Lattice model of living polymerization. III. Evidence for particle clustering from phase separation properties and "rounding" of the dynamical clustering transition

Equilibrium polymerization is studied here as a prototype for clustering tr ansitions that commonly occur in systems of interacting particles at equili brium. These transitions are often difficult to locate because of transitio n "rounding" associated with a limited extent of cluster growth, competing association or dissociation processes that initiate or inhibit clustering, and other constraints on the particle clustering dynamics. Instead of singu larities in thermodynamic and transport properties, more subtle property ch anges signal the onset of particle clustering, explaining why clustering tr ansitions are often overlooked or misinterpreted. We utilize a Flory-Huggin s model for the equilibrium ("living") polymerization of linear polymer cha ins to identify experimental signatures (features in the osmotic pressure, osmotic compressibility, and specific heat) that can be used to locate and quantify the transition "rounding" in general clustering transitions. The c omputation of a flattening in the concentration dependence of the osmotic p ressure in the one-phase region motivates our consideration of the temperat ure dependence of the second virial coefficient and the variation of the th eta temperature T-theta with "sticking energy" Delta h as possible importan t indicators of particle clustering. The ratio of the critical temperature T-c for phase separation to T-theta, along with other "critical constant" r atios, such as the osmotic compressibility factor Z(c), are also calculated and discussed in connection with establishing criteria for identifying par ticle clustering transitions and for quantifying the relative "strength" of these transitions. (C) 2000 American Institute of Physics. [S0021- 9606(00 )50825-3].