Scaled particle theory for hard sphere pairs. II. Numerical analysis

We use the extension of scaled particle theory presented in the accompanying paper [F. H. Stillinger et al., J. Chem. Phys. 125, 204504 (2006)] to calculate numerically the pair correlation function of the hard sphere fluid over the density range 0< or =rhosigma(3)< or =0.96. Comparison with computer simulation results reveals that the new theory is able to capture accurately the fluid's structure across the entire density range examined. The pressure predicted via the virial route is systematically lower than simulation results, while that obtained using the compressibility route is lower than simulation predictions for rhosigma(3)< or =0.67 and higher than simulation predictions for rhosigma(3)> or =0.67. Numerical predictions are also presented for the surface tension and Tolman length of the hard sphere fluid.     

Equation of state for systems of hard non-spherical molecules

The equation of state for systems of hard prolate spherocylinders has been obtained using a Monte Carlo simulation method. The result in the fluid region are compared with the predictions of scaled particle theory, and are found to agree quite well. The equation of state is significantly different from that for hard sphere molecules, and it is concluded that the effects of non-spherical shape must be explicitly dealt with.     

一个新的桥泛函及其在非均一流体密度泛函理论中的应用

基于对OZ 方程的渐近行为与Taylor级数展开的分析，提出了一个新的桥泛函，桥泛函被表达为间接相关函数的函数，Taylor级数展开的重整化导致了一个可调参数，通过将所提出的桥泛函与一个最近提出的密度泛函理论方法学，以及单个硬墙的sum 规则结合，可以确定可调参数.所提出的桥泛函能预言如下非均一流体的密度分布：硬球流体接近一个硬墙与在球形空隙内，Lennard-Jones 流体与缔合硬球流体在两个硬墙之内.理论预言与文献所报导的模拟数据符合很好.     

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.     

A fundamental measure theory for the sticky hard sphere fluid

We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the hard sphere fluid [Y. Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)], is based on a set of weighted densities and an exact result from scaled particle theory (SPT). It is demonstrated that the excess free energy density of the inhomogeneous SHS fluid Φ(SHS) is uniquely defined when (a) it is solely a function of the weighted densities from Kierlik and Rosinberg's version of FMT [E. Kierlik and M. L. Rosinberg, Phys. Rev. A 42, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c) it yields any given direct correlation function (DCF) from the class of generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J. Chem. Phys. 120, 4742 (2004)]. The resulting DFT is shown to be in very good agreement with simulation data. In particular, this FMT yields the correct contact value of the density profiles with no adjustable parameters. Rather than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT produces them. Interestingly, although equivalent to Kierlik and Rosinberg's FMT in the case of hard spheres, the set of weighted densities used for Rosenfeld's original FMT is insufficient for constructing a DFT which yields the SHS DCF.     

Two-body integrals for hard sphere fluid in the first coordination layer

Hard sphere is a commonly used reference fluid, its two-body integrals are of great significance in perturbation theory. However, in order to model the highly orientated strong interactions, such as associating and ionic solvating with perturbation theory, the upper limit of the two-body integral should be restricted within the first coordination layer instead of infinite. In this paper, the two-body integrals confined to the first coordination shell for hard sphere fluid are calculated, which might be useful in representing semi-bonding interaction, such as hydrogen bonding and ionic solvating and pairing.     

Transport properties of the rough hard sphere fluid

Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct extensive benchmark calculations of self-diffusion, shear and bulk viscosity, and thermal conductivity coefficients. As well, the validity of several kinetic theory equations have been examined at various levels of approximation as a function of density and translational-rotational coupling. In particular, expressions from Enskog theory using different numbers of basis sets in the representation of the distribution function were tested. Generally Enskog theory performs well at low density but deviates at larger densities, as expected. The dependence of these expressions upon translational-rotational coupling was also examined. Interestingly, even at low densities, the agreement with simulation results was sometimes not even qualitatively correct. Compared with smooth hard sphere behaviour, the transport coefficients can change significantly due to translational-rotational coupling and this effect becomes stronger the greater the coupling. Overall, the rough hard sphere fluid provides an excellent model for understanding the effects of translational-rotational coupling upon transport coefficients.     

Scaled particle theory for hard sphere pairs. I. Mathematical structure

We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper.     

Does confining the hard-sphere fluid between hard walls change its average properties?

We use grand canonical transition-matrix Monte Carlo and discontinuous molecular dynamics simulations to generate precise thermodynamic and kinetic data for the equilibrium hard-sphere fluid confined between smooth hard walls. These simulations show that the pronounced inhomogeneous structuring of the fluid normal to the confining walls, often the primary focus of density functional theory studies, has a negligible effect on many of its average properties over a surprisingly broad range of conditions. We present one consequence of this insensitivity to confinement: a simple analytical equation relating the average density of the confined fluid to that of the bulk fluid with equal activity. Nontrivial implications of confinement for average fluid properties do emerge in this system, but only when the fluid is both (i) dense and (ii) confined to a gap smaller than approximately three particle diameters. For this limited set of conditions, we find that "in-phase" oscillatory deviations in excess entropy and self-diffusivity (relative to the behavior of the bulk fluid at the same average density) occur as a function of gap size. These paired thermodynamic/kinetic deviations from bulk behavior appear to reflect the geometric packing frustration that arises when the confined space cannot naturally accommodate an integer number of particle layers.     

