Further observations on the polarized absorption spectrum of benzene crystals at 2000 Å

The structure of a hard sphere fluid confined by model slit and cylindrical pores is investigated. Results from grand canonical Monte Carlo (GCMC) simulations and from the hypernetted chain/mean spherical approximation (HNC/MSA) equation are reported. GCMC results are compared with those from the HNC/MSA equation, and agreement is good. The effect of confinement on liquids at the same chemical potentials is that the absorption of the hard sphere fluid into the pores decreases with increasing confinement, i.e., when going from planar to cylindrical geometry or by narrowing the pores. The adsorption on the pore walls has, in general, the opposite behaviour. For high bulk concentrations and certain values of cylindrical pore diameter the concentration profile is higher at the centre of the pore than next to the pore wall. A very strong, but continuous, transition occurs in the concentration profile, as a function of the cylinder's diameter. These results could be of some interest in catalysis studies.     

Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral b ₂(V) related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.     

Equation of State for Parallel Rigid Spherocylinders

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto’s method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto’s original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto’s original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

Second-order Percus-Yevick theory for a confined hard-sphere fluid

A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions depend upon the positions of four particles (two hard spheres and two walls treated as giant hard spheres), this is the most demanding application of the second-order theory that has been attempted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations showed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a singlet approximation (in the sense that correlation functions that depend on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard spheres, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.     

Equation of state of a mixture of hard spheres with non-additive diameters

The equation of state of a mixture of hard spheres with non-additive diameters has been found by molecular dynamical simulation. The mixture undergoes a fluid-fluid phase transition at high densities. A perturbation equation of state using a multicomponent reference fluid was found to give good agreement with the simulation results.     

Turbulence temperature spectra: Scaling theory

Grand canonical Monte Carlo, histogram reweighting and finite-size scaling methods are used to determine the phase transitions of bulk (three-dimensional) and confined (quasi-two-dimensional) neutral colloid–polymer systems. The colloids are modeled as hard spheres and the polymer molecules as hard chains, and the only attractive forces are effective ones induced by depletion effects. In contrast to the predictions of mean field and other approximate theories, the nature of the coexistence phases is found to not depend solely on the polymer-to-colloid size ratio, q, but on the colloid diameter, the polymer radius of gyration, and the polymer monomer size. The threshold values of q for the onset of liquid–liquid phase separation differ significantly from earlier predictions, and depend strongly on the dimensionality of space. Extrapolation to the “protein limit” of very small colloid and very long polymer indicates that immiscibility persists at this limit in three dimensions, while it does not always do so for confined systems.     

方阱链流体在固液界面分布的密度泛函理论研究

应用Yethiraj的加权密度近似泛函理论研究平板狭缝中方阱链流体的密度分布，系统的Helm holtz自由能泛函分为理想气体的贡献利剩余贡献两部分，其中剩余贡献部分分别采用刘洪 来等人建立的基于空穴相关函数的方阱链流体状态方程和Gil-Villegas等人提出的统计缔合 流体理论状态方程(SAFT-VR)结合简单加权密度近似计算.考察了不同链长、温度、系统密度 和壁面吸引强度下平板狭缝中方阱链流体的密度分布，并与Monte Carlo(MC)模拟结果进行 了比较.结果表明采用不同的状态方程对密度分布的计算有明显的影响，对于受限于硬壁狭 缝中的方阱链流体，温度和密度比较高时，两种状态方程计算的结果均与MC模拟符合得比较 好，在低温和低密度下效果变差，SAFT-VR方程的计算结果更接近于MC模拟结果.对于受限于 方阱壁狭缝中的方阱链流体，由于系统密度分布的非均匀性加强，采用两种状态方程计算的 结果均与MC模拟结果有一定偏差，寻找更合适的权重函数是进一步改进的关键. 关键词： 密度泛函理论 非均匀流体 密度分布 固液界面 方阱链     

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.     

