Effect of attractive interactions on the structure of polymer melts confined betweensurfaces: A density-functional approachTeena Goel, Chandra N. Patra, Swapan K. Ghosh, and Tulsi Mukherjee Citation: The Journal of Chemical Physics 122, 214910 (2005); doi: 10.1063/1.1924451 View online: http://dx.doi.org/10.1063/1.1924451 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/122/21?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Structure of cylindrical electric double layers: A systematic study by Monte Carlo simulations and densityfunctional theory J. Chem. Phys. 129, 154906 (2008); 10.1063/1.2992525 Effect of attractions on the structure of polymer solutions confined between surfaces: A density functionalapproach J. Chem. Phys. 126, 074905 (2007); 10.1063/1.2567271 Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory J. Chem. Phys. 123, 194902 (2005); 10.1063/1.2117009 An improved density functional description of hard sphere polymer fluids at low density J. Chem. Phys. 119, 1889 (2003); 10.1063/1.1595646 Structure of nonuniform fluid mixtures: A self-consistent density-functional approach J. Chem. Phys. 117, 8933 (2002); 10.1063/1.1514650

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Effect of attractive interactions on the structure of polymer melts confinedbetween surfaces: A density-functional approach

Teena Goel, Chandra N. Patra,a! Swapan K. Ghosh, and Tulsi MukherjeeTheoretical Chemistry Section, Radiation Chemistry and Chemical Dynamics Division, Chemistry Group,Bhabha Atomic Research Centre, Mumbai 400 085, India

sReceived 1 February 2005; accepted 30 March 2005; published online 2 June 2005d

A density-functional theory is presented to study the structure of polymers, having attractiveinteractions, confined between attractive surfaces. The theory treats the ideal-gas free-energyfunctional exactly and uses weighted density approximation for the hard-chain contribution to theexcess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained fromgeneralized Flory equation of state and the attractive interactions are calculated using the directcorrelation function obtained from the polymer reference interaction site model theory along withthe mean spherical approximation closure. The theoretical predictions are found to be in quite goodagreement with the Monte Carlo simulation results for varying densities, chain lengths, and differentinteraction potentials. The results confirm important implications of using different approximationsfor the hard-sphere and attractive interactions. ©2005 American Institute of Physics.fDOI: 10.1063/1.1924451g

I. INTRODUCTION

The structural behavior of polymer melts confined be-tween surfaces has found various practical applications suchas processing, lubrication, thin-film coatings, etc. Variousliquid state methods, such as computer simulation,1–7 integralequation,8 and density-functional theories,9–16have been sys-tematically developed to study these systems. The computersimulations, because of being computationally intensive,have been restricted to simple models like freely jointed hardchains or short chains of more complex models. In that case,semianalytic theories such as integral equation theorysIETdand density-functional theorysDFTd have been successfullydeveloped to study long chains of more realistic models.Among all the methods, the DFT has been found to apply,quite widely, to more complex systems such as polyelectro-lyte solutions,17 electric double layers,18 DNA-salt binding,19

etc.In classical DFT,20 the grand potential functional is mini-

mized with respect to the density profile, at equilibrium den-sity, to get the statistical mechanical properties of the system.The system of polymers confined between surfaces has beenstudied using many density-functional theories differing inapproximations for the ideal and excess free-energy func-tionals and also in methodologies for applying weighted den-sity approximationssWDAd. Thus, Yethiraj and Woodward14

sYWd used a density-functional approach, which treats theideal-gas functional exactly through single-chain simulationand uses weighted density approximation21,22 with a simpleweight function23,24 for excess free-energy functional. Thetheory was later improved by Yethiraj,15 employing a more

sophisticated choice of weight function based on the Curtin–Ashcroft sCAd recipe.25 Both the theories are found to bequite successful, although the latter predicts quite accurateresults on comparing with the simulation data.

