Genuine Non-Self-Averaging and Ultra-Slow Convergence in Gelation

TL;DR

This paper reveals that gelation transitions can exhibit non-self-averaging and ultra-slow convergence, challenging the traditional understanding of gelation as a self-averaging process, with implications for controlling gelation.

Contribution

It introduces a framework showing diverse gelation transition patterns, including non-self-averaging and ultra-slow convergence, based on the growth rate of the largest clusters.

Findings

Gelation transition can be non-self-averaging.

Transition points can converge ultra-slowly.

Multiple stochastic discontinuous transitions observed.

Abstract

In irreversible aggregation processes droplets or polymers of microscopic size successively coalesce until a large cluster of macroscopic scale forms. This gelation transition is widely believed to be self-averaging, meaning that the order parameter (the relative size of the largest connected cluster) attains well-defined values upon ensemble averaging with no sample-to-sample fluctuations in the thermodynamic limit. Here, we report on anomalous gelation transition types. Depending on the growth rate of the largest clusters, the gelation transition can show very diverse patterns as a function of the control parameter, which includes multiple stochastic discontinuous transitions, genuine non-self-averaging and ultra-slow convergence of the transition point. Our framework may be helpful in understanding and controlling gelation.