Many-particle effects in kinetics of bimolecular diffusion-controlled reactions

Starting from the generalized theory of bimolecular diffusion-controlled reactions between reagents in solids and liquids, we have performed calculations of the A + B → AB (Frenkel defect annihilation) and A + A → B (exciton annihilation) reaction kinetics over a wide time interval and for high initial concentrations. The predicted lowering at long times of the reaction rate in the course of the A + B → AB reaction and acceleration at short times of the A + A → B reaction due to dynamical aggregation of similar non-interacting reagents are demonstrated. The possibility of experimental checks of these effects is discussed.     

Multiparticle effects in the kinetics of diffusion-controlled reactions

We present the equations for the kinetics of the bimolecular reaction A + B AB, taking into account both the competition of adjacent reagents and strong interaction with the environment. For the electrostatic forces we give a modification of the equations with self-consistent determination of the effective potential. We have shown that multiparticle effects are apparent in the time dependence of the reaction rate constant and the deviation from the formal kinetics laws.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 1, pp. 33–38, January–February, 1985.     

Molecular-dynamics simulations for nonclassical kinetics of diffusion-controlled bimolecular reactions

Molecular-dynamics simulations are presented for the diffusion-controlled bimolecular reaction A+B<==>C in two and three dimensions. The reactants and solvent molecules are modeled as spheres interacting via continuous potential-energy functions. The interaction potential between two reactants contains a deep well that results in a reaction. When the solvent concentration is low and the reactant dynamics is essentially ballistic, the system reaches equilibrium rapidly, and the reaction follows classical kinetics with exponential decay to the equilibrium. When the solvent concentration is high the particles enter the normal diffusion regime quickly and nonclassical behavior is observed, i.e., the reactant concentrations approach equilibrium as t(-d/2) where d is the dimensionality of space. When the reaction well depth is large, however, the reaction becomes irreversible within the simulation time. In this case the reactant concentrations decay as t(-d/4). Interestingly this behavior is also observed at intermediate times for reversible reactions.     

On some errors committed in the studies of kinetics of thermal dissociation of solids

The methods of preparing the samples for kinetic studies are critically discussed with particular consideration to the effect of granulometric characteristics and structure of the material, conditions of performing the measurements, and choice of proper kinetic equation on the reliability of the results obtained.     

Analytical solutions for diffusion-controlled adsorption kinetics with non-linear adsorption isotherms

A regular perturbation series method provides a solution to the diffusion equation when the boundary condition is a non-linear adsorption isotherm. For adsorption at the interface the Freundlich and Langmuir isotherms yield power series in the square root of time. Convergence of the power series solutions is improved by applying the Shanks transformation. The solutions are compared to limiting cases and to published numerical solutions. The results are most accurate for small time where the numerical finite difference method is least reliable.     

Theory of diffusion-controlled reaction between non-simple molecules. I

A new vibrational principle is presented for reaction rates of diffusion-controlled chemical reaction. The variational principle is obtained by a modification of the closure approximation of Wilemski and Fixman. The closure approximation is found to correspond to a special choice of the trial function in this formation and to yield a lower bound of the reaction rate. This formulation is found to be especially useful for the analysis of reaction between non-simple molecules, such as macromolecules.     

Theory of diffusion-controlled reaction between non-simple molecules. II

A simplified version of the closure approximation, presented in the preceding paper, is applied to the reaction of rigid or flexible macromolecular systems. Two effects are found to be important for understanding the characteristic features of the reaction rates of these systems: (i) the orientation effect, which expresses the accessibility of the active sites, and (ii) the relaxation effect, which reflects the nature of the brownian motion of the active sites.     

Features of diffusion-controlled bimolecular reaction of fluorescence quenching in sol-gel-xerogel transitions

Reaction kinetics have been investigated in the diffusion-controlled quenching of pyrene fluorescence by N,N-dimethylaniline in a medium that gradually changes from homogeneous to heterogeneous as a result of solution-sol-gel-xerogel transitions. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 34, No. 2, pp. 122–125, March–April, 1998.     

Theory and simulation of diffusion-controlled Michaelis-Menten kinetics for a static enzyme in solution

We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem. Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by utilizing the Green function previously derived for excited-state reversible geminate recombination with different lifetimes (Gopich, I. V.; Agmon, N. J. Chem. Phys. 2000, 110, 10433). Running the simulation for representative parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense patches of membrane-bound enzymes.     

