Comparative study of recent phenomenological potentials for the NaCl-type alkali halides derived from elastic and dielectric data

A comparative study is presented of various phenomenological potentials for the NaCl-type alkali halides-based on elastic and dielectric data and on a “combination” of the Born model with a deformable ion mode-reported in recent years by Catlow, Diller and Norgett, by Corish, Parker and Jacobs, by Sangster et al. and by Hardy and Karo. First a critical analysis is made of the models adopted by the various AA and of the procedures to determine the pertinent parameters, emphasizing the different, often crude approximations used and the thermodynamic inconsistencies present in them. The quality of the fits achieved, and of the predictions made with the different models is then discussed. Finally, one compares directly the resulting effective pair potentials for the short-range interactions cation-anion, anion-anion and cation-cation, as well as the various types of parameters (specifically the potential parameters (Born repulsive parameters and van der Waals coefficients) and the shell-model parameters). One finds that the effective short-range potentials for each pair interaction in a given salt reported by the various AA-taken as a whole-have a sizeable indeterminacy, due both to the Born repulsive and vdW contributions.     

二分量胶体悬浮系统的短时间动力学

研究了二分量带电粒子悬浮系统的短时间平动和转动自扩散系数.由于存在静电相互作用和流体力学作用,扩散系数与两种粒子的尺寸比,它们的体积分数,以及所带的有效电荷都有关.计入了流体力学相互作用对扩散张量的二体贡献和首项三体贡献.计算结果表明,流体力学作用对于带电粒子系统的影响要小于它对硬球粒子系统的影响.扩散系数随两种粒子的尺寸比和它们的体积分数变化的关系可以用有效硬球模型来解释,而其定性结果与实验相符合.     

Discreteness inducing coexistence

Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.     

Rotational diffusion of a tracer colloid particle: I. Short time orientational correlations

We extend the generalized Smoluchowski equation to descrbe the diffusional relaxation of position and orientation in a suspension of interacting spherical colloid particles. Considering a tracer particle which interacts with other particles through spherically symmetric pair potentials and with an external field we obtain a cluster expansion representation of the orientational time correlation functions for the tracer. The one and two body cluster contributions are studied explicitly at short times. Working to first order in volume fraction φ we show that the initial slope of the time correlation functions is described by a modified diffusion coefficient D^r = D^r₀(1 −C^rφ) where C^r is a number determined by hydrodynamic and potential interactions. We evaluate C^r numerically for spheres with slip-stick hydrodynamic boundary conditions and also for permeable spheres.     

Topological analysis of charge density in heptasulfur imide (S7NH) from isolated molecule to solid

Intra and intermolecular interactions of heptasulfur imide (S₇NH) are investigated in terms of topological properties analyses, such analyses are applied to both experimental (multipole model) and theoretically calculated (DFT and PDFT calculations) charge densities of the isolated molecule and of the crystal. The same analyses are also applied to a multipole model density obtained from theoretically (PDFT) derived structural amplitudes. The covalent bond character of S-N, N-H and S-S bonds are well described in terms of density, ρ_b, and total energy density, H_b, at the bond critical point r_c, though it is clear that the S-S bonds are weaker shared interactions than those of N-H and S-N bonds. Lone pair electron regions of sulfur and nitrogen atoms are revealed as the local charge concentration site from the Laplacian of charge density. The even weaker intermolecular interactions are well characterized; these include the N-H?S hydrogen bonding, N?S binding interactions and S?S binding interactions. All these intermolecular binding interactions are closed-shell interactions. The Laplacian of charge density demonstrates a directional intermolecular binding interaction. The corresponding intermolecular binding energies are derived by MP2/6-311+G(d,p) calculations. Atomic graph of each atom of the molecule is described in detail by the vertices, edges and faces of the polyhedron around the nucleus to illustrate such directional interactions.     

