Numerical analysis of kinetic rate constants derived from stochastic computer simulation

A numerical approach has been developed to determine the individual rate constants (k(f-s) and k(s-f)), as well as the equilibrium constant from the ratio of the rate constants (k(f-s)/k(s-f)), by using stochastic simulation. This approach is illustrated for simulations of the absorption (partition) process between homogeneous fluid and surface phases under diffusion-limited conditions. A pair of regression methods is derived from the chemical system with the initial distribution of molecules entirely in either the fluid or surface phase. These two methods are complementary in determining the rate constants for distribution coefficients that are lower or higher than unity respectively. A standard exponential (two-parameter) regression equation is compared with a biexponential (four-parameter) equation, which provides for inherent correction of numerical error The effects of the number of molecules, as well as the time increment and range, are examined in detail. This provides guidance to optimize the computational parameters of the simulation. The proposed approach has been successfully applied for distribution coefficients ranging from 0.01 to 100.0, yielding individual rate constants k(f-s) and k(s-f) with +/- 0.84% and +/- 0.57% average relative standard deviation and the ratio of the rate constants with +/- 1.04% average relative standard deviation and +/- 1.14% average relative error.