Thermodynamics of Viscoelasticity in Liquids

A tensorial ordering parameter, obeying a linear relaxation equation, is introduced to describe the elastic shearing strain exhibited by a liquid at high frequencies. The coefficients in the relaxation-rate equation and the shear modulus in the stress tensor are linked by the Onsager-Casimir reciprocal relations with the result that the total rate of deformation is divided into elastic and viscous parts, in agreement with a hypothesis made by Frenkel to derive the viscoelastic stress relaxation equation of Maxwell. The hypersound wave velocity is computed from the thermal conductivity by an adaptation of a theory of Debye and from it the shear modulus and shear relaxation time are computed, effects of thermal relaxation being taken into account. In three nonassociated liquids, order-of-magnitude agreement is found with values calculated from a theory by Mooney.