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.     

A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres

We introduce an expansion of the equation of state for additive hard-sphere mixtures in powers of the total packing fraction with coefficients which depend on a set of weighted densities used in scaled particle theory and fundamental measure theory. We demand that the mixture equation of state recovers the quasiexact Carnahan-Starling [J. Chem. Phys. 51, 635 (1969)] result in the case of a one-component fluid and show from thermodynamic considerations and consistency with an exact scaled particle relation that the first and second orders of the expansion lead unambiguously to the Boublik-Mansoori-Carnahan-Starling-Leland [J. Chem. Phys. 53, 471 (1970); J. Chem. Phys. 54, 1523 (1971)] equation and the extended Carnahan-Starling equation introduced by Santos et al. [Mol. Phys. 96, 1 (1999)]. In the third order of the expansion, our approach allows us to define a new equation of state for hard-sphere mixtures which we find to be more accurate than the former equations when compared to available computer simulation data for binary and ternary mixtures. Using the new mixture equation of state, we calculate expressions for the surface tension and excess adsorption of the one-component fluid at a planar hard wall and compare its predictions to available simulation data.     

Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.     

A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. IV. The short time behavior of the memory function

Using a recently developed diagrammatic formulation of the kinetic theory of fluctuations in liquids, we investigate the short time behavior of the memory function for density fluctuations in a classical atomic fluid. At short times, the memory function has a large contribution that is generated by the repulsive part of the interatomic potential. We introduce a small parameter that is a measure of the softness of the repulsive part of the potential. The diagrams in the memory function that contribute to lowest order in that small parameter are identified and summed to give an explicit expression for the dominant contribution to the memory function at short times. The result leads to a theory for fluids with continuous potentials that is similar to the Enskog theory for hard sphere fluids.     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

极性—非极性双液体系汽液平衡盐效应参数的测定与计算

测定了苯—甲醇— 1_1型电解质 (LiCl、NaBr、KI)、四氯化碳—甲醇— 1_1型电解质 (LiCl、NaBr、KI)两个体系在恒压 ( 1 0 1 .3kPa)条件下的汽液平衡盐效应参数。理论计算以Pierotti的定标粒子理论为基础 ,硬球作用项采用Masterton -Lee方程计算 ,软球作用项采用胡英等人建议的简化的径向分布函数 ,分子间力在Lennard -Jones位能函数基础上计入极性分子间偶极—偶极、偶极—诱导偶极 ,离子与极性分子间的电荷—偶极以及离子与分子间的电荷—诱导偶极的贡献 ,并根据溶剂性质和溶液结构作出一些合理的假设。在此基础上 ,理论计算与实验结果基本相符。     

Structures and dynamics of thermosensitive microgel suspensions studied with three-dimensional cross-correlated light scattering

The structure factors, short- and long-time diffusion coefficients, and hydrodynamic interactions of concentrated poly(N-isopropylacryamide) microgel suspensions were measured with simultaneous static and dynamic three-dimensional cross-correlated light scattering. The data are interpreted through comparison to hard sphere theory. The structure factors are known to be described well by the hard sphere approximation. When the structure factor is fit to an effective hard sphere volume fraction and radius, the diffusion and hydrodynamic interactions are also well described by the hard sphere model. We demonstrate that one single hard sphere volume fraction is sufficient to describe the microgel structures, hydrodynamic interactions, and long- and short-time collective diffusion coefficients. This result is surprising because the particle form of the microgels at these temperatures is not rigid, but rather "fuzzy" spheres with dangling polymer chains.     

Water’s surface tension and cavity thermodynamics

The relationship between cavity thermodynamics in water and air-water surface tension is investigated in the present study. The effective hard sphere diameter of water molecules over a large temperature range is estimated from the experimental air-water surface tension, and cavity thermodynamics is calculated by means of classic scaled particle theory. The work of cavity creation proves to be a decreasing function of temperature and the cavity entropy change is a positive, practically constant, quantity, regardless of the cavity diameter, in marked contrast with well established theoretical and computer simulation results. This finding suggests that the relationship between cavity thermodynamics and surface tension is not a simple matter in the case of water.     

Freezing of hard spheres confined in narrow cylindrical pores

Monte Carlo simulations for the equation of state and phase behavior of hard spheres confined inside very narrow hard tubes are presented. For pores whose radii are greater than 1.1 hard sphere diameters, a sudden change in the density and the microscopic structure of the fluid is neatly observed, indicating the onset of freezing. In the high-density structure the particles rearrange in such a way that groups of three particles fit in sections across the pore.     

The van Hove distribution function for brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self?" component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.     

Partial molar volume of n-alcohols at infinite dilution in water calculated by means of scaled particle theory

The partial molar volume of n-alcohols at infinite dilution in water is smaller than the molar volume in the neat liquid phase. It is shown that the formula for the partial molar volume at infinite dilution obtained from the scaled particle theory equation of state for binary hard sphere mixtures is able to reproduce in a satisfactory manner the experimental data over a large temperature range. This finding implies that the packing effects play the fundamental role in determining the partial molar volume at infinite dilution in water also for solutes, such as n-alcohols, forming H bonds with water molecules. Since the packing effects in water are largely related to the small size of its molecules, the latter feature is the ultimate cause of the decrease in partial molar volume associated with the hydrophobic effect.