molecular dynamics simulation of the water|nitrobenzene interface

Journal of Electroanalytical Chemistry 450 (1998) 335–345

Molecular dynamics simulation of the water�nitrobenzene interface

David Michael *, Ilan Benjamin

Department of Chemistry, Uni6ersity of California, Santa Cruz, CA 95064, USA

Received 11 September 1997; received in revised form 3 November 1997

Abstract

The structure and dynamics of the neat water�nitrobenzene liquid�liquid interface are studied at 300 K using molecular dynamicscomputer simulations. The water is modeled using the flexible SPC potential, and the nitrobenzene is modeled using an empiricallydetermined nitrobenzene potential energy function. Although nitrobenzene is a polar liquid with a large dielectric constant, thestructure of the interface is similar to other water�non-polar organic liquid interfaces. Among the main structural features wedescribe are an enhancement of interfacial water hydrogen bonds, the specific orientation of water dipoles and nitrobenzenemolecules, and a rough surface that is locally sharp. Surface roughness is also characterized dynamically. The dynamics ofmolecular reorientation are shown to be only mildly modified at the interface. The effect due to the polarizable many-bodypotential energy functions of both liquids is investigated and is found to affect only mildly the above results. © 1998 ElsevierScience S.A. All rights reserved.

Keywords: Molecular dynamics; Simulation; Water�nitrobenzene interface

1. Introduction

The interface between water and nitrobenzene is oneof the most commonly studied condensed phase environ-ments for understanding electrochemical phenomena atliquid�liquid interfaces [1,2]. Many studies of ion transferacross the liquid�liquid interface are carried out in thissystem [3–5]. In many cases, the interpretation of thesestudies requires us to make certain assumptions aboutthe structure of this interface [4,6,7]. For example, someinterpretations of ion transfer kinetic data assume a wideregion of homogeneous mixture separating the two bulkregions [7]. Other models speculate that specific molecu-lar orientations at the interface give rise to stronganisotropic forces.

In recent years, new spectroscopic techniques haveenabled workers to gain valuable information about thestructure of liquid interfaces in general [8–10], and aboutliquid�liquid interfaces in particular [11], including theelectrochemical water�1,2-dichloroethane interface [12].

In parallel, theoretical and computational studies havebeen successful in providing new microscopic insightsabout these interfaces [13,14]. Yet, despite the enormousinterest in electrochemical processes at the wa-ter�nitrobenzene interface, there are neither direct exper-imental data nor theoretical or computational studies ofthe microscopic structure of this interface.

In this paper, we employ the much used flexiblesimple point charge (FSPC) model of water, togetherwith an empirically derived intermolecular (all atoms)flexible model of nitrobenzene, to gain insight into themicroscopic structure and dynamics of the interfacebetween these two liquids. As a comparison, we havealso studied the interface when the two liquids aredescribed using fully polarizable model potentials. Ingeneral, despite the relatively large polarity of the ni-trobenzene, many of the properties of the neat interfaceare similar to those of other water�non-polar organicliquids. In particular, our calculations suggest that atthe nanometer length scale, the interface should bethought of as a sharp and rough transition between thebulk of the two liquids.* Corresponding author.

0022-0728/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved.PII S0022-0728(97)00653-0

D. Michael, I. Benjamin / Journal of Electroanalytical Chemistry 450 (1998) 335–345336

Table 1Lennard–Jones parameters, charges and polarizabilities for water and nitrobenzene

Polarizable modelsaNon-polarizable modelsAtom

e/kJ mol−1 Q/au s/nm e/kJ mol−1s/nm Q/au 10−3 a/nm3

0.4184 0.1500 0.3296C (bonded to NO2) 0.37660.3296 0.135 1.5C (ortho) 0.3296 0.4184 −0.050 0.3296 0.3766 −0.045 1.5

0.4184 −0.150C (meta) 0.32960.3296 0.3766 −0.135 1.50.4184 −0.050 0.32960.3296 0.3766C (para) −0.045 1.5

0.3274N 0.4184 0.3000 0.3274 0.3766 0.27 1.40.6276 −0.3000 0.2994O (Nitro) 0.56480.2994 −0.27 0.80.0335 0.1500 0.27440.2744 0.0302H (ortho) 0.135 0.2

0.2744H (meta) 0.0335 0.1000 0.2744 0.0302 0.09 0.2H (para) 0.03350.2744 0.1000 0.2744 0.0302 0.09 0.2

0.6502 −0.82 0.31960.3165 0.6694O (water) −0.73 0.5280.0000 0.41H (water) 0.00000.0000 0.0000 0.365 0.170

a The parameters for water were taken from Ref. [28].

