Transport of matter and energy in a mesoscopic thermo-hydrodynamic approach

We derive a thermo-hydrodynamic theory for particles and energy flow, based on a nonequilibrium grand-canonical ensemble formalism. The time-dependent kinetic coefficients are explicitly given in terms of microscopic mechanical quantities. The time evolution equations describing the coupled flow of energy and particles are derived. The second-rank tensorial fluxes of current of energy and particles present in the nonequilibrium ensemble are nondiagonal. We obtain a generalized Fick's Law, which presents the effect of the energy flow on the particle diffusion equation.     

简并谱的涨落统计特征分析

通过引入权重的方式,使简并谱的积累函数形式上连续递增,并用带权重的多元线性拟合提取涨落谱,由此建立一套适用于分析简并谱的NNS分布、谱刚度、能谱分维函数等涨落统计特征的方法,并具体分析了H2O、NH3及CH4分子的振动能谱进行涨落统计特征分析:发现它们的规则谱和约化非简并谱的涨落统计特征均已非Poigson化;而且约化非简并谱的非Poisson化程度较规则谱明显,即前者的能级斥力较后者大;此外,随着简并度的增加,H2O、NH3、CH4的涨落统计特征由非Poisson型向近Poisson型过渡.     

用可解的六次势研究9-羟基苯嵌萘酮的基态能级劈裂

质子转移（PT）得到了理论和实验方面广泛的研究［1-10],9－羟基苯嵌萘酮（9－HPO）是一个典型体系．在荧光光谱中,观测到氖化的9－HPO的基态能级劈裂,结合其它光谱和X射线衍射数据,提出用四次函数V（R）=A（R4-BR2）作为势能函数［1]．迄今,这一势能函数对应的Schr dinger方程还不能精确求解,且得到的结果与实验值[4]有较大差异．本文用可解的六次势V（R,γ）＝C[R6＋2γR4+(γ2＋μ）R2] 来描述该体系质子转移时的势能面,得到这一势能对应的Schr dinger方程的解析解,再用变分法并结合得到的解析解可计算9－HPO的基态能级劈裂．     

Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects

This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three-dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 571(3) can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono- and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.     

聚合物-溶剂相互作用参数研究

根据液体混合的通用Gibbs自由能模型,导得了一个能满意地描述高分子溶液中聚合物-溶剂相互作用参数随浓度和温度变化的方程。它由焓贡献和熵贡献两部分组成,在形式上与Koningsveld-Kleintijen关系式相同,但它的熵贡献是浓度的复杂函数,而不象Koningsveld建议的是一个随意的常数。该方程能够很好地解释高分子溶液的某些特性。     

Calculation of diffusion impedance in the terms of locally nonequilibrium diffusion

An equation for diffusion impedance is derived in the terms of the lattice diffusion model based on the assumption as to the local nonequilibrium distribution of diffusing particles across the sites of different types. This equation is valid at low lattice occupation. Unlike the multiple trapping model, all site types are interpreted symmetrically. In the boundary condition, it is assumed that there is a unique relationship between the electric potential variation, on one side of the interface and variation of the generalized particle activity on the other side.     

Two-dimensional colloidal crystal in nonlinear Poisson-Boltzmann model

A two-dimensional hexagonal colloidal crystal of charged particles obeying the general nonlinear Poisson-Boltzmann equation is studied by the numerical method. Force constants and pressure in a system, as well as elastic constants of a crystal, are calculated on the basis of the solutions of the equation. Calculation procedures are described briefly and numerical data are reported. The effect of nonlinearity of charge distribution on the manifestation of many-body interactions and on the validity of the approximation of interaction of the nearest neighbors is considered.     

Distribution of colloidal particles in a spherical cavity

The spatial distribution of colloidal particles in a confined space is frequently a key issue to many phenomena of practical significance. This problem is investigated by considering the distribution of colloidal particles in a spherical cavity under the conditions of relatively large cavities, low cavity and colloidal particles potentials, and low monovalent electrolyte and colloidal concentrations. The analytical expression for the particle-cavity pair interaction energy is derived under various surface conditions. The results obtained are used to evaluate the direct correlation functions in the hypernetted chain approximation employed for the resolution of an Ornstein-Zernike equation. For a fixed particle number concentration at the center of a cavity, we make the following conclusions: (i) the spatial distribution of particles increases in an oscillatory manner with the distance away from the cavity surface, (ii) increasing the particle-cavity pair interaction energy has the effect of reducing the free space of particles inside a cavity, and (iii) the greater the pair interaction energy between two particles, the higher the average concentration of particles.     

