molecular dynamics simulation of water near nanostructured hydrophobic surfaces: interfacial...

Molecular Dynamics Simulation of Water NearNanostructured Hydrophobic Surfaces:Interfacial EnergiesSandeep Pal,*[a] Danilo Roccatano,[a] Horst Weiss,[b] Harald Keller,[b] andFlorian M�ller-Plathe*[a]

1. Introduction

We investigated the effect of a hole and a protrusion indent-ed/raised on a planar hydrophobic surface on the structuraland thermodynamic properties of water at the interface withit. As a model of the surface, we used an alkane crystal. Theproperties of interest are the density distribution of water nearthe hydrophobic surface, the potential of mean force calculat-ed from the density distribution and the contacts betweenwater and the structured crystal. Finally, we compare the differ-ence in hydration free energy between a structured crystal anda planar crystal.

To see how surface structuring can increase the hydropho-bicity of a surface, a view to the so-called lotus effect isuseful.[1–10] The water on the surface of a lotus leaf is very un-stable and on rolling off it takes off any dirt with it. Many plantleaves use this phenomenon. The surface of the lotus leaf isstructured on a micrometer length scale. The water drop restsonly on the tips of the peaked microstructures, the contactarea between leaf and droplet is minimized.

Recently, some detailed theoretical and experimental studieshave been done on the lotus effect.[11–14] The problem of droproll-off from the surface was dealt with by a very simple theo-retical model of the protrusions on a planar surface byMarmur.[11] In their article, the wetting on rough surfaces wasstudied in two regimes: the homogeneous regime, where theliquid completely penetrates the rough grooves; and heteroge-neous wetting, where air is trapped underneath the liquidinside the rough grooves. The dynamic electrical control of thewetting behaviour of liquids on nanostructured surfaces hasbeen dealt with by Krupenkin et al.[13] The method primarilyrelies on using electrowetting to adjust the local contact anglethat the liquid forms with the nanosized features of the sur-face.

Lee and Rossky[15] have compared the structure and dynam-ics of water near two different hydrophobic surfaces, one near

a flat surface and the other near an atomic Lennard–Jones sur-face. The range of the surface-induced perturbation in thestatic and dynamical properties of water was found within twolayers of water molecules (�0.8 nm) from the surface. Thedensity profiles of the water molecules near an atomic Len-nard–Jones surface is slightly higher and is shifted more to-wards the hydrophobic surface than the perfectly planar sur-face.

Whereas the recent theoretical and experimental articles onthe lotus effect describe how the hydrophobicity changes dueto microstructuring, herein we consider comparing two differ-ent surface structures, a hole and protrusion, of nanometre di-mensions. The motivations for performing the calculations arebasically two. Firstly, we supplement our previous article[16,17]

which found enhanced hydrophobicity for structured hydro-phobic surfaces having different indentations (hexagonal,stripes, triangular) compared to flat surfaces. Although inden-tations are easier to manufacture technically, it is not clear ifthey are as efficient as protrusions for increasing the hydro-phobicity of the surface. We therefore report here the most ef-ficient hole geometry (diameter �2.5 nm) in comparison witha protrusion of the same size.

Secondly, this article goes beyond the analysis of water den-sity and structure presented in ref. [16] . We also report hereinthe differences in interfacial free-energy between a planar sur-face, a surface with a hole and a surface with a protrusion.There exist simulation approaches for finding the absolute hy-

[a] S. Pal, Dr. D. Roccatano, Prof. F. M�ller-PlatheInternational University Bremen, P.O. Box 750561, 28725 Bremen (Germany)Fax (+49) 421-200-3249E-mail : [email protected]

[email protected]

[b] Dr. H. Weiss, Dr. H. KellerBASF Aktiengesellschaft, 67056 Ludwigshafen (Germany)

We present results from molecular dynamics simulations of waternear structured hydrophobic surfaces. The surface structures re-ported herein are a planar alkane crystal as a reference and crys-tals with a hole and a protrusion of approximately 2.5 nm diam-eter and 0.5 nm depth or height. All indicators show that surfacestructuring increases the hydrophobicity: The water density is re-duced near the structure elements, and the number of residual

contacts between water and the surface decreases by about 40%with respect to the planar surface. Thermodynamic integrationshows that the interfacial energy of the structured surfaces isabout 7 mJm�2 higher for structured surfaces than for the planarsurface. The hydrophobicity increases by a similar amount for thehole and the protrusion geometries compared to the planar sur-face.