The rest of the paper is organized as follows. InSection 2, we discuss the development of the potentialenergy surfaces for the nitrobenzene and wa-ter�nitrobenzene interactions using both non-polariz-able and polarizable potentials, and we describe thesimulated system and the simulation parameters. InSection 3, we discuss the results, focusing on globalstructural and dynamical features as well as micro-scopic details. Among the properties we discuss are thedensity profiles, the surface roughness and surface ten-sion, the molecular orientation, the surface potentials,the anisotropic diffusion and reorientation dynamics,and the hydrogen bonding. We also examine briefly theeffect that the polarizable liquid models introduce. Weconclude in Section 4 with a summary of the mainresults.

2. Methods

2.1. Potential energy functions

2.1.1. Non-polarizable potentialsFor the intermolecular water potential we use the

flexible simple point charge model [15]. In this model,each water molecule is represented by a Lennard–Jonessphere centered at the position of the oxygen atom.Three fixed point charges at the location of the oxygenand the hydrogens are selected to reproduce a numberof the experimental properties of water. These chargesgive rise to a fixed molecular electric dipole moment ofmbulk

eff =2.27 D at the equilibrium position. The relativelocation of the charges is allowed to change accordingto an intramolecular (vibrational) potential selected toreproduce the IR spectra of the gas phase watermolecule [16]. This results in a slight increase in theeffective dipole moment. The Lennard–Jones parame-

ters and the fixed charges are given in Table 1. Thismodel of water has been used in a large number ofsimulations of bulk and interfacial water [14].

The nitrobenzene intermolecular potential is de-scribed by a central force model. Each atom (includingthe hydrogens) is represented by a Lennard–Jonessphere and a fixed point charge. The magnitude of thefixed charges were initially selected from recent abinitio calculations of the ground state electronic struc-ture of nitrobenzene [17]. These calculations give toobig a dipole moment, and thus the charges were scaleddown to reproduce the experimental dipole moment,while their relative size was kept constant. Final adjust-ments of charges and of the Lennard–Jones parametersto reproduce the enthalpy of vaporization of the liquid(55 kJ mol−1) were made. These parameters are givenin Table 1. The resulting diffusion constant of theliquid (D=1.3×10−9 m2 s−1) and its dielectric con-stant (e=42) are found to be in reasonable agreementwith experimental data [18]. The model nitrobenzenemolecule used in this work is flexible. The intramolecu-lar potential is represented by a sum of the harmonicbond stretching and angle bending, and of the standardtorsional and improper torsional terms. The parametersare taken from the Amber force field [19].

The water–nitrobenzene interaction potential is alsodescribed using Coulomb plus Lennard–Jones termsbetween atomic sites. In principle, the parameters ofthis potential can be selected to reproduce the experi-mental surface tension of the liquid�liquid interface.However, for simplicity we have used the combinationrule for mixtures [20] for the interactions between dif-ferent atoms in molecules that belong to the sameliquid, as well as between molecules that belong to thetwo different liquids. In summary, the total potentialenergy function of the system in this non-polarizablemodel is given by:

D. Michael, I. Benjamin / Journal of Electroanalytical Chemistry 450 (1998) 335–345 337

U=U intra+S(z) %iB j

4eij

��sij

rij

�12

−�sij

rij

�6n+

QiQj

rij

S(z)=1−10z3+15z4−6z5

z= (R2ij−L2

min)/(L2max−L2

min)e ij=eiej, sij= (si+sj)/2

(1)

where Uintra is the total intramolecular (vibrational)potential energy of all the molecules in the system. Thesum in Eq. (1) is over all atomic sites in the systemwhich belong to different molecules (in the same liquidor in different liquids). rij is the distance between atomsi and j in the two molecules. S(z) is a switchingfunction which smoothly decays to zero in the interval[Lmin,Lmax], where Lmax is taken to be half the box sizein the x (or y) directions, and Lmin is typically taken tobe Lmax−1 A. The distance Rij is between two pointsfixed in the molecular frame of the two molecules.These image points can be taken to be the center ofmass, or better, the center of charge (SkQkrk, where thesum is over the atoms in the molecule). In the calcula-tions described below, the large cut-off distance usedmakes the results not sensitive to the exact choice.Thus, for simplicity, we take the image point of waterto be the oxygen atom and the image point of nitroben-zene to be the carbon atom bonded to the nitro group.

