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.

On Viscous Flow in Glass-Forming Organic Liquids

“…At intermediate temperatures, the activation energy of the viscous flow Q(T) is a function of the temperature, e.g., it can be used in an Arrhenius-type equation η(T) = A•T•exp(Q/RT), where it formally depends on the temperature. There are many effective models of viscosity to account for this [39][40][41][42][43], with two of the most frequently used models being the Williams-Landel-Ferry (WLF) equation for polymers and the Vogel-Fulcher-Tammann (VFT) equation for inorganic materials. The WLF equation typically used for polymers is [39]:…”

“…At intermediate temperatures, the activation energy of the viscous flow Q(T) is a function of the temperature, e.g., it can be used in an Arrhenius-type equation η(T) = A·T·exp(Q/RT), where it formally depends on the temperature. There are many effective models of viscosity to account for this [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 39 , 40 , 41 , 42 , 43 ], with two of the most frequently used models being the Williams–Landel–Ferry (WLF) equation for polymers and the Vogel–Fulcher–Tammann (VFT) equation for inorganic materials. The WLF equation typically used for polymers is [ 39 ]: η(T) = η 0 ·exp[−C 1 ·(T − T 0 )/(C 2 + T − T 0 )] where η 0 is a constant and T 0 is taken as T g , whereas C 1 and C 2 are universal constants for most polymeric materials.…”

“…As seen from Figure 1 , this is also the case for B 2 O 3 , which is also a fragile liquid, with R D = 3.28 [ 8 , 30 ]. Analysis of the activation energy for the viscosity of silica, which is a strong (long) liquid, shows that Q(T) changes over a wider range within the glassy state [ 43 ], although this range is narrow compared to T g . Accounting for this, we can conclude that the Arrhenius-type behavior of the viscosity with low activation energy Q L occurs when exp(T/T g ) > 1 rather than requesting T/T g >> 1, which is a very strong requirement when processing experimental data [ 30 ].…”

Study of Activation Energy for Viscous Flow of Mixtures as a Measure of Dilution Efficiency for Heavy Oil-Diluent Systems

“…To derive an equation for the activation energy change due to dilution of heavy crude oil using a suitable diluent, A E in Eq. (1) will be regarded as the activation energy for viscous flow (Ojovan, 2015). In this regard, the viscous flow activation energy for the original viscous heavy oil will be different from that of the mixture consisting containing a known fraction of diluent due to change in molar volume following the dilution.…”

Structural Changes in Metallic Glass-Forming Liquids on Cooling and Subsequent Vitrification in Relationship with Their Properties

“…More generally the universal temperature relationship for the activation energy of viscous flow of liquids is [ 108 ]: E(T) = E L + RT∙ln[1 + exp(−S d /R)∙exp((E H − E L )/RT)] which depends on these two asymptotic energies and on the entropy of configurons S d . Also, spatial heterogeneities (soft and hard zones) can alter the dynamics of supercooled liquids and glasses [ 109 , 110 ].…”