SCALING THEORY FOR MIXTURES OF RANDOMLY BRANCHED AND LINEAR-POLYMERS IN THE MELT

We study theoretically mixtures of linear and branched chains in the melt using a Flory theory and scaling concepts. For one isolated branched chain immersed in a melt of linear chains we find three possible behaviors. If the molecular weight of the branched chain is large enough, it has the same behavior as in a monomeric solvent. If the branched chain has a smaller weight than the linear chains, it takes a compact conformation when the branching fraction is large and displays the Zimm-Stockmayer ideal statistics if the branching fraction is small. The statistics of semidilute solutions of branched chains in a polymeric solvent is deduced from the single-chain behavior with the help of a blob model. The important results is that in most regimes different branched chains do not interpenetrate. Above a critical value of the Flory interaction parameter, branched and linear chains phase separate: the phase separation is well described by the classical Flory theory for a small branching fraction. At higher branching fraction the classical theory is inappropriate and the critical demixing concentration is the overlap concentration of the branched chains in the linear-chain melt.