ChemPhysChem 2005, 6, 1641 – 1649 DOI: 10.1002/cphc.200500074 ? 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 1641

dration free-energy of a hydrophobic interface.[18,19] They are,however, in the present form suitable only for interfaces be-tween two isotropic phases (vacuum, fluid, structureless walls,crystal/melt interface). Herein, we use thermodynamics integra-tion to calculate the difference in the Helmholtz free-energy ofhydration between a structured (hole or protrusion) and aplanar crystal. If the free-energy change is positive then thestructured surface is more hydrophobic than the planar surfaceand vice versa.

Computational Details

Details of the Surface Structure: A crystal of n-eicosane molecules(C20H42) (one layer of 7E12 molecules) serves as the model of ourhydrophobic surface. Crystallography of n-eicosane shows that ithas a triclinic crystal structure with a hexagonal packing of themolecules.[20,21] The model of our n-eicosane crystal has been de-scribed in refs. [16, 17] . The crystal structure is triclinic (a=67.68,b=83.98, c=2.544 nm) and close to the experimental crystal (a=68.28, b=85.78, c=2.743 nm).[21–24] The eicosane crystal (thickness2.5 nm) was separated from its periodic image by a water layer(thickness 2.6 nm). Two different topographies were created on thesurface (Figure 1): A hexagonal hole (19 alkane chains, which forma regular hexagon, shortened by four carbon atoms) and a hexago-nal protrusion of the same size (65 alkane chains shortened byfour carbon atoms resulting in the remaining 19 chains forming ahexagonal protrusion on the surface of the planar crystal). The per-

centage of raised/indented surface, is therefore approximately100E19/84=21%. The height or depth of the protrusion or hole,respectively, is about 0.5 nm. Shortening chains, by turning off in-teractions between water and the corresponding carbon and thehydrogen atoms of the crystal is technically the most convenientway of achieving surface structuring. Figure 2 shows the schematic

and the labels of the different surface segments used for the re-mainder of this article. In all analyses, z=0 refers to the surface ofthe planar crystal defined by the arithmetic mean of the z coordi-nates of all the unindented/unraised surface carbon atoms, so thehole carries a negative z and the protrusion a positive z (Figure 2).The protrusion was created on only one side of the crystal, to keepthe water on both the sides of the surface well separated. Howev-er, holes were created on both the sides of the crystal and offsetby 2 nm in the y direction and 1 nm in the x direction to havemore statistics. Measuring between carbon chain positions flankingthe hole/protrusion, the hole and protrusion have a diameter ofapproximately 2.5 nm. To convert to the inner widths, the diameterof a CH3 group should be subtracted from these values. The totalsurface area of the side-walls of the hole and the protrusion is�2.5EpE0.5 m2=4 nm2.

Simulation Model: Our periodic simulation box (3.3E5.3E5.1 nm3)contained 1500 molecules of water and 84 n-eicosane molecules.The details of the simulation setup are discussed in ref. [16]. Wehave used the YASP simulation package[25] for the molecular dy-namics (MD) simulations. The system was weakly coupled to thedesired temperature (298 K) with a relaxation time of 0.2 ps.[26,27]

The Cartesian diagonal components of the pressure tensor wereFigure 1. The system chosen for our molecular dynamics simulation. a) Hole;b) protrusion.

Figure 2. a) Schematic of the hole. The reference height (z=0) is the aver-age of the terminal methyl carbon atoms. The depth of the hole is�0.5 nm. b) Schematic of a protrusion. The reference height (z=0) is theaverage of the terminal methyl carbon atoms. The height of the protrusionis �0.5 nm.

