Effect of attractive interactions on the structure of polymer melts confined between surfaces: a density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.     

A hybrid method for predicting the microstructure of polymers with complex architecture: combination of single-chain simulation with density functional theory

A hybrid method is proposed to investigate the microstructure of various polymeric fluids confined between two parallel surfaces. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of the Helmholtz energy and a density functional theory (DFT) for the excess part that arises from nonbonded intersegment interactions. The latter consists of a modified fundamental measure theory for excluded-volume effect, the first-order thermodynamics perturbation theory for chain connectivity, and a mean-field approximation for the van der Waals attraction. In comparison with a conventional DFT, the hybrid method avoids calculation of the time-consuming recursive functions and is directly applicable to polymers with arbitrary molecular architecture. Its numerical performance has been validated by extensive comparisons with MC data for the density distributions of totally flexible, semiflexible, or rigid polymers and those with starlike architecture. Special attention is also given to the formation of a nematic monolayer by rigid molecules laying perpendicular to a planar surface. The hybrid method predicts the surface pressure versus surface coverage in good agreement with experiment.     

Isotropic-nematic transition of hard rods immersed in random sphere matrices

Using replica density functional theory and Monte Carlo computer simulations we investigate a system of annealed hard spherocylinders adsorbed in a matrix of quenched hard spheres. Theoretical predictions for the partition coefficient, defined as the ratio of density of rods in the matrix and that in a reservoir, agree well with simulation results. Theory predicts the isotropic-nematic transition to remain first order upon increasing sphere packing fraction, and to shift towards lower rod densities. This scenario is consistent with our simulation results that clearly show a jump in the nematic order parameter upon increasing the rod density at constant matrix packing fraction, corresponding to the isotropic-nematic transition, even for sphere matrix packing fractions < or approximately equal to 0.3.     

Microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces: A hybrid density functional approach

We use a hybrid density functional approach to investigate the microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces, i.e., two hard walls. In the calculation, the rodlike molecule is modeled as a rigid rod linearly connected by the tangent sphere beads. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of Helmholtz energy and a DFT approach for the excess Helmholtz energy. The DFT approach includes a modified fundamental measure theory for the excluded-volume effect, the first order thermodynamics perturbation theory for chain connectivity, and the mean field approximation for the van der Waals attraction. We investigate the effect of the chain length (i.e., aspect ratio) of the rodlike molecule and the separation between two surfaces on the microstructure and self-assembly of inhomogeneous rigid rodlike chains. For the athermal systems, the rodlike chain fluids present a smaller partitioning coefficient compared to the flexible chain fluids. For the thermal systems, lamellar thin films formed by the rigid rodlike molecules perpendicular to the neutral surface are observed. The effects of the head-head interaction and the separation on the self-assembly of the rodlike chain fluids in the slit are investigated.     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

The behavior of fluids near solutes: a density functional theory and computer simulation study

The density distribution of solvent near a solute particle is studied using density functional theory and Monte Carlo simulation. The fluid atoms interact with each other via a hard sphere plus Yukawa potential, and interact with the solute via a hard sphere potential. For small solute sizes, the solvent displays liquidlike ordering near the particle. When the solute become larger, a drying transition is observed at state points near the coexistence conditions of the solvent. These predictions are similar to those of a recent theory for the hydrophobic effect by Lum, Chandler, and Weeks [J. Phys. Chem. 103, 4570 (1999)], although a comparison with simulations shows that the theory of this work is quantitatively more accurate. The connection between density functional methods and the LCW approach is also established.     

Structures and adsorption of binary hard-core Yukawa mixtures in a slitlike pore: grand canonical Monte Carlo simulation and density-functional study

The grand canonical ensemble Monte Carlo simulation and density-functional theory are applied to calculate the structures, local mole fractions, and adsorption isotherms of binary hard-core Yukawa mixtures in a slitlike pore as well as the radial distribution functions of bulk mixtures. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu [J. Chem. Phys. 117, 10156 (2002)] for the hard-core contribution and a corrected mean-field theory for the attractive contribution. A comparison of the theoretical results with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of binary hard-core Yukawa mixtures in the vicinity of contact over the original mean-field theory. Both the present corrected theory and the simulations suggest that depletion and desorption occur at low temperature, and the local segregation can be observed in most cases. For binary mixtures in the hard slitlike pore, the present corrected theory predicts more accurate surface excesses than the original one does, while in the case of the attractive pore, no improvement is found in the prediction of a surface excess of the smaller molecule.     

