Structural and thermodynamic properties of a multicomponent freely jointed hard sphere multi-Yukawa chain fluid

The product-reactant Ornstein-Zernike approach, represented by the polymer mean-spherical approximation (PMSA), is utilized to describe the structure and thermodynamic properties of the fluid of Yukawa hard sphere chain molecules. An analytical solution of the PMSA for the most general case of the multicomponent freely jointed hard sphere multi-Yukawa chain fluid is presented. As in the case of the regular MSA for the hard sphere Yukawa fluid, the problem is reduced to the solution of a set of nonlinear algebraic equations in the general case, and to a single equation in the case of the factorizable Yukawa potential coefficients. Closed form analytical expressions are presented for the contact values of the monomer-monomer radial distribution function, structure factors, internal energy, Helmholtz free energy, chemical potentials and pressure in terms of the quantities, which follows directly from the PMSA solution. By way of illustration, several different versions of the hard sphere Yukawa chain model are considered, represented by one-Yukawa chains of length m, where m = 2, 4, 8, 16. To validate the accuracy of the present theory, Monte Carlo simulations were carried out and the results are compared systematically with the theoretical results for the structure and thermodynamic properties of the system at hand. In general it is found that the theory performs very well, thus providing an analytical route to the equilibrium properties of a well defined model for chain fluids.     

LJ模型的热力学特性、相平衡及用于真实分子的研究

结合描述硬球固体Helmholtz自由能的自由体积方法与描述硬球固体径向分布函数的拟合的分析表达式与一阶热力学摄动理论,用于描述Lennard Jones(LJ)固体的Helmholtz自由能.按照一个修正的WCA方法将LJ势分为短程排斥部分与长程吸引部分,将文献中一个用于求取液相的等价的硬球直径的简单的迭代法扩展到固相,用于求取固相的等价的硬球直径.在固体Helmholtz自由能的计算中,使用200壳层,以便获得精确的结果.体相LJ液体的热力学特性由一个最近提出的状态方程求取.该方法很好地描述了LJ固体的过量Helmholtz自由能与状态方程,满意地描述了Lennard Jones模型的相平衡;通过选取合适的LJ势参数,能很好地描述了真实分子的融化曲线.     

Weighted-density approaches for polymer structure at solid–polymer interfaces

Weighted-density approximations (WDAs), which are based on the weighting function for the second-order direct correlation functions (DCFs) of the uniform polymeric fluids, have been developed to investigate the structural and thermodynamic properties of polymer melts at interfaces. The advantage is the simplicity of calculation of the weighting functions and their accuracies in the applications. They were applied to study the local density distributions and adsorption isotherms of the freely jointed tangent hard-sphere chain, Yukawa chain, and hard-sphere chain mixture in slit pores. The polymer reference interaction model (PRISM) integral equation with the Percus–Yevick (PY) closure has been used to calculate the second-order DCF of the polymeric fluids required as inputs. The mean-field approximation (MFA) has been used to calculate the weighting function for the attractive contribution of a freely jointed tangent Yukawa chain fluid, having attraction among the beads. The calculated results show that (i) for the freely jointed tangent hard-sphere chain, the present theory is in excellent agreement with the computer simulations over a wide range of chain lengths and bulk densities, (ii) the WDA approach for the attraction provides an accurate method for the local density distributions of a freely jointed tangent Yukawa chain fluid, and that (iii) the present theory also yields a reasonably good result for the structural properties of the freely jointed hard-sphere chain mixtures composed of the chain and monomer.     

扩展桥密度泛函近似于非匀一非硬球流体

为了将非匀一硬球流体的桥密度泛函近似扩展到非匀一非硬球流体,提出了一个理论方案．所得的LJ流体的密度泛函近似计算简单,精确．特别是密度泛函近似仅仅需要共存体相流体的二阶直接相关函数作为输入,因而可以应用于超临界与亚临界温度．所提出的理论方案可以认为是热力学理论的非匀一对应物．     

Structure of a tethered polymer under flow using molecular dynamics and hybrid molecular-continuum simulations

We analyse the structure of a single polymer tethered to a solid surface undergoing a Couette flow. We study the problem using molecular dynamics (MD) and hybrid MD-continuum simulations, wherein the polymer and the surrounding solvent are treated via standard MD, and the solvent flow farther away from the polymer is solved by continuum fluid dynamics (CFD). The polymer represents a freely jointed chain (FJC) and is modelled by Lennard-Jones (LJ) beads interacting through the FENE potential. The solvent (modelled as a LJ fluid) and a weakly attractive wall are treated at the molecular level. At large shear rates the polymer becomes more elongated than predicted by existing theoretical scaling laws. Also, along the normal-to-wall direction the structure observed for the FJC is, surprisingly, very similar to that predicted for a semiflexible chain. Comparison with previous Brownian dynamics simulations (which exclude both solvent and wall potential) indicates that these effects are due to the polymer–solvent and polymer–wall interactions. The hybrid simulations are in perfect agreement with the MD simulations, showing no trace of finite size effects. Importantly, the extra cost required to couple the MD and CFD domains is negligible.     

