Rheothermodynamics of transient networks

Abstract

The transient network model of Green-Tobolsky [1946], Yamamoto [1956] and Tanaka-Edwards [1992] is formulated within the frame of thermodynamics of irreversible processes, using as a fundamental quantity the chemical potential associated to the connection of strands to the network and treating these connections as chemical-like reactions. All thermodynamic quantities are thus naturally defined in and out of equilibrium. Constitutive equations are derived, giving the stress and the heat production as functions of the thermomechanical history. The Clausius-Duhem inequality, stating that the source of entropy is non-negative, is shown to hold for any thermomechanical history, ensuring the thermodynamic consistency of our model. The presented model includes the Green-Tobolsky model, whereas those of Yamamoto and Tanaka-Edwards fit within ours on the condition that their free parameters obey a detailed balance condition stemming form Boltzmann equilibrium statistics.