Scaling in Kinetics of Supercooled Liquids

Abstract: The present study introduces a renormalization based approach to investigate the relaxation dynamics within supercooled liquids. By applying a numerical scale transformation to potential energies along the temporal axis, we have established a novel framework that elucidates the underlying kinetics of supercooled liquids. Our findings indicate that the skewness of the potential energy distribution attains its maximum at a characteristic time scale, D, which exhibits a Curie like scaling relationship with temperature. This scaling relationship is characterized by an exponent, g, that experiences a discontinuous transition at a critical cooling rate, signifying a kinetic like phase transition.We further demonstrate that g maintains an approximate scaling relationship with the cooling rate, where the product of g and the logarithm of the cooling rate is approximately constant.This constant, however, varies depending on whether the cooling rate is above or below the critical value, effectively classifying supercooled liquids into two distinct categories: the glass transition as the destiny of supercooled liquid, GDL, and the crystallization as the destiny of supercooled liquid, CDL. Furthermore, we identify that Ts corresponds to the glass transition temperature for GDL and the crystallization temperature for CDL, respectively. We have successfully developed a theoretical model,which not only derives the Curie like power law but also provides profound insights into the physical implications of D, g and Ts. This research delineates the differences between GDL and CDL, and offers a fresh perspective for exploring the nature of glasses. The findings contribute to the broader understanding of the dynamics of supercooled liquids and the mechanisms of glass formation.