A Unified Theoretical Treatment on Statistical Properties of the Semi-batch Self-condensing Vinyl Polymerization System

TL;DR

This paper introduces a new generating function method for analyzing semi-batch self-condensing vinyl polymerization, enabling explicit calculation of molecular weights and polydispersity, and guiding the design of hyperbranched polymers.

Contribution

A novel generating function approach that provides a unified analytical framework for semi-batch SCVP systems with customizable feeding strategies.

Findings

Explicit formulas for molecular weights and polydispersity index.

Validation of analytical results through Monte Carlo simulations.

Guidance for designing hyperbranched polymers with desired properties.

Abstract

We present a novel generating function (GF) method for the self-condensing vinyl polymerization (SCVP) system with any initial distribution of preexisted polymers. Such a method was proven to be especially useful to investigate the semi-batch SCVP system allowing a sequence of feeding operations during the polymerization. Consequently, the number-, weight-, and z-average molecular weights as well as polydispersity index of hyperbranched polymers can be explicitly given, which are determined by predetermined feeding details and conversions in each polymerization step. These analytical results are further confirmed by the corresponding Monte Carlo simulation. Therefore the present GF method has provided a unified treatment on the semi-batch SCVP system. Accordingly, hyperbranched polymers with desired properties can be prepared by designing feeding details and presetting conversions at each step based on the present GF method.