Fluctuation kinetics of diffusion-controlled processes: Strong effects due to correlations and fluctuations

We summarize some recent results related to fluctuation-induced kinetics of diffusion-controlled processes. We show that kinetic behavior can be drastically changed due to fluctuation effects, spatial correlations between particles, and anomalous transport properties. In addition, we show that correlation-induced kinetics in some systems can govern the temporal evolution over the entire time domain.     

一种液晶环氧树脂固化中扩散控制动力学研究

根据扩散控制反应的基本原理 ,建立了合适的反应模型 ,描述了 4 ,4′ 二 ( 2 ,3 环氧丙氧基 )偶氮苯(DGEAP) / 4,4′ 二氨基二苯甲烷 (DDM)环氧树脂的固化行为 .该模型认为 ,随着环氧基团反应程度的提高 ,基团的反应半径将受到影响 .当体系中出现了介晶基元的有序排列时 ,与之相连的反应基团的分布也受到影响 ,有序区内的局部浓度将变大 ,产生假浓度效应 ,并最终影响扩散控制反应动力学 .通过与普通环氧树脂固化动力学的比较 ,证实了这一效应 .     

Simultaneous establishing of stationary growth rate and composition of supercritical droplets at isothermal binary condensation in the diffusion-controlled regime

General integral relations expressing the droplet radius and time of the droplet nonstationary growth as nonlinear functions of solution concentration in the droplet have been derived. These relations are valid for a supercritical droplet (i.e., sufficiently large droplet, for which the Laplace pressure effect on the concentration at saturation of vapors is negligible) isothermally growing via stationary diffusion in the mixture of two condensing vapors and an incondensable carrier gas. The initial composition in the droplet may be arbitrary and partial molecular volumes of components are not fixed. Explicit analytical relations have been found for droplet composition and the droplet size as functions of time at small deviations from the stationary concentration in the growing droplet. These relations show that the assumption of the steady droplet growth rate is not valid for non-small deviations from the stationary concentration. Some illustrations of the general nonlinear theory have been done in situation when solution in the droplet can be considered ideal.     

Time evolution of the size distribution of nano-sphere droplets in the hexadecane-in-water miniemulsion stabilized by nonionic surfactants

Time evolutions of the droplet size distribution in miniemulsions, which is constituted of water/n-hexadecane/nonionic surfactants, were investigated by using light scattering techniques. A hard-sphere model is applied to characterize the polydispersity of miniemulsion droplets. Measuring the relative scattering intensity as a function of the volume fraction of dispersed phase, the variance of the droplets size distribution, σ², was evaluated. Miniemulsions developed gradually from monodisperse systems (σ²≅0.02) to polydisperse ones (σ²≥0.13) over 12 days after preparation. σ² increased rapidly in the early stage, and ceased to develop at about 6 days after preparation. The z-average hydrodynamic radius of miniemulsion droplets grew with time over the whole time range. The change with time of the total droplet number of miniemulsion is in agreement with that predicted by Smoluchowski's theory for diffusion-controlled coagulation. Although the characteristic coagulation time obtained here was much larger than that estimated by Smoluchowski's theory, the qualitative agreement between the theory and the experimental results obtained here is good. At the earlier stage of the destabilization process of miniemulsions, the growth mechanism of droplets may be explained in terms of a diffusion-controlled coagulation. Received: 1 April 2000 Accepted: 10 August 2000     

Concentration dependence of diffusion-controlled processes among stationary reactive sinks

A multiple scattering theory of competition effects in diffusion-controlled reactions are presented. We consider a random array of stationary sinks which react with a density field of another reactant. Using the radiation boundary condition to describe the reaction at the surfaces of the sinks, we treat the modification of the density field due to reaction with sinks exactly. By keeping only the most divergent terms in a given order of scattering and summing them, we obtain the rate constant as a function of the sink concentration in the steady state. We also calculate the concentration-dependent diffusion constant of the density field. Both the rate and diffusion constants have nonanalytic behavior in the sink concentration.Alfred P. Sloan Foundation Fellow 1976–1980; John Simon Guggenheim Memorial Fellow 1979–1980.     

