Substrate concentration dependence of the diffusion-controlled steady-state rate constant
Abstract
The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B_2*. Comparisons to Brownian dynamics simulations excluding HI show excellent agreement up to bulk number densities of B_2* rho_0 < 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.
Cite
@article{arxiv.cond-mat/0412541,
title = {Substrate concentration dependence of the diffusion-controlled steady-state rate constant},
author = {J. Dzubiella and J. A. McCammon},
journal= {arXiv preprint arXiv:cond-mat/0412541},
year = {2009}
}
Comments
7 pages, 3 figures