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J. Phys. Chem. B 2007, 111, 3336-3341
ARTICLES Enhanced Hydrophobicity of Rough Polymer Surfaces Janne T. Hirvi and Tapani A. Pakkanen* Department of Chemistry, UniVersity of Joensuu, P.O. Box 111, FIN-80101, Joensuu, Finland ReceiVed: NoVember 9, 2006; In Final Form: January 29, 2007
Molecular dynamics simulations were used to study the effect of periodic roughness of PE and PVC polymer surfaces on the hydrophobicity. Pillars of different lateral dimensions and heights were derived from flat crystalline surfaces, and the results of nanoscale simulations on the structured surfaces were compared with theoretical predictions of the Wenzel and Cassie equations. Hydrophobicity increased on all rough surfaces, but the increase was greater on the structured PE surfaces because of the larger water contact angle on the flat PE surface than the corresponding PVC surface. Equally sized pillar structures on the two polymers resulted in different equilibrium wetting geometries. Composite contacts were observed on rough PE surfaces, and the contact angle increased with decreasing contact area between the solid and the liquid. Opposite results were obtained for rough PVC surfaces; the contact angle increased with the solid-liquid contact area, in agreement with Wenzel’s equation. However, the composite contact was observed if the energies of the wetted and composite contacts were almost equal. Good agreement was obtained between the simulated contact angles and equilibrium droplet shapes and the theories but there were also some limitations of the nanoscale simulations.
Introduction Wettability of solid surfaces is a property with great importance in daily life, industry, and agriculture. Topographical structure as well as chemical composition of a surface or coating influences the wettability. The self-cleaning property of certain plant leaves has recently been attracting considerable attention.1,2 This unusual wetting phenomenon and many other cases of superhydrophobicity have been linked to unique micro- or nanostructures.3 Both experimental and theoretical studies are needed to obtain a comprehensive understanding of the phenomenon and then to mimic nature in the fabrication of artificially designed hydrophobic surfaces. The earliest modeling of the effect of surface roughness on the contact angle was done by Wenzel4 and Cassie.5 Wenzel proposed a theoretical model assuming that liquid follows the solid surface and fills up the grooves on a rough surface according to Figure 1a. For the wetted contact the apparent contact angle θW r is expressed by equation
cosθW r ) r cosθe
(1)
where r is the ratio of the area of the rough surface to the projected area and θe is the equilibrium contact angle of the liquid droplet on the flat surface. The roughness factor (r) is always larger than unity and the hydrophobicity is augmented by the increase of the solid-liquid contact area. For very rough hydrophobic materials, however, the wetted contact is energetically more unfavorable than trapping air in the grooves of the rough surface. In Cassie’s approach, the liquid forms a composite surface and contacts the solid only at the top of the asperities according to Figure 1b. The apparent contact * Address correspondence to this author. Phone: +358 13 2513345. Fax: +358 13 2513344. E-mail:
[email protected].
Figure 1. Hydrophobic equilibrium states for (a) wetted and (b) composite contacts.
