CALCULATION OF THE NON-LINEAR STRESS OF POLYMERS IN OSCILLATORY SHEAR FIELDS

Complex moduli are calculated for the lowest-order deviations from linearity of the stress in an oscillatory shear field. The calculations involve solution of an equation, recently proposed by Doi, which goes beyond the ″independent alignment approximation″ of the Doi-Edwards theory of polymer dynamics. The new equation incorporates various reptative motions of a polymer in the effective constraining tube induced by entanglements, viz. Brownian motion along the tube and the systematic motion in response to changes in the length of the tube accompanying affine deformation.