There are only few systematic theoretical studies doneon the systems of hard chains hard walls incorporating theeffects of wall-fluid and fluid-fluid attractive interactions.Thus, Patra and Yethiraj26 extended the YW theory to studythe effect of added attractions on the system of fused sphere,freely rotating chain fluids confined between attractive sur-faces, using van der Waals approximation for the attractiveinteractions. They further improved27 the theory by treatingthe attractions through direct correlation functionsDCFd ob-tained from polymer reference interaction site modelsPRISMd theory,28 indicating the importance of using differ-ent approximations for the hard-sphere and attractive inter-actions. The results obtained were quite accurate for a widerange of chain lengths and densities. In our previous work,29

we studied the effect of bulk and wall attractions on thestructure of freely jointed hard-sphere chains at the surfaces,by utilizing the concept of universality of free-energy func-tional to obtain the self-consistent field with Verlet-modifiedbridge function30 and the second-order DCF was calculatedthrough PRISM along with mean spherical approximationsMSAd closure relation. Many-chain Monte Carlo simulationcarried out on such systems gives29 the apparent idea of thedensity profiles and the conformational properties of chainsin the vicinity of the walls.

In this work, we extend the YW theory to study thestructure of freely jointed polymer melts, having attractiveinteractions, confined between surfaces. The ideal-gas free-energy functional is treated exactly via single-chain simula-tion and the excess free-energy functional is obtained usingweighted density approximation with the Curtin–Ashcroftweight functions.25 The thermodynamic properties of the

adAuthor to whom correspondence should be addressed. Present address:Department of Materials Science & Engineering, University of Utah, 122South Central Campus Drive, Room 304, Salt Lake City, Utah 84112.Electronic mail: patra@cluster2.mse.utah.edu.

THE JOURNAL OF CHEMICAL PHYSICS122, 214910s2005d

0021-9606/2005/122~21!/214910/6/$22.50 © 2005 American Institute of Physics122, 214910-1

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hard-chain fluid are calculated from generalized Flory equa-tion of state31 and the attractive interactions are treated usingPRISM theory along with MSA. The theoretical predictionsare compared with that of many-chain simulations and foundto be in quite good agreement. Our present results are foundto be superior than the previously proposed theory,29 whichuses Verlet-modified bridge function to obtain the self-consistent field. The accuracy of the results shows importantimplications of using separate approximations for the hard-sphere and attractive interactions. Furthermore, the incorpo-ration of correlation effects in the attractive contribution andits coupling with the hard-chain contribution are also impor-tant parts of the present work. The rest of this paper is orga-nized as follows. The density-functional theory is describedin Sec. II and tested via comparison with simulations in Sec.III. Some conclusions are presented in Sec. IV.

II. THEORETICAL FORMULATION

A. Molecular model

We study a polymer model consisting ofNm number offreely jointed tangential hard spheres of diameters confinedbetween two infinite parallel walls. The intramolecular po-tential, VsRd, which includes the bonding potential,yb, andthe interaction potential,uffsrd, is given by

VsRd = oi=2

Nm

oj=1

i−1

uffsr ijd + oj=2

Nm

ybsur j − r j−1ud, s1d

whereR denotes the positions of all theNm monomerssorsitesd on a polymer molecule, i.e.,R=hr ij, where r i is theposition of theith bead of the polymer andyb constraintsadjacent beads to a fixed separations.

The fluid-fluid site-site interaction potential between anytwo sites,uffsrd, is the sum of a hard sphere and Yukawapotential and is represented as

buffsrd = ` for r , s, s2d

=− effexpf− ksr/s − 1dg

r/sfor r . s, s3d

wherer is the distance between any two beads,b=1/kBT, kB

is Boltzmann’s constant, andT is the absolute temperature.The attractive interactionsuwfszd, between the perfectly

smooth impenetrable planar walls and the fluid, given byYukawa potential as

buwfszd = − ewffexps− kz/sd + exph− ksH

− zd/sjg for 0 , z, H, s4d

=`, elsewhere, s5d

wherek is the inverse range of the Yukawa potentialsset tok=2.5d, ewf andeff are thesdimensionlessd strengths of wall-fluid and fluid-fluid attractive interactions, andH is the sepa-ration between the walls. We define the length scale by set-ting s=1.

