# Nucleation theory of polymer crystallization with conformation entropy

## TL;DR

This paper develops theoretical models based on classical nucleation theory to understand polymer crystallization, explicitly considering conformation entropy and chain interactions, revealing differences in nucleation behavior between single and multi-chain systems.

## Contribution

It introduces two models for polymer nucleation that explicitly incorporate conformation entropy and chain interactions, advancing understanding of nucleation mechanisms.

## Key findings

- Multi-chain nucleation is easier than single-chain nucleation for semi-flexible polymers.
- Nucleation probability depends on chain stiffness and system type.
- Adding chains into the nucleus facilitates growth in multi-chain systems.

## Abstract

Based on classical nucleation theory, we propose a couple of theoretical models for the nucleation of polymer crystallization, i.e. one for a single chain system (Model S) and the other for a multi-chain system (Model M). In these models, we assume that the nucleus is composed of tails, loops and a cylindrical ordered region, and we evaluate the conformation entropy explicitly by introducing a transfer matrix. Using these two models, we evaluate the occurrence probability of critical nucleus as a function of the polymer chain stiffness. We found that the critical nucleus in Model M is easier to occur than in Model S because, for semi-flexible chains, the nucleus in Model M can grow by adding a new polymer chain into the nucleus rather than to diminish the loop and tail parts as in the case of Model S.