2.1.2. Polarizable model potentialsAlthough the model described above is labeled ‘non-

polarizable’, the electronic polarizability of each atomis effectively taken into account by adjusting the magni-tude of the fixed point charges to reproduce the esti-mated dipole moment of the molecule in the condensedphase. For example, the water gas phase electric dipolemoment (1.86 D; 1 D=3.335×10−30 C m) is muchsmaller than the value one calculates from the fixedcharges in the SPC model (2.27 D). This difference isdue to the electronic polarizable nature of each atom,which results in an induced dipole in each watermolecule produced by the dipoles of neighboring watermolecules. This ‘effective polarizability’ approach seemsto be justified for the description of certain aspects ofbulk liquids. However, there is reason to suspect that itmay not be as accurate for the description of theinterfacial properties of liquids. In particular, the effec-tive dipole moment of a water molecule at the interfacebetween water and a liquid of lower polarity (or watervapor) is expected to be lower than the one in bulkwater due to the weaker local electric field. Addition-ally, local density fluctuations will produce fluctuatingelectric fields and thus fluctuating induced dipoles.These fluctuations are neglected in the non-polarizablemodel.

The rigorous way of treating fluctuating induceddipoles due to the electronic structure of each atom is

by using a fully quantum description of the system.This is not feasible for the water�nitrobenzene interface,and an approximate approach must be used. Severalsuch approximate schemes have been suggested [21–23]. We choose to use the method which solves itera-tively the self-consistent equations for the induceddipoles at each step of the molecular dynamics. Briefly,the following term is added to the total potential energyof the system:

Upol= −12 %

k

mk ·Ek (2)

where the sum is over all atomic sites in the system. Ek

is the electric field at the location of site k due to all thefixed charges in the system, and mk is the induced dipolemoment vector at the location k. The induced dipolesare determined by iteratively solving the equation:

mk=ak�

Ek− %k" l

Tkl ·mln

(3)

where ak is the atomic polarizability assigned to site k,and Tkl is the dipole–dipole tensor given by

Tkl=3

r5kl

ÃÁ

Ä

x2kl

xklykl

xklzkl

xklykl

y2kl

yklzkl

xklzkl

yklzkl

z2kl

ÃÂ

Å=

1r3

kl

(4)

More details about the above method can be foundelsewhere [24,25].

In the above approach, one needs to readjust theLennard–Jones parameters and the charges for eachatom, and to assign atomic polarizability to each atom.This has been done for water by many workers[21,22,25–27]. Our polarizable water model is onlyslightly modified from a model discussed by Dang [28].It includes the intramolecular potential of the non-po-larizable model mentioned earlier. For the nitrobenzenepolarizable model, we have kept the same Lennard–Jones size parameters (s) and scaled down the parame-ters e and the charges by a factor of 0.9. The atomicpolarizabilities are selected to approximately reproducethe experimental polarizabilities of nitrobenzene, ben-zene, NO2 and O2. The parameters of the polarizablewater and nitrobenzene models are given in Table 1.

2.2. Simulation parameters

The simulated system includes 986 water moleculesand 252 nitrobenzene molecules in a box of cross-sec-tion 3.129×3.129 nm. The long axis of the box is takento be the Z-axis. The interface between the two liquidsis on average located at Z=0. The total thickness ofthe slab along the Z-axis is approximately 8 nm. How-ever, the length of the simulation box along the Z-axisis chosen to be long enough to avoid a second contactbetween the two liquids. Thus, the geometry of the


system is such that a single liquid�liquid interface is‘sandwiched’ between two bulk liquids, each of which isat equilibrium with its own vapor. Note that althougha periodic boundary condition in the Z-direction isassumed, in practice, during the simulation time-scale,no mixing of the two vapor phases takes place. Otherchoices of simulation geometries and connections withstatistical mechanical ensembles are discussed elsewhere[29].

The system is prepared by first equilibrating the twobulk liquids in separate boxes of the same cross-sectionlisted above, but with a thickness selected according tothe bulk density. The two boxes are joined togetheralong the two equal sized faces. An equilibration periodof 250 ps is followed by a 1.5-ns trajectory, which isused to collect the statistics. All the trajectories aredone at a temperature of T=30093 K using thevelocity version of the Verlet algorithm [30] with a timestep of 1 fs.