B. Density-functional theory

In DFT, one starts with an approximation for the grandpotential,V, as a functional of the molecular density distri-bution,rMsRd. The density profile and thermodynamic prop-erties of the system are then obtained by minimizingV withrespect torMsRd, at the condition of equilibrium

dVfrMsRdgdrMsRd

= 0. s6d

The grand potential functionalVfrMsRdg is related to theHelmholtz free-energy functional,FfrMsRdg, via a Legendretransform

VfrMsRdg = FfrMsRdg +E fFsRd − mgrMsRddR, s7d

wherem is the chemical potential andFsRd is the externalpotential responsible for the density inhomogeneity.

The free energyFfrMsRdg can be expressed as the sumof an idealFidfrMsRdg and an excess partFexfrsr dg

FfrMsRdg = FidfrMsRdg + Fexfrsr dg, s8d

where the ideal-gas free-energy functionalFid is given by

FidfrMsRdg = kBTE dRrMsRdfln rMsRd − 1g

+E dRVsRdrMsRd, s9d

and VsRd describes the internal potential generated due tointramolecular interactions, as is described in Eq.s1d. Theexcess free-energy term can be shown to be a functional ofthe average density distributionrsr d which is related to thepolymer molecule density distributionrMsRd via

rsr d =E dRoi=1

Nm

dsr − r idrMsRd. s10d

The excess free-energy functionalFexfrsr dg can be usedto define its second-order functional derivative with respectto rsr d in terms of second-order DCF. This excess free-energy functional does not differentiate between differentsites on the molecules, thereby ignoring the end effects andassuming all the sites on the chain identical; thus

d2Fexfrgdrsr ddrsr 8d

= − kBTcsr ,r 8d, s11d

wherecsr ,r 8d is the site-averaged direct correlation function.On integrating the above equation, it gives

Fexfrsr dg = − kBTE drE dr 8rsr drsr 8dE0

1

dl

3E0

l

dl8csr ,r 8;l8d, s12d

where l is a parameter varying between 0 and 1. Thesecond-order DCF can be decomposed into the sole repulsivehard-chain partchcsr ,r 8d and direct attraction part, whichincludes site-site interaction potentialuffsr −r 8d;

214910-2 Goel et al. J. Chem. Phys. 122, 214910 ~2005!

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csr ,r 8d = chcsr ,r 8d − buffsur − r 8ud + Dcsr ,r 8d. s13d

The last term, i.e.,Dc denotes the correlations between thehard-core interactions and attractive interactions. Substitut-ing these terms in Eq.s12d, the excess free-energy functionalcan be rewritten as the sum of three terms

Fexfrsr dg = Fhcfrsr dg + Fattrfrsr dg + Fcorrfrsr dg. s14d

The hard-core interactions are obtained using WDA,whereFhcfrsr dg is expressed as

Fhcfrsr dg =E rsr dfhcsrddr , s15d

where fhcsrd is the excesssover ideal-gasd free-energy persite of the bulk hard-chain fluid evaluated at a site densityrsr d,

rsr d =E rsr 8dwsur − r 8uddr 8, s16d

which is called weighted density, andwsrd is the weightfunction, normalized so thatewsr ddr =1. The excess free-energy per site,fsrd, is obtained from the generalized Florydimer sGFDd equation of state,31 the general form of whichis given by

NbP

r=

1 + ah + bh2 + ch3

s1 − hd3 , s17d

whereh=p /6rs3 is the packing fraction,r is the site den-sity, anda, b, andc are constants.