Vapour pressure of non-polar fluids and their repulsive and attractive contributions

Using a simple equation of state, based on the Weeks-Chandler-Andersen separation of the intermolecular potential, we have obtained the contributions of repulsive and attractive intermolecular forces to the thermodynamic properties of coexisting vapour and liquid phases of a Lennard-Jones (LJ) fluid.

In order to obtain the vapour pressure of real non-polar fluids, we take the LJ fluid as a reference model, and propose a new perturbative contribution, which is dependant on the temperature and on the acentric factor of the substance. Using the complete perturbed equation, we determine the corresponding repulsive and attractive contributions to the vapour pressure of non-polar fluids. The results show that the attractive vapour pressure of non-polar fluids increases with increasing acentric factor, i.e., larger deviation of the molecular shape from spherical symmetry.

This procedure could be extended to separate the repulsive and attractive contributions of the intermolecular forces to other thermodynamic properties of non-polar fluids as well as of polar fluids and fluid mixtures.     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

Phase diagram of highly asymmetric binary mixtures: A study of the role of attractive forces from the effective one-component approach

The phase diagram of an asymmetric solute-solvent mixture is investigated at the level of the effective one-component fluid. The solvent is taken into account by computing the potential of mean force between solute particles at infinite dilution for different models of solvent-solvent and solute-solvent short range interactions. Fluid-fluid and fluid-solid coexistence lines are determined from the free energy in the reference hypernetted chain theory for the fluid branch and from a variational perturbation theory for the solid one. The phase boundaries so determined compare well with recently published Monte Carlo data for mixtures of pure hard spheres. The influence of solute-solvent and solvent-solvent short range attractive forces is then investigated. When compared with pure hard core interactions, these forces are found to produce dramatic changes in the phase diagram, especially on the solvent packing fractions at which a dense fluid of solutes can be stable and on the separation of the fluid-fluid and fluid-solid coexistence lines. Finally, the connection of these results with the behavior of some colloidal suspensions is emphasized.     

Statistical Mechanics Approach for Uniform and Non-uniform Fluid with Hard Core and Interaction Tail

One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.     

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered matrix of hard spheres: attractive wall-hard sphere interaction

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered hard sphere matrix is studied using the inhomogeneous Ornstein-Zernike equation with hypernetted chain closure. In contrast to previous studies, an attractive wall-hard sphere interaction is considered. The adsorption is affected by the attractive interaction both directly by the fluid-wall interaction and indirectly by the change in the structure of the matrix. Density profiles and pair distribution functions are reported. For comparison, grand canonical Monte Carlo simulation data are obtained. The agreement of the theoretical and simulation results is satisfactory but somewhat less pleasing than for the purely repulsive case.     

A molecular dynamics study on the role of attractive and repulsive forces in excess heat capacity at constant volume of dense fluids

The curves of experimental heat capacity against density show a minimum around and below the critical temperature (Tc), but at higher temperatures, this minimum is not observed. In this study, the role of attractive and repulsive forces on excess heat capacity of Lennard–Jones (LJ) dense fluids has been investigated using a molecular dynamics simulation technique. LJ potential is divided into attractive and repulsive parts. From the molecular dynamics calculations, potential energy and heat capacities have been obtained for Argon at temperatures of 100–500?K. The repulsive forces play the main role in causing the heat capacities at temperatures greater than critical point. Around and below the critical temperature, the role of repulsion is dominant at high densities, but attraction has the main role at low densities, consequently at middle densities, a minimum is formed.     

Dense and nearly jammed random packings of freely jointed chains of tangent hard spheres

Dense packings of freely jointed chains of tangent hard spheres are produced by a novel Monte Carlo method. Within statistical uncertainty, chains reach a maximally random jammed (MRJ) state at the same volume fraction as packings of single hard spheres. A structural analysis shows that as the MRJ state is approached (i) the radial distribution function for chains remains distinct from but approaches that of single hard sphere packings quite closely, (ii) chains undergo progressive collapse, and (iii) a small but increasing fraction of sites possess highly ordered first coordination shells.     