3. Results

3.1. Global structural and dynamical aspects

As a standard measure for the average width of theinterface, we consider the density profiles of the twoliquids, shown in Fig. 1 (calculated from a 1.5-nstrajectory). The behavior is very similar to many otherliquid�liquid interfacial systems [31]. There is amonotonic decrease in the density of each liquid as oneapproaches the interface from the respective bulk re-gions. The density of each liquid varies from its bulkvalue to near zero over a di3 stance of 0.7–0.9 nm.Another feature of the density profiles that has beenobserved in a number of simulations is the existence ofdensity oscillations in the bulk region of the organicphase, but few or none in the bulk water region. Theseoscillations could be a result of the relatively smallnumber of nitrobenzene molecules used, or more likely,

Fig. 2. (a) Probability distribution of the position (dotted line) andwidth (solid line) of the water�nitrobenzene interface. The positionand width variables are defined in Eq. (5). (b) Time-dependentaverage (over 5-ps intervals) position of the water molecules mostprotruding into the organic phase.

due to the small surface area of the system [32]. Al-though we have observed that these oscillations dimin-ish as the length of the trajectory increases, asimulation of a system with a much larger surface areawould help to clarify this issue.

A more detailed (although somewhat incomplete)view of the gross structural features of the interface canbe obtained by defining the two dynamical variables:

w(t)=max(ZH2O)−min(ZNB)h(t)=1

2[max(ZH2O)+min(ZNB)](5)

where max(ZH2O) is the location of the water moleculewith the largest value of Z (largest protrusion into theorganic phase) at time t, and similarly, min(ZNB) is theposition of the nitrobenzene molecule with the smallestvalue of Z (largest protrusion into the aqueous phase)at time t. The study of the statistics of these variables asa function of surface area has been found to be veryuseful for the characterization of local surface deforma-tion [33]. The probability distributions P(w) and P(h)are shown in Fig. 2a (each is normalized to unit area).The interface location probability distribution is nearlyGaussian, with a width that can be related to thesurface tension through capillary wave theory [34]. Theinterface width probability distribution peaks around0.38 nm, which can also be related to the surfacetension. Using the relation [31]

s2=kT4pg

lnSj2

b

(6)Fig. 1. Density profiles of water and nitrobenzene at T=300 K. Theliquid�liquid interface is around Z=0.


Fig. 3. Snapshot of two configurations from the MD simulations showing the water molecules in contact with the nitrobenzene. The two framesare taken 15 ps apart. For clarity, the nitrobenzene molecules and the bulk water molecules are not shown.

where s is the average interfacial width, kT has theusual meaning, g is the interfacial tension, S is thesurface area and jb is the bulk correlation length. Thelatter quantity is the distance over which the bulk radialdistribution function decays to 1, which is not well-defined here but can be taken to be around 0.6 nm (thefinal result for the interfacial tension is not sensitive tothe exact value of jb). Using s=0.19 nm (we take halfthe width because of the definition in Eq. (5)), weobtain g=0.03 N m−1. The direct calculation of theinterfacial tension using the virial expression [13,34]gives the value 0.035 N m−1. The experimental value is0.026 N m−1 (estimated from the surface tension of thetwo liquids).

The probability distribution P(w) has a long tail atpositive values which represents configurations in whichwater molecules are extended into the organic phase.These protrusions can be thought of as microscopicdistortions of an otherwise sharp interface. A simpleway to demonstrate the size and time-scale of these‘fingers’ is given in Fig. 2b. In this figure, we show theaverage location of the uppermost water molecule as afunction of time. The average is taken over a timeinterval of 5 ps. At some period of time, the mostprotruding water molecule can go from a distance of0.8 to 0.3 nm over a period of about 15 ps. Snapshotsshowing the water side of the interface with two suchconfigurations are shown in Fig. 3a and b. A quite


Fig. 4. A snapshot of the complete simulated water�nitrobenzene system.

representative snapshot of the whole system is shown inFig. 4. There are corresponding protrusions of ni-trobenzene molecules (but with smaller amplitudes). Anexamination of the water–nitrobenzene interaction en-ergy on the same time-scale as Fig. 2b shows, asexpected, that configurations in which water moleculesare significantly extended into the organic phase arecorrelated with a more negative water–nitrobenzeneinteraction energy than configurations in which theinterface is relatively smooth. Nevertheless, these higharea configurations (high entropy) are associated withhigh free energy because they correspond to less favor-able water–water interactions. Specifically, as will beshown below, water molecules that are extended intothe organic phase are hydrogen-bonded to one or twoother water molecules, compared with an average of 2.5molecules for interfacial water and 3.5 molecules forbulk water.

3.2. Molecular orientations and surface potential

Direct experimental information about molecular or-dering at liquid�liquid interfaces is beginning to be

provided by the polarization dependence of the secondharmonic signal from the interface [35]. This methodhas been mainly applied to the determination of mono-layer and solute orientations [36–39] and, to a lesserextent, to the molecular orientation at the neat liq-uid�liquid interface [40,41].

