van der Waals-Tonks-type equations of state for hard-hypersphere fluids in four and five dimensions

Recently, we developed accurate van der Waals-Tonks-type equations of state for hard-disk and hard-sphere fluids by using the known virial coefficients. In this paper, we derive the van der Waals-Tonks-type equations of state. We further apply these equations of state to hard-hypersphere fluids in four and five dimensions. In the low-density fluid regime, these equations of state are in good agreement with the simulation results and existing equations of state.     

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.     

Voronoi cell volume distribution and configurational entropy of hard-spheres

The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume vf, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2gamma) or a three-parameter (3gamma) gamma distribution. The free parameter m in both the 2gamma and 3gamma models is identified as the "regularity factor." The regularity factor is the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of vf. Simulations carried out using a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural inhomogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)] for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system, D, is found necessary for the hard-disk and hard-sphere systems. Thus, for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.     

Structural and optical properties of liquid CO2 for pressures up to 1 TPa

We report on the use of first-principles molecular dynamics calculations to examine properties of liquid carbon dioxide in the pressure-temperature range of 0-1 TPa and 200-100 000 K. The computed equations of state points are used to predict a series of shock Hugoniots with initial starting conditions that are relevant to existing and ongoing shock-wave experiments. A comparison with published measurements up to 70 GPa shows excellent agreement. We find that the liquid undergoes a gradual phase transition along the Hugoniot and have characterized this transition based on changes in bonding and structural properties as well as the conductivity and reflectivity of the fluid.     

Atomistic molecular dynamics simulations of shock compressed quartz

Atomistic non-equilibrium molecular dynamics simulations of shock wave compression of quartz have been performed using the so-called BKS semi-empirical potential of van Beest, Kramer, and van Santen [Phys. Rev. B 43, 5068 (1991)] to construct the Hugoniot of quartz. Our scheme mimics the real world experimental set up by using a flyer-plate impactor to initiate the shock wave and is the first shock wave simulation that uses a geometry optimised system of a polar slab in a three-dimensional system employing periodic boundary conditions. Our scheme also includes the relaxation of the surface dipole in the polar quartz slab which is an essential pre-requisite to a stable simulation. The original BKS potential is unsuited to shock wave calculations and so we propose a simple modification. With this modification, we find that our calculated Hugoniot is in good agreement with experimental shock wave data up to 25 GPa, but significantly diverges beyond this point. We conclude that our modified BKS potential is suitable for quartz under representative pressure conditions of the Earth core, but unsuitable for high-pressure shock wave simulations. We also find that the BKS potential incorrectly prefers the β-quartz phase over the α-quartz phase at zero-temperature, and that there is a β → α phase-transition at 6 GPa.     

A diffuse‐interface modeling for liquid solution–solid gel phase transition of physical hydrogel with nonlinear deformation

A diffuse‐interface model is presented in this paper for simulation of the evolution of phase transition between the liquid solution and solid gel states for physical hydrogel with nonlinear deformation. The present domain covers the gel and solution states as well as a diffuse interface between them. They are indicated by the crosslink density in such a way that the solution phase is identified as the state when the crosslink density is small, while the gel as the state if the crosslink density becomes large. In this work, a novel order parameter is thus defined as the crosslink density, which is homogeneous in each distinct phase and smoothly varies over the interface from one phase to another. In this model, the constitutive equations, imposed on the two distinct phases and the interface, are formulated by the second law of thermodynamics, which are in the same form as those derived by a different approach. The present constitutive equations include a novel Ginzburg–Landau type of free energy with a double‐well profile, which accounts for the effect of crosslink density. The present governing equations include the equilibrium of forces, the conservations of mass and energy, and an additional kinetic equation imposed for phase transition, in which nonlinear deformation is considered. The equilibrium state is investigated numerically, where two stable phases are observed in the free energy profile. As case studies, a spherically symmetrical solution‐gel phase transition is simulated numerically for analysis of the phase transition of physical hydrogel.     

Equations of state for tetra-dimensional hard-sphere fluids

An equation of state, a kind of generalised Padé approximants, first proposed for the hard-sphere fluid in cases of two, three, four and five dimensions is extended for the tetra-dimensional case with new simulation data available. The corresponding equations of state show good to excellent agreement with the above-mentioned data.     

On the relation between virial coefficients and the close-packing of hard disks and hard spheres

The question of whether the known virial coefficients are enough to determine the packing fraction η(∞) at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pade? approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η(∞) is equal to the maximum packing fraction corresponding to an ordered crystalline structure.     

Shock wave propagation in dissociating low-Z liquids: D2

We present direct molecular dynamics simulations of shock wave propagation in liquid deuterium for a wide range of impact velocities. The calculated Hugoniot is in perfect agreement with the gas-gun data as well as with the most recent experimental data. At high impact velocities we observe a smearing of the shock wave front and propagation of fast dissociated molecules well ahead of the compressed region. This smearing occurs due to the fast deuterium dissociation at the shock wave front. The experimental results are discussed in view of this effect.     

Thermophysical properties of liquid carbon dioxide under shock compressions: quantum molecular dynamic simulations

Quantum molecular dynamics were used to calculate the equation of state, electrical, and optical properties of liquid carbon dioxide along the Hugoniot at shock pressures up to 74 GPa. The principal Hugoniot derived from the calculated equation of state is in good agreement with experimental results. Molecular dissociation and recombination are investigated through pair correlation functions and decomposition of carbon dioxide is found to be between 40 and 50 GPa along the Hugoniot, where nonmetal-metal transition is observed. In addition, the optical properties of shock compressed carbon dioxide are also theoretically predicted along the Hugoniot.     

