Graph theory of configurational and viscoelastic properties of polymers, 3. Cyclic and star‐shaped chains containing small copolymeric blocks

Abstract

AbstractGraph theory of configurational and viscoelastic properties of polymers has been extended to treat cyclic and star‐shaped chains containing small copolymeric blocks in the free‐draining limit. Analytical expressions of the zero‐shear‐rate viscosity η4 and the steady‐state recoverable compliance J of these types are obtained. In the Rouse theory of viscoelastic behaviour η0 and J are directly related to the moments of the radius of gyration 〈S2〉 and 〈S4〉, hence both can be obtained simultaneously. Particularly, the relaxation spectrum of cyclic alternating block copolymer chains can also be obtained. The results obtained in this paper indicate that the structures of these types of chains are altered locally by the incorporation of a small concentration of another type of segments; the variation in viscoelasticities cannot be ignored and shows a strong dependence on block configuration. The results obtained may prove useful for understanding and interpreting the rheological data of block copolymers.