Phase equilibria and fractionation of linear homopolymers in solution: A thermodynamic numerical interpretation

A numerical procedure is described for the quantitative interpretation of experimental fractionations by successive precipitations. The analysis is based on a thermodynamic relationship (mp″/mp′ = A·Bp) between the masses of a polymeric component with degree of polymerization, p, distributed between two liquid phases in equilibrium (mp″ and mp′) and the parameters A and B, which are independent of the degree of polymerization but functions of the thermodynamic variables. An individual pair of A and B parameters corresponds to every individual fraction. The numerical procedure, which is iterative in nature, provides the means for calculating the molecular‐weight distribution of the individual fractions. The procedure requires data from the experimental fractionation (number‐average degree of polymerization and total mass fraction of each fraction) and knowledge of the molecular‐weight distribution function of the whole, starting polymer. The procedure was applied to the analysis of the results of two experimental fractionations of polyamide 11, whereby covergence was quickly reached after a few iterations in the calculations of every set of A and B parameters.