Solution of the compressibility equation of the adhesive hard-sphere model for mixtures

The solution of the generalized equations of Percus and Yevick is obtained for mixtures of molecules interacting via the adhesive hard-sphere potential. It is shown that the possibility of a discontinuous phase or fluid-fluid transition appears only in such binary systems where the adhesion acts between like particles of at least one of the components. The found distribution functions are used to obtain from the compressibility equation the expression for the pressure of a mixture consisting of v components in arbitrary concentration. The pressure, chemical potential and other thermodynamic properties are calculated explicitly in the limit when several components (the solutes) are dilute and one component (the solvent) is in its “liquid” phase. The solubility of substances of small molecules is shown to increase when the temperature T rises. The same regularity is found in the case when the interaction between solvent and solute consists only of a hard-sphere potential. In the general case of the presence of adhesion between solvent and solute molecules and for arbitrary ratio of particles sizes a minimum appears on the solubility cuves versus T. If the attraction is sufficiently big the drop in the solubility may be very sharp and reach the value zero at a certain temperature. The results obtained are qualitatively supported by examples from experiment.     

Equation of state for hard-spheres and excess function calculations of binary liquid mixtures

Using our previously proposed matrix method, an equation of state for hard spheres is presented, which can reproduce the exact values of the first-eight virial coefficients. This equation meets both the low density and the close-packed limits and can predicts the first order fluid–solid phase transition of hard spheres. The results obtained show that the new equation of state can correlate the simulation data of compressibility factor up to high densities better than other equations of state.The new equation of state is extended to mixtures of hard spheres and excess functions of various binary liquid mixtures are calculated using the perturbation theory of Leonard–Henderson–Barker. The results are compared with existing theoretical and experimental data and with those calculated by other hard-sphere equations of state.It is seen that the results obtained by the new equation of state is quite satisfactory compared to other equations of state for the hard spheres and mixture of hard spheres.     

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.     

Application of Restrictive Primitive SAFT Coupled with Different Hard-Sphere Equations to Model Mean Ionic Activity Coefficients of Electrolyte Solutions

In this work, the primitive SAFT equation of state along with three different hard-sphere equations was used to correlate and predict mean ionic activity coefficients of aqueous electrolyte solutions. The mean ionic activity coefficient of aqueous electrolyte solutions was considered as the contribution of hard-sphere and dispersion effects. The Mansoori (M), Wang-Khoshkbarchi-Vera (WKV) and Ghotbi-Vera (GV) hard-sphere equations were applied in correlating the mean ionic activity coefficient of electrolyte solutions. The comparison among above indicated equations was shown. First, vapor pressure and densities of water in the temperature range of 373.15 to 423.15 K was regressed by SAFT equation of state. In the restrictive primitive mean spherical model, ions were hard spheres without any chain structure. Neither association effects were considered in this study. Clearly, in common used five SAFT parameters were decreased to three, which were calculated by using the experimental mean ionic activity coefficients of electrolyte solutions. The comparison among three hard-sphere equations of state approved that Ghotbi-Vera hard-sphere model (GV) correlated the experimental data accurately than the others; two hard-sphere models. The mean ionic activity coefficients of some electrolyte solutions were being predicted by taking the advantage of the regressed values surely, in a wide range of molality.     

Optimal transition paths of stochastic chemical kinetic systems

We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system sizes. The optimal transition paths are identified, in terms of reaction advancement coordinates, to be the most probable paths according to large deviation theory for the limiting dynamics governed by stochastic differential equations. Dynamical equations for the optimal transition paths are obtained using the variational principle. A multiscale minimum action method is proposed as a numerical scheme to solve the optimal transition paths. Applications to the toggle switch model are presented.     

Thermodynamic properties of benzene under shock conditions

We present in this paper a thermodynamic analysis of benzene properties under shock conditions as given by molecular dynamics (MD) simulations. Reactive MD simulations of benzene predict a decomposition threshold corresponding to the flection point on the experimental Hugoniot curve. A polymerlike carbonated structure is observed for pressures above this threshold, but the calculated Hugoniot curve is in disagreement with the experimental one at high pressure. On the contrary, a system consisting of a diamond cluster in hydrogen gas leads to a correct prediction of the pressure on the Hugoniot curves. The central question is then linked to the kinetics of the transition between the polymerlike structure and the diamond cluster.     

线型高聚物分子量分布函数的另一种推导方法

针对自由基聚合歧化终止和偶合终止两类机理生成的线型高聚物,应用统计物理的基本原理,对其分子量分布重新进行了理论推导,其方法简洁清晰,无须任何附加假定,导出FlorySchulz分布.结果有助于从另一方面理解FlorySchulz分布的物理学基础.     

Slow dynamics and re-entrant melting in a polydisperse hard-sphere fluid

Extensive molecular dynamics simulations are performed at 6% polydispersity to investigate the phase diagram of a polydisperse hard-sphere fluid and the dynamical behavior in each phase. As the volume fraction phi is increased, the existence of a supercooled liquid is suggested above phi = 0.5524 by the mean-field analysis proposed recently. The first-order phase transition from supercooled liquid to crystal is then shown to occur around phi = 0.5630. The occurrence of re-entrant melting, a first-order phase transition from crystal to supercooled liquid, is also found around phi = 0.5715. The existence of the glass transition is thus suggested, even in the hard-sphere fluid with small polydispersity.