Diffusion of colloidal particles in swimming suspensions

Previously, we have proposed to analyse the hydrodynamic interactions in a suspension of swimmers with respect to an effective hydrodynamic diffusion coefficient, which only considers the fluctuating motion caused by the stirring of the fluid. In this work, we study the diffusion of colloidal particles immersed in a bath of swimmers. To accurately resolve the many-body hydrodynamic interactions responsible for this diffusion, we use a direct numerical simulation scheme based on the smooth profile method. We consider a squirmer model for the self-propelled swimmers, as it accurately reproduces the flow field generated by real microorganisms, such as bacteria or spermatozoa. We show that the diffusion coefficients of the colloids are comparable with the effective diffusion coefficients of the swimmers, provided that the concentration of swimmers is high enough. At low concentrations, the difference in the way colloids and swimmers react to the flow leads to a reduction in the diffusion coefficient of the colloids. This is clearly seen in the appearance of a negative-correlation region for the velocity-correlation function of the colloids, which does not exist for the swimmers.     

Size and average density spectra of macromolecules obtained from hydrodynamic data

It is proposed to normalize the Mark-Kuhn-Houwink-Sakurada type of equation relating the hydrodynamic characteristics, such as intrinsic viscosity, velocity sedimentation coefficient and translational diffusion coefficient of linear macromolecules to their molecular masses for the values of linear density M_L and the statistical segment length A. When the set of data covering virtually all known experimental information is normalized for M_L, it is presented as a size spectrum of linear polymer molecules. Further normalization for the A value reduces all data to two regions: namely the region exhibiting volume interactions and that showing hydrodynamic draining. For chains without intachain excluded volume effects these results may be reproduced using the Yamakawa-Fujii theory of wormlike cylinders. Data analyzed here cover a range of contour lengths of linear chains varying by three orders of magnitude, with the range of statistical segment lengths varying approximately 500 times. The plot of the dependence of [η]M on M represents the spectrum of average specific volumes occupied by linear and branched macromolecules. Dendrimers and globular proteins for which the volume occupied by the molecule in solution is directly proportional to M have the lowest specific volume. The homologous series of macromolecules in these plots are arranged following their fractal dimensionality.     

Dynamics in dense suspensions of charge-stabilized colloidal particles

The dynamic behavior of charge-stabilized colloidal particles in suspension was studied by photon correlation spectroscopy with coherent X-rays (XPCS). The short-time diffusion coefficient, D(Q) , was measured for volume concentrations φ ⩽ 0.18 and compared to the free particle diffusion constant D₀ and the static structure factor S(Q) . The data show that indirect, hydrodynamic interactions are relevant for the system and hydrodynamic functions were derived. The results are in striking contrast to the predictions of the PA (pairwise-additive approximation) model, but show features typical for a hard-sphere system. The observed mobility is however considerably smaller than the one of a respective hard-sphere system. The hydrodynamic functions can be modelled quantitatively if one allows for an increased effective viscosity relative to the hard-sphere case.     

Fick's law and Fokker-Planck equation in inhomogeneous environments

In inhomogeneous environments, the correct expression of the diffusive flux is not always given by the Fick's law Γ=−D∇n. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck equation (FPE). The microscopic dynamics of each specific system may affect the form of the FPE, either establishing connections between the diffusion and the convection term, as well as providing supplementary terms. In particular, the Fick's form for the diffusion equation may arise only in consequence of a specific kind of microscopic dynamics. It is also shown how, in the presence of sharp inhomogeneities, even the hydrodynamic FPE limit may becomes inaccurate and mask some features of the true solution, as computed from the Master equation.     

Diffusion of spheres in a concentrated suspension II

We evaluate the wavevector dependent (short-time) diffusion coefficient D(k) for spherical particles in suspension, by extending a previous study of selfdiffusion (which corresponds to the case of large k). Our analysis is valid up to high concentrations and fully takes into account the many-body hydrodynamic interactions between an arbitrary number of spheres, as well as the resummed contributions from a special class of correlations. Results obtained which agree well with available experimental data.     

The ferromagnetic phase of quark matter in the framework of one gluon exchange and thermodynamics with the density-temperature-dependent particle mass model

In the current work we examine the possibility of ferromagnetism phase of quark matter by using the one gluon exchange interaction and the thermodynamics with the density-temperature-dependent particle masses as well as the normal thermodynamics (with constant masses). We calculate the free energy per particle of the polarized and unpolarized states to discuss the difference between these two phases at various densities and temperatures. In our calculations we assume that the QCD coupling, α_c, is constant (the simple model) or varies with the temperature and the density (the asymptotic freedom); but we keep α_c less than one, because we intend to use the perturbation method to calculate the exchange energy. We also assume that the up and down quarks are massless and do not interact. Only the strange quarks interact with each other via the one gluon exchange interaction. The free and internal energies as well as the effective masses and the pressure are calculated at different densities and temperatures. The results are discussed and a comparison is made with those of Tatsumi. Finally it is shown that the present models do not predict any transition for the strange quark matter to its ferromagnetic phase.     

