New Insights into the Dependence of Glass Transition Temperature and Dynamic Fragility on Molecular Weight in Oligomers and Polymers

TL;DR

This paper explores how the glass transition temperature and dynamic fragility of polymers depend on molecular weight, revealing linear relationships and unifying behavior across oligomers and high polymers through theoretical modeling.

Contribution

It demonstrates that T_{g} and relaxation times scale linearly with 1/M, unifying oligomer and polymer behavior using the SL-TS2 theory and thermodynamical scaling.

Findings

Relaxation time curves collapse onto a master curve across oligomers and polymers.

T_{g} and fragility are linear functions of 1/M, consistent with Fox-Flory.

Theoretical interpretation aligns with thermodynamical and thermal expansion principles.

Abstract

In an earlier preprint (V. V. Ginzburg, O. V. Gendelman, R. Casalini, and A. Zaccone, arxiv:2409.17291), we demonstrated that the dynamic (relaxation time) and volume equations of state for many amorphous polymers are near-universal -- each material is characterized by two governing parameters -- the glass transition temperature, T_{g}, and the elementary relaxation time, /tau_{el}. The dynamic fragility, m, is uniquely related to /tau_{el}. The earlier analysis was based on the data for high polymers (degree of polymerization, N > 200, and molecular weight, Mw > 20,000 g/mol). Here, we investigate the dependence of T_{g} and /tau_{el} on N (or, equivalently, on the molecular weight, M). We consider the dielectric spectroscopy data for homologous series of four polymers: polystyrene (PS), poly-(2-vinylpyridine) (P2VP), poly(dimethylsiloxane) (PDMS), and polybutadiene (PB). It is shown that the relaxation time curves for various oligomers can be successfully collapsed onto the same master curve as the high polymers. The glass transition temperature and the dynamic fragility are found to be linear functions of 1/M, in agreement with the Fox-Flory equation. The scaling results are interpreted based on the SL-TS2 theory, ensuring that the model description is consistent with the Boyer rules for the coefficients of thermal expansion above and below T_{g}, as well as the thermodynamical scaling for the pressure dependence of the relaxation time.