Polymerization with Freezing

TL;DR

This paper studies irreversible aggregation with reactive and frozen clusters, showing how freezing influences the cluster size distribution and gel formation, with different behaviors depending on the aggregation rate.

Contribution

It introduces a rate equation model for aggregation with freezing, revealing how freezing rate affects cluster distributions and gel formation scenarios.

Findings

Power-law tail in cluster size distribution with exponent depending on freezing rate

Different exponents (1 and 3) for constant and product aggregation rates

Various gel formation outcomes, including no gel, single gel, or multiple gels

Abstract

Irreversible aggregation processes involving reactive and frozen clusters are investigated using the rate equation approach. In aggregation events, two clusters join irreversibly to form a larger cluster, and additionally, reactive clusters may spontaneously freeze. Frozen clusters do not participate in merger events. Generally, freezing controls the nature of the aggregation process, as demonstrated by the final distribution of frozen clusters. The cluster mass distribution has a power-law tail, F_k ~ k^{-gamma}, when the freezing process is sufficiently slow. Different exponents, gamma=1, 3 are found for the constant and the product aggregation rates, respectively. For the latter case, the standard polymerization model, either no gels, or a single gel, or even multiple gels may be produced.