Lattice model of living polymerization. II. Interplay between polymerization and phase stability

Representative spinodal curves and polymerization lines for the equilibrium polymerization of linear polymers in a solvent have been calculated using a Flory–Huggins-type mean-field theory. The calculations are primarily restricted to systems that polymerize upon cooling, but examples are also given for systems that polymerize upon heating. In the former case, we find that an increase in the magnitude of enthalpy of propagation |Δh| (“sticking energy”) leads to an elevation of the critical temperature Tc and to a decrease of the critical composition φc when |Δh| exceeds a critical value |Δhc|. The shifts in the critical temperature and composition, ΔTc≡Tc(Δh)−Tc(Δh=0) and Δφc≡φc(Δh)−φc(Δh=0), vary linearly with Δh for |Δh|>|Δhc| over a large range of sticking energies |Δh|, so that ΔTc is proportional to Δφc for a sufficiently large sticking energy. Variations in the phase boundaries with Δh are also evaluated for systems that polymerize upon heating, but the presence of multiple critical points in this case renders a general description of these changes difficult. The polymerization line is found to be independent of solvent quality (χ interaction parameter) within the simple Flory–Huggins model, but the phase stability is strongly influenced by the magnitude of both χ and Δh. Similarities between living polymers and other types of associating polymers (thermally reversible gels, micelles) suggest that some of the thermodynamic consequences of particle association in these self-assembling systems are insensitive to the detailed nature of the clustering process. Thus, our results may have a much broader range of applicability than living polymer solutions (e.g., gelation in clay and other colloidal suspensions, polyelectrolyte solutions, cell aggregation, and self-organization of biologically significant structures that exist at equilibrium).