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We develop a simple yet comprehensive nonlinear model to describe relaxationphenomena in amorphous glass-formers near the glass transition temperature. Themodel is based on the two-state, two-(time)scale (TS2) framework, and describesthe isothermal relaxation of specific volume, enthalpy, or shear stress via asimple first-order nonlinear differential equation (the Trachenko-Zaccone [TZ]equation) for local cooperative events. These nonlinear dynamics ofcooperatively rearranging regions (CRR) naturally arise from the TS2 framework.We demonstrate that the solutions of the TZ equation comprehensively encompassthe Debye exponential relaxation, the Kohlrausch-Williams-Watts (KWW) stretchedand compressed relaxations, and the Guiu-Pratt logarithmic relaxation.Furthermore, for the case of stress relaxation modeling, our model recovers, asone of its limits, the Eyring law for plastic flow, where the Eyring activationvolume is related to thermodynamic parameters of the material. Using theexample of polystyrene (PS), we demonstrate how our model successfullydescribes the Kovacs "asymmetry of approach" specific volume and enthalpyexperiments, as well as the stress relaxation. Other potential applications ofthe model, including the dielectric relaxation, are also discussed. Thepresented approach disentangles the physical origins of different relaxationlaws within a single general framework based on the underlying physics.

Unified physical framework for stretched-exponential, compressed-exponential, and logarithmic relaxation phenomena in glassy polymers