Determination of cooperatively rearranging regions in a binary glass former

Cooperative motions are important for understanding the divergence of viscosity of glassy materials at a finite temperature, since the elementary process of the structural relaxation occurs within the smallest cooperative region as suggested by Adam and Gibbs. On the basis of the definition of a cooperatively rearranging region (CRR) by Adam and Gibbs and by Odagaki, we determine the size of CRR for the Kob-Andersen model as a function of temperature using molecular dynamics simulations. We first confine particles in a spherical region and, varying the radius of that region, we determine the CRR size as the smallest radius of the region in which particles can change their relative positions. The size of the CRR increases as the temperature is reduced and seems to diverge below the glass transition temperature. The temperature dependence of the number of particles in the CRR obeys the equation derived from the Adam-Gibbs relation and the Vogel-Fulcher-Tammann equation.