Tetracritical and novel tricritical points in sulfur solutions: A Flory model for polymerization of rings and chains in a solvent

摘要

A model for equilibrium polymerization of rings and chains in a solvent is solved in a Floryhyphen;like approximation. The presence of polymeric rings leads to interesting new kinds of phase equilibrium and higher order critical points. We find a higher order critical point analogous to a tetracritical point in a corresponding magnet, at which four phases come into simultaneous equilibrium, as well as novel tricritical points where three critical lines meet at a cusp. The resulting phase diagrams give improved agreement with those of sulfur solutions withcishyphen;decalin and with orthohyphen;xylene. The model has interesting consequences for the predicted behavior of magnets as well. It reduces to the earlier theories of Tobolsky and Eisenberg, Scott, Wheeler, and Pfeuty, and Petschek, Pfeuty, and Wheeler in various limits, but exhibits new behavior not seen in any of the previous theories.