Phase Behavior of Reversibly Polymerizing Systems with Narrow Length Distributions

The lattice models of Flory and DiMarzio for rigid linear polymers of fixed length have been extended to describe reversibly polymerizing systems with narrowly distributed polymer lengths (i.e., it is assumed that the system remains approximately monodisperse as the average polymer length varies with concentration and other variables). Whereas irreversibly polymerized systems are expected to form a relatively dilute, partially aligned anisotropic phase unless sufficiently strong attractions between polymers are present to condense them, we find that reversibly polymerizing systems are expected to form a highly concentrated and highly ordered anisotropic phase unless sufficiently strong repulsions between polymers are present to separate them. The predicted temperature dependence of the phase behavior for the two systems is markedly different. For the reversibly polymerizing system there exists a temperature below which there is no phase transition at any concentration of solute. Just above this temperature there is a wide two-phase region in which a dilute isotropic phase, consisting of monomers or very short polymers, is in equilibrium with a quasi-crystalline phase consisting of very long, highly aligned polymers which essentially completely exclude solvent. The decrease in the concentration of the isotropic phase, with increasing temperature, occurs at a progressively decreasing rate to give an “elbow-shaped” phase boundary. The anisotropic phase remains very dense at high temperatures unless the interactions between polymers are sufficiently repulsive to separate them and admit solvent. The temperature dependence of the viscosity of sickle-cell hemoglobin solutions is consistent with the theoretical predictions. Interpretation of the experimental data in terms of the model suggests that domain dimensions could be a major determinant of the viscous properties of these sickle-cell hemoglobin solutions and could account for some of the hysteresis observed in these systems.