Orientation and relaxation of nonlinear elastic dumbbells in electric fields: Modeling transient electric birefringence

Abstract

The orientation and extension of a finitely extensible nonlinearly elastic (FENE) dumbbell in an electric field is analyzed to model the nonlinear phenomena observed during orientation and relaxation of flexible polymer molecules in transient electric birefringence measurements. In the model the dumbbell interacts with the electric field via an induced dipole with a dipole moment proportional to the end-to-end separation of the dumbbell. The electric field produces a strong ‘‘elongational’’ deformation of the molecule which has analogies with the deformations produced by elongational flow. The steady state birefringence, as a function of field strength, is calculated in two ways: first using matched expansions around low and high field conditions, and then using Peterlin’s approximation of preaveraging the connector force law. Both techniques yield similar results: Kerr law behavior is observed at low field strengths and saturation of birefringence at high field strengths. Birefringence relaxation after the field is removed shows a strong field dependence on the initial rate of relaxation. Previously proposed means of analyzing birefringence relaxation data for flexible molecules are discussed in light of this observation.