用渗流理论计算高分子溶液中溶剂的自扩散系数

基于微观渗流理论建立了溶剂小分子在高分子溶液中的自扩散模型,并据此模型对不同温度和浓度下的聚苯乙烯(PS)-苯、PS-甲苯、PS-乙苯和PS-四氢呋喃4个体系中小分子的自扩散系数进行了关联,计算出在不同温度下溶剂分子扩散所需的临界浓度。结果表明,在PS玻璃化温度以下,本模型对于温度和浓度具有很好的适用性和关联精度。     

Predicting the proton conductivity of perfluorosulfonic acid membrane via combining statistical thermodynamics and molecular dynamics simulation

The electrochemical properties of a perfluorosulfonic acid (PFSA) membrane are estimated using a combination of molecular dynamics simulation and statistical thermodynamic model. We obtain all parameters in an ionic conductivity model from an atomistic simulation and remove all adjusted model parameters. From a microscopic point of view, the hydrated PFSA membrane shows micro‐phase segregation which separated into hydrophilic and hydrophobic phases. Our present work originates with this phenomenon and we treat this phase segregation as if it is a continuous phase for each of which the proton (H⁺) is transported inside the PFSA membrane/solvent (water and alcohols) mixture. The chemical potential for a given system is estimated using a molecular simulation technique to predict the van der Waals interaction energy between the polymer and solvent. In addition, the self diffusion coefficients are calculated from the molecular dynamics simulation. We study various polymer/solvent compositions to understand the concentration dependence of self diffusion coefficient. Our self diffusion coefficients and also the predicted final ionic conductivity agree well with previously reported experimental data. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1455–1463, 2011     

用于聚合物溶液扩散系数计算的活度系数模型比较

用40个聚合物溶液体系的实验数据,对三个有代表性的活度系数模型用于计算联系自扩散系数和互扩散系数的热力学因子的精度进行了比较,结果表明三个模型的精度相近,误差一般在20％左右。,因而本工作揭示了聚合物溶注保由自扩散系数计算与扩散系数的一个潜在问题。即由于活度系数模型计算热力学因子误差较大所带来的较大不确定性。     

The “fast” and “slow” mode theories of interdiffusion in polymer mixtures: Resolution of a controversy

The theory of interdiffusion of a pair of components in multicomponent polymer mixtures is reviewed from a statistical point of view, and the foundation of the “fast” and “slow” mode theories, as well as the more recent “ANK” theory of interdiffusion is critically examined. The ANK theory reproduces the results of the slow and fast mode theories as the two limits when the vacancy concentration is varied from zero to a large value, and shows that the interdiffusion coefficient in a binary compressible mixture at finite vacancy concentrations can not in general be expressed only in terms of the tracer diffusion coefficients of the components, but it involves in addition the cooperative diffusion coefficient which characterizes the relaxation of total density fluctuations. The predictions of the ANK expression for the molecular dependence of the kinetic factor is compared with recent scattering experiments.     

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.     

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Hydrodynamic approximation for distinct diffusion coefficients

The distinct diffusion coefficient is a measure of the coupling of the diffusive motions of two particles. It is given as the integral over a velocity cross correlation rather than the velocity self correlation that determines the self-diffusion coefficient. A hydrodynamic approximation for the distinct diffusion coefficient is proposed and then tested by comparison with data for a wide range of non-ionic binary mixtures. The hydrodynamic approximation gives negative distinct diffusion coefficients and is in qualitative agreement with most of the data. In many cases, deviations from the model results can be explained in terms of interactions which are not accurately treated by the model.     

Self Diffusion in Isotopic Fluid

Abstract

Expressions for the second and fourth frequency sum rules of the velocity auto-correlation function have been obtained for an isotopic fluid. These expressions and Mori memory function formalism have been used to study the influence of the particle mass and mole fraction on the self diffusion coefficient. Our results confirm the weak mass dependence of the self diffusion. The influence of the mole fraction of the light particles on the self diffusion constant has been found to increase for the larger particle mass.     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008     

Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile,and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

The self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D₀ exp(?αc^ν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003     

Computer‐Aided Estimation of Diffusion Coefficients in Non‐Solvent/Polymer Systems

A novel method for estimating the mutual and self‐diffusion coefficients of a non‐solvent/polymer system is proposed in this work. The idea is to study the evaporation process from non‐solvent/solvent/polymer systems as a one‐dimensional numerical experiment and to use polymer solution weight versus time data to fit the unknown parameters of the diffusion‐coefficient correlations based on free‐volume theory. For this purpose, the evaporation process is modeled as a coupled heat‐ and mass‐transfer problem with a moving boundary, and the Galerkin finite‐element method is used to solve simultaneously the non‐linear governing equations. This method is successfully applied to the estimation of water–cellulose acetate diffusion coefficients and is valid over the whole range of temperatures and concentrations for practical applications in membrane technology. Additionally, there is a detailed discussion on if water affects the morphology of the final cellulosic membrane by studying the concentration profiles of the constituents of the casting solution.     