KINETIC MODEL FOR DIFFUSION-CONTROLLED INTERMOLECULAR REACTION OF HOMOGENOUS POLYMER UNDER STEADY SHEAR

The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated to get a new equation, which directly correlates the rate constant with shear rate. It was found that the rate constant is not monotonic with shear rate. The scale of rate constant is N^-1.5 （N is the length of chains）, which is in consistent with de Gennes＇s result.     

A review of anomalous diffusion phenomena at fractal interface for diffusion-controlled and non-diffusion-controlled transfer processes

This article reviewed anomalous diffusion phenomena coupled with facile and sluggish charge-transfer reactions at fractal interface. Firstly, the generalised diffusion equation (GDE) involving a fractional derivative which describes diffusion towards and from fractal interface was briefly introduced. And then, anomalous diffusion coupled with facile charge-transfer reaction at fractal interface, i.e., diffusion-controlled transfer process across fractal interface, was mathematically examined by the generalised Cottrell, Sand, Randles-Sevcik and Warburg equations theoretically derived from the analytical solutions to the GDE under the semi-infinite boundary condition. Finally, in order to provide a guideline in analysing anomalous diffusion coupled with sluggish charge-transfer reaction at fractal interface, i.e., non-diffusion-controlled transfer process across fractal interface, this review covered the recent researches into the effect of surface roughness on non-diffusion-controlled transfer process within the intercalation electrodes.     

Thermally stimulated depolarization measurements on NaF:02-, NaCI:S2-.and KC1:S2-

In NaCl:S^2-, KC1:S² and NaF:0^2-(i) optical absorption and emission spectra and (ii) electric conductivity measurements show that after suitable heat treatment the bivalent anion impurities are paired with anion vacancies. Conventional dielectric absorption measurements and sensitive measurements of thermally stimulated depolarizing (t. s. d.) currents (ionic thermocurrent) have failed to detect the presence of bivalent anion-anion vacancy dipoles in these crystals. We suggest that derealization or sharing of the electron of the bivalent impurity ion, possibly with the vacancy, considerably reduces the dipole moment.     

Experimental study of a diffusion-controlled reaction involving a chain molecule with terminal reactive sites

Diffusion-controlled reaction of electron transfer from diphenylsilane radical anions to the series of α- and α,ω-bromoalkanes with alkane chain length up to 18 atoms has been studied in n-dodecane solutions. At room temperature, reaction rate constants have been determined and corresponding reaction radii have been evaluated. It has been shown that a not-too-long chain molecule, which contains two terminal reaction sites and participates in the diffusion-controlled reaction, may be considered as a rapidly rotating pair of reacting sinks with a distance between their centers equal to the mean-square end-to-end distance of the molecule.     

Brownian dynamics simulation of protein association

Summary The Brownian Dynamics (BD) method is applied to study the diffusive dynamics and interaction of two proteins, cytochrome c (CYTC) and cytochrome c peroxidase (CYP). We examine the role of protein electrostatic charge distribution in the facilitation of protein-protein docking prior to the electron transfer step, assessing the influence of individual charged amino acid residues. Accurate interaction potentials are computed by iterating the linearized Poisson-Boltzmann (PB) equation around the larger protein CYP. The low dielectric constant inside proteins, electrolyte screening effects and irregular protein surface topography are taken into account. We observe a large ensemble of electrostatically stable encounter complexes seemingly with acceptable geometric requirements for electron transfer rather than a single dominant complex. Stabilities of the large variety of docking complexes are rationalized in terms of generalized charged residue complementarities. However, it is found that the electrostatic interactions giving rise to complex stabilities are somewhat nonspecific in nature. A large series of additional simulations are performed in which individual charged residues on CYTC have been chemically modified. Resulting perturbations of the association rate are significant and qualitatively similar to results observed in comparable kinetics experiments. We therefore demonstrate the potential of the Brownian dynamics method to estimate the effects of site-directed mutagenesis on protein-protein and protein-ligand diffusional association rates.