Tracer diffusion in the presence of segregating obstacles

Tracer diffusion in an alloy in which the trajectories of one of the species is biased is examined as a model of mass transport with attendant segregation to extended defects (e.g., dynamic strain ageing, grain-boundary segregation). More specifically, we employ Monte Carlo simulation to describe the nonequilibrium diffusive behavior of the components of a two-dimensional lattice gas comprising A and B atoms wherein one of the species (B) interacts with randomly distributed line defects to create equilibrium atmospheres at late times. Various kinetic assumptions and defect densities are explored to highlight the role of B-atom mobility and defect interaction strength on the transport behavior of the A atoms. From the calculated instantaneous diffusivity, several diffusive regimes are then identified and related to evolving segregation profiles and, in particular, to the free area available for diffusion.     

Kinetic phase transitions and tricritical point in an Ising model with competing dynamics

The nonequilibrium phase diagram of an Ising model in which the evolution of the spins reflects diffusion as well as ordering, is determined via dynamic mean-field theory (pair approximation). There is a first-order transition (in zero field) for sufficiently large diffusion rates.     

Simulation studies of bilayers of N2 adsorbed on graphite at 25 and 35 K

Molecular dynamics simulations of bilayers of model nitrogen molecules adsorbed on the graphite basal plane at 25 and 35 K are reported. Systems considered include commensurate bilayers and three uniaxially compressed films, namely, two with different compressions along the X-axis (perpendicular to the herringbone lattice glideline) and one with a compression along the Y-axis, relative to the commensurate spacing. For comparison, commensurate and X-compressed monolayer films were also simulated. Properties simulated include: center-of-mass (COM) molecule-surface densities as a function of separation distance: in-plane COM pair correlation functions; in-plane and out-of-plane distributions of the molecular axis orientations; average potential energies for N₂-surface and for N₂-N₂ interactions; and velocity time-correlation functions for translational and orientational motion perpendicular to and parallel to the surface. These results indicate that the N₂ layers at these temperatures are nearly harmonic oscillator solids, with considerable orientational freedom. Molecules tend to be coplanar with the surface in both layers. The in-plane orientations for the compressed films form a herringbone lattice, in both layers, with variable angles between the molecular axis and the crystal glidliines; the commensurate film does not show herringbone ordering for the potential model used in this work. It is concluded that both the orientational and translational the degrees of freedom strongly coupled, between layers as well as within the layer. It is also shown that the Y-compressed film is unstable and that both layers in the bilayer spontaneously rearrange into a (rotated) uniaxially X-compressed structure.     

On the temperature dependence of the F-coloring efficiency in KCl

A simple model is presented to account for the major features of the temperature dependence of the primary F-coloring efficiency in KCl. It assumes that irradiation creates Frenkel pairs in three basic configurations followed by some correlated diffusion, leading either to annihilation of the pair or formation of a “surviving” primary pair. Steady irradiation as well as fast pulse data are analyzed in terms of the model.     

Infrared spectra and intermolecular potentials of matrix isolated methyl nitrate and methyl-d3-nitrate

The infrared spectra of protonated and deuterated methyl nitrate isolated in a nitrogen matrix have been recorded from 4000 to 250 cm⁻¹. Peaks have been assigned to monomers, pairs, and higher-ordered species by varying the concentration of methyl nitrate in the matrix and also by inducing diffusion of molecules in the matrix. Monomer frequencies were used to calculate the normal coordinates, force constants, and cartesian displacements. Configurations of a pair of methyl nitrate molecules were calculated using an approximate nonbonded atom-atom potential including both Lennard-Jones and electrostatic potentials. The position of minimum energy was established as a function of the distance between molecules as well as angular rotation of the two molecules with respect to one another. Calculations of exciton splittings and shifts for the pair configuration computed to be most stable were evaluated by two site exciton theory and compared to the assigned pair frequencies.     