Structure and adsorption of a hard-core multi-Yukawa fluid confined in a slitlike pore: grand canonical Monte Carlo simulation and density functional study

Because of the increasing interest in studying the phenomenon exhibited by charge-stabilized colloidal suspensions in confining geometry, we present a density functional theory (DFT) for a hard-core multi-Yukawa fluid. The excess Helmholtz free-energy functional is constructed by using the modified fundamental measure theory and Rosenfeld's perturbative method, in which the bulk direct correlation function is obtained from the first-order mean spherical approximation. To validate the established theory, grand canonical ensemble Monte Carlo (GCMC) simulations are carried out to determine the density profiles and surface excesses of multi-Yukawa fluid in a slitlike pore. Comparisons of the theoretical results with the GCMC data suggest that the present DFT gives very accurate density profiles and surface excesses of multi-Yukawa fluid in the slitlike pore as well as the radial distribution functions of the bulk fluid. Both the DFT and the GCMC simulations predict the depletion of the multi-Yukawa fluid near a nonattractive wall, while the mean-field theory fails to describe this depletion in some cases. Because the simple form of the direct correlation function is used, the present DFT is computationally as efficient as the mean-field theory, but reproduces the simulation data much better than the mean-field theory.     

Evaluating the accuracy of a density functional theory of polymer solutions with additive hard sphere diameters

We assess the accuracy of a density functional theory for athermal polymer solutions, consisting of solvent particles with a smaller radius than that of the monomers. The monomer and solvent density profiles in a slit bound by hard, flat, and inert surfaces are compared with those obtained by a Metropolis Monte Carlo simulation. At the relatively high density at which the comparison is performed, there are considerable packing effects at the walls. The density functional theory introduces a simple weight function to describe nonlocal correlations in the fluid. A recent study of surface forces in polymer solutions used a different weighting scheme to that proposed in this article, leading to less accurate results. The implications of the conclusions of that study are discussed.     

The density profile of hard sphere liquid system under gravity

The density profile of hard sphere liquid under gravity is calculated by using density functional theory and Monte Carlo simulation method. The two methods give consistent results for a wide range of parameters. Meanwhile, the validity range of the density functional theory is also established. The results are quite different from the barometric height distribution rho(z)=rho(0) exp(-zL(G)) in almost all cases studied, which indicates that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the crystallizing phenomenon is also predicted at the bottom part of the system under strong gravitation.     

Structure of short polymers at interfaces: a combined simulation and theoretical study

The structure of polymers confined between surfaces is studied using computer simulation and a density functional approach. The simple model system considers the polymer molecule as a pearl necklace of freely jointed hard spheres, having attractions among the beads, confined between attractive surfaces. This approach uses the universality of the free-energy functional to obtain the self-consistent field required in the single chain simulation. The second-order direct correlation function for the uniform bulk fluid required as input has been calculated from the reference interaction site model integral equation theory using mean spherical approximation. The theoretical results are shown to compare well with the Monte Carlo simulation results for varying densities, chain lengths, and with different attractive interaction parameters. The simulation results on the conformational properties give important indications regarding the behavior of chains as they approach the surfaces.     

从统计力学推导流体状态方程——方阱势硬球微扰理论的解析表达式

本文在Zwanzlg微扰理论的基础上, 对二级以上的高级微扰项采用Barker与Henderson的近似方法, 得到一个简单的微扰理论表达式。以硬球势为参考势, 方阱势为微扰势,用一新的级数表达式g(R)=1/ηgj(η/(1-η))~j为径向分布函数, 导出了自由能。内能、比热、压缩因子的级数表达式。为了检验理论的正确性, 取g(R)级数的前四项代入各热力学性质的表达式, 与Monte-Carlo(MC)及分子动力学(MD)计算机模拟数据作了比较, 结果符合较好。     

Structure of inhomogeneous attractive and repulsive hard-core yukawa fluid: grand canonical Monte Carlo simulation and density functional theory study

A density functional theory is proposed for an inhomogeneous hard-core Yukawa (HCY) fluid based on Rosenfeld's perturbative method. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-core repulsion and a quadratic functional Taylor expansion for the long-ranged attractive or repulsive interactions. To test the established theory, grand canonical ensemble Monte Carlo simulations are carried out to simulate the density profiles of attractive and repulsive HCY fluid near a wall. Comparison with the results from the Monte Carlo simulations shows that the present density functional theory gives accurate density profiles for both attractive and repulsive HCY fluid near a wall. Both the present theory and simulations suggest that there is depletion for attractive HCY fluid at low temperature, but no depletion is found for repulsive HCY fluid. The calculated results indicate that the present density functional theory is better than those of the modified version of the Lovett-Mou-Buff-Wertheim and other density functional theories. The present theory is simple in form and computationally efficient. It predicts accurate radial distribution functions of both attractive and repulsive HCY fluid except for the repulsive case at high density, where the theory overestimates the radial distribution function in the vicinity of contact.     

