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 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.