A.B. Doktorov

Kinetics of diffusion‐influenced reversible reaction A+B ⇌C in solutions

Reversible diffusion‐influenced pseudo first order reaction A+B ⇌C with static particles in excess is rigorously studied. Under most general assumptions, the problem of the reversible reaction kinetics is reduced to the consideration of the effective irreversible reaction studied by conventional methods. In the framework of the average t‐matrix approximation (ATA) we reproduce some results derived earlier and establish their applicability limits. Rigorous investigation of the kinetics behavior at long times shows that the t−3/2 law predicted earlier and reproduced by ATA has a different concentration‐dependent amplitude. On the basis of diagrammatic summation, providing correct long‐time asymptotics, a modified theory has been developed. The range of validity of the modified theory is much wider than that of ATA and similar theories.

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.

A many-particle treatment of the reversible reaction A+B⇔C+B

A many-particle consideration of diffusion-influenced reversible pseudo-first order reaction A+B⇌C+B is presented. It is shown that the lowest order (in concentration) of the memory matrix is not sufficient for describing the binary kinetics of the reaction. Binary kinetic equations describing both stationary and nonstationary stages of the kinetics have been obtained using diagrammatic representation and selecting the necessary diagrams. Comparison with the fully renormalized kinetic theory is made by considering the contact approximation for reactivity.

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.

Theory of geminate recombination of radical pairs with instantaneously changing spin-Hamiltonian. I. General theory and kinematic approximation

Abstract A general theory of geminate recombination of radical pairs with instantaneously changing spin-Hamiltonian has been constructed on the basis of the formalism of Green functions which characterize the molecular motion of reagents. The kinematic approximation has allowed us to reduce the calculation of the values determining the spin state of the products to matrix operations. The operator matrices, involved in the resulting expressions, are determined by the “convolution” of spin dynamics with a function describing molecular motion. The form of such a function has been established for a well-known phenomenological two-positional model of radical pair.