angle θCr for the composite contact is given by
cosθCr ) φs cosθe - (1 - φs)
(2)
where φs is the area fraction of the horizontal projected solid surface in contact with the liquid. This is a special case of the general equation for a heterogeneous surface composed of two different materials. The area fraction of the solid-liquid contact (φs) is always less than unity and the hydrophobicity increases with decrease in the area of the solid-liquid contact. Wenzel’s and Cassie’s equations predict different contact angles or at least different equilibrium states for a droplet on the same fractal surface. Experimental observations of micromachined surface structures6-10 have been compared with predictions from the two models, although there has generally been some ambivalence about the correct one. The energy analysis performed by Patankar11 demonstrated that an equilibrium drop shape with a smaller value of the apparent contact angle on a rough surface would have lower energy. In fact, both Wenzel and Cassie equilibrium states are possible, but usually they are separated by an energy barrier, which may be overcome even by the gravitational potential energy.9,11,12 This result needs to be taken into account in the design of hydrophobic surfaces. Transition from the composite contact in a local energy minimum to the wetted contact in a global energy minimum
10.1021/jp067399j CCC: $37.00 © 2007 American Chemical Society Published on Web 03/09/2007
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J. Phys. Chem. B, Vol. 111, No. 13, 2007 3337
TABLE 1: Dimensional Parameters for the Periodic Pillar Structures on PE and PVC Surfacesa ax (Å)
ay (Å)
bx (Å)
by (Å)
H (Å)
13.6 8.5 8.5 8.5 3.5
9.7 7.3 7.3 7.3 2.3
22.2 11.1 14.8 22.2 22.2
13.5 8.5 8.5 5.9
8.9 8.9 8.9 3.7
30.7 15.4 30.7 30.7
PEb S6 M3 M4 M6 L6
6.7 11.8 11.8 11.8 16.9
10.0 12.5 12.5 12.5 17.4
S6 M3 M6 L6
6.9 11.9 11.9 14.4
12.0 12.0 12.0 17.3
PVCb
a See Figure 2 for explanations of parameters. b Letters S, M, and L refer to small, medium, and large lateral size of the pillar, and numerical values 3, 4, and 6 to the number of partial hydrocarbon layers.
would be unfavorable because the sliding angle of a droplet on the composite surface is much smaller than that on the wetted surface.8,9 The sliding angle can also be decreased by increasing the tortuosity of the three-phase contact line, using either posts of more complicated shape8 or hierarchical structures.3,13 Molecular dynamics simulations have been applied in wetting research for almost two decades. We recently studied the effect of the amorphicity of the surface on the contact angle of a water droplet on polymer surfaces.14 The simulated crystalline and amorphous polymer surfaces differed from each other in roughness as well as in density and overall surface characteristics, making direct estimation of the effect of atomic-scale roughness difficult. Where a single liquid droplet has been replaced by a liquid layer, even atomistic surface roughness has been reported to increase hydrophobicity.15-17 A fractal surface was found to have reduced wettability relative to the smooth surface when surface roughness was modeled either with another partial monolayer on a smooth surface of fcc-lattice15 or by cutting larger pits into an alkane crystal.16,17 In this paper we extend our previous wetting studies on polyethylene (PE) and poly(vinyl chloride) (PVC) polymer surfaces.14 Regular and controlled nanoscale surface roughness is modeled with periodically arranged rectangular pillars of different heights and lateral dimensions cut from the experimental crystal structures. The effect of the controlled surface roughness on the hydrophobicity is studied by extracting the water contact angles on the structured surfaces and comparing them with the contact angle on the flat surface. The simulation results can be compared directly with Wenzel’s and Cassie’s theoretical predictions, enabling the evaluation of these theories in nanoscale. The two equilibrium states are seen for the different pillar sizes on the two materials, and the different equilibration and spreading mechanisms are visualized at the atomic level. Simulations The GROMACS 3.3 molecular dynamics simulation package18 with single-precision compilation was applied in wetting simulations of structured polymer surfaces. A constant volume and temperature (NVT) ensemble with periodic boundary conditions at 300 K employed the Berendsen algorithm19 for temperature coupling with coupling time constant τT ) 0.1 ps. Models. The unit cells of experimental crystal structures were duplicated to produce smooth crystalline (100) surface planes with lateral dimensions of approximately 160 Å. An orthorhombic structure20 with density of 1.008 g/cm3 was used to build the crystalline PE surface and an orthorhombic structure21 with
Figure 2. The highest and narrowest pillars (S6) of the structured PE surfaces viewed from (a) the side and (b) the top.
