Modeling the Slow Arrhenius Process (SAP) in Polymers

Amorphous glass-forming polymers exhibit multiple relaxation processes, including the structural α-relaxation associated with the glass transition and faster secondary relaxations that typically follow Arrhenius behavior. Recently, a distinct slow Arrhenius process (SAP) has been observed at frequencies well below the α-process. Although Arrhenian in its temperature dependence, the SAP involves much longer relaxation times and its microscopic origin remains unclear. Here, we extend the two-state, two-timescale (TS2) theory to describe both the α-relaxation and the SAP within a unified framework. We propose that the SAP represents the high-temperature limit of an α-like process in a coarse-grained fluid of dynamically correlated clusters. With renormalized interaction energies and coordination parameters, the same model quantitatively reproduces both α and SAP data across multiple polymers without additional adjustable parameters and explains the observed Meyer-Neldel compensation behavior. The theory further predicts that the SAP should deviate from Arrhenius behavior at sufficiently low temperatures, transitioning to Vogel-Fulcher-Tammann-Hesse-like dynamics, thereby offering a physically transparent interpretation of cluster-scale relaxation in glass-forming polymers.

💡 Research Summary

The paper presents a unified theoretical description of the slow Arrhenius process (SAP) observed in amorphous glass‑forming polymers, extending the previously developed two‑state, two‑timescale (TS2) framework that successfully captured the conventional α‑relaxation (structural glass transition) and the faster β‑relaxation (Johari‑Goldstein secondary relaxation). The authors begin by reviewing experimental evidence that SAP appears at frequencies far below the α‑process, follows a strict Arrhenius temperature dependence, and obeys a Meyer‑Neldel (entropy‑enthalpy compensation) relationship across a variety of polymers. Existing models, such as the Collective Small Displacement (CSD) approach of White, Napolitano, and Lipson, attribute SAP to the reshaping of large clusters but do not provide a comprehensive quantitative link to the α‑process.

The TS2 model treats a glass‑former as a mixture of “liquid” and “solid” domains, each of which can be in one of two states. The model introduces two characteristic relaxation times: a fast β‑time τβ that follows a simple Arrhenius law, and a slow α‑time τα that incorporates a solid‑fraction ψ(T) and a thermodynamic glass‑liquid transition temperature Tx. The α‑time expression is
τ_α = τ_el exp