Flow pattern in a polymer coil placed into a stationary longitudinal flow

The flow pattern of solvent in a polymer coil placed into a stationary flow is examined. In contrast to the previous works, the flow of solvent at large distances from the macromolecule has a constant longitudinal gradient. The calculations are based on a simple model of macromolecule dynamics in flowing solutions proposed earlier. An analysis of the results shows that, in the first-order approximation in the longitudinal velocity at a certain threshold value of the parameter of hydrodynamic interactions P, the coil acquires a hydrodynamic boundary at which the radial component of the flow velocity is zero. The threshold value of P coincides with that for a stationary shear flow, determined earlier. At large P, i.e., large molecular mass, the hydrodynamic boundary of the coil encompasses a major part of the macromolecule, while the longitudinal intrinsic viscosity takes a form analogous to that characteristic of a suspension of solid balls with a radius equal to the radius of inertia of the polymer coil. In the second-order approximation in the flow velocity, the radial component of the flow velocity is nonzero. As a result, the mass transfer of solvent between the regions separated by the hydrodynamic boundary only slows down, without hindering the speedup of reactions by mixing the reagents and macromolecules.     

Brownian particles with long- and short-range interactions

We develop the kinetic theory of Brownian particles with long- and short-range interactions. Since the particles are in contact with a thermal bath fixing the temperature T, they are described by the canonical ensemble. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean field Smoluchowski equation including a mean field potential due to long-range interactions and a generically nonlinear barotropic pressure due to short-range interactions. This equation describes various physical systems such as self-gravitating Brownian particles (Smoluchowski-Poisson system), bacterial populations experiencing chemotaxis (Keller-Segel model) and colloidal particles with capillary interactions. We also take into account the inertia of the particles and derive corresponding kinetic and hydrodynamic equations generalizing the usual Kramers, Jeans, Euler and Cattaneo equations. For each model, we provide the corresponding form of free energy and establish the H-theorem and the virial theorem. Finally, we show that the same hydrodynamic equations are obtained in the context of nonlinear mean field Fokker-Planck equations associated with generalized thermodynamics. However, in that case, the nonlinear pressure is due to the bias in the transition probabilities from one state to the other leading to non-Boltzmannian distributions while in the former case the distribution is Boltzmannian but the nonlinear pressure arises from the two-body correlation function induced by the short-range potential of interaction. As a whole, our paper develops connections between the topics of long-range interactions, short-range interactions, nonlinear mean field Fokker-Planck equations and generalized thermodynamics. It also justifies from a kinetic theory based on microscopic processes, the basic equations that were introduced phenomenologically to describe self-gravitating Brownian particles, chemotaxis and colloidal suspensions with attractive interactions.     

Collective diffusion of Brownian particles with square well and hydrodynamic interaction

The low wavenumber collective diffusion coefficient of a semi-dilute suspension of spherical Brownian particles interacting via square well potential and hydrodynamic pair interaction is considered. The first two nonvanishing terms of an expansion in powers of the wavenumber are calculated. Analytical expressions are found for extremely narrow wells and in the limit of large well diameters.     

Modeling the sound transmission between rooms coupled through partition walls by using a diffusion model

In this paper, a modification of the diffusion model for room acoustics is proposed to account for sound transmission between two rooms, a source room and an adjacent room, which are coupled through a partition wall. A system of two diffusion equations, one for each room, together with a set of two boundary conditions, one for the partition wall and one for the other walls of a room, is obtained and numerically solved. The modified diffusion model is validated by numerical comparisons with the statistical theory for several coupled-room configurations by varying the coupling area surface, the absorption coefficient of each room, and the volume of the adjacent room. An experimental comparison is also carried out for two coupled classrooms. The modified diffusion model results agree very well with both the statistical theory and the experimental data. The diffusion model can then be used as an alternative to the statistical theory, especially when the statistical theory is not applicable, that is, when the reverberant sound field is not diffuse. Moreover, the diffusion model allows the prediction of the spatial distribution of sound energy within each coupled room, while the statistical theory gives only one sound level for each room.