One of the most suitable choice forwsrd is the simpleweight function23,24which uses Heaviside step functionQsrdand is given as

wsrd =3

4ps3Qss − rd, s18d

where s is the bead diameter on the chain. In the case ofhigh-density polymer melts, where the density profile showsstrong oscillations, the predicted oscillations are generallyshown14 to be way off from the simulation results, thus therearises the need to use a more sophisticated choice of weightfunction. Thus, we also used the Curtin–Ashcroft weightfunction obtained from25

− kBTchcskd = 2fhc8 srdwskd + rfhc9 srdw2skd

+ 2rfhc8 srdwskddwskd

dr, s19d

where primes denote derivatives with respect to density andcarets denote Fourier transforms. The required direct corre-lation function is obtained by solving the nonlinear PRISMintegral equation,

hskd = vskdcskdvskd + r0vskdcskdhskd, s20d

simultaneously with the MSA closure,

hsrd = − 1, r , s,

s21d

csrd = − buffsrd, r . s,

wherevskd is the single-chain structure factor, obtained fromKoyama distribution,32 andhsrd denotes the total correlationfunction. By puttingb=0, the prism equation will give thevalue of chcsrd, which is DCF of a hypothetical fluid inter-acting via only hard-core interactions.

To obtain the correlation term,Fcorrfrsr dg, further ap-proximation is used,27 which is

Dcsr ,r 8d = Dcsur − r 8ud, s22d

whereDcsrd=csrd+buf fsrd−chcsrd andcsrd denotes the totalDCF of Yukawa fluids. Thus the final expression forFcorrfrsr dg is

Fcorrfrsr dg = −kBT

2E drdr 8rsr drsr 8dDcsur − r 8ud. s23d

C. Numerical implementation

The final nonlinear density equation, obtained after mini-mizing V, is expressed as

rsr d =E dRFoi=1

Nm

dsr − r idGrav expF− bVsRd + bm

+ boi=1

Nm

huwfsr id + lsr idjG , s24d

where the effective fieldlsrd is given by

lsrd = fhcfrsr dg +E dr 8rsr 8dwsur − r 8udfhc8 frsr 8dg

− kBTE dr 8rsr 8dfcsur − r 8ud − chcsur − r 8udg, s25d

and fhc8 =dfhc/dr.An ensemble of all possible configurations of a single

chain confined between defined boundaries is generated byMonte Carlo simulation under full intramolecular interac-tions. Assuming that the configurations generated by thesimulation are independent of the effective field, the densityprofile obtained from the single-chain simulation is substi-tuted in the above expression, which incorporates intramo-lecular interactionsVsRd in an effective field due to otherchain molecules and the attractive walls, to get a new densityprofile. Hence, the density profile is calculated by iterativelysolving this equation

rszd =Koi=1

Nm

dsz− zidL . s26d

The average density obtained through single-chain simula-tion is normalized at each iteration so thaterszddz/H=rav isfixed. Final theoretical predictions are compared with thealready available many-chain Monte Carlo simulationresults.29 It should, however, be mentioned at this point thatthe use of a DCF, obtained from the self-consistent PRISMwith the vskd generated through a single-chain simulationwith intramolecular potentials, does not indicate any change

214910-3 Polymer melts confined between surfaces J. Chem. Phys. 122, 214910 ~2005!

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in the density profiles of polymers calculated through thepresent theoretical prescription. The reason can be attributedto approximate nature of the PRISM theory as well as theclosure relation used here.

