A Constraint-Modulated Rate Law Outperforming VFT and Its Modern Alternatives Across Canonical Glass-Forming Liquids

TL;DR

This paper introduces a new constraint-modulated rate law called CPA+C for modeling viscosity in glass-forming liquids, outperforming traditional models like VFT and modern alternatives across multiple datasets.

Contribution

The paper proposes the CPA+C model that incorporates a temperature-dependent constraint load, providing a more accurate and generalizable description of glass transition behavior.

Findings

CPA+C outperforms VFT, MYEGA, and Avramov-Milchev on most datasets.

CPA+C achieves lower prediction errors and better model ranking metrics.

A sigmoid variant of CPA+C fits data as well or better, indicating flexibility.

Abstract

A constraint-modulated rate law for viscosity in glass-forming liquids is reported. The key assumption is that each configurational state is resolved independently under its current structural constraints, rather than as a point on a predetermined free-energy surface. This approach, termed Continuous Present Actualization (CPA), requires a rate law that tracks resolution cost as it changes with temperature. The formulation, CPA + Constraint (CPA+C), introduces a temperature-dependent constraint load C(T) that quantifies how configurational access narrows as a liquid approaches the glass transition. Tested against VFT and its modern divergence-free successors MYEGA and Avramov-Milchev on canonical datasets for ortho-terphenyl, salol, and boron trioxide, CPA+C outperforms all three on four of five datasets after full AIC penalization for its two additional parameters, with margins reaching Delta-AIC = 141. On two datasets the baseline kinetic parameter vanishes, reducing the effective model to four free parameters. BIC confirms the same ranking. A smooth sigmoid variant fits equally well or better. The single exception occurs on the narrowest-range dataset, where the temperature range is too narrow for the constraint transition to separate the model from simpler alternatives. Leave-one-out cross-validation on salol (n=95) confirms that CPA+C generalizes to held-out data with mean prediction error 3x lower than the next-best model.