TABLE 2: Partial Charges for Water Molecules and Polymer Surfaces Atoms PE water
CH2
PVC CH3
CHCl
CH2
CH3
qO (e) -0.820 qH (e) 0.410 0.053 0.053 0.1486 0.0990 0.0628 qC (e) -0.106 -0.159 0.0313 -0.1792 -0.1790 qCI (e) -0.1987
density of 1.523 g/cm3 to build the syndiotactic PVC surface. Structured surfaces were cut from the smooth surfaces, and broken C-C bonds were replaced by C-H bonds with the original direction maintained, but with a shorter bond length equal to other C-H bond lengths in the crystal in question. Pillars with three lateral and three vertical dimensions were underlain by two complete layers of hydrocarbons. Dimensional parameters of the structured PE and PVC surfaces are summarized in Table 1, and side and top views of the structured PE surface with pillars of largest height-width aspect ratio (S6) are shown in Figure 2. The largest distance in the x- and y-dimensions is presented. The van der Waals radii of the atoms were taken into account and the surface roughness factors were calculated for rectangular pillars with these dimensions. At the initial configuration of the wetting simulation, a freely relaxed water droplet consisting of 8788 molecules was centered on top of the structured surface, which was kept fixed at the bottom of a high simulation box. A rigid version of the simple point charge model (SPC)22 was used in view of the relatively good agreement between the simulated and experimental water
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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
3.553 232 2 0.650 194 0
3.737 844 8 0.383 278 3
3.230 334 5 0.233 255 7
3.674 593 5 0.548 771 0
3.326 908 2 0.219 434 0
3.699 265 2 0.947 202 1
contact angles.14 Bond distances and bond angles were fixed with the SETTLE algorithm.23 The use of frozen surfaces and rigid water molecules eliminates all intramolecular interactions, and thus models only include Coulombic and nonbonded Lennard-Jones 12-6 interactions (3) among water molecules and between water molecules and surface atoms. Parameters for nonbonded interactions and partial charges for PE were taken from the polymer consistent force field (PCFF) of the Cerius2 program24 and analogously for PVC from a specific force field25,26 derived from ab initio calculations. The different forms of the Lennard-Jones potential for the PE force field and the SPC water model were also combined to Lennard-Jones 12-6 form 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
6
(3)
A cutoff radius of 12 Å was used for the van der Waals interactions while the Particle Mesh Ewald method (PME)27,28 with slab correction (3dc)29 and three times elongated simulation box in the dimension perpendicular to the surface plane was used for the long-range electrostatic interactions. The direct space cutoff radius was likewise 12 Å, and a maximum grid spacing of 1.2 Å with cubic interpolation was employed in the reciprocal space. With the tolerance dir ) 10-5 the Ewald parameter β was 0.26 Å-1. All simulations were carried out for 1.0 or 1.5 ns, using an integration time step of 2 fs,30 while neighbor lists were updated every tenth integration time step. Contact Angles. Contact angles were calculated by using a three-step procedure where the water isochore profile was first obtained by introducing a cylindrical binning to the momentary coordinate datum of the water droplet stored at intervals of 0.25 ps.31 The analyses were started after the height of the center of mass of the water droplet had stabilized, and the analysis time was 0.4-0.9 ns. The liquid-vapor interface was defined from the isochore profile as the location where the density falls to less than one-half that of the bulk. Finally, a circle was fitted to the liquid-vapor profile, excluding data points less than about 8 Å above the surface, and the contact angle was determined at the point where the fitted circle and the zero reference level of the solid surface meet.32 The surface reference level was defined as the topmost atomic layer.14 Results and Discussion Molecular dynamics simulations were performed to study the influence of periodic roughness of PE and PVC polymer surfaces on the hydrophobicity. The contact angles of microscopic water droplets were extracted by taking advantage of the spherical shape of the cap of the liquid droplet. Occasional evaporation of water molecules, which has only minor influence on the total volume of the droplet, was taken into account in calculating the time-averaged density profiles.14 The three-phase contact line of a water droplet with small contact angle can also be pinned to a certain extent to the two-dimensional surface
W TABLE 4: Simulated (θSIM r ) and Theoretical Wenzel (θr ) C and Cassie (θr ) Contact Angles for Structured PE Surfaces, and the Contact Angle on the Flat PE Surface Where the Wetted and Composite Contact Angles for a Given Surface Roughness are Equal (θW)C ) e
PE
θSIM (deg)a r
θW r (deg)
θCr (deg)
θW)C (deg)b e
S6 M3 M4 M6 L6
156.4C 139.0W 145.8C 145.8C 127.9C
>180 167.2 >180 >180 >180
154.5 141.8 141.8 141.8 125.0
108.1C 108.7C 105.2C 101.0C 93.8C
a W refers to the observed wetted contact and C to the observed composite contact. b W refers to the predicted wetted contact and C to the predicted composite contact.