Modified cell theory: Equation of state for hard spheres

A modified cell theory - introducing a distribution of different cell sizes - is applied to hard spheres. Using a relation developed by Hoover a successful uniform equation of state is given for both the solid and the dense fluid phase.     

Theory of the interface between a classical plasma and a hard wall

The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a “contact theorem”, fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. It is also shown that the interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile.     

Depletion from a hard wall induced by aggregation and gelation

Diffusion-limited cluster aggregation and gelation of hard spheres is simulated using off-lattice Monte Carlo simulations. A comparison is made of the wall-particle correlation function with the particle-particle correlation function over a range of volume fractions, both for the initial system of randomly distributed spheres and for the final gel state. For randomly distributed spheres the correlation functions are compared with theoretical results using the Ornstein-Zernike equation and the Percus-Yevick closure. At high volume fractions (φ > 40%) gelation has little influence on the correlation function, but for φ < 10% it is a universal function of the distance normalized by correlation length (ξ) of the bulk. The width of the depletion layer is about 0.5ξ. The concentration increases as a power law from the wall up to r ≈ ξ, where it reaches a weak maximum before decreasing to the bulk value.     

Entropic wetting and many-body induced layering in a model colloid-polymer mixture

We develop an efficient simulation scheme to study a model suspension of equally sized colloidal hard spheres and nonadsorbing ideal polymer coils, both in bulk and adsorbed against a planar hard wall. The many-body character of the polymer-mediated effective interactions between the colloids yields a bulk phase diagram and adsorption phenomena that differ substantially from those found for pairwise simple fluids; e.g., we find an anomalously large bulk liquid regime and, far from the bulk triple point, three layering transitions in the partial wetting regime prior to a transition to complete wetting by colloidal liquid.     

Probing the phase transition behavior of acetonitrile confined in mesoporous silica by FT Raman spectroscopy

Phase transitions of acetonitrile confined in mesoporous silica SBA‐15 and mesocellular silica foam (MCF) having different pore diameters of 39.0, 39.9, 28.4, 8.7, and 4.6 nm with corresponding pore openings of 20.9, 12.1, 10.0, 8.7, and 4.6 nm were investigated by FT Raman spectroscopy. Melting and freezing temperature depressions were found for acetonitrile confined in mesoporous silica with pore opening sizes of 20.9, 12.1, 10.0 and 8.7 nm. A thermal hysteresis between the cooling and heating cycles was also observed. It appears that the smaller the pore opening, the larger the depression of melting or freezing temperature. Although two solid ( and ) phases exist in bulk acetonitrile, only the liquid →β phase transition was detected for acetonitrile confined in the nanopores of mesoporous silica. The solid‐to‐solid phase transition was not observed. For the mesoporous silica with the smallest pore size of 4.6 nm, neither the liquid nor the transition was observed for the confined acetonitrile. The results demonstrate that FT Raman spectroscopy is a useful technique for studying the phase transition behavior of organic compounds confined in silica‐based hosts. Copyright © 2011 John Wiley & Sons, Ltd.     

Hartree-Fock approximation of bipolaron state in quantum dots and wires

The bipolaronic ground state of two electrons in a spherical quantum dot or a quantum wire with parabolic boundaries is studied in the strong electron-phonon coupling regime. We introduce a variational wave function that can conveniently conform to represent alternative ground state configurations of the two electrons, namely, the bipolaronic bound state, the state of two individual polarons, and two nearby interacting polarons confined by the external potential. In the bipolaron state the electrons are found to be separated by a finite distance about a polaron size. We present the formation and stability criteria of bipolaronic phase in confined media. It is shown that the quantum dot confinement extends the domain of stability of the bipolaronic bound state of two electrons as compared to the bulk geometry, whereas the quantum wire geometry aggravates the formation of stable bipolarons.     

Wannier exciton in microcrystals

A simple variational calculation is presented of the ground state properties of the electron-hole system confined in three-dimensional quantum wells with spherical shape. As the radius of the wall is reduced to a few times the effective Bohr radius of the bulk exciton, the character of the ground state changes abruptly but continuously from that of a Wannier exciton confined as a quasiparticle to that of the electron and the hole confined as individual particles. The optical experiments on CuCl microcrystals in alkali halides and in silicate glasses are briefly discussed.     