III. RESULTS AND DISCUSSION

A. Density profiles

The density profile of polymer melts confined betweenhard walls sewf =0.0 in Yukawa wallsd is governed by thecompetition between the configurational and packing en-tropic effects. The loss in the configurational entropy ofchain molecules near the wall promotes the depletion ofchain sites near the surface whereas the preferred packing ofchains against the walls promote their enhancement near thewall. The results of the above-mentioned theoretical formu-lations have been compared with the Monte Carlo simulationdata of Goelet al.29 The present results are also comparedwith the theoretical results of Goelet al., which utilizes theVerlet-modified bridge function to obtain the self-consistentfield. The predictions from the present theory agree quitewell with the simulation results as compared to the earlierVerlet-modified theory. The layering of the chains is alsoquite well reproduced by the present prescription. The oscil-lations in the density profiles predicted from the theory uti-lizing simple weight function are found to be little awaywhen compared with the simulation results. This problem,which may be more prevalent at higher densities, has beenimproved using a better Curtin–Ashcroft weight function.

The density profiles of 10-mer freely jointed hard-sphereathermal chains are shown in Fig. 1 at different packing frac-tionsh=0.1, 0.2, and 0.4. It is seen that at low densities, theconfigurational entropic effects predominate, thus there is adepletion in the layering of chains on the surface. The chainstend to pack against the wall with increasing bulk density inorder to utilize the available free volume most efficiently,hence the layering of chains increases on the surface athigher densities. The predominance of configurational en-tropic effects on increasing chain length, resulting in deple-tion of site density at the surface, can be seen in Fig. 2,

which shows the density profiles for athermal chains of poly-mer melts of packing fractionh=0.2, at different chainlengthsNm=5, 10, and 20.

On introducing the attractions in the wall and/or in bulk,the layering of the chains at the surface is significantly af-fected as is seen in Fig. 3, which shows the density profilesof 10-mer chains ofh=0.2 at varying interaction potentials.There is a net enhancement of chain density at the surface onintroducing the wall attractionssewf =0.2d; provided that thebulk attractions are absent. The chains prefer the bulk whenthe fluid-fluid attractions are introducedseff =0.2d, resultingin depletion of chain density from the walls. The effect offluid-fluid interactions predominates, on introducing bothfluid-fluid and wall-fluid attractions of comparable strengthssewf =eff =0.2d, indicating a depleted chain density near thewalls. The enhancement and/or depletion effects at the sur-face become more predominant when higher interaction po-tentials, viz.sewf =eff =0.5d are applied. Figure 4 depicts thedensity profiles of 10-mers ath=0.2 for higher values of

FIG. 1. Comparison of DFT predictions of this workslined to the theory ofGoel et al. sdashd and to Monte Carlo simulationsssymbolsd sRef. 29d forthe density profiles of athermalfi.e., sewf ,effd=s0.0,0.0dg 10-mers for vari-ous packing fractionssas markedd.

FIG. 2. Comparison of DFT predictions of this workslined to the theory ofGoel et al.sdashd and to computer simulation datassymbolsd sRef. 29d forathermal chains ofh=0.2 and for different chain lengthssas markedd.

FIG. 3. Comparison between DFT predictions of this workslined to thetheory of Goelet al.sdashd and to Monte Carlo simulationsssymbolsd sRef.29d for the density profiles of 10-mers forh=0.2 and for various values ofinteraction potentialssewf ,effd sas markedd.

214910-4 Goel et al. J. Chem. Phys. 122, 214910 ~2005!

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interaction potentials. It is found that the packing effects aremore prevalent than the configurational effects for short-chain high-density polymers even if bulk attractions pre-dominate in the system. Thus, Fig. 5 shows an increasedlayering of chains at the surface for 5-mers havingh=0.4, atdifferent interaction potentials. Similarly, for long-chain low-density polymers, the configurational effects are more impor-tant even in significant wall attractions, resulting in netdepletion at the surface as is seen in Fig. 6, for 20-mers ath=0.1.

