"Burning and sticking" model for a porous material: suppression of the topological phase transition due to the backbone reinforcement effect

TL;DR

This paper introduces the burning-and-sticking lattice model for porous materials, demonstrating that backbone reinforcement prevents the topological phase transition, unlike traditional models.

Contribution

It presents a novel burning-and-sticking model showing the suppression of phase transition due to backbone reinforcement effects.

Findings

Backbone exists at arbitrarily low concentrations in the model.

Phase transition is suppressed by sticking and reinforcement effects.

Hybrid models with probabilistic sticking also lack a phase transition.

Abstract

We introduce and study the "burning-and-sticking" (BS) lattice model for the porous material that involves sticking of emerging finite clusters to the mainland. In contrast with other single-cluster models, it does not demonstrate any phase transition: the backbone exists at arbitrarily low concentrations. The same is true for hybrid models, where the sticking events occur with probability $q$: the backbone survives at arbitrarily low $q$. Disappearance of the phase transition is attributed to the backbone reinforcement effect, generic for models with sticking. A relation between BS and the cluster-cluster aggregation is briefly discussed.