Theoretical reaction kinetics of reversible living polymerization

Abstract

AbstractAmplifying an early study by SZWARC and BROWN, we have investigated the mathematical problem of the reversible living polymer system without transfer or termination reactions, concentrating particularly on the molecular weight distribution. This problem is identical to that for the kinetics of BET adsorption. A complete analytical solution is obtained when the monomer concentration is kept constant. In the much harder case of polymerization in a closed system, numerical solutions of the equations are used as guides to analytical approximations, and a perturbation approach is also helpful. The time required for the initial narrow POISSON distribution to go over into the final „most probable”︁ equilibrium or SCHULZ distribution is proportional to the square of the average chain length. For polystyrene at room temperