Abstract: Several equilibrium properties of typical polycondensation system of Aa-Bb type were studied by the principle of statistical thermodynamics. Starting with the canonical partition functions constructed from two viewpoints, the explicit expressions of the equilibrium free energy and the law of mass action are obtained. Meanwhile, two new methods were proposed to derive the equilibrium size distribution, and the gelation condition was carried out by the isothermal compressibility. Furthermore, based on the invariant property of the equilibrium size distribution, the equilibrium free energies of sol and gel phases in postgel regime were given, and the relevant issues on the sol-gel phase transition were discussed.

Key words: Equilibrium free energy, Law of mass action, Size distribution, Sol-gel phase transition