Influence of Solvent-Solvent and Solute-Solvent Interaction Properties on Solvent-Mediated Potential

A recently proposed universal calculational recipe for solvent-mediated potential is applied to calculate excess potential of mean force between two large Lennard-Jones (LJ) or hard core attractive Yukawa particles immersed in small LJ solvent bath at supercritical state. Comparison between the present prediction with a hypernetted chain approximation adopted for solute-solute correlation at infinitely dilute limit and existing simulation data shows high accuracy for the region with large separation, and qualitative reliability for the solute particle contact region. The calculational simplicity of the present recipe allows for a detailed investigation on the effect of the solute-solvent and solvent-solvent interaction details on the excess potential of mean force. The resultant conclusion is that gathering of solvent particles near a solute particle leads to repulsive excess PMF, while depletion of solvent particles away from the solute particle leads to attractive excess PMF, and minor change of the solvent-solvent interaction range has large influence on the excess PMF.     

Influence of Solvent-Solvent and Solute-Solvent Interaction Properties on Solvent-Mediated Potential

A recently proposed universal calculational recipe for solvent-mediated potential is applied to calculate excess potential of mean force between two large Lennard-Jones （LJ） or hard core attractive Yukawa particles immersed in small LJ solvent bath at supercritical state. Comparison between the present prediction with a hypernetted chain approximation adopted for solute-solute correlation at infinitely dilute limit and existing simulation data shows high accuracy for the region with large separation, and qualitative reliability for the solute particle contact region. The calculational simplicity of the present recipe allows for a detailed investigation on the effect of the solute-solvent and solvent-solvent interaction details on the excess potential of mean force. The resultant conclusion is that gathering of solvent particles near a solute particle leads to repulsive excess PMF, while depletion of solvent particles away from the solute particle leads to attractive excess PMF, and minor change of the solvent-solvent interaction range has large influence on the excess PMF.     

The effective interactions between colloidal hard spheres in microporous media: Hypernetted chain approximation for replica Ornstein-Zernike equations

In this work, the effective interaction between hard sphere colloidal particles in the presence of a hard sphere solvent, both dispersed either in a disordered quenched matrix of hard spheres or in the random matrix of freely overlapping obstacles is analyzed, using the replica Ornstein-Zernike (ROZ) integral equations. The ROZ equations are supplemented by the hypernetted chain closure. The presence of either disordered or random matrix is manifested in the attractive minima of the colloid-colloid potential of mean force (PMF), in addition to a set of minima due to the presence of solvent species. The effects of matrix microporosity and solvent density on the PMF and the intercolloidal forces are investigated. This project has been supported in part by the National Council for Science and Technology of Mexico (CONACyT) under Grant 25301-E.     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

TPT2 and SAFTD equations of state for mixtures of hard chain copolymers

We present the second-order thermodynamic perturbation theory (TPT2) and the dimer statistical associating fluid theory (SAFTD) equations of state for mixtures consisting of hetero-nuclear hard chain molecules based on extensions of Wertheim's theory for associating fluids. The second-order perturbation theory, TPT2, is based on the hard sphere mixture reference fluid. SAFTD is an extension of TPT1 (= SAFT) and is based on the non-spherical (hard disphere mixture) reference fluid. The TPT2 equation of state requires only the contact values of the hard sphere mixture site-site correlation functions, while the SAFTD equation of state requires the contact values of site-site correlation functions of both hard sphere and hard disphere mixtures. We test several approximations for site-site correlation functions of hard disphere mixtures and use these in the SAFTD equation of state to predict the compressibility factor of copolymers. Since simulation data are available only for a few pure copolymer systems, theoretical predictions are compared with molecular simulation results for the compressibility factor of pure hard chain copolymer systems. Our comparisons show a very good performance of TPT2, which is found to be more accurate than TPT1 (= SAFT). Using a modified Percus-Yevick site-site correlation function SAFTD is found to represent a significant improvement over SAFT and is slightly more accurate than TPT2. Comparison of SAFTD with generalized Flory dimer (GFD) theory shows that both are equivalent at intermediate to high densities for the compressibility factor of copolymer systems investigated here.     

Simulations of stretching a flexible polyelectrolyte with varying charge separation

We calculated the force-extension curves for a flexible polyelectrolyte chain with varying charge separations by performing Monte Carlo simulations of a 5000 bead chain using a screened Coulomb interaction. At all charge separations, the force-extension curves exhibit a Pincus-like scaling regime at intermediate forces and a logarithmic regime at large forces. As the charge separation increases, the Pincus regime shifts to a larger range of forces and the logarithmic regime starts are larger forces. We also found that force-extension curve for the corresponding neutral chain has a logarithmic regime. Decreasing the diameter of bead in the neutral chain simulations removed the logarithmic regime, and the force-extension curve tends to the freely jointed chain limit. This result shows that only excluded volume is required for the high force logarithmic regime to occur.