About activation energy of viscous flow of glasses and melts
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About activation energy of viscous flow of glasses and melts Michael I. Ojovan1 1 Department of Materials, Imperial College London, London SW7 2AZ, UK 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 QH at low temperatures and low QL 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)=QL+RT·ln[1+exp(-Sd/R) exp((QH-QL)/RT)] which depends on asymptotic energies QL (for the liquid phase) and QH (for the glassy phase), and on entropy of configurons Sd. This equation has two asymptotes, namely Q(TTg) = QL. Moreover we demonstrate that the equation for Q(T) practically coincides in the transition range of temperatures with known Sanditov equation. INTRODUCTION Interest in the physics of disordered state of matter and in particular to study the rheology is high, and in recent years a number of results have shed light on the nature of the changes occurring at the glass transition [1-7]. Vitrification according to the IUPAC definition is considered as a quasi-second order transition in which a supercooled melt yields, on cooling, a glassy structure so that below the glass-transition temperature the physical properties of glasses vary in a manner similar to those of the crystalline phases. The physical picture of the glass transition in amorphous materials with decrease of temperature involves the representation of the topology change of disordered bonds lattice (network) and of increase of Hausdorff dimension of the network [3, 4] with supporting evidences on short and medium range order structural changes at glass transition given in [4-7]. Rearrangements that occur in an amorphous material at the glass transition temperature lead to characteristic jumps of derivative thermodynamic parameters such as the coefficient of thermal expansion or the specific heat. These discontinuities allow to detect the glass transition temperature however for practical purpose the arbitrary glass transition temperature is found from the viscosity-temperature relationship as a temperature at which viscosity reaches 1012 Pa s [8]. Note that for some materials this value belongs to the glasstransition region defined by specific heat capacity measurement, but it is not the case for other materials [9]. A significant interest is also seen to study the visco
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