A Laplace Transform Method for Molecular Mass Distribution Calculation from Rheometric Data

TL;DR

This paper introduces a Laplace transform method for calculating molecular mass distributions of linear polymer melts from rheometric data, offering a mathematically simple and effective alternative to light scattering techniques.

Contribution

A novel Laplace transform approach for molecular mass distribution calculation that is easy to implement and applicable to multimodal distributions in polymer melts.

Findings

Method accurately computes multimodal distributions.

Compared favorably with classical light scattering results.

Applicable within modern polymer dynamics frameworks.

Abstract

Polydisperse linear polymer melts can be microscopically described by the tube model and fractal reptation dynamics, while on the macroscopic side the generalized Maxwell model is capable of correctly displaying most of the rheological behavior. In this paper, a Laplace transform method is derived and different macroscopic starting points for molecular mass distribution calculation are compared to a classical light scattering evaluation. The underlying assumptions comprise the modern understanding on polymer dynamics in entangled systems but can be stated in a mathematically generalized way. The resulting method is very easy to use due to its mathematical structure and it is capable of calculating multimodal molecular mass distributions of linear polymer melts.