Concentrated solutions of polydisperse rodlike polymers in the isotropic and lyotropic liquid‐crystalline phases. I. The effects of molecular length distribution on phase behavior

The earlier calculations of Moscicki and Williams of the phase behavior of rodlike macromolecules in solution incorporating a Gaussian distribution of rod lengths have been extended to include, in addition to a “basic” Gaussian distribution, a small amount of high‐molecular‐weight species which are characterized by a δ‐function or “box‐function” distribution. It is shown that C*p, the concentration of polymer at which the biphasic material (isotropic plus anisotropic phase) first appears may be substantially lowered in comparison with that for the system comprising only the basic distribution. The volume fraction ΦA of anisotropic phase, the compositions of the two phases, and the distribution of species between the phases are calculated for a range of polymer concentration which spans the isotropic, biphasic, and anisotropic phase and, among several features obtained, it is shown that the high‐molecular‐weight species are essentially responsible for the initial formation of anisotropic phase in the biphasic system. The results of the calculations have important implications for the interpretation of published dielectric relaxation data for polyalkylisocyanates in solution at high concentration and for published shear‐flow viscosity data for polyalkylisocyanates and poly(p‐benzamide) in solution at high concentration and these are discussed in some detail.