About activation energy of viscous flow of glasses and melts

Abstract

Data on a viscous flow model based on network defects–broken bonds termed configurons–were analysed. An universal equation has been derived for the variable activation energy of viscous flow Q(T) of the generic Frenkel equation of viscosity η(T)=A∙exp(Q/RT) which is known to have two constant asymptotes–high Q_H at low temperatures and low Q_L at high temperatures. The defect model of flow used by e.g. Doremus, Mott, Nemilov, Sanditov states that higher the concentration of defects (e.g. configurons) the lower the viscosity. We have used the configuron percolation theory (CPT) which treats glass–liquid transition as a percolation-type phase transition. Additionally the CPT results in a continuous temperature relationship for viscosity valid for both glassy and liquid amorphous materials. We show that a particular result of CPT is the universal temperature relationship for the activation energy of viscous flow: Q(T)=Q_L+RT∙ln[1+exp(-S_d/R) exp((Q_H-Q_L)/RT)] which depends on asymptotic energies Q_L (for the liquid phase) and Q_H (for the glassy phase), and on entropy of configurons S_d. This equation has two asymptotes, namely Q(T<<T_g) = Q_H, and Q(T>>T_g) = Q_L. Moreover we demonstrate that the equation for Q(T) practically coincides in the transition range of temperatures with known Sanditov equation.