1642 ? 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemphyschem.org ChemPhysChem 2005, 6, 1641 – 1649

S. Pal, F. M�ller-Plathe et al.

www.chemphyschem.org

coupled separately to an external pressure of 0.1013 MPa with arelaxation time of 5 ps.[26–29] Bond lengths were constrained usingthe SHAKE algorithm.[30] The time step for the leapfrog integrationscheme[26,27] was set to 0.002 ps and the trajectory frames weresaved every 1 ps. The total simulation run was 2 ns, with 1 ns forthe equilibration and the production runs, respectively. Nonbond-ed interactions were evaluated at every time step, with a cutoffradius of 0.9 nm and using a neighbour list (update every 20 steps,neighbour list cutoff 1.0 nm). The n-eicosane was described by theall-atom OPLS model.[31, 32] Water was treated with the SPC/Emodel.[33] Lennard–Jones parameters for interactions betweenunlike atoms were evaluated using the Lorentz–Berthelot mixingrules,[26] electrostatic interactions were treated with the reactionfield approximation,[26] using an effective dielectric constant of 72.The intra/intermolecular interactions (Lennard–Jones + Coulombicinteraction) between the chains were switched off in the calcula-tions of nonbonded interactions between alkane molecules;springs were used between adjacent carbon atoms of any chainand the carbon atoms of its six nearest-neighbours, taking into ac-count periodic boundary conditions. The springs were used be-tween carbon atoms of the same index (i.e. , Ci–Ci’, length:0.497 nm) and carbon one index apart (Ci–Ci+1’, length: 0.89 nm).The spring constants were chosen as 2000 kJmol�1 L�2. Theselengths were chosen to maintain the crystal structure of n-eico-sane[16,17] under constant pressure simulations. This rigidificationwas necessary, not so much for the native planar alkane slab, butto prevent surface reconstruction of structured alkane surfaces,which also contained shorter alkane chains.

The thermodynamic integration calculations[34–36] were carried outwith the GROMACS molecular dynamics simulation package.[34–36]

The details of the procedure are discussed in Section 2.3. The po-tential parameter interactions are the same as described above forthe simulations using YASP. GROMACS uses the softcore nonbond-ed potentials for the thermodynamic integration procedure. Inorder to avoid singularities, the soft-core potential Vsc is given byEquation (1):

VscðrÞ ¼ ð1�lÞVAðrAÞ þ lVBðrBÞ ð1Þ

where rA and rB are given by Equations (2) and (3), respectively:

rA ¼ ðas6Al

2 þ r6Þ1=6 ð2Þ

rB ¼ ðas6Bð 1�lÞ2 þ r6Þ1=6 ð3Þ

and l is the coupling parameter which varies from 0 to 1; VA andVB are the normal “hard core” van der Waals or electrostatic poten-tials in states A (l=0) and B (l=1), respectively; a=1.51 is thesoft-core parameter, which mainly controls the height of the po-tential around r=0;[35] s is the radius of the interaction defined as

s=

�C12

C6

�1=6

, or s=0.3 nm when C12 or C6 (Lennard–Jones 12 and 6

terms) is zero.

The simulations were established at constant pressure (normalpressure and temperature, NPT, ensemble) using anisotropic cou-pling during the equilibration run of 1 ns for each value of the cou-pling parameter l : The compressibility in the xy directions waschosen at a very small value (109 times less than the compressibili-ty of water) to keep the crystal geometry rigid in the xy direction,whereas in the z direction the value was equal to the compressibil-ity of water. The box geometry was then fixed and a productionrun of 4 ns was performed at every l at a constant volume (normalvolume and temperature, NVT). This procedure does not introduce

a pDV term, owing to fluctuation of the box during a productionrun at an individual l value. The bond lengths were constrainedusing SHAKE[30] and the leapfrog algorithm was used to integratethe equations of motion. The cutoff for the different nonbondedinteractions was 0.9 nm. The Coulombic interactions were treatedwith a reaction field technique (e=72). As in the MD simulationusing YASP (no thermodynamic integration), the only interactionpotential present inside the crystal is the spring potential and thebonded interactions within a molecule, which do not change withthe coupling parameter l. The masses of the atoms being switchedon/off were not changed.

