Slow Time Phenomena in Heterogeneous Materials: from Microscopic Fluctuations to Macroscopic Relaxation

Abstract

Slow time relaxation of elastic moduli with typically logarithmic time dependence is observed in many media interesting for materials science. This phenomenon is related to internal structure and is, hence, important for the development of present-day materials. Here, we provide a general explanation showing a close link between slow time phenomena and fluctuations on the microscopic and mesoscopic scales. We look for the origin of slow time phenomena in random walk or diffusion processes on microscopic scales. Some bonds occurring in the metastable state make a transition through the energy barriers due to small fluctuations slightly perturbing the statistical equilibrium. If the number of the excited bonds is small compared to the total number of bonds in a heterogeneous material, the process of the transition as a whole can be considered as mesoscopic fluctuations. Averaging over all transient bonds or states is revealed in the observed macroscopic relaxation of elastic moduli, velocities, and others. The functional dependence on time in the relaxation process has been shown to be controlled by the profile of energy barriers. The results obtained point to their possible applications in materials science.