Dynamics of helical worm-like chains. X. Oscillatory flow birefringence

Abstract

Oscillatory flow birefringence of flexible chain polymers in dilute solution is studied on the basis of the discrete helical worm-like chain such that a local polarizability tensor is attached rigidly to each of the subbodies composing the chain. The mechano-optic coefficient S is formulated by the time-correlation function formalism, and is expressed in terms of the (1,1)- and (1,2)-body time-correlation functions of ‘‘total angular momentum quantum number’’ L=2. The (1,2)-body time-correlation functions are evaluated following a procedure analogous to the one developed previously in the higher-order subspace approximations. It is then shown that the three branches (one global and two local) of the viscoelastic eigenvalue spectrum and the five local branches of the magnetic one make contributions to S. With these results, examination is made of the frequency behavior of the phase angle θs of S and also of its dependence on the local polarizability tensor. It is found that the high-frequency behavior of observed θs, which deviates from the prediction for the Zimm spring–bead model, may well be explained by the contributions from the local chain motions with proper local polarizability tensors. A comparison of theory with experiment is made for atactic polystyrene with respect to the frequency dependence of θs, and the good agreement is found with the model parameters determined from an analysis of experimental data for equilibrium properties.