structures. However, neglecting the layered structure of the water closer than 8 Å to the surface in the circular fitting gives a spherically averaged contact angle in good agreement with the projected contact angles parallel to pillar structures. Polyethylene. Simulated contact angles (θSIM r ) on the structured PE surfaces are presented in Table 4. Increased hydrophobicity is observed for all rough surfaces compared with the contact angle of a similarly sized SPC water droplet on the flat crystalline PE surface (114.6°).14 For pillars with the largest height-width aspect ratio (S6), the water contact angle is over 40° larger. The final configurations of the simulations on the highest pillar structures with the three lateral dimensions (S6, M6, and L6) are presented in Figure 3. Here the decrease of the contact angle from S6 to L6 can be seen to follow the increase in the contact area of the liquid with the solid. The spherical shape of the liquid-vapor interface above the surface reference level is well-preserved, and the droplets, all with composite contact, are only weakly pinned to the edges of the pillars. The energy barrier for the rolling of the water droplet decreases with decreasing solid-liquid contact area. Simulated contact angles are dependent on the truncation of the long-range van der Waals interaction,33 and the stability of the simulated composite contacts on high pillar structures of PE was ensured by simulations employing a Lennard-Jones cutoff radius of 40 Å. The larger cutoff enabled van der Waals interactions of the water droplet with the two complete layers of hydrocarbons at the bottom of the effective roughness. No transition to the wetted contact was observed, although the contact angle extracted in the test case M6 was a few degrees smaller than the angle reported in Table 4. The effect of the bulk hydrocarbon layers on the water contact angle in the composite contact was found to be negligible at least without their direct influence on the van der Waals interactions. Theoretical contact angles for the wetted (θW r ) and composite contacts (θCr ) were calculated by using a rectangular approximation for the pillar geometries. The angles are presented in Table 4. Also included in the table is the contact angle on the flat PE surface where the apparent Wenzel and Cassie ). contact angles for a given surface roughness are equal (θW)C e The expected wetting geometry can be deduced from the apparent contact angles on the rough surface because the lower contact angle corresponds to an equilibrium drop shape in the
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J. Phys. Chem. B, Vol. 111, No. 13, 2007 3339
Figure 3. Final configurations of water droplets on structured PE surfaces. The highest pillars with three different lateral dimensions are visualized in the order (a) S6, (b) M6, and (c) L6, which also corresponds to decreasing height-width aspect ratio. W TABLE 5: Simulated (θSIM r ) and Theoretical Wenzel (θr ) and Cassie (θCr ) Contact Angles for Structured PVC Surfaces, and the Contact Angle on the Flat PVC Surface Where the Wetted and Composite Contact Angles for a Given Surface Roughness Are Equal (θW)C ) e
PVC
θSIM (deg)a r
θW r (deg)
θCr (deg)
θW)C (deg)b e
S6 M3 M6 L6
104.5W
107.7 102.9 111.4 117.2
145.5 133.8 133.8 117.6
103.3W 106.2W 99.3W 94.8W,C
111.1W 106.2W 116.9C
a W refers to the observed wetted contact and C to the observed composite contact. b W refers to the predicted wetted contact and C to the predicted composite contact.
