A Relation Between Fragility, Specific Heat, and Shear Modulus Temperature Dependence for Simple Supercooled Liquids

摘要

It is often said that the fragility and specific heat discontinuity at the glass transition are related characteristic features of glasses. We give a relation bwtween these quantities for simple liquids, and also find that the temperature dependence of the shear modulus should be closely related to these quantities. According to the interstitialcy theory, the liquid stte shear modulus G=G sub 0 exp(gbetac)=G sub 0 exp {-lambda[(T/T sub 0)-1]}, where G sub 0 is the shear modulus at a reference temeprature T sub o, which can be taken to be the galss temperatur. In these relations, beta is the diaelastic shear susceptibility, c is the interstitialcy concentration, T is the tmerpature, and dc/dT=lambda/beta T sub 0. It has been proposed by Dyre, Olsen and Christensen that U iin the viscosity eta=eta sub 0 exp (U/kT) be given as the work done in shoving aside particles during a diffusion step, and therefore be proportional to the shear modulus. If so, then combining the above relations, the fragility F=[d log eta/d (T sub g/T] sub T=Tg becomes F=(1+gamma) log [eta (T sub g)/eta sub 0], where U sub f is the interstitialcy formation energy, one obtains further with reasonable simplifying approximations , where G sub oo is the zero temperature crystalline shear modulus. For a typical fragile glass gamma-2(F-50) with G(T sub g)/G sub 00-1/2, then deltaC sub v/C sub v-1, but close to xero for strong glasses, in fir agreement with available experimental results. The perspecitve given by the Interstititialcy Theory is then that the fragility is given phenomenoogically by the temperature dependence of the shear modulus, or microscopically by the rate of increase of the equilibrium interstitialcy concentration with temperature.