A number of workers have demonstrated that accu-rate molecular orientations can be obtained by MonteCarlo and molecular dynamics simulations (for a reviewsee Refs. [13,14]). In Figs. 5 and 6 we show the proba-bility distribution functions P(u) for several molecularorientations in the water�nitrobenzene system. Theseprobability distributions are normalized such that& p

0

P(u) sin u du=1

The water molecular orientation is quite similar toother water�organic liquid interfacial systems. On thewater side of the liquid�liquid interface, the waterdipoles tend to lie parallel to the interface, with only aslight tendency to point toward the organic phase. Onthe organic side of the interface, there is a clear ten-dency for the water dipoles to point toward the bulk


Fig. 5. The probability distribution for the angle (u) between theinterface normal and the water dipole (top panel) and for the angle(u) between the interface normal and the water OH bond (bottompanel).

Fig. 7. The electric potential change across the water�nitrobenzeneinterface calculated using the charge density profile. Solid line, totalpotential; dashed line, contribution of the water molecules; dottedline, contribution of the nitrobenzene molecules.

Indirect information about molecular orientations atinterfaces can be obtained from surface potential mea-surements. These measurements are important for eluci-dating the structure of the diffuse ion layer at theelectrochemical liquid�liquid interface [42] because themain contribution to the electric potential changeacross the interface comes from the ionic distribution.At the neat liquid�liquid interface, the surface potentialis generated by specific molecular orientations.

It is straightforward to compute the electrostaticpotential change across the interface using moleculardynamics simulations. One first determines the chargedensity profile rq(z) using the same procedure as isused to compute the density profile. Direct integrationof the one-dimensional Poisson equation gives:

Df(z)=1e0

& z

z%

rq(u)(z−u) du (7)

where z % is a point in the charge-free region, and thepotential change Df is relative to this point. Fig. 7shows the separate contributions of the water and thenitrobenzene, as well as the total potential drop. Thereis an increase in the electrostatic potential contributedby each liquid as one crosses the interface, but thelarger contribution of water results in a total potentialdrop of about 400 mV as one goes from the organicphase into water. This is somewhat larger than onewould expect by considering the dipole orientationmentioned earlier, which suggests a significant contribu-tion of quadrupolar terms. A similar situation exists atthe water liquid�vapor interface [43,44].

3.3. Rotational and translational dynamics

We have already discussed the dynamics associatedwith the liquid surface motion. Here we focus on themolecular reorientation and the self diffusion of eachliquid at the interface compared with the bulk region.

organic phase (top panel of Fig. 5). The water OHvector distribution (bottom panel of Fig. 5) clearlyshows that one OH bond points into the organic phase.It is interesting to compare this behavior with thebehavior of the water dipoles at the water liquid�vaporinterface (the region ZB−3 nm). Here, the waterdipoles also tend to lie parallel to the surface, but witha slight tilt towards the bulk water. The nitrobenzenemolecule also exhibits a preferential orientation. Fig. 6shows that the main axis of the nitrobenzene molecule(as well as the plane of the benzene ring) lies parallel tothe interface plane.

Fig. 6. The probability distribution for the angle (u) between theinterface normal and the main axis of the nitrobenzene molecule.


The single-molecule reorientation correlation func-tion is defined as

Cn(t)=�Pn [r(t+t) · r(t)]� (8)

where r is a unit vector fixed in the molecular frame, Pn

is the nth order Legendre polynome, and the angularbrackets represent an average over all molecules andover all time origins t such that the molecules are in theregion of interest during the time interval [t,t+t ]. Withthe choice of n=1, P1(x)=x, Fig. 8a and b show theresults for the water dipole and the water H–H reorien-tation, respectively, in the bulk (solid line) and at thewater�nitrobenzene interface (dotted line). Fig. 8c showsthe results for the reorientation along the main axis ofthe nitrobenzene molecule.

The water dipole reorientation is the same in the bulkand at the water�nitrobenzene interface, a result that isquite similar to the reorientation dynamics at otherliquid�liquid interfaces and reflects the similarity in thefrictional forces exerted on the rotation of the watermolecule’s main axis. The same is true for the waterH–H vector. The slightly slower reorientation at theinterface is consistent with the stronger water hydrogenbonding at the interface, as will be discussed below. Onthe other hand, one observes a somewhat faster reorien-tation of nitrobenzene at the interface than in bulknitrobenzene. This is probably due to the ability ofwater molecules to adjust rapidly to the slowly movingnitrobenzene molecule and thus to exert less frictionthan that felt by a nitrobenzene molecule in bulknitrobenzene.