Analysis: The simulations were analysed in terms of the density ofwater at and near the interface. We have analysed the local densi-ties by dividing the simulation box into cells (nm3) and finding thedensity in each cell. As the crystal is not space-fixed and has thefreedom to diffuse in the x and y directions, the grid geometry wasattached to it in order to get consistent density distributions in thecourse of the MD simulations. Fixing grid points to the surfacecarbon atoms of the crystal does this. The density distribution[gcm�3] was evaluated using Equation (4):

1ð r!Þ ¼

�N

�r!,ðx� Dx

2 ,x þ Dx2 Þ,ðy�

Dy2 ,y þ Dy

2 Þ,ðz�Dz2 ,z þ Dz

2 Þ��

Mw

DxDyDz

ð4Þ

where r!= (x,y,z) is the centre of the cell ; Dx, Dy, Dz are thelengths of the sides of the cell ; Mw is the molecular weight ofwater; and hN[ r!]i is the number of water oxygen atoms inside thecell at r! averaged over the 103 trajectory frames. The density dis-tributions were converted to local excess chemical potentials usingBoltzmann inversion, Equation (5):[37]

Dmð r!Þ ¼ �RT ln

�1ð r!Þ1Bulk

�ð5Þ

where 1Bulk is the bulk density of water away from the surface cal-culated at the centre of the water layer; Dm( r!) is the difference inthe excess chemical potential between position r! and the bulkwater excess chemical potential. For Dm( r!)<0, position r! is hy-drophilic and if Dm( r!)>0 it is hydrophobic.

For the thermodynamic integration calculations, the hole/protru-sion was created by reversibly switching on/off the interaction be-tween four carbon atoms and the associated hydrogen atoms of19 chains, from the 84 chains, and water.[34–36] Care has been takento turn the fourth carbon atom from the surface to a hydrogenatom and the bond length of the resulting carbon hydrogen bondvalue was equal to 0.109 nm. The torsional and the angle poten-tials were not altered during this change. The difference in thefree-energy between two states A and B of a molecular system,with Hamiltonians denoted by HA( r

!) and HB( r!), is expressed by

Equation (6):

DABA ¼ AB�AA ¼Z1

0

�@Hð r!;lÞ

@l

�l

dl ð6Þ

where r! is the (3N-dimensional) position vector of the N atoms ofthe system; and H( r!;l) is the Hamiltonian parameterized by thecoupling variable l, and satisfying Equations (7a) and (7b):

Hð r!;0Þ ¼ HAð r!Þ ð7aÞ

Hð r!;1Þ ¼ HBð r!Þ ð7bÞ

ChemPhysChem 2005, 6, 1641 – 1649 www.chemphyschem.org ? 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 1643

Water Near Nanostructured Hydrophobic Surfaces


The angle brackets in Equation (6) denote averaging over an equi-librium ensemble generated with the Hamiltonian function H( r!;l).We employed the multiconfiguration thermodynamic-integrationmethod[34–36] to evaluate the integral in Equation (6). This methodperforms a separate simulation at a number of discrete l. At each

l point, the value of h@Hð r!

;lÞ@l i is calculated. The integral in Equa-

tion (6) is then determined numerically using the trapezoidal rule.

The error bars at each l point were found by block averaging[27]

(150 blocks were used in our simulations) of h@Hð r!

;lÞ@l i points. The

error in the thermodynamic integration was determined using

Equation (8):[34]

dðDAÞ ¼� XNl

n¼1

wðlnÞd2ðh@H=@lilnÞ�1=2

ð8Þ

where w(ln) is the weight factor from the trapezoidal integration

and d is the error.

2. Results and Discussion

2.1. Density Distribution of Water Near the Two SurfaceStructures

The grid geometry, Equation (4), was used to describe the vari-ous density distributions discussed below. Figure 3 shows thedensity profile in a yz slab of thickness Dx=0.5 nm positionedbetween x1=�0.25 nm and x2=0.25 nm relative to the centralreference carbon atom. This slab vertically cuts through the

surface and the protrusion/hole. For comparison, the waterdensity near a planar crystal is also plotted.

From Figures 3a and 3b, the following observations are evi-dent. 1) The water density is lower at the side walls of the holeand the protrusion; it avoids contact with the side of the sur-face structures. 2) The density of water at the surface of thecrystal in all cases is higher than in the bulk water region. Thisis due to the structuring of water at the interfacial region ofwater and the crystal surface. 3) The density of water at the“base carbon atoms” (compare with Figure 2) of the hole is�0.5 gcm�3 Figure 3a, at the “top carbon atoms” (comparewith Figure 2) of the protrusions it is �1.4 gcm�3, Figure 3b.

