Modeling the slow Arrhenius process (SAP) in polymers

Abstract

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 αβ-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.