Fig. 9. Ensemble average of the mean squared displacement of waterand nitrobenzene molecules in the bulk and at the water�nitrobenzeneinterface. Panel (a) bulk water; panel (b) interfacial water; panel (c)bulk nitrobenzene; and panel (d) interfacial nitrobenzene. In eachpanel, the solid line is for the displacement parallel to the interface(divided by 4), and the dotted line is for the displacement normal tothe interface (divided by 2).

The self diffusion coefficient of each liquid is deter-mined using the center-of-mass distance time correla-tion function [45]. Because of the cylindrical symmetryof the system, one can define two distinct correlations:

R2z (t)=1

2�[z(t+t)−z(t)]2� �t��

DÞt

R2xy(t)=1

4{�[x(t+t)−x(t)]2

+ [y(t+t)−y(t)]2�} �t��

D t (9)

where (x,y,z) is the center of mass position of anindividual molecule, and the ensemble average is overall molecules that are in the region of interest (bulk orinterface) during the time [t,t+t ] interval. The longtime behavior indicated in Eq. (9) enables one to obtainthe lateral and normal diffusion coefficients.

Fig. 9 shows the results for surface and bulk waterand nitrobenzene molecules. In all cases, the linearbehavior at long times shows that we are indeed look-ing at diffusive motion. In the bulk, one must haveDÞ=D , and the small deviation we observe gives anindication of the sampling error, which is mainly due tothe small number of nitrobenzene molecules. The com-puted bulk diffusion coefficients of the two liquids arein reasonable agreement with experiments:Dbulk(H2O)=2.690.1×10−9 m2 s−1 (experiment:2.4×10−9 m2 s−1), Dbulk(C6H5NO2)=1.390.1×10−

9 m2 s−1 (experiment: 1.1×10−9 m2 s−1). Bulk wateris faster than bulk nitrobenzene, reflecting the higherviscosity of the latter liquid. As one moves to theinterface, the diffusion of each liquid becomes an-isotropic, with DÞBD (the motion normal to theinterface is slower than the one parallel to the interfaceplane). Specifically, for each liquid, D (bulk):

Fig. 8. Orientational time correlation functions for (a) water dipole,(b) water H–H vector and (c) nitrobenzene main axis, in the bulk(solid lines) and at the water�nitrobenzene interface (dotted lines) atT=300 K.


D (interface), and it is the perpendicular motion thatslows down. There is some indication that the lateralmotion is slightly faster in both liquids relative to thebulk, but the change is small and nearly within thesampling error. On the other hand, the lateral motionat the liquid�vapor interface of nitrobenzene (and to alesser degree also for water) is significantly faster thanin the bulk (D:4×10−9 m2 s−1).

3.4. Hydrogen bonding

More detailed information about molecular interac-tions at the liquid�liquid interface is provided by ananalysis of the hydrogen bonding between watermolecules at the interface compared with those in thebulk water. We define two water molecules to be hy-drogen bonded if their pair interaction energy is morenegative than −10 kJ mol−1. Other definitions thatare based on geometric criteria give similar results towhat is discussed below. Simulations of a number ofwater�organic liquid interfaces show that the numberof hydrogen bonds per water molecule varies fromabout 3.6 in the bulk to near 2 at the interface. Whenthese numbers are divided by the number of watermolecules in the first coordination shell, one finds thatthe probability that any given hydrogen bond existsincreases from about 0.8 in bulk water to 0.9 at theinterface. Fig. 10 demonstrates that essentially thesame behavior is found at the water�nitrobenzene in-terface.

Fig. 11. The magnitude of the average induced electrical dipolemoment per molecule as a function of the distance normal to theinterface. The solid and dotted lines are for water and nitrobenzenemolecules, respectively.

3.5. Polarizable liquids

To determine the possible effects of polarizablemany-body interactions on the structure and dynamicsof the neat water�nitrobenzene interface, we have usedthe model polarizable potentials described in Section2.1.2 to run a 0.5-ns trajectory. The error tolerance inthe iterative calculation of the induced dipoles is set to0.001 D. Typically, two iterations per time step (1 fs)are sufficient for achieving convergence of the com-puted dipoles.

The main new feature that the polarizable potentialintroduces into the interfacial system is the inhomoge-neous variation in the magnitude of the induceddipoles. This has already been noted by Chang andDang for the water�CCl4 liquid�liquid interface [46],and it is even more dramatic here because of the largepolarizability of the nitrobenzene molecule. Fig. 11shows the magnitude of the induced dipole momentper molecule as a function of the distance along theinterface normal. Near the liquid�liquid interface, thestrong electric fields produced by the fixed charges onthe water molecules and the large polarizability of thenitrobenzene molecule are responsible for the largeincrease in the induced dipole on the interfacial ni-trobenzene molecules. Because of the relatively weakelectric field produced by the nitrobenzene molecule,the induced dipoles on the water molecules are smallerthan in the bulk, and this is quite similar to thesituation at the liquid�vapor interface.

