Polymer Glass-Formation in Variable Dimension

TL;DR

This study investigates how polymer glass-formation varies with spatial dimension using a generalized entropy theory, revealing critical dimensional thresholds and correlations with packing frustration.

Contribution

It introduces a generalized entropy framework to analyze polymer glass-formation across different dimensions, highlighting a transition near dimension 8 and linking fluid properties to fragility.

Findings

Structural relaxation becomes Arrhenius as dimension approaches infinity.

A dense amorphous state with residual entropy appears above dimension 8.

Fluid properties correlate strongly with fragility of glass-formation.

Abstract

We explore the nature of glass-formation in variable spatial dimensionality ($d$) based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established statistical mechanical model. We find that structural relaxation in the fluid state asymptotically becomes Arrhenius in the $d\rightarrow\infty$ limit and that the fluid transforms upon sufficient cooling above a critical dimension near $d=8$ into a dense amorphous state with a finite positive residual configurational entropy. Direct computations of the isothermal compressibility and thermal expansion coefficient, taken to be physical measures of packing frustration, demonstrate that these fluid properties strongly correlate with the fragility of glass-formation.