Theory of Gel Formation

TL;DR

This paper develops a theoretical framework for drop-wise addition polymerization, introducing a new distribution function for cyclic species and deriving a gel point formula, extending conventional homogeneous polymerization theory.

Contribution

It presents a novel distribution function accounting for dilution effects and derives a gel point formula specific to drop-wise addition polymerization.

Findings

New distribution function includes dilution effects

Derived gel point formula for drop-wise addition polymerization

Theoretical results align with recent experimental observations

Abstract

A theory of drop-wise addition polymerization is developed. Because of the linear growth of the reaction volume V, the system gives rise to a new type of distribution function for cyclic species that can be expressed by the sum of two terms: the conventional distribution term and a extra term due to the dilution effect. The present result is an extension of the conventional homogeneous polymerization that corresponds to a special case without the extra term. Making use of the result we derive the gel point formula for this unique polymerization. The theoretical result is compared with the recent observations.