Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids

The Prandtl number is evaluated for the three-dimensional hard-sphere and one-component plasma fluids, from the dilute weakly coupled regime up to a dense strongly coupled regime near the fluid-solid phase transition. In both cases, numerical values of order unity are obtained. The Prandtl number increases on approaching the freezing point, where it reaches a quasi-universal value for simple dielectric fluids of about ≃1.7. Relations to two-dimensional fluids are briefly discussed.     

Simple analysis of the thermodynamic properties of the one-component plasma

The one-component plasma model describing a fluid of identically charged point-like ions moving in a uniform continuum background charge density neutralizing the total system is a chemically relevant special case of the primitive models used in theories of electrolyte solutions. It poses, due to its lack of hard-sphere repulsion, an unusual and particularly difficult problem for both the traditional Debye—H$\text{u}$ckel theory and the modern pair correlation theories. We show that the gross error of the Debye—H$\text{u}$ckel predictions for thermodynamic properties at high coupling strength (as compared to Monte Carlo simulation results) can be effectively removed by an extremely simple modification of the theory based on the recognition that the exponential particle density must be truncated close to the ion so as not to become negative.     

Electronic and Ionic Ordering in Condensed Matter Plasmas. (Phase Transitions Induced by Coulomb Interactions)

Abstract

Recent progress in treating phase transitions induced by Coulomb interactions is reviewed. This is done by appealing to simple models, and in particular to the one-component plasma, with its quantum-mechanical counterpart jellium. The relevance of the phase transition, to a body-centred-cubic crystal in the classical one-component plasma, to the freezing of liquid metals Na and K is stressed. By generalizing these arguments to a two-component system, regularities in the freezing of the molten alkali halides are understandable. Sublattice disorder in superionics, driven by Coulomb forces, is then discussed. Finally, the ordering of electrons in jellium, in the limit of complete degeneracy, is considered; evidence being presented for the existence of electron liquids in molten Na and K.     

Freezing line of the Lennard-Jones fluid: a phase switch Monte Carlo study

We report a phase switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard-sphere freezing and builds on a previous PSMC study of the LJ system by Errington [J. Chem. Phys. 120, 3130 (2004)]. The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results of which we compare with a previous Gibbs-Duhem integration study. Additionally, we provide new background material regarding the statistical-mechanical basis of the PSMC method and extensive implementation details.     

Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.     

Structure of spherical electric double layers: a density functional approach

A density functional theory is presented for the structure of spherical electric double layers within the restricted primitive model, where the macroion is considered as a hard sphere having uniform surface charge density, the small ions as charged hard spheres, and the solvent is taken as a dielectric continuum. The theory is partially perturbative as the hard-sphere contribution to the one-particle correlation function is evaluated using suitably averaged weighted density and the ionic part is obtained through a second-order functional Taylor expansion around the uniform fluid. The theory is in quantitative agreement with Monte Carlo simulation for the density profiles and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations. The theory is able to provide interesting insights about the layering and the charge inversion phenomena occurring at the interface.     

烷烃电离能和生成焓的相关性

根据化合物形成过程中价电子能量变化与生成焓之间的关系, 推导出烷烃的生成焓和电离能之间的关系. 以21个烷烃化合物为模型将实验测定的电离能与标准生成焓进行直接关联, 证实了模型方程的适用性, 所得回归方程的相关系数达到0.9999, 估算值与实验值之间的标准偏差仅为0.03 eV. 同时还利用实验测定的标准生成焓对一系列烷烃的电离能作了预测.     

Test of athermal terms of activity coefficient models by Monte Carlo simulation with hard-core models

The infinite dilution activity coefficients of exactly athermal fluids were calculated by Monte Carlo simulation with hard-core models. The hard-core models used in this work were hard-sphere and hard-spherocylinder models. The Widom test particle method was adopted to calculate the residual chemical potentials of solutes in pure solvent and in pure solute solutions. The infinite dilution activity coefficients of solutes were obtained from the residual chemical potentials of solutes. The infinite dilution activity coefficients calculated by Monte Carlo simulation were compared with those of athermal terms in activity coefficient equations. Staverman–Guggenheim equation overestimates the activity coefficients. The deviations of activity coefficients increase with increasing the hard-core volume of solute. Flory–Huggins equation based on molar volume gives good results for the hard-spherocylinder systems. Elbro-FV equation gives good results for both the hard-sphere and hard-spherocylinder systems.     