Neutron spin echo measurements of monolayer and capillary condensed water in MCM-41 at low temperatures

Neutron spin echo measurements of monolayer and capillary condensed heavy water (D(2)O) confined in MCM-41 C10 (pore diameter 2.10 nm) were performed in a temperature range of 190-298 K. The intermediate scattering functions were analyzed by the Kohlrausch-Williams-Watts stretched exponential function. The relaxation times of confined D(2)O in the capillary condensed state follow remarkably well the Vogel-Fulcher-Tammann equation between 298 and 220 K, whereas below 220 K they show an Arrhenius type behavior. That is, the fragile-to-strong (FTS) dynamic crossover occurs, which has never been seen in experiments on bulk water. On the other hand, for monolayer D(2)O, the FTS dynamic crossover was not observed in the temperature range measured. The FTS dynamic crossover observed in capillary condensed water would take place in the central region of the pore, not near the pore surface. Because the tetrahedral-like water structure in the central region of the pore is more preserved than that near the pore surface, the FTS dynamic crossover would be concerned with the tetrahedral-like water structure.     

Freezing and melting of binary mixtures confined in a nanopore

This paper reports on a Grand Canonical Monte Carlo study of the freezing and melting of Lennard–Jones Ar/Kr mixtures confined in a slit pore composed of two strongly attractive structureless walls. For all molar compositions and temperatures, the pore, which has a width of 1.44?nm, accommodates two contact layers and one inner layer. Different wall/fluid interactions are considered, corresponding to pore walls that have a larger affinity for either Ar or Kr. The solid/liquid phase diagram of the confined mixture is determined and results compared with data for the bulk mixture. The structure of the confined mixture is studied using 2D order parameters and both positional g(r) and bond orientational G₆(r) pair correlation functions. It is found that in the confined solid phase, both the contact and inner layers have a hexagonal crystal structure. It is shown that the freezing temperature of the Ar/Kr confined mixture is higher than the bulk freezing point for all molar compositions. Also, it is found that the freezing temperature becomes larger as the ratio α of the wall/fluid to the fluid/fluid interactions increases, in agreement with previous simulation studies on pure substances confined in nanopores. In the case of pore walls having a stronger affinity for Kr atoms (ε _Ar/W<ε _Kr/W), it is observed that both the contact and inner layers of the confined mixture undergo, at the same temperature, a transition from the liquid phase to the crystal phase. The freezing of Ar/Kr mixtures confined between the walls having a stronger affinity for Ar (ε _Ar/W?>?ε _Kr/W) is more complex: for Kr molar concentration lower than 0.35, we observe the presence of an intermediate state between all layers being 2D hexagonal crystals and all the layers being liquid. This intermediate state consists of a crystalline contact layer and a liquid-like inner layer. It is also shown that the qualitative variations of the increase of freezing temperature with the molar composition depend on the affinity of the pore wall for the different components. These results confirm that, in addition to the parameter α the ratio of the wall/fluid interactions for the two species, η=?_Ar/W/?_Kr/W, is a key variable in determining the freezing and melting behaviour of the confined mixture.     

A new method to obtain the Carnahan–Starling equation and its generalization

We obtain the Carnahan–Starling equation for a system of hard spheres using the Euler method of accelerated series convergence. For this purpose, the virial series is transformed into a new series with coefficients that differ slightly from each other, even when considering the eleven currently known virial coefficients. The method of accelerated convergence was applied to this series; it allowed us to obtain the Carnahan–Starling equation. In this work, this equation is derived for the first time using the method of accelerated convergence. It is generalized to accurately reproduce all of the known virial coefficients and the asymptotic behavior of the free energy at high densities. This also makes it possible to describe a metastable region with a high degree of accuracy and to obtain the equation of state for a homogeneous system of hard spheres with the accuracy of a computer experiment.