A general theory of kinetics and thermodynamics of steady-state copolymerization

TL;DR

This paper develops a unified truncation method to solve complex kinetic equations in steady-state copolymerization, including depropagation effects, and introduces a thermodynamic framework incorporating sequence entropy.

Contribution

It presents a novel truncation approach for higher-order models with depropagation and derives a general thermodynamic equality involving sequence entropy.

Findings

Exact solutions for steady-state kinetic equations with depropagation.

A thermodynamic equality incorporating Shannon entropy of sequences.

Unified treatment applicable to any-order terminal models.

Abstract

Kinetics of steady-state copolymerization has been investigated since 1940s. Irreversible terminal and penultimate models were successfully applied to a number of comonomer systems, but failed for systems where depropagation is significant. Although a general mathematical treatment of the terminal model with depropagation was established in 1980s, penultimate model and higher-order terminal models with depropagation have not been systematically studied, since depropagation leads to hierarchically-coupled and unclosed kinetic equations which are hard to be solved analytically. In this work, we propose a truncation method to solve the steady-state kinetic equations of any-order terminal models with depropagation in an unified way, by reducing them into closed steady-state equations which give the exact solution of the original kinetic equations. Based on the steady-state equations, we also derive a general thermodynamic equality in which the Shannon entropy of the copolymer sequence is explicitly introduced as part of the free energy dissipation of the whole copolymerization system.