Phase Behavior of Linear/Branched Polymer Blends

Abstract

The phase behavior of a linear/branched polymer blend is predicted within the framework of the Flory-Huggins theory. The linear polymer is treated as monodisperse and the branched polymer as polydisperse with power law statistics, O(N) ∞ N -(τ-1) , cut off at some upper degree of polymerization N 2 . The latter is dependent on the reacted fraction, α, and the functionality, f, of the functional groups of the branched polymer. We calculate analytically the spinodal curves for various α up to the gel point and find unusual behavior of the critical point. In particular, it is found to be very sensitive to the exponent of the power law distribution function, e.g., whether τ takes the classical value of 2.5 or the percolation value of 2.20. Example cloud point curves and coexistence curves have been calculated numerically, again for various α, and a picture of the evolution of the phase diagram during cross-linking has been constructed. The coexistence curves are surprisingly steep as χ is varied over a large range ; this is particularly evident for the parameters of the linear-rich phase. Hence it is found that although the distribution of the branched polymer in the linear-rich phase varies considerably with increasing χ, the ratio of linear and branched polymer volume fractions within this phase does not. From our results we are able to predict, at least qualitatively, a secondary phase separation that is known to occur in such blends.