To understand the effect of the two surface topographies onthe interfacial water in a systematic way, horizontal slabs (xy -layers) of 0.2 nm thicknesses were placed at different heights(z) above the surface, Figures 4 and 5. The heights consideredfor the holes were �0.4 to �0.2 nm, �0.2 to 0 nm, 0 to0.2 nm, 0.2 to 0.4 nm, 0.4 to 0.6 nm and 0.6 to 0.8 nm, respec-tively, for Figures 4a–f. A comprehensive discussion can befound in ref. [17] . The salient points in Figure 4 are the waterdensity showing the underlying crystal structure in Figures 4a–d, and the influence of the hole present in the water densityprofile at heights up to 0.2–0.4 nm from the surface of thecrystal. In the case of the protrusions, the following slabs ofthickness 0.2 nm, from Figures 5a–f were chosen: 0 to 0.2 nm,0.2 to 0.4 nm, 0.4 to 0.6 nm, 0.6 to 0.8 nm, 0.8 to 1.0 nm and1.0 to 1.2 nm, respectively. Figure 5a (0–0.2 nm) clearly depictsthe excluded volume due to the presence of the protrusion.Figure 5b, 0.2–0.4 nm, shows a not-so-sharp interface between

water and the sidewalls of theprotrusion. Interestingly, thedensity is lower on the surfacewest and east (x) of the protru-sion than north and south (y).This is owing to the fact thatthe periodic images of the pro-trusions stand closer in the xthan in the y direction. Similarobservations of density reduc-tion were made for holes of dif-ferent sizes and shapes.[16] Fig-ure 5c shows the density distri-bution of water in the regionbetween 0.4 and 0.6 nm slab.The water molecules have ahigher density above the edgesof the protrusion than above itscentre. Figure 5d, the layer be-tween 0.6–0.8 nm, shows thewater density is slightly greaterabove the protrusion than thesurrounding region. In Figur-es 5e and 5 f, the water densityis similar to the bulk water andthe influence of the surfacestructures on the water densityis barely evident.

Figure 3. Water density [gcm�3] in a vertical (yz) slab of thickness Dx=0.5 nm cutting through the centre of thehole/protrusion: a) Hole; b) Protrusion; c) Planar crystal. Black represents the crystal, from which water is excluded;the colours in the legend quantify the water density.




2.2. Water Density Normal to the Surface

Figure 6a shows the density averaged in the x and y directionas a function of z. The same grid as before was used for the

analysis. Recall that z=0 corresponds to the height of the sur-face carbon atoms. Thus, cells inside the alkane crystal are ex-cluded. In all cases, the water density approaches the same

Figure 4. Water density [gcm�3] in the vicinity of the hole for horizontal (xy) slabs placed in the xy direction at the following range of heights a) z=�0.4 to�0.2 nm; b) z=�0.2 to 0 nm; c) z=0 to 0.2 nm; d) z=0.2 to 0.4 nm; e) z=0.4 to 0.6 nm; f) z=0.6 to 0.8 nm. Black represents the crystal, from which water isexcluded; the colours in the legend quantify the water density.




Figure 5. Water density [gcm�3] in the vicinity of the protrusions for horizontal (xy) slabs at the following range of heights a) z=0 to 0.2 nm; b) z=0.2 to0.4 nm; c) z=0.4 to 0.6 nm; d) z=0.6 to 0.8 nm; e) z=0.8 to 1.0 nm; f) z=1.0 to 1.2 nm. Black represents the crystal, from which water is excluded; the col-ours in the legend quantify the water density.




bulk value of �0.98 gcm�3 away from the crystal surface. Thewater density in the case of a hole and a planar crystal showsthe same height of the first peak 1.38 gcm�3 at 0.25 nm fromthe surface. Lee and Rossky[15] have reported the height of thedensity first peak is 1.25 gcm�3 and at the same position withrespect to a flat atomistic (using a much smaller system and adifferent water model) hydrophobic surface. The density ofwater inside the hole is �0.2 gcm�3. For the protrusion, thewater density has a shoulder at 0.28 nm and peaks at 0.42 nmand 0.68 nm. Their height is 1.0 gcm�3, whereas the density incase of the hole and the planar surface are similar and is signif-icantly different in case of the protrusion.