The local site density distributions obtained above canbe used to calculate the related thermodynamical quantities,e.g., the adsorption isotherms. Thus, the quantity, surface ex-cessfGsrdg can be defined as33

Gsrbulkd =E0

zbulk

frszd − rbulkg, s27d

wherezbulk is the distance from a single wall whererszd hasattained a constant valuerbulk. Figure 7 depicts the surfaceexcess versus the bulk density for athermal 10-mers. It canbe seen that both the theories are able to predict the negativeadsorption at low bulk density which is the result of thesingle-chain configurational entropic effects. Similar behav-ior has already been observed in simulations as well as inother versions of DFT.33

IV. CONCLUDING REMARKS

The structure of polymer melts confined between sur-faces is studied using a density-functional theory. The poly-mer system is modeled as the pearl necklaces of freelyjointed hard spheres, having attractions, confined betweenattractive surfaces. The theory combines an exact expressionfor the ideal-gas free-energy functional with a weighted den-sity approximation for the hard-chain contribution to the ex-cess free-energy functional. Two different weight functionsare used in the same approach, viz., simple Heaviside stepfunction and Curtin–Ashcroft weight function, in order to see

FIG. 4. Comparison between DFT predictions of this workslined to thetheory of Goelet al.sdashd and to Monte Carlo simulationsssymbolsd sRef.29d for the density profiles of 10-mers forh=0.2 at higher strengths ofinteraction potentialssewf ,effd sas markedd.

FIG. 5. Comparison between DFT predictions of this workslined to thetheory of Goelet al.sdashd and to Monte Carlo simulationsssymbolsd sRef.29d for the density profiles of 5-mers forh=0.4 and for various values ofinteraction potentialssewf ,effd sas markedd.

FIG. 6. Comparison between DFT predictions of this workslined to thetheory of Goelet al.sdashd and to Monte Carlo simulationsssymbolsd sRef.29d for the density profiles of 20-mers forh=0.1 and for various values ofinteraction potentialssewf ,effd sas markedd.

FIG. 7. Comparison between DFT predictions of this workslined to thetheory of Goelet al.sdashd and to Monte Carlo simulationsssymbolsd sRef.29d for the surface excess for athermal 10-mers.

214910-5 Polymer melts confined between surfaces J. Chem. Phys. 122, 214910 ~2005!

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the effect of choosing proper weight function on the densityprofiles. The hard-sphere bulk interactions are obtainedthrough generalized Flory dimer equation of state and theattractive interactions are obtained through the polymer ref-erence interaction site model theory using mean sphericalapproximation. The theoretical predictions are found to be ingood agreement with the many-chain Monte Carlo simula-tion results for varying densities, chain lengths, and differentinteraction potentials. To compare the accuracy of differenttheories, the present results are compared with the theoryproposed in our previous work,29 which uses the Verlet-modified bridge function to calculate the bulk interactions. Itis found that the present results are more accurate than theprevious results, in terms of the layering of chain sites at thesurfaces.

The effect of average density on the density profilesclearly show the interplay of configurational and the packingentropic effects governing the oscillatory behavior of thedensity profiles. The configurational effects predominate onincreasing the chain length, causing depletion of chain lay-ering at the surface. The wall attractions introduced in thesystem cause enhanced chain densities near the wallswhereas the bulk attractions cause depletion of chain densi-ties near the walls. The bulk attractions predominate whenboth wall and the bulk attractive interaction potentials are ofequal strengths. The enhancement and/or depletion effectspredominate when interaction potentials of higher strengthare applied.

The present theory slightly overestimates the layering ofchains near the surface, which becomes prevalent at higherdensities. Although the chain densities are nearly the samenear the surface as predicted through two different weightfunctions, the Curtin–Ashcroft approach shows oscillationsin the density profiles which are quite accurate with thesimulation results as compared to the simple step functionresults. The results of both the approaches are exactly thesame at low densities. The theory uses different approxima-tions for hard-core repulsive interactions and for attractiveYukawa-type interactions, which have important implica-tions in the accuracy of the results. Furthermore, the incor-poration of the coupling between the correlation effects dueto hard-chain and the attractive interactions has importantsignificance. The simplicity of the theoretical approach andaccurate results encourage to further apply the same for more

complex fluids, such as branched polymer behavior on thesurface and to more complex interactions, such as in poly-electrolyte solutions.

