Charged Aggregation

TL;DR

This paper introduces a charged aggregation model where oppositely charged monomers form neutral clusters that irreversibly grow, analyzing the kinetics, gelation phenomena, and extending the model to multiple monomer types.

Contribution

The paper presents a solvable mean-field model of charged aggregation, including gelation and multi-type extensions, providing new insights into aggregation dynamics.

Findings

Cluster concentration scales as A_k/t with non-trivial A_k dependence.

Gelation occurs when reaction rate equals the product of cluster masses.

Model extended to three or more monomer types.

Abstract

We introduce an aggregation process that begins with equal concentrations of positively and negatively `charged' monomers. Oppositely charged monomers merge to form neutral dimers. These dimers are the seeds for subsequent aggregation events in which neutral clusters of necessarily even mass join irreversibly to form neutral aggregates of ever-increasing size. In the mean-field approximation with mass independent reaction rates, we solve for the reaction kinetics and show that the concentration of clusters of mass $k$, $c_k(t)$, asymptotically scales as $A_k/t$, with $A_k$ having a non-trivial dependence on $k$. We also investigate the phenomenon of gelation in charged aggregation when the reaction rate equals the product of the two incident cluster masses. Finally, we generalize our model to the case of three and more types of monomers.