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.     

Liquid polymorphism and density anomaly in a three-dimensional associating lattice gas

The authors investigate the phase diagram of a three-dimensional associating lattice gas (ALG) model. This model combines orientational icelike interactions and "van der Waals" that might be repulsive, representing, in this case, a penalty for distortion of hydrogen bonds. These interactions can be interpreted as two competing distances, making the connection between this model and continuous isotropic soft-core potentials. The authors present Monte Carlo studies of the ALG model showing the presence of two liquid phases, two critical points, and density anomaly.     

The simulation of metallic hydrogen-helium solutions under the conditions of internal Jupiter regions

Several series of liquid metallic hydrogen, liquid helium, and hydrogen-13 at % helium solution models were constructed by the method of molecular dynamics at state parameters corresponding to three levels of the Jupiter shell. The one-component classical plasma approximation including electronic contributions to energy and pressure was used for hydrogen. Helium was described by the interparticle potential suggested by Aziz et al., and hydrogen-helium pairs, by the Lennard-Jones potential with adjustment parameters (the models contained from 1968 to 2048 particles in the basic cube). The thermodynamic, structural, and diffusion characteristics of solutions and viscosity at 10 000, 15 000, and 20 300 K and molar volumes V of from 0.35 to 1.3 cm³/mol were determined. The mass fraction of the heavy component was found to be approximately 6% at the higher and 14% at the lower level. Hydrogen-helium solutions exhibited very weak positive deviations from ideality. Their viscosity was close to 0.002 Pa s at V = 0.35 cm³/mol and 0.0004 Pa s at V = 1.3 cm³/mol and very weakly depended on temperature at a constant volume. The velocity of sound was 25–50 km/s; it decreased as the density lowered. The form of the partial pair correlation functions was characteristic of metallic liquids and close to the data on the one-component classical plasma at plasma parameter values Γ = 12–16.     

Structure and anomalous solubility for hard spheres in an associating lattice gas model

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.     

Solvation potentials for flexible chain molecules in solution: on the validity of a pairwise decomposition

The effects of a solvent on the conformation of a flexible n-site solute molecule can be described formally in terms of an n-body solvation potential. Given the practical difficulty in computing such multibody potentials, it is common to carry out a pairwise decomposition in which the n-body potential is approximated by a sum of two-body potentials. Here we investigate the validity of this two-site approximation for short interaction-site chain-in-solvent systems. Using exact expressions for the conformation of an isolated chain, we construct a mapping between the full chain-in-solvent system and its solvation potential representation. We present results for both hard-sphere and square-well systems with n=5 that show that the two-site approximation is sufficient to completely capture the effects of an explicit solvent on chain conformation for a wide range of conditions (which include varying the solvent diameter in the hard-sphere system and varying the chain-solvent coupling in the square-well system). In all cases, a set of two-site potentials (one for each distinct site-site pair) is required. We also show that these two-site solvation potentials can be used to accurately compute a multisite intramolecular correlation function.     

Hard sphere perturbation theory for fluids with soft-repulsive-core potentials

The thermodynamic properties of fluids with very soft repulsive-core potentials, resembling those of some liquid metals, are predicted with unprecedented accuracy using a new first-order thermodynamic perturbation theory. This theory is an extension of Mansoori-Canfield/Rasaiah-Stell (MCRS) perturbation theory, obtained by including a configuration integral correction recently identified by Mon, who evaluated it by computer simulation. In this work we derive an analytic expression for Mon's correction in terms of the radial distribution function of the soft-core fluid, g(0)(r), approximated using Lado's self-consistent extension of Weeks-Chandler-Andersen (WCA) theory. Comparisons with WCA and MCRS predictions show that our new extended-MCRS theory outperforms other first-order theories when applied to fluids with very soft inverse-power potentials (n< or =6), and predicts free energies that are within 0.3 kT of simulation results up to the fluid freezing point.     

