Kinetic theory of bimolecular reactions in liquid. II. Reversible reaction A+B⇄C+B

Manifestation of macroscopic correlations in elementary reaction kinetics. I. Irreversible reaction A+A-->product

Using an modern many-particle method for the derivation of non-Markovian binary kinetic equations, we have treated theoretically the applicability of the encounter theory (ET) (the prototype of the collision theory) concepts to the widely known diffusion assisted irreversible bulk reaction A+A-->product (for example, radical reaction) in dilute solutions. The method shows that the agreement with the ET is observed when the familiar integral ET is employed which in this method is just a step in the derivation of kinetic equations. It allows for two-particle correlations only, but fails to take account of correlation of reactant simultaneously with the partner of the encounter and the reactant in the bulk. However, the next step leading to the modified ET under transformation of equations to the regular form both extends the time range of the applicability of ET rate equation (as it was for reactions proceeding with one of the reactants in excess), and gives the equation of the generalized ET. In full agreement with physical considerations, this theory reveals macroscopic correlations induced by the encounters in the reservoir of free walks. This means that the encounters of reactants in solution are correlated on a rather large time interval of the reaction. Though any nonstationary (non-Markovian) effects manifest themselves rather weakly in the kinetics of the bimolecular reaction in question, just the existence of the revealed macroscopic correlations in the binary theory is of primary importance. In particular, it means that the well-known phenomena which are generally considered to be associated solely with correlation of particles on the encounter (for example, chemically induced dynamic nuclear polarization) may be induced by correlation in the reservoir of free random walks of radicals in solution.

Excited-state reversible geminate recombination in two dimensions

Excited-state reversible geminate recombination with two different lifetimes and quenching is investigated in two dimensions. From the exact Green function in the Laplace domain, analytic expressions of two-dimensional survival and binding probabilities are obtained at short and long times. We find that a new pattern of kinetic transition occurs in two dimensions. The long-time effective survival probabilities show a pattern of (ln t)(-1)-->constant-->e(t) depending on the rate constants while the effective binding probabilities show t(-1)(ln t)(-2)-->t(-1)-->e(t).

The influence of interactions between reagents on the excess in the rate of quenching reaction: Molecular dynamics study

The influence of the interactions between reagents on the excess in the rate coefficient, Deltak, for the instantaneous reaction A+B-->C+B have been investigated by performing large scale molecular dynamics simulations for simple soft spheres. The simulation method has enabled us to determine the contributions to Deltak coming from A-B as well as B-B interactions. The simulations have shown that positive values of Deltak that appear both for the liquid and for the Brownian system [M. Litniewski, J. Chem. Phys. 123, 124506 (2005); 124, 114501 (2006)] result from B-B interactions. If B-B interactions were absent, Deltak was always negative. The influence of B-B interactions was about three times higher for the Brownian system than for the liquid. A qualitative explanation for the effect has been proposed basing on a simple model and analyzing the influence of B-B interactions on fluctuations in concentrations of reagents. The influence of A-B interactions was completely negligible except for the liquid at short times, for which the cancellation of A-B interaction noticeably decreased Deltak.

Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.

The influence of the quencher concentration on the rate of simple bimolecular reaction: Molecular dynamics study. II

In this paper new results of the simulations [M. Litniewski, J. Chem. Phys. 123, 124506 (2005)] on the influence of the quencher concentration on the reaction A+B-->C+B for the identical soft sphere system are presented. The problem is generalized by considering also the case when the spheres are immersed in the Brownian medium. A significant difference between simple deterministic systems and the Brownian ones is found: the excess in the rate coefficient for the Brownian system is constant and positive, except for very short times. The reaction has been simulated for a very long time, but any tendency to decrease the excess has not been noted. It is also shown that the relative excess in the surviving probability is a universal quadratic function of the quencher concentration for the range of time much longer than the result from the previous simulations. A very strong correlation between the excess in the relative value of spatial correlations between the reagents and the excess in the rate coefficient is shown. It is also shown that the A-A and A-C interactions have some influence on the excess values. A simple model for this effect is presented.

The influence of the quencher concentration on the rate of simple bimolecular reaction: Molecular dynamics study

The paper presents the results of large-scale molecular dynamics simulations of the irreversible bimolecular reaction A+B --> C+B for the simple liquid composed of mechanically identical soft spheres. The systems with the total number of molecules corresponding to 10(7)-10(9) are considered. The influence of the concentration of a quencher (B) on the surviving probability of A and the reaction rate is analyzed for a wide range of the concentrations and for two significantly different reduced densities. It is shown that the quencher concentration dependence effect (QCDE) is, in fact, a composition of two QCDE effects: the short-time QCDE that increases the reaction rate and the long-time QCDE that decreases it. The paper also analyzes the influence of the concentration on the steady-state rate constant, k(ss), obtained by integrating the surviving probability. The excess in k(ss) due to finite quencher concentration changes the sign from negative to positive while going from low to high concentrations. Generally, the excess is extremely weak. It attains a 1% level only if the concentration is very high.

Mesoscopic model for diffusion-influenced reaction dynamics

A hybrid mesoscopic multiparticle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum, and energy so that hydrodynamic effects are fully taken into account. Reactive and nonreactive interactions with catalytic solute particles are described by full molecular dynamics. Results are presented for large-scale, three-dimensional simulations to study the influence of diffusion on the rate constants of the A + C <==> B + C reaction. In the limit of a dilute solution of catalytic C particles, the simulation results are compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction phi of catalytic spheres is high are also presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants are studied.

Kinetics of diffusion-assisted reactions in microheterogeneous systems

This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.