The density distributions were converted to excess chemicalpotential differences (potential of mean force) by Boltzmanninversion, (Figure 6b) using Equation (5). Figure 6b shows thatat z�0.25 nm, the value of Dm is �0.25RT, in the case of thehole and the planar slab, implying a small free-energy benefitfor water to be at the interface rather than in the bulk. Howev-er the value Dm/RT rises sharply inside the hole. In case of theprotrusion, there is no region with Dm/RT<0, which meansthat water is not attracted to the surface preferentially.

2.3. Contacts of Water with the Surface Carbon Atoms

The number of contacts that the water makes with the surfaceatoms can also be used to judge the hydrophobicity of an in-terface. The more contacts there are, the larger is the residualdispersive attraction between water and surface, and the loweris the hydrophobicity. As surface carbon atoms, we count allmethyl carbon atoms at chain ends, as well as the three follow-ing methylene carbon atoms of the chains forming the sidesof the hole/protrusion. The contacts are calculated from thecorresponding radial distribution function, g(r). Figure 7ashows the radial distribution functions between oxygen atomsof the water molecules and all surface carbon atoms. For com-parison, the corresponding g(r) for a completely planar surfaceis also included. Figures 7b and 7c show the different contri-butions to the radial distribution function between water andsurface carbon atoms.

The number of contacts is obtained by integrating the firstpeak of the radial distribution function (0 to 0.5 nm) (Table 1).The number of contacts is analysed in two ways, per wateroxygen atom (water side) and per surface carbon atom (sur-face carbon side). The total number of contacts from the waterside is the sum of all the three contributions. The surfacecarbon atoms, in the case of the protrusion (on one side), are65 reference plane carbon atoms, 36 side-wall carbon atomsand 19 top surface carbon atoms. In the case of the hole,there are 130 reference plane carbon atoms, 108 side-wallcarbon atoms and 38 hole base carbon atoms, consideringboth sides of the alkane crystal. A water molecule has consid-erably fewer contacts with either of the structured surfacesthan with the planar surface. The number of contacts is similarfor the hole and the protrusion geometry, with the latter beingslightly lower. The contacts are, however, being made with dif-ferent atoms. The reference plane has 1.5 times more contactsfor the hole than for the protrusion. The protruding carbonatoms, however, have three times more contact than thehole’s base carbon atoms. The number of contacts from of theside-walls is approximately the same for both the protrusionand the hole.

Comparing the number of contacts from the carbon side,the number of contacts of the reference plane is 1.5 timeshigher for the hole than for the protrusion. The protrudingcarbon atoms have 3 times more contacts than the basecarbon atoms. The side-wall carbon atoms show 1.2 timesmore number of contacts in case of protrusion than the hole.The total number of contacts between all the surface carbonatoms and water is the same in case of the hole/protrusion,however it is 40% less than for the planar crystal. From this weconclude that the surface structuring does impart a higher hy-drophobicity to the crystal. Both ways of structuring the sur-face (hole or protrusion) have a similar total effect.

2.4. Free-Energy Calculations

The Gibbs free-energy difference between a crystal with sur-face structuring and a planar crystal is calculated in this sec-tion. The coupling variable l is used to scale the potential pa-

Figure 6. a) Density of water as a function of z, the distance from the sur-face. b) Difference in the water excess chemical potential from the bulkvalue as a function of z from the surface.




rameters of atoms that participate in reversibly changing thecrystal from planar (l=0) to structured (l=1). The transforma-tion during the free-energy calculations, from an interacting toa non-interacting ghost or dummy atoms in the slab, was per-formed using at least 23 points, which was sufficient to ensurea smooth integrand.