On the application of quantitative models of diffusion-controlled adsorption kinetics at fluid interfaces

The model of diffusion-controlled adsorption kinetics can be solved by different mathematical procedures. For the most important case of a Langmuir isotherm, useful solutions are summarized and extended and the ranges of application are given. New approximations are presented which can be applied to most experiments in practice.Nomenclature a _i coefficients of the collocation solution - a _L Langmuir parameter - a interaction parameter of the Frumkin isotherm - _n coefficients of a power series - c surfactant bulk concentration - c ₀ equilibrium bulk concentration - D diffusion coefficient - surface concentration - ₀ equilibrium surface concentration - _t8 maximum surface concentration - ( _x ) Gamma function - t time - dimensionless time Dedicated to the 60th birthday of G. Kretzschmar.     

Solid-phase reaction kinetics

It is argued that, for the macroscopic parameters of conventional kinetic models to become meaningful, they may be and must be expressed in terms of elementary single-barrier processes. To accomplish this means to associate some (external) extensional measure with a single-barrier elementary act, remaining within the logic of the existing geometrical-probabilistic scheme. A manner of doing this involving the use of Dirichlet fragmentations is suggested.     

A study of the thermodynamic properties and dehydration reaction kinetics of some salt-hydrates

Correlations were determined between heat capacity and temperature and phase change enthalpy of Ba(OH)₂·8H₂O. The phase diagram and DSC curve of the binary system Na₂CO₃·10H₂O?Na₂HPO₄·12H₂O were determined The kinetics of the dehydrating reaction of Ba(OH)₂·8H₂O, Na₂CO₃·10H₂O and Na₂HPO₄·12H₂O were measured and theoretically analyzed by TG.     

Identifiability classes in reaction kinetics

Some difficulties of eliciting reliable rate constants from experimental data are considered. Different classes of ill-posed estimation problems are given and demonstrated by simple examples.

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Fluctuation effects in the solid-phase kinetics of diffusion-controlled radiation-chemical processes: A Monte Carlo simulation

The model problem of the recombination of free radicals was considered with consideration for the following three types of events: the generation (homogeneous and inhomogeneous), migration, and recombination of particles of the same type in a cubic lattice. A simple formula, which was checked using the Monte Carlo method, was proposed to describe this kinetics with an inhomogeneous initial distribution. This model was used to describe experimental data on the recombination of free radicals in a real system of γ-irradiated ammonia. Reasonable values were obtained for the characteristic spur radius and diffusion coefficient. It was found that the character of fluctuation noise in the system depends on the mechanism of elementary processes occurring in this system; consequently, it can be a source of information on process parameters.     

Experimental verification of the Smoluchowski theory for a bimolecular diffusion-controlled reaction in liquid phase

We report experimental verification of the Smoluchowski theory for diffusion-controlled reactions in solution at the steady-state limit. We have determined both the diffusion coefficients and the self-termination reaction rates of the diphenylmethyl radical simultaneously. Smoluchowski theory is insufficient to discuss the reaction rate for the self-termination reaction of the diphenylmethyl radical, so the reaction rate of an encounter complex based on the Collins-Kimball treatment is estimated.     

Current transient study of the kinetics of nucleation and diffusion-controlled growth of bimetallic phases

A model to describe the kinetics of nucleation and diffusion-controlled growth of bimetallic phases has been developed, and analytical expressions have been obtained for the elucidation of nucleation kinetics through determination of the number density N ₀ of active sites and their nucleation frequency A, from experimental current transients obtained under potentiostatic control. The validity of the model has been demonstrated with the electrodeposition of Ag–Hg phases at two distinct compositions.     

Kinetics of partly diffusion-controlled reaction XXI: A simple algorithm for computing the apparent rate of reaction

Starting from Smoluchowski's hypothesis, a simple algorithm is developed in order to obtain the apparent rate constant at large values of time, t, with some physical and chemical processes, as in the case of diffusion controlled reactions. Some practical examples are illustrated, assuming nonuniform distribution function, space-dependent diffusion coefficient or short-range interaction leading to an asymptotic analytical expression of the form α + β/√t, where α and β are constants function of the system of interest.