One might expect that this could have an importanteffect on the structure and dynamics of the neat inter-face. However, this is not the case. The variation wefind in a number of properties are well within thetypical statistical errors. As a demonstration of thispoint, we show in Fig. 12 the potential change acrossthe interface calculated by adding the contribution ofthe fixed charge density (Eq. (7), but with the new

Fig. 10. Water hydrogen bond statistics as a function of the distanceZ along the interface normal. Panel (a) shows the number of watermolecules which are hydrogen-bonded to a given water molecule, andin panel (b) this number is normalized by the number of watermolecules in the first coordination shell.


charges), and the contribution due to the normal com-ponent of the induced dipole density (rm):

Dfm(z2)−Dfm(z1)=1e0

& z2

z 1

rm(u %) du % (10)

where rm is calculated by binning the component nor-mal to the interface of the induced dipole moment oneach atom. This contribution is shown in Fig. 12 to-gether with the total potential across the interface, andthis is compared with the non-polarizable results. Thedifference is quite small. This can be traced to the factthat although the magnitude of the induced dipole oneach nitrobenzene molecule is large, the induced dipoleson nearby nitrobenzene and water molecules are ori-ented in such a way as to make the net increase of thedipole density at the interface quite small.

4. Conclusions

We have described the first molecular dynamics simu-lation of the water�nitrobenzene interface—one of themost important electrochemical liquid�liquid interfaces.Calculated properties are in reasonable agreement withavailable experimental data. The simulations provideinsight into the microscopic structure and dynamics ofthis system. The interface is locally sharp but rough.The roughness can mainly be described as protrusionsof water molecules hydrogen-bonded to the bulk water.The length of these protrusions can reach up to 0.8 nmand vary on the tens of ps time scale. Water moleculesare preferentially oriented with their dipoles parallel tothe interface and slightly tilted into the organic phase.One OH bond is pointed into the organic phase. Ni-trobenzene molecules are also oriented with their mainaxis parallel to the interface. The surface potential iscomputed, and a potential drop of 0.4 V is found on

moving from the organic phase to the aqueous phase.The enhancement of interfacial water hydrogen bondsis similar to that of many other water�organic liquidinterfaces. Molecular reorientation dynamics and selfdiffusion are shown to be only mildly modified at theinterface.

The calculations have been repeated using polariz-able many-body potentials for the water and nitroben-zene. Although significant variation in the induceddipole moment is observed across the liquid�liquid in-terface, calculated properties are only mildly affected.An important future issue is to examine how the inclu-sion of the many-body polarizability affects the solva-tion of ions at this interface.

Acknowledgements

This work has been supported by the National Sci-ence Foundation Grant number CHE-9628072.

References

[1] H.H. Girault, D.J. Schiffrin, in: A.J. Bard (Ed.), Electroanalyti-cal Chemistry, Dekker, New York, 1989, p. 1.

[2] P. Vanysek, Electrochim. Acta. 40 (1995) 2841.[3] C. Gavach, B. D’Epenoux, J. Electroanal. Chem. 55 (1974) 59.[4] T. Kakiuchi, M. Senda, Bull. Chem. Soc. Jpn. 56 (1983) 1753.[5] T. Kakiuchi, Y. Teranishi, J. Electroanal. Chem. 396 (1995) 401.[6] Z. Samec, V. Marecek, D. Homolka, J. Electroanal Chem. 187

(1985) 31.[7] H.H. Girault, in: J.O.M. Bockris, B.E. Conway, R.E. White

(Eds.), Modern Aspects of Electrochemistry, vol. 25, PlenumPress, New York, 1993, p. 1.

[8] R. Superfine, J.Y. Huang, Y.R. Shen, Phys. Rev. Lett. 66 (1991)1066.

[9] K.B. Eisenthal, Annu. Rev. Phys. Chem. 43 (1992) 627.[10] R.M. Corn, D.A. Higgins, Chem. Rev. 94 (1994) 107.[11] P.F. Brevet, H.H. Girault, in: A.G. Volkov, D.W. Deamer

(Eds.), Liquid-Liquid Interfaces, CRC Press, Boca Raton, FL,1996, p. 103.