We have Equation (9) for the Hamiltonian of a planar crystalwith water Hi :

Hi ¼ ½Hww þ Hwc�i ð9Þ

where Hww and Hwc are the Ham-iltonian for water–water andwater–crystal interactions. (Thesubscript i indicates initial). Simi-larly, we can write the Hamiltoni-an of the final system, that is,water + structured crystal, Equa-tion (10):

Hf ¼ ½Hww þ Hwc þ Hsw�f ð10Þ

where Hsw is the Hamiltoniandue to the surface structure(hole/protrusion) on the surfaceof the crystal. It consists of addi-tional interactions with theadded carbon units in the caseof the protrusion. For the holecase, however, Hsw correspondsto removing the appropriatewater–carbon and water–hydro-gen interactions. The water–water Hamiltonian does notchange with the coupling pa-rameter l. With the change incoupling variable l, Hwc and Hsw

change. The results of the inte-gration are shown in Table 2with the associated error barscalculated from Equation (8)

after 4 ns of production run. As the volume is allowed to equi-librate at each l point, the free-energy allows for a pDV termand is the Gibbs free-energy for the process of creating a holeor protrusion. From the volume change (�2%), the pDV con-tribution can be estimated. It amounts to �10�2 mJm�2,which is small compared to the free-energy changes and theirerror bars. The Gibbs and Helmholtz energies for the surfacestructuring can therefore be considered numerically equal.

The change in the surface free-energy is positive in bothcases. This implies that both the hole geometry and the pro-trusion geometry impart higher hydrophobicity to the crystalcompared to a flat surface. For both, the gain of free-energy isof similar order.

Figure 7. a) Radial distribution function between all surface carbon atoms and water. Radial distribution functionbetween different types of surface carbon atoms and water a) Hole; b) Protrusion. For definition of types, seeFigure 2.

Table 1. Number of contacts between water and the surface carbonatoms from the water side. In the parentheses, the number of contactsfrom the surface carbon side is given.

Surfacestructuring

Referenceplane

Base/Protrusion Sidewalls

Allsurface

hole 0.19 (4.4) 0.03 (2.0)(base carbonatoms)

0.05 (1.5) 0.27(3.0)

protrusion 0.13 (2.9) 0.07 (5.7)(top carbon atoms)

0.05 (1.9) 0.25(3.1)

planarcrystal

0.45 (4.0) – – 0.45(4.0)

Table 2. Difference in the Gibbs free-energy of hydration between astructured crystal (hole/protrusion) and a planar crystal.

Free-energy process DA [kJmol�1] DA/Area [mJm�2]

Planar crystal!Hole geometry 75�13 7.1�1.0Planar crystal!Protrusion geometry 66�13 6.3�1.0




3. Conclusions

Nanostructuring enhances the hydrophobicity of a surface,which is intrinsically hydrophobic. We have created structures�2.5 nm in diameter and �0.5 nm in depth or height onalkane crystals serving as models for a hydrophobic material.Both indentations and protrusions increase the hydrophobicityby approximately the same amount. The increased hydropho-bicity is evident in the average number of contacts experi-enced by a water molecule. It drops from 0.45 for a planar sur-face to 0.27 and 0.25 for the surface with a hole and a protru-sion, respectively. The effect can be quantified by thermody-namic integration calculations which show that the interfacialtension increases by 7.1 mJm�2 and 6.3 mJm�2 for the holeand the protrusion topographies, respectively, compared tothe planar surface. Although the precise values of these incre-ments depend on details of the simulation, such as force-fieldparameters, the qualitative result is clear: Both ways of surfacestructuring increase the interfacial tension and hence the hy-drophobicity. A methodological side result is that the simplereasoning based on water–surface contacts (fewer contacts!less interactions!higher hydrophobicity) is borne out by ther-modynamic integration calculations of the surface free-energyincrements. As counting the number of contacts is much sim-pler and computationally cheaper than thermodynamic inte-gration, it might be a quick, qualitative estimator for compar-ing the hydrophobicities of different surfaces. More work is,however, needed to determine how universal this relation be-tween contacts and surface tension is.

Keywords: alkanes · hydrophobic effect · moleculardynamics · surface chemistry · water chemistry

[1] N. K. Adam, The Physics and Chemistry of Surfaces ; Oxford UniversityPress, London, 1941.

[2] J. N. Israelachvili, Intermolecular and Surface Forces, Academic Press, SanDiego, 1991.

[3] C. Neinhuis, W. Barthlott, Ann. Bot.-London 1997, 79, 667–677.[4] E. A. Baker, E. Parsons, J. Microsc. 1971, 94, 39–49.[5] W. Barthlott in Scanning Electron Microscopy in Taxonomy and Functional

Morphology (Ed. : D. Claughter), Oxford, Clarendon Press, 1990, pp. 69–94.

