Transient biaxial orientation of flexible polymer chains in a wide range of deformation conditions

Abstract

Transient distribution function of chain ends in non-linear polymer fluids subjected to a constant biaxial flow deformation is approximated by an affine evolution of initial Gaussian distribution function. A non-linear elastic dumbbell potential is used in the evolution equation for the distribution function, with the Peterlin and Padè approximations of inverse Langevin function. With the approximations, the evolution equation reduces to a system of ordinary first order differential equations for axial components of affine molecular deformation tensor.Numerical and a self-consistent analytical method of solving the system of evolution equations are proposed. Example computations are performed for uniaxial, incompressible elongational flow.The non-linear model covers entire range of deformation rates, and predicts molecular deformation tangential to macroscopic deformation at the beginning of the process, and asymptotically converging to the equilibrium chain deformation in the limit of infinite time. The model describes time evolution of the chain distribution function between the macroscopic affine limit at the beginning of the process and the equilibrium asymptote. The evolution deviates from the asymptotes the more, the lower is the deformation rate. For slow processes, linear Gaussian model is valid, and for very fast ones, solid-like behavior takes place with minor deviation between the molecular and macroscopic deformations, up to the level of full chain extension.