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory (cited: 2)

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa-tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site modelwith Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode-coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.     

Comparison of Ethene Diffusion Characteristics in H[Al]ZSM‐5 at 300 K and 400 K by Molecular Dynamics

The ethene diffusion characteristics in the framework of H[Al]ZSM‐5 at 300 K and 400 K have been studied by molecular dynamics (MD) simulation. The data have been obtained for the molecular kinetic, potential and total energies, mean square displacement and self‐diffusion coefficient, interaction and beat of adsorption. The dependence of molecular diffusion on temperature has been explored.     

Geometrical aspects of self diffusion in liquid water

In the late 1950s Cohen and Turnbull proposed a model for the self diffusion process in high density fluids, which considers the diffusion process as driven by the free volume fluctuations. An explicit expression was derived for the diffusion coefficient on hard sphere systems, and the results were consistent with molecular dynamic simulations. However the model is not able to reproduce experimental or simulation results for associated fluids, particularly in liquid water, where there is a huge variation of the diffusion coefficient without a significant change in the density. This implies that other properties, besides the free volume, have to be considered in modelling the diffusion process. The model we propose here takes into account both the volume and the shape of the “cage” surrounding the molecules. The “cage” is defined through the Voronoi polyhedra which are calculated from molecular dynamics simulations. The resulting diffusion coefficients, which have been calculated making use only of structural properties, are in good agreement with those evaluated directly from the long time behaviour of the molecular mean square displacements during the molecular dynamics runs.     

Light scattering measurement and theoretical interpretation of mutual diffusion coefficients in binary liquid mixtures

Mutual diffusion coefficients for eleven binary systems of simple organic liquids have been measured by laser light scattering. By separating the mutual diffusion coefficient into a kinetic diffusion coefficient and a thermodynamic factor, we have been able to analyze the dynamical information contained in the kinetic coefficient in terms of a simple hard sphere theory of molecular motion. The hard sphere model of the kinetic diffusion coefficient is shown to be accurate for ideal and moderately nonideal solutions, and for both spherical and very nonspherical molecules. Only for extremely nonideal solutions were we unable to interpret diffusion coefficient data by our methods of analysis.     

When can the Ogston-Morris-Rodbard-Chrambach model be applied to gel electrophoresis?

The Ogston-Morris-Rodbard-Chrambach theory of gel electrophoresis is consistent with predictions from the volume averaging method with respect to the equivalence of the accessible volume fraction to the ratios of gel mobility to free solution mobility and the gel diffusion coefficient to free solution diffusion coefficient for the limiting case of small molecule electrophoresis with low electrical fields, low gel concentrations, and nonconductive gel fibers. When these conditions are not valid, more extensive calculations are required to determine the mobility and diffusion coefficient ratios as functions of the geometry and electrical field within the gel. The volume averaging theory shows that it is important to account for the electrical conductivity properties of the fibers that make up a gel electrophoresis medium, and this aspect is consistent with early theories of transport phenomena in gel electrophoresis.     

Anomalous nanoparticle diffusion in polymer solutions and melts: a mode-coupling theory study

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.     

Diffusion in polymer—solvent systems. I. Reexamination of the free-volume theory

The free-volume theory describing diffusion in polymer–solvent systems is reexamined. Calculation of the specific free volume for such systems is discussed, and equations are presented for the determination of the self-diffusion coefficients of the polymer and the solvent. Conditions under which the mutual diffusion coefficient can be deduced solely from free-volume considerations are clarified, and a more general version of the free-volume diffusion theory proposed by Fujita is presented. The further restrictions needed for the theory of Fujita are discussed, and it is concluded that these additional restrictions are responsible for failures of the Fujita theory.     

Limiting law for distinct diffusion coefficients in ionic solutions

The limiting laws for the distinct diffusion coefficient and the corresponding Onsager phenomenological coefficient are obtained from the cluster theory of electrolyte conductance. Results are given for single electrolytes and common-ion mixtures with unrestricted charges and friction coefficients in both cases.     

Momentum and stress relaxation in fluids illustrating caging

The self diffusion coefficient, shear viscosity, and velocity time correlation function are calculated for a hard sphere fluid under a severe assumption, namely, the friction arises from uncorrelated binary collisions and from correlated backscattering (caging) collisions as represented in the memory function. Relaxation of the memory function from its zerotime caging value is described as a diffusion process. Derived diffusion coefficients and the shear viscosities, relative to their Enskog values decrease and increase with density, respectively, in a monotonic and gradual fashion in contrast with simulation values that show a precipitous change near the fluid-solid transition. In the present pair diffusion model, the velocity time correlation function vanishes at the proper time but its tail is overly damped relative to the simulation data. A weak breakdown of the Stokes-Einstein relation is also predicted.