polymer layer, smallscale surface roughness had only a minor influence on the hydrophobicity increasing the contact angles by only a few degrees. Two partial layers of PE increased the contact angles more noticeably, but the results were still 5-10° smaller than the predicted Wenzel contact angles. The theoretical roughnessinduced increase in hydrophobicity on the studied PVC surfaces was less than on PE surfaces. The contact angle for the only observed composite contact on the grooved PVC surfaces was just 2 to 3° larger than that of the flat surface and did not reach the theoretical increase of about 10° in the Cassie contact angle. Droplets with wetting contact on PVC surfaces exhibit anisotropy, and the projected contact angles were either smaller than the
Langmuir, Vol. 23, No. 14, 2007 7729
Wenzel contact angle or the Wenzel prediction lay between the two values. The three-phase contact line of nanoscale water droplets on the grooved PE and PVC surfaces with composite contact was almost spherical, and no anisotropy was observed in the droplet shape. For the wetted contacts on the structured PE surfaces, anisotropy was either nonexistent or minor, but on the corresponding PVC surfaces, the droplet tended to adopt a highly anisotropic shape with a corrugated three-phase contact line as a result of weaker hydrophobicity. The apparent contact angle in the direction of the grooves was as much as 40° smaller than that in the perpendicular direction as a consequence of pinning to the stripes. The difference between the projected contact angles decreased with increasing size of the water droplet as a spherical shape was approached. LA700558V