Quantum dynamics in continuum for proton transport--generalized correlation

As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and boundary method, the Dirichlet to Neumann mapping, Gummel iteration, and Krylov space techniques, is employed to improve the accuracy, efficiency, and robustness of model simulations. Finally, comparisons between the present model predictions and experimental data of current-voltage curves, as well as current-concentration curves of the Gramicidin A channel, verify our new model.     

Interaction Between Fine Diamond Particles in Electroless Nickel Solutions

The classical DLVO theory was applied to calculate the interaction potential energy between diamond particles in electroless nickel (EN) solution and its diluted solutions with deionized (DI) water to predict their dispersion and sedimentation rates. Sedimentation tests and particle size distribution for all particle dispersions were measured to verify the DLVO calculations. Results show that the curve features of interaction potential energy vary with the dilution ratio of dispersions. The energy barrier in the curves requires the minimum 1:100 dilution of the EN solution. A sufficient energy barrier results in an extremely slow sedimentation rate of particles by keeping them separate. Otherwise, they settle down quickly due to the agglomeration resulting from their attractive forces at any separation distance. The prediction results are in good agreement with the measurement of sedimentation tests and particle size distribution. The classical DLVO theory is applicable to the field of electroless plating.     

Preparation and Properties of Hybrid Nanostructures of Zinc Tetraphenylporphyrinate and an Amphiphilic Copolymer of <Emphasis Type="Italic">N</Emphasis>-Vinylpyrrolidone in a Neutral Aqueous Buffer Solution

Water-soluble forms of a hydrophobic dye, zinc tetraphenylporphyrinate, are obtained via its solubilization by polymer particles of the micellar type formed by a copolymer of N-vinylpyrrolidone with triethylene glycol dimethacrylate. Hydrodynamic radii R_h and the size distribution of such particles in neutral aqueous buffer solutions are determined via dynamic light scattering. The electrochemical activity of the encapsulated dye is found, and its photochemical properties (absorption and fluorescence) are studied.     

A study of the collisional fragmentation problem using the Gamma distribution approximation

The nonlinear fragmentation population balance formulation has been elevated in recent years from a prototype for studying nonlinear integro-differential equations to a vehicle for analyzing and understanding several physicochemical processes of technological interest. The so-called pure collisional fragmentation, which is the particular mode of nonlinear fragmentation induced by collisions between particles, is studied here. It is shown that the corresponding population balance equation admits large time asymptotic (self-similarity) solutions for homogeneous fragmentation and collision functions (kernels). The self-similar solutions are given in closed form for some simple kernels. Based on the shape of the self-similar solutions the method of moments with Gamma distribution approximation is employed for transient solution (from initial state to establishment of the asymptotic shape) of the collisional fragmentation equation. These solutions are presented for several sets of parameters and their behavior is discussed rather extensively. The present study is similar to the one has already been performed for the case of the much simpler linear fragmentation equation [G. Madras, B.J. McCoy, AIChE J. 44 (1998) 647].     

Influence of magnetic interactions between clusters on particle orientational characteristics and viscosity of a colloidal dispersion composed of ferromagnetic spherocylinder particles: analysis by means of mean field approximation for a simple shear flow

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones that belong to the neighboring clusters, besides those that belong to its own cluster. The basic equation of the orientational distribution function, which is an integrodifferential equation, has approximately been solved by Galerkin's method and the method of successive approximation. Some of the main results obtained here are summarized as follows. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significant with increasing volumetric fraction of particles; the orientational distribution function exhibits a sharper peak in the direction nearer to the magnetic field one as the volumetric fraction increases. Such a significant inclination of the particle in the field direction induces the large increase in viscosity in the range of larger values of the volumetric fraction. The above-mentioned characteristics of the orientational distribution and viscosity come to appear more significantly when the influence of the applied magnetic field is not so strong compared with that of magnetic particle-particle interactions.     

