Modeling creep and strain relaxation as an anomalous diffusion-limited mixed 2nd order reaction

Relaxation dynamics of disordered systems can be modeled as a reaction process limited by diffusion. In the case of a mechanical relaxation of a polymer or glass, "reactant A" corresponds to a concentration of strained bonds, and "reactant B" corresponds to a concentration of energetic catalyst such as a diffusing void or phonon above a certain energy cutoff, which permits the strained bond to relax upon contact. When the limiting diffusion is anomalous, stretched exponential relaxations (Kohlrausch-Williams-Watts law) or power-law decays (Curie-von Schweidler law) can result. These slow relaxations have been observed in a wide range of cases including stress relaxation in polymers, conductivity in amorphous solids, photocurrent in organic and inorganic materials, and dielectric relaxation in glasses among others. A microscopic model that can describe the dynamics of both standard and anomalous diffusion is the continuous-time random walk theory (CTRW), whereby each step of the diffusive random walk is governed by a wait-time distribution function ψ(τ ) predicting the probability ψ(τ )dτ for the subsequent step to be taken within dτ of the wait time τ. Working from the CTRW framework, this work will fit both analytical expresions and stochastic simulations to experimental data of relaxation phenomena to elucidate the role that different CTRW parameters play in the resulting random walk and, in turn, the relaxation dynamics.