A.A. Kipriyanov

A modification of the non-Markovian encounter theory. III. Hopping and diffusion mechanisms of reactions

Abstract The exact kinetic law has been calculated for the hopping mechanism of the reaction A + B → B with allowance for the mobility of both reactants. The binary kinetics depending solely on the relative motion parameters has been extracted. It is shown that in the same time interval the binary kinetics is correctly described by both the non-Markovian differential theory and the encounter theory. The binary kinetics extraction principle is formulated. Generalization of this principle to diffusion motion shows that the encounter theory does not allow for all necessary binary terms, and, therefore, needs modification. The required modification of the kernel of the encounter theory equation for the reactions A + B → B and A + B → C has been performed.

A many-particle approach to the derivation of binary non-Markovian kinetic equations for the reaction A+B→B

Many-particle methods of physical kinetics have been adapted to a many-particle consideration of irreversible reactions A+B→B in liquid solutions. The correctness of the diagrammatic approach developed is demonstrated using the exactly solvable problem. Appropriate scaling procedure has been devised for the extraction of a binary kinetics. On its basis, the conception of pair uncorrelated encounters of reactants in liquid solutions has been generalized, and the concept of the effective pair has been introduced. Binary non-Markovian kinetic equations of the reaction for uniform initial distribution of B species obtained earlier are reproduced. For the first time, integro-differential kinetic equations of the reaction in spatially non-uniform normal systems have been derived.

A modification of non-Markovian encounter theory. I: Markovian description in non-Markovian theories

Abstract Non-Markovian theories based on two commonly used many-particle approaches to the derivation of kinetic equations of elementary bimolecular reactions in diluted liquid solutions are analyzed. The first approach conforms to superposition decoupling of the BBGKI hierarchy, and the second one conforms to the expansion in terms of the reactants density parameters of the mass operator in the memory function formalism. Within the scope of these theories, the discrepancy between the time bounds of the Markovian description of the kinetics (obeying the law of mass action) is established with irreversible diffusion-controlled reactions A + B → B as an example

A new approach to the derivation of binary non-Markovian kinetic equations

A universal method of derivation of infinite hierarchies for partial distribution functions and correlation forms in the thermodynamic limit has been developed. It is based on the consideration of reacting systems in the Fock space. Hierarchy closure methods available in the literature are shown to give incorrect binary kinetic equations of the reaction A+B→B in some critical cases. A new approach to hierarchy closure has been proposed. It consists in neglecting contributions from four-particle correlations and in adapting the Faddeev method of the three-body theory to the extraction of a binary part of three-particle evolution. For the model of the reaction A+B→B the proposed method gives correct kinetic equations obtained earlier on the basis of diagram summation. It gives the theoretical basis for derivation of binary kinetic equations for realistic reacting systems.

T-MATRIX REPRESENTATION AND LONG TIME BEHAVIOR OF OBSERVABLES IN THE THEORY OF MIGRATION-INFLUENCED IRREVERSIBLE REACTIONS IN LIQUID SOLUTIONS

The theory of migration-influenced irreversible reactions upon binary encounters of reactants in liquid solutions is formulated in terms similar to those of quantum scattering theory. Free motion of a reacting pair in the configuration space is a random walk in three-dimensional infinite space and arbitrary Markovian motion over internal degrees of freedom. In the case of mixing by free motion, general asymptotic properties of the free resolvent describing this motion have been established. General long-time kinetic law of the attainment of steady-state values by the observables in bulk and geminate reactions has been deduced. Thermodynamically, not only the universality of their long-time dependence is important, but also the fact that the rate of attaining the steady-state values is completely determined by macroscopic quasi-equilibrium observables.

Many-particle treatment of nonuniform reacting systems A+B→C and A+B→C+D in liquid solutions

Abstract The recently developed method of deriving binary non-Markovian (non-stationary) kinetic equations of reactions in liquid solutions has been applied to irreversible reactions A+B→C and A+B→C+D in spatially nonuniform systems. The method is based on the derivation and subsequent closure of hierarchies for correlation forms. Physically clear kinetic equations for local concentrations of reactants showing that the method can be applied to a wide class of the reacting systems have been obtained in the hydrodynamic approximation.

The effect of chemical displacement of B species in the reaction A+B→B

The non-Markovian binary kinetic equations of the irreversible reaction A+B→B taking into account B reactant displacement due to chemical conversion events have been derived for the first time. The derivation is based on the many-particle closure method recently proposed by the authors. It is shown that a conventional view of the reaction A+B→B as a pseudomonomolecular reaction is true only for spatially uniform systems. In the case of spatially non-uniform systems additional macroscopic flows arise. They can transform an originally uniform distribution of one of the species into a non-uniform one in the course of the reaction.

Exactly solvable models in the theory of irreversible reactions in liquids

Exact kinetic equations defining the A + B → B reaction in liquid solutions are obtained on the basis of a many-particle approach and the notion of point-reacting particles with remote reactivity. For any initial correlations in the system of reactants, the calculation of many-particle kinetics is shown to reduce to the calculation of survival probability of one particle A in the ensemble of particles B. In the context of the most general model the exact equations in the thermodynamic limit are obtained. The equations define the process which develops from two classes of initial correlations: those of the same type corresponding to the reactions in the bulk, and polytypic correlations corresponding to the reactions in non-isolated geminate pairs.

A scaling procedure in a many-particle derivation of the non-Markovian binary kinetic equations of the reaction A+B→B in liquid solutions

Abstract A mathematically rigorous scaling procedure for the derivation of binary non-Markovian kinetic equations has been developed. Though the procedure refers to the irreversible reaction A + B → B , it can serve as a reliable basis for selecting diagrams in regular many-particle derivation of non-Markovian kinetic equations for other types of elementary chemical reactions in liquid solutions.

A modification of non-Markovian encounter theory. II. Exactly solvable models

Abstract Exact kinetic equations defining A + B → B reaction in liquid solutions are obtained on the basis of many-particle approach and the notion of point reacting particles with space dependent reactivity. Mobility of both types of reactants is taken into account. It is assumed that particles A move by infinite stochastic jumps, whereas the motion of particles B is of arbitrary Markovian character.