Eigensolutions,virial theorem and molecular study of nonrelativistic Krazer-Fues potential

A Kratzer-Fues potential is coupled with its self to form a double Kratzer-Fues potential. The solutions of the radial Schrödinger equation with the combined potential are obtained via two different methodologies. Using the supersymmetric approach, the energy equation for a non-approximated centrifugal term is obtained. The energy equation for the approximated centrifugal term is obtained using the parametric Nikiforov-Uvarov method. Numerical results are computed for five molecules using MATLAB software program. The computed numerical values are compared with the experimental values and the ground state energy obtained from Herzberg's energy level equation. The study revealed that the results of the approximated centrifugal term are better than the results of the non-approximated centrifugal term for four molecules.     

Sorption of aluminate from alkaline solutions on D-403 anion exchanger

The sorption of aluminate from alkaline solutions on D-403 anion exchanger is studied. The sorption isotherm is described by the Langmuir and Freindlich classical equations and the Redlich-Peterson generalized equation. Thermodynamic parameters of sorption are determined using the Langmuir equation, modified to describe ion-exchange eqiulibria. A method for determining the type of the sorbed ion in the solid phases is proposed.     

A Model for Calculating Electrostatic Interactions between Colloidal Particles of Arbitrary Surface Topology

A numerical model for calculating the electrostatic interaction between two particles of arbitrary shape and topology is described. A key feature of the model is a generalized discretization program, capable of simulating any desired analytical shape as a set of flat, triangular elements. The relative sizes of the elements are adjusted using a density function to better match the desired shape and the spatial variation of the electrical surface properties on each particle. The distribution of either surface potential or surface charge density is then calculated using a boundary element approach to solve the linearized Poisson-Boltzmann equation. Example interaction energy profiles are calculated for three different types of roughness-bumps, pits, and surface waves. It is found that the interaction energy between rough particles remains different from that between two equivalent smooth spheres at all separations, even for gap widths much larger than either the solution Debye length or the characteristic roughness size. This behavior at large gap widths arises from the nature of the decay of the electric potential away from each particle. In addition, the magnitude of the roughness effect is found to depend greatly on the size and shape of the nonuniformity as well as the electrostatic boundary conditions. For example, for a sphere containing asperities of height equal to 0.2 times the particle radius, the interaction energy can be as much as 50% greater than that between two equivalent spheres under the condition of constant surface potential. At constant surface charge density, the ratio of the interaction energies between rough and smooth spheres was found to either diverge or become zero as contact between the two particles is approached, depending on the nature of the roughness. Changes of this magnitude could clearly have a substantial impact on the stability behavior of a dispersion of such particles. Copyright 2001 Academic Press.     

Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye-Hückel approximation and Deryagin formulation

We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may dramatically change depending on the interplay between characteristic Debye length, thickness of ion-permeable layers and their respective protolytic features (e.g. location, magnitude and sign of charge density). This formalism extends a recent model by Ohshima which is strictly limited to interaction between soft mono-shell particles within Deryagin and Debye-Hückel approximations under conditions where ionizable sites are completely dissociated.     

凝并和成核机理下颗粒尺度分布的Monte Carlo求解

颗粒的凝并和成核现象影响其尺度分布,现有的MonteCarlo方法描述颗粒尺度分布的时间演变过程存在若干困难.提出了一种新的多重MonteCarlo(MMC)算法,基于时间驱动,利用加权的虚拟颗粒的思想,在模拟过程中保持虚拟颗粒总数不变和计算区域体积不变.利用该算法对“常凝并核,一阶成核”的情况下颗粒尺度分布的时间演变过程进行了数值求解,所得结果与数值解相符,表明MMC算法具有高且稳定的计算精度.另外,MMC算法由于跟踪比实际颗粒数目少得多的虚拟颗粒而具有较低的计算代价.     

Generalized diffusion equation of interacting brownian particles

Macroscopic behavior of a system of brownian particles interacting with each other through potential forces is described by a generalized diffusion equation (GDE) for the density of particles. The diffusion coefficient in the GDE is given by the generalized Stokes—Einstein relation and generally depends on the density. In the presence of long-range interactions, the GDE becomes non-local in space. When a Coulomb interaction exists, the GDE corresponds to an improvement of the Poisson—Boltzmann equation.