Is perturbation DFT approach applicable to purely repulsive fluids?

A recently proposed third order + second order perturbation density functional theory (DFT) approach is tested for the validity and applicability to purely repulsive model fluids subjected to various external fields. Hard core repulsive Yukawa potential, point particle Yukawa potential, and inverse power potential are employed as sample models. Theoretical DFT results are compared with the corresponding simulation data obtained by grand canonical ensemble Monte Carlo simulation. This comparison indicates that the third order + second order perturbation DFT approach is suitable for these purely repulsive fluids only on condition of high accuracy of the imported bulk second order direct correlation function (DCF). However, in this case the origin of the successful performance somewhat differs from that observed for the mean field approximation applied to van der Waals fluids. In the present case it originates from the observation that the bulk second order DCF is strongly dependent on the density argument for the hard-core part, while for the distances exceeding the core dimension this dependence is considerably weaker.     

Computational methods in coupled electron-ion Monte Carlo simulations.

In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.     

Direct correlation functions of binary mixtures of hard Gaussian overlap molecules

We study the direct correlation function (DCF) of a classical fluid mixture of nonspherical molecules. The components of the mixture are two types of hard ellipsoidal molecules with different elongations, interacting through the hard Gaussian overlap (HGO) model. Two different approaches are used to calculate the DCFs of this fluid, and the results are compared. Here, the Pynn approximation [J. Chem. Phys. 60, 4579 (1974)] is extended to calculate the DCF of the binary mixtures of HGO molecules, then we use a formalism based on the weighted density functional theory introduced by Chamoux and Perera [J. Chem. Phys. 104, 1493 (1996)]. These results are fairly in agreement with each other. The pressure of this system is also calculated using the Fourier zero components of the DCF. The results are in agreement with the Monte Carlo molecular simulation.     

Theory of repulsive charged colloids in slit-pores

Using classical density functional theory (DFT) we analyze the structure of the density profiles and solvation pressures of negatively charged colloids confined in slit pores. The considered model, which was already successfully employed to study a real colloidal (silica) suspension [S. H. L. Klapp et al., Phys. Rev. Lett. 100, 118303 (2008)], involves only the macroions which interact via the effective Derjaguin-Landau-Verwey-Overbeek (DLVO) potential supplemented by a hard core interaction. The solvent enters implicitly via the screening length of the DLVO interaction. The free energy functional describing the colloidal suspension consists of a hard sphere contribution obtained from fundamental measure theory and a long range contribution which is treated using two types of approximations. One of them is the mean field approximation (MFA) and the remaining is based on Rosenfeld's perturbative method for constructing the Helmholtz energy functional. These theoretical calculations are carried out at different bulk densities and wall separations to compare finally to grand canonical Monte Carlo simulations. We also consider the impact of charged walls. Our results show that the perturbative DFT method yields generally qualitatively consistent and, for some systems, also quantitatively reliable results. In MFA, on the other hand, the neglect of charge-induced correlations leads to a breakdown of this approach in a broad range of densities.     

修正的格子空间的密度泛函理论在狭缝中的应用

对描述单原子分子溶液在狭缝中的吸附现象的格子空间的密度泛函理论 (LDFT, lattice density functional theory)进行了修正, 在系统Helmholtz函数的推导中引入了平均场近似校正和Gibbs-Helmholtz方程. 对比Monte Carlo (MC)模拟结果, 发现LDFT理论对吸附分子在狭缝中的吸附浓度分布的预测与模拟数据有较大的偏差, 而修正模型的结果与模拟数据吻合较好 .随着体相浓度的变化,分子在狭缝中具有多级吸附行为, 具体表现为在特定体相浓度区, 对相同的体相浓度,狭缝中同时存在不同的分子浓度分布, 而在Gibbs等温线上可以明显看出多级吸附的性质. 对比修正前后的结果发现,两者均可以预测多级吸附行为, 但仍存在着较大的差异.     

Density functional approach to the adsorption of spherical molecules on a surface modified with attached short chains

A density functional and Monte Carlo simulation study of end-grafted polymers immersed by simple fluids is presented. The polymer molecules are modeled as freely jointed tangent hard spheres with the end segments linked to the surface. The authors analyze an influence of the chain length, the grafting density, and a nature of solvent on the brush structure. Adsorption of hard-sphere mixtures on the modified surface is also discussed. The theory precisely approximates simulation data.