EFFECT OF DYNAMICAL ASYMMETRY ON THE VISCOSITY OF A RANDOM COPOLYMER MELT

The variation of the viscosity as a function of the sequence distribut ion in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, t he parameter lambda which determines the correlation in the monomer id entities along a chain and the Flory chi parameter chi(F) which determ ines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlik e monomers are more likely to be adjacent to each other. The tradition al Markov model for the random copolymer melt is altered to remove ult raviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type t ransition for lambda>0 and does not exhibit a phase transition for lam bda<0. A mode coupling analysis is used to determine the renormalizati on of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupl ing. there are nonlinearities both in the transport equation and in th e noise correlation. The concentration dependence of the transport coe fficient presents additional difficulties in the formulation due to th e Ito-Stratonovich dilemma, and there is some ambiguity about the choi ce of the concentration to be used while calculating the noise correla tion. In the Appendix, it is shown using a diagrammatic perturbation a nalysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provid es a consistent formulation that satisfies stationarity and the fluctu ation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present p roblem as well. The upper critical dimension for this type of renormal iaation is 2, and so there is no divergence in the viscosity in the vi cinity of a critical point. The results indicate that there is a syste matic dependence of the viscosity on lambda and chi(F). The fluctuatio ns tend to increase the viscosity for lambda<0, and decrease the visco sity for lambda>0, and an increase in chi(F) tends to decrease the vis cosity. (C) 1996 American Institute of Physics.