Figure 4. Contact angle (θr) according to Wenzel’s and Cassie’s equations as a function of PE surface roughness (φs). The Wenzel curve corresponds to pillars with the ratio of the lateral dimensions equal to the ratio of the crystal dimensions. The simulated contact angles for the highest pillar structures (S6, M6, and L6) are presented with a half sphere and the theoretical ones with similarly colored dotted lines.
global energy minimum.11 An equilibrium contact angle on a stabilizes the wetting contact flat surface smaller than θW)C e with Wenzel’s contact angle, and the corresponding angle larger than θW)C stabilizes the composite contact with Cassie’s e contact angle. Except for the lowest pillars (M3), the composite contacts with good agreement between the simulated and calculated contact angles were observed on structured PE surfaces. Simulation results for the highest pillar structures (S6, M6, and L6) are compared with the theoretical counterparts in Figure 4, where the apparent contact angles of Wenzel’s and Cassie’s equations are plotted as a function of PE surface roughness. The Cassie contact angle is solely dependent on the roughness parameter (φs), whereas the Wenzel contact angle is also dependent on the pillar shape. Thus only the curve corresponding to the pillars with ratio of the lateral dimensions (ax, ay) equal to the ratio of the almost square crystal dimensions is visualized. The simulated contact angles are only a few degrees larger than the theoretical ones predicted by Cassie’s equation, whereas Wenzel’s contact angles on the modeled rough PE surfaces are mostly unrealistic, with values larger than 180°. The rectangular approximation for the pillar shapes slightly overestimates the solid-liquid contact area and decreases the Cassie contact angles. The wetting contact would be stabilized either by increasing the distance between the pillars or by lowering the pillars.
The water contact angle on PE surfaces with the highest pillar structures (S6, M6, and L6) increases, according to Cassie’s equation, with decreasing contact area between the solid and the liquid. The apparent contact angle is theoretically independent of pillar height if the composite contact is energetically favorable in that scale, and no transition to the wetting contact takes place. The simulated contact angle of 114.6° on the flat ) crystalline PE surface is larger than the limiting values (θW)C e for the pillars with different heights (M6, M4, and M3) and composite contacts should be observed. The apparent contact angles for the two highest pillar structures on crystalline PE (M6 and M4) are equal, and agreement with the theoretical predictions is obtained. In the case of the lowest pillars (M3), however, the contact angle is decreased by about 7°; and while still in good agreement with Cassie’s contact angle, in fact the wetted contact is observed. This may be because the depth of the surface roughness is smaller than the employed van der Waals cutoff. Poly(vinyl chloride). The same results as presented for the structured PE surfaces in Table 4 are presented for the structured PVC surfaces in Table 5. Relative to the contact angle of a SPC water droplet of equal size on the flat crystalline surface (94.7°),14 the hydrophobicity is increased for all rough PVC surfaces. However, the largest increase of the contact angle on the rough surface is only slightly over 20° compared with 40° on PE. Figure 5 shows the final configurations of the simulations on the highest pillar structures, with three different lateral dimensions (S6, M6, and L6). Wetted contact is observed on the two smallest pillar structures (S6 and M6), which have almost equal lateral and even higher vertical pillar dimensions than the corresponding structures on PE. Wetting of the grooves takes place slowly, following the sides of the pillars, instead of an instant collapse occurring from the midpoint between the adjacent pillars as in the macroscopic situation. The water
3340 J. Phys. Chem. B, Vol. 111, No. 13, 2007
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Figure 5. Final configurations of water droplets on structured PVC surfaces. The highest pillars with three different lateral dimensions are visualized in the order (a) S6, (b) M6, and (c) L6, which also corresponds to decreasing height-width aspect ratio.