ACKNOWLEDGMENTS

One of the authorssC.N.P.d is greatly indebted to Profes-sor Arun Yethiraj for introducing him to the subject of poly-mer theory. He also thanks Professor Yethiraj for helpful dis-cussions during this work.

1Computer Simulations of Polymers, edited by R. J. RoesPrentice-Hall,Englewood Cliffs, NJ, 1991d.

2G. J. Fleer, M. A. Cohen-Stuart, J. M. H. Schetjens, T. Cosgrove, and B.Vincent,Polymers at InterfacessChapman and Hall, London, 1993d.

3R. Dickman and C. K. Hall, J. Chem. Phys.89, 3168s1988d.4S. K. Kumar, M. Vacatello, and D. Y. Yoon, J. Chem. Phys.89, 5206s1988d.

5S. K. Kumar, M. Vacatello, and D. Y. Yoon, Macromolecules23, 2189s1990d.

6A. Yethiraj, Phys. Rev. Lett.74, 2018s1995d.7A. Yethiraj and C. K. Hall, Macromolecules24, 709 s1991d.8A. Yethiraj and C. K. Hall, J. Chem. Phys.95, 3749s1991d.9D. Chandler, J. D. McCoy, and S. J. Singer, J. Chem. Phys.85, 5971s1986d.

10W. E. McMullen and K. F. Freed, J. Chem. Phys.92, 1413s1990d.11C. E. Woodward, J. Chem. Phys.94, 3183s1991d.12E. Kierlik and M. L. Rosinberg, J. Chem. Phys.100, 1716s1994d.13M. S. Wertheim, J. Stat. Phys.42, 477 s1986d.14A. Yethiraj and C. E. Woodward, J. Chem. Phys.102, 5499s1995d.15A. Yethiraj, J. Chem. Phys.109, 3269s1998d.16S. Tripathi and W. G. Chapman, Phys. Rev. Lett.94, 087801s2005d.17C. N. Patra, R. Chang, and A. Yethiraj, J. Phys. Chem. B108, 9126

s2004d.18C. N. Patra and S. K. Ghosh, J. Chem. Phys.117, 8938s2002d.19C. N. Patra and A. Yethiraj, Biophys. J.78, 699 s2000d.20R. Evans, inFundamentals of Inhomogeneous Fluids, edited by D. Hend-

ersonsDekker, New York, 1992d.21A. R. Denton and N. W. Ashcroft, Phys. Rev. A44, 1219s1991d.22P. Tarazona, Phys. Rev. A31, 2672s1985d.23G. Stell, in The Equilibrium Theory of Classical Fluids, edited by H. L.

Frisch and J. L. LebowitzsW. A. Benjamin, New York, 1964d.24S. Nordholm, M. Johnson, and B. C. Freasier, Aust. J. Chem.33, 2139

s1980d.25W. A. Curtin and N. W. Ashcroft, Phys. Rev. A32, 2909s1985d.26C. N. Patra and A. Yethiraj, J. Chem. Phys.112, 1579s2000d.27C. N. Patra and A. Yethiraj, J. Chem. Phys.118, 4702s2003d.28J. G. Curro and K. S. Schweizer, Adv. Polym. Sci.116, 321 s1994d.29T. Goel, C. N. Patra, S. K. Ghosh, and T. Mukherjee, J. Chem. Phys.121,

4865 s2004d.30L. Verlet, Mol. Phys. 41, 183 s1980d.31K. G. Honnell and C. K. Hall, J. Chem. Phys.90, 1841s1989d.32K. G. Honnell, J. G. Curro, and K. S. Schweizer, Macromolecules23,

3496 s1990d.33J. B. Hooper, J. D. McCoy, J. G. Curro, and F. van Swol, J. Chem. Phys.

113, 2021s2000d.

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