Abstract
This paper is the fourth in a series exploring the physical consequences of the solidity of highly viscous liquids. It is argued that the two basic characteristics of a flow event (a jump between two energy minima in configuration space) are the local density change and the sum of all particle displacements. Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k space of the form Gamma0 + Dk2 with D >> Gamma0a2 where a is the average intermolecular distance. The inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) may be taken to be ultralocal. As an illustration of the theory the case with the simplest nontrivial Hamiltonian is solved to second order in the Gaussian approximation, where it predicts an asymmetric frequency dependence of the isothermal bulk modulus with Debye behavior at low frequencies and an omega(-1/2) decay of the loss at high frequencies. Finally, a general formalism for the description of viscous liquid dynamics, which supplements the density dynamics by including stress fields, a potential energy field, and molecular orientational fields, is proposed.
Highlights
Glasses are made by cooling viscous liquids
Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k space of the form ⌫0 + Dk2 with D ӷ ⌫0a2 where a is the average intermolecular distance
We argued above that in view of Eq ͑1͒ viscous liquid dynamics are basically to be identified with the “inherent dynamics” ͓10͔ consisting of jumps between potential energy minimainherent structures
Summary
Glasses are made by cooling viscous liquids. The liquid relaxation time increases dramatically upon cooling, and the glass transition takes place when exceeds the inverse cooling rate: ӷ 1 / ͉d ln T / dt. The incoherentsingle-particlediffusion constant Ds is extremely small, and in the well-known expression for Ds in terms of the velocity autocorrelation function Ds = ͐0ρvx0͒vxt͘dt there is a most delicate cancellation of contributions This fact was emphasized in 1984 by Brawer7͔ who pointed out that if one wishes to apply conventional liquid-state theory to viscous liquids approaching the calorimetric glass transition, the approximations used should be accurate to many digits in order to give reasonable results. In terms of the average intermolecular distance adefined by writing the volume per molecules as a3͒, the ␣ relaxation time , and the high-frequency sound velocity c, the solidity length is given by l4 = a3c This expression was derived by noting that a flow event is followed by the emission of a spherical sound wave; l is determined by requiring that elastic equilibrium be just about established throughout a sphere with radius l before the flow event inside the sphere typically takes place16͔. We propose principles for the general description of viscous liquid dynamics
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
