The free energy of a deforming Lodge rubber-like liquid

Abstract

The Lodge network model for concentrated polymer solutions is used to develop a free energy expression in the limit of small deformation rate. Departing from the previous practice of postulating an ad hoc expression analogous to that for a single Gaussian chain with a fixed end-to-end vector, we derive an expression which is consistent with the mechanical picture of the concentrated solution as a network of Hookean springs. By doing this we show that the expression currently in use is actually the internal energy change upon deformation of the network segments. In the case of steady shear and elongational flows the entropic contribution of the springs to the solution free energy is shown to be as large as 50% of the internal energy contribution. For these flows the procedure adopted in this paper, enables us to have a unified treatment of dilute and concentrated polymer solutions and leads to identical free energy expressions in both these limiting cases.