Higer order calculations of the renormalization group flow for multicomponent polymer solutions

(Received 19 July 1990, accepted 25 October 1990)

Abstract
We calculate to three-loop order the renormalization group flow of the interaction constants for polymer solutions containing several chemically different polymer species. Close to the fixed points we determine the flow by a Padé-Borel analysis using information on the asymptotic behaviour of the perturbation expansion. We furthermore derive exact relations which connect the correction to scaling exponents of binary solutions or of star polymers, and in the cross over region we integrate the flow equations numerically to get a global picture. To clarify the relation to previous work based on "direct renormalization" we present a detailed discussion of the interpenetration ratio for two chains of different chemistry or size.