A small-angle X-ray scattering study of the interactions in concentrated silica colloidal dispersions

The structure factors of colloidal silica dispersions at rather high volume fractions (from 0.055 to 0.22) were measured by small-angle X-ray scattering and fitted with both the equivalent hard-sphere potential model (EHS) and the Hayter-Penfold/Yukawa potential model (HPY). Both of these models described the interactions in these dispersions successfully, and the results were in reasonable agreement. The strength and range of the interaction potentials decreased with increasing particle volume fractions, which suggests shrinkage of the electrical double layer arising from an increase in the counterion concentration in the bulk solution. However, the interactions at the average interparticle separation increased as the volume fraction increased. The interaction ranges (delta) determined by the two models were very similar. Structure factors were also used to determine the size and volume fraction of the particles. The values of the size obtained from the structure factors were slightly larger than those obtained from the form factors; this difference is ascribed to the nonspherical shape and polydispersity of the colloidal particles. The volume fractions measured by these two methods were very similar and are both in good agreement with the independently measured results.     

Voronoi neighbor statistics of hard-disks and hard-spheres

The neighbor distribution in hard-sphere and hard-disk fluids is analyzed using Voronoi tessellation. The statistical measures analyzed are the nth neighbor coordination number (Cn), the nth neighbor distance distribution [fn(r)], and the distribution of the number of Voronoi faces (Pn). These statistics are sensitive indicators of microstructure, and they distinguish thermodynamic and annealed structures. A sharp rise in the hexagon population marks the onset of hard-disk freezing transition, and Cn decreases sharply to the hexagonal lattice values. In hard-disk random structures the pentagon and heptagon populations remain significant even at high volume fraction. In dense hard-sphere (three-dimensional) structures at the freezing transition, C1 is close to 14, instead of the value of 12 expected for a face-centered-cubic lattice. This is found to be because of a topological instability, where a slight perturbation of the positions in the centers of a pair of particles transforms a vertex in the Voronoi polyhedron into a Voronoi surface. We demonstrate that the pair distribution function and the equation-of-state obtained from Voronoi tessellation are equal to those obtained from thermodynamic calculations. In hard-sphere random structures, the dodecahedron population decreases with increasing density. To demonstrate the utility of the neighbor analysis, we estimate the effective hard-sphere diameter of the Lennard-Jones fluid by identifying the diameter of the spheres in the hard-sphere fluid which has C1 equal to that for the Lennard-Jones fluid. The estimates are within 2% deviation from the theoretical results of Barker-Henderson and Weeks-Chandler-Andersen.     

Mean-field cage theory for the freezing of hard-sphere fluids

Using some observations and some mean-field approximations, we develop a mean-field cage theory for the freezing of hard-sphere fluids with v(f) > or =a(d) and obtain the freezing densities as functions of the closest-packing densities and the spatial densities, which are in good agreement with the experimental and simulation results.     

Study of ground state EDA complex formation between [70]fullerene and a series of polynuclear aromatic hydrocarbons.

[70]fullerene has been shown to form 1:1 EDA complex with anthracene, naphthalene, phenanthrene, pyrene and acenaphthene in CCl4 medium. Charge transfer (CT) bands have been detected in all the cases. Isosbestic points have been observed in the cases of phenanthrene and acenaphthene complexes. Ionisation potentials of the donors and CT transition energies have been found to correlate in accordance with Mulliken equation and from this correlation the electron affinity of C70 has been found to be 2.59 eV. Enthalpies and entropies of formation of the complexes have been estimated from the formation constants of the complexes determined spectrophotometrically at three different temperatures.     

Influence of the chain length on the dynamic viscosity at high pressure of some amines: Measurements and comparative study of some models

This work reports the dynamic viscosity data (a total of 72 points) of a series of primary amines which exhibit small association consisting of pentylamine, hexylamine and heptylamine at four temperatures between (293.15 and 353.15) K (every 20 K), and pressures up to 100 MPa (every 20 MPa) which allows to study the influence of the chain length. A falling body viscometer with an uncertainty of ±2% was used to perform these measurements.The variations of dynamic viscosity are discussed with respect to their behavior due to chain length. Six different models, most of them with a physical and theoretical background, are studied in order to investigate how they take the chain length influence and effect into account through their required model parameters. The evaluated models are based on the empirical Vogel–Fulcher–Tamman (VFT) representation (combined with Tait-like equation), the rough hard-sphere scheme, the concept of the free-volume, the friction theory and a correlation derived from molecular dynamics. A recent scaling viscosity model has also been considered. These models need some adjustable parameters except the molecular dynamic correlation which is entirely predictive. Overall a satisfactory representation of the viscosity of these amines is found for the different models within the considered T, p range taking into account their simplicity. Moreover it has been verified that the viscosity is a unique function of TV^γ where the exponent γ is related to the steepness of the intermolecular repulsive potential (T: temperature, and V: specific volume).