[12] J.C. Conboy, G.L. Richmond, Electrochim. Acta 40 (1995) 2881.[13] A. Pohorille, M.A. Wilson, J. Mol. Struct. (Theochem) 284

(1993) 271.[14] I. Benjamin, Chem. Rev. 96 (1996) 1449.[15] H.J.C. Berendsen, J.P.M. Postma, W.F.V. Gunsteren, J. Her-

mans, in: B. Pullman (Ed.), Intermolecular Forces, D. Reidel,Dordrecht, 1981, p. 331.

[16] K. Kuchitsu, Y. Morino, Bull. Chem. Soc. Jpn. 38 (1965) 814.[17] V.A. Shlyapochnikov, L.S. Khaikin, O.E. Grikina, C.W. Bock,

L.V. Vilkov, J. Mol. Struct. 326 (1994) 1.[18] D.R. Lide, Handbook of Chemistry and Physics, 71st ed., CRC

Press, Boca Raton, FL, 1990.[19] S.J. Weiner, P.A. Kollman, D.T. Nguyen, D.A. Case, J. Comp.

Chem. 7 (1986) 230.[20] J.-P. Hansen, I.R. McDonald, Theory of Simple Liquids, 2nd

ed., Academic Press, London, 1986.[21] M. Sprik, M.L. Klein, J. Chem. Phys. 89 (1988) 7556.[22] J. Caldwell, L.X. Dang, P.A. Kollman, J. Am. Chem. Soc. 112

(1990) 9144.

Fig. 12. The electric potential change across the water�nitrobenzeneinterface, calculated using the polarizable models. Solid line, totalpotential from the non-polarizable model (same as in Fig. 7); dashedline, total potential from the polarizable model; dotted line, contribu-tion of the induced dipoles.


[23] S.W. Rick, S.J. Stuart, B.J. Berne, J. Chem. Phys. 101 (1994)6141.

[24] F.J. Vesely, J. Comput. Phys. 24 (1977) 361.[25] P. Ahlstrom, A. Wallqvist, S. Engstrom, B. Jonsson, Mol. Phys.

68 (1989) 563.[26] A. Wallqvist, Chem. Phys. 148 (1990) 439.[27] G.W. Robinson, S. Singh, M.W. Evans, Water in Biology,

Chemistry and Physics, World Scientific, Singapore, 1996.[28] L.X. Dang, J. Chem. Phys. 97 (1992) 2659.[29] I. Benjamin, in: D.L. Thompson (Ed.), Modern Methods for

Multidimensional Dynamics Computations in Chemistry, WorldScientific, Singapore, 1997.

[30] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids,Clarendon, Oxford, 1987.

[31] I. Benjamin, Annu. Rev. Phys. Chem. 48 (1997) 401.[32] S. Toxvaerd, J. Stecki, J. Chem. Phys. 102 (1995) 7163.[33] I. Benjamin, J. Chem. Phys. 97 (1992) 1432.[34] J.S. Rowlinson, B. Widom, Molecular Theory of Capillarity,

Clarendon, Oxford, 1982.[35] Y.R. Shen, The Principles of Nonlinear Optics, Wiley, New

York, 1984.

[36] T.F. Heinz, H.W.K. Tom, Y.R. Shen, Phys. Rev. A. 28 (1983)1883.

[37] S.G. Grubb, M.W. Kim, T. Raising, Y.R. Shen, Langmuir 4(1988) 452.

[38] A.J. Bell, J.G. Frey, T.J. Vandernoot, J. Chem. Soc. FaradayTrans. 88 (1992) 2027.

[39] D.A. Higgins, R.R. Naujok, R.M. Corn, Chem. Phys. Lett. 213(1993) 485.

[40] J.C. Conboy, J.L. Daschbach, G.L. Richmond, J. Phys. Chem.98 (1994) 9688.

[41] A.A. Tamburello, P. Hebert, P.F. Brevet, H.H. Girault, J.Chem. Soc. Faraday Trans. 91 (1995) 1763.

[42] A. Watts, T.J. VanderNoot, in: A.G. Volkov, D.W. Deamer(Eds.), Liquid-Liquid Interfaces, CRC Press, Boca Raton, FL,1996, p. 77.

[43] M.A. Wilson, A. Pohorille, L.R. Pratt, J. Chem. Phys. 88 (1988)3281.

[44] V.L. Kuzmin, Colloid J. 56 (1994) 593.[45] D. Chandler, Introduction to Modern Statistical Mechanics,

Oxford University Press, Oxford, 1987.[46] T.M. Chang, L.X. Dang, J. Chem. Phys. 104 (1996) 6772.

.

molecular dynamics simulation of the water|nitrobenzene interface

Documents