volume between the pillars below the surface reference level leaves a larger volume of liquid to form a visible droplet on the top of a surface and leads to a larger contact angle if the three-phase contact line is pinned equally. This finding applies to all the results involving wetted contact in nanoscale. Conclusions
Figure 6. Contact angle (θr) according to Wenzel’s and Cassie’s equations as a function of PVC surface roughness (φs). The Wenzel curve corresponds to pillars with the ratio of the lateral dimensions equal to the ratio of the crystal dimensions. The simulated contact angles for the highest pillar structures (S6, M6, and L6) are presented with a half sphere and the theoretical ones with similarly colored dotted lines.
droplet is supported only by the asperities of the largest pillars of the PVC surface (L6), and a composite contact is formed. The simulated water contact angle on the highest pillar structures (S6, M6, and L6) increases in agreement with Wenzel’s equation, with increase in the roughness factor (r), which is equivalent to an increase in the lateral dimensions of the pillars. The surface hydrophobicity increases in the opposite order to that of the structured PE surfaces because the contact angle on the flat crystalline PVC surface (94.7°) is now equal to or smaller than θW)C . The results compiled in Table 5 are e visually compared with the theoretical ones in Figure 6. The simulated contact angles are at most a few degrees smaller than the predictions of Wenzel’s equation but, with one exception, 20-40° smaller than Cassie contact angles. The exception is L6, where the wetted and composite contacts produce almost identical contact angles. With this construction, the ratio of the lateral dimensions of the pillars to their separation is increased sufficiently to enable the formation of a composite contact with the PVC surface. For the wetted contact, in contrast to the composite contact, the theoretical contact angle is dependent on the height of the pillars. Surface roughness, and the hydrophobicity, increases with the pillar height. Simulated contact angles on the pillars of different heights (M6 and M3) show the opposite behavior: the contact angle on the lower pillar structure (M3) is 5° larger than that on the higher one (M6). This behavior can be explained by the strong pinning to the edges of the pillars. Smaller free
Hydrophobicity induced by surface roughness on structured PE and PVC polymer surfaces was studied by molecular dynamics simulations. Nanoscale pillar structures with three different lateral dimensions and heights were cut from the flat crystalline polymer surfaces. Contact angles of microscopic water droplets on the frozen structured surfaces were extracted and compared with the theoretical angles predicted by Wenzel’s and Cassie’s equations. The difference between the water contact angles on the flat PE and PVC surfaces led to different equilibrium wetting geometries on pillar structures of approximately the same size. Simulations on rough PE surfaces exhibited composite contacts, and the contact angle increased with decreasing contact area between the solid and the liquid, in good agreement with Cassie’s theory. Moreover, the contact angle was independent of the pillar height, although a surface roughness depth-scale smaller than the van der Waals cutoff radius led to the wetted contact. Results for rough PVC surfaces indicated mostly the opposite wetting behavior. The simulated contact angles coincided with the predictions of Wenzel, and the contact angle increased with the lateral dimensions of the pillars and thus with the roughness in wetted contact. The wetted and the composite contacts were energetically about the same on the largest pillars of PVC, and the composite contact was observed. The theoretically predicted dependency of the contact angle on the height of the pillars was not observed for the wetted contact. The contrary behavior was a consequence of the strong pinning to the surface structures associated with the decreasing volume of the microscopic droplet above the surface reference level with the increasing surface groove volume. Relative to the smooth surfaces hydrophobicity increased on all surfaces with nanopillars. The maximal increase in the water contact angle was about 20° larger on structured PE surfaces than on structured PVC surfaces, reflecting the larger contact angle on the flat PE surface. Good agreement was obtained between the simulated nanoscale roughness and the theoretical predictions of Wenzel and Cassie for macroscopic surface roughness. Acknowledgment. The research was partially supported by TEKES as a part of a national technology program on surface sciences called Clean Surfaces (2002-2006).
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