Accurate analytical calculation of the rate coefficient for the diffusion-controlled reactions due to hyperbolic diffusion

Using an approach based on the diffusion analog of the Cattaneo-Vernotte differential model, we find the exact analytical solution to the corresponding time-dependent linear hyperbolic initial boundary value problem, describing irreversible diffusion-controlled reactions under Smoluchowski's boundary condition on a spherical sink. By means of this solution, we extend exact analytical calculations for the time-dependent classical Smoluchowski rate coefficient to the case that includes the so-called inertial effects, occurring in the host media with finite relaxation times. We also present a brief survey of Smoluchowski's theory and its various subsequent refinements, including works devoted to the description of the short-time behavior of Brownian particles. In this paper, we managed to show that a known Rice's formula, commonly recognized earlier as an exact reaction rate coefficient for the case of hyperbolic diffusion, turned out to be only its approximation being a uniform upper bound of the exact value. Here, the obtained formula seems to be of great significance for bridging a known gap between an analytically estimated rate coefficient on the one hand and molecular dynamics simulations together with experimentally observed results for the short times regime on the other hand. A particular emphasis has been placed on the rigorous mathematical treatment and important properties of the relevant initial boundary value problems in parabolic and hyperbolic diffusion theories.

Molecular dynamics study on the influence of quencher concentration on the reaction rate for ionic systems

The influence of concentrations of reagents on the rate of reaction: A+B-->C+B for low density equimolar mixtures of spherically symmetric ions immersed in the Brownian medium has been investigated by performing large scale molecular dynamics simulations. The Coulomb potential of ion-ion interactions is truncated at the cutoff distance large enough to make the kinetics of the reaction independent of its value. The simulations have been performed at conditions close to that for quenching reactions for fluophores. One of the simulation results is that the excess in the rate coefficient Delta k is always positive and converges to a constant value which is two to three orders in magnitude higher than that for the soft spheres immersed in the Brownian medium [Litniewski, J. Chem. Phys. 124, 114502 (2006)]. Delta k is approximately proportional to c however, if the concentration is high, positive deviations [O(c(2))] are noticeable. The simulation results are compared with simple model that bases on the superposition approximation. The model predicts most of the properties of Delta k. The predicted values are about 30%-40% lower than that from the simulations.

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.

Kinetics of fluorescence quenching for electron transfer and for energy transfer: Molecular dynamics tests for spherical molecules

The Smoluchowski approach to description of fluorescence quenching is tested by comparing the theory with computer simulations for the case of spherical molecules. The distance dependent sink terms describing the electron transfer mechanism and the Forster model for the energy transfer are considered. It is shown that the agreement between the rate coefficient from the model and from simulations depends on the strength of the solute-solvent interactions as well as on the speed of reaction itself. Comparing results of simulations for different quencher concentrations we estimate the strength of quencher concentration dependence effect and the range of times the effect may be significant. In the long time limit the increase in quencher concentration decreased the rate coefficient.