Eshelby description of highly viscous flow—Half model, half theory

Abstract

A recent description of the highly viscous flow ascribes it to irreversible thermally activated Eshelby transitions, which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. The description is extended to include reversible Eshelby transitions, with the Kohlrausch exponent β as a free parameter. The model answers several open questions in the field.

Long-time structural relaxation of glass-forming liquids: Simple or stretched exponential?

“…We conjecture that the existence of a terminal relaxation rate is a general feature of glass-forming liquids, which any reliable theory of viscous liquid dynamics must account for. 34,[42][43][44][45][46][47]…”

Theory of the highly viscous flow

“…where G is the high frequency shear modulus and η is the viscosity. The normalized decay time distribution in the barrier variable v = ln(τ /τ c ) is [9]…”

“…Eq. ( 6) for the relaxation time distribution of the irreversible processes turned out to be able to describe dynamic heat capacity data with the Maxwell time from shear data for four different glass formers, among them two hydrogen bonded substances [5,9].…”

Eshelby ensemble of highly viscous flow out of equilibrium

“…This was first shown [13] for PPE, a vacuum pump oil consisting of five connected phenylene rings and later [14] for a metallic glass, for glycerol and for propylene glycol. The present paper will add more examples.…”

“…Very recently, the distinction between reversible and irreversible processes has been introduced into the Eshelby shear transformation picture, with the irreversible processes responsible for the viscous flow, and the reversible ones responsible for the recoverable shear compliance J 0 and the short-time Kohlrausch time dependence [13,14].…”