[6] E. A. Baker, G. M. Hunt, New Phytol. 1986, 102, 161–173.[7] A. B. D. Cassie, S. Baxter, Trans. Faraday Soc. 1944, 40, 546–551.

[8] N. K. Adam in Waterproofing and Water-Repellency (Ed. : J. L. Moilliet),Elsevier, Amsterdam, 1963, pp. 1–23.

[9] H. F. Linsken, Planta 1950, 38, 591–600.[10] I. Rentshler, Planta 1971, 96, 119–135.[11] A. Marmur, Langmuir 2004, 20, 3517–3519.[12] R. N. Wenzel, Ind. Eng. Chem. 1936, 28, 988–993.[13] T. N. Krupenkin, J. A. Taylor, T. M. Schneider, S. Yang, Langmuir 2004, 20,

3824–3827.[14] A. Otten, S. Herminghaus, Langmuir 2004, 20, 2405–2408.[15] S. H. Lee, P. J. Rossky, Proceedings of the 10th Korean Scientists and Engi-

neers Conference, Inchen, Korea, 1987, pp. 150–155.[16] S. Pal, H. Weiss, H. Keller, F. M�ller-Plathe, Langmuir 2005, 21, 3699–

3709.[17] S. Pal, F. M�ller-Plathe, J. Phys. Chem. B 2005, 109, 6405–6415.[18] D. M. Huang, D. Chandler, J. Phys. Chem. B 2002, 106, 2047–2053.[19] R. L. Davidchack, B. B. Laird, J. Chem. Phys. 2003, 118, 7651–7657.[20] J. G. Kirkwood, F. P. Buff, J. Chem. Phys. 1949, 17, 3–9.[21] E. M. Blokhuis, D. Bedaux, C. D. Holcomb, J. A. Zollweg, Mol. Phys. 1995,

85, 665–669.[22] S. C. Nyburg, J. A. Potworowski, Acta Crystallogr. , Sect. B 1973, B29,

347–352.[23] N. Waheed, M. S. Lavine, G. C. Rutledge, J. Chem. Phys. 2001, 116, 2301–

2309.[24] D. M. Small, The Physical Chemistry of Lipids : From Alkanes to Phospholi-

pids ; Plenum, New York, 1986, pp. 183–190.[25] F. M�ller-Plathe, Comput. Phys. Commun. 1993, 78, 77–94.[26] M. P. Allen, D. J. Tildesly, Computer Simulation of Liquids, Clarendon

Press, Oxford, 1987.[27] D. Frenkel, B. Smit, Understanding Molecular Simulation, Academic Press,

San Diego, 2002.[28] F. Jensen, Introduction to Computational Chemistry, Wiley VCH, Chiches-

ter, 1998.[29] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, J. R.

Haak, J. Chem. Phys. 1984, 81, 3684–3690.[30] J. P. Ryckaert, G. Ciccotti, H. J. C. Berendsen, J. Comp. Physiol. 1977, 23,

327–341.[31] E. M. Duffy, W. L. Jorgensen, J. Am. Chem. Soc. 2000, 122, 2878–2888.[32] G. Kaminski, E. M. Duffy, T, Matsui, W. L. Jorgensen, J. Phys. Chem.

1994, 98, 13077–13082.[33] H. J. C. Berendsen, J. R. Grigera, T. P. Straatsma, J. Phys. Chem. 1987, 91,

6269–6271.[34] X. Daura, A. E. Mark, W. F. van Gunsteren, J. Comput. Chem. 1998, 19,

535–547.[35] H. J. C. Berendsen, D. van der Spoel, R. van Drunen, Comput. Phys.

Commun. 1995, 91, 43–56.[36] E. Lindahl, B. Hess, D. van der Spoel, J. Mol. Model. 2001, 7, 306–317.[37] O. Biermann, E. HSdicke, S. Koltzenburg, F. M�ller-Plathe, Angew. Chem.

2001, 113, 3938–3942; Angew. Chem. Int. Ed. 2001, 40, 3822–3825.

Received: February 3, 2005

Revised: May 4, 2005




molecular dynamics simulation of water near nanostructured hydrophobic surfaces: interfacial...

Documents