Mass action kinetics and equilibria of reversible aggregation

Abstract

The kinetics and equilibrium of particle aggregation are studied using the general mass action model. In this approach, the reversibility of aggregation is treated explicitly and yields a direct calculation of the equilibrium distribution of aggregates. Very simple expressions are obtained for the distribution of aggregates at equilibrium for a general class of rate constants. The mass action kinetic equations for aggregation are solved numerically using a straightforward Taylor series expansion. These solutions all yield the same equilibrium distribution of aggregate sizes as was obtained directly from the solutions of the detailed balance equations. At sufficiently short times, i.e. not too close to the equilibrium, there is a topological similarity between the mass action and Smoluchowski's solutions. This similarity is used to obtain accurate closed form estimates for the time development of various systems. The analysis demonstrates that light scattering data may yield an apparent second-order dependence on particle concentration even when the fraction of higher-order aggregates is significant. These calculations explain the characteristics of Na⁺-induced aggregation of sonicated phosphatidylserine vesicles. The distinction between the rate and extent of aggregation is examined and it is illustrated that while the addition of electrolyte may initiate fast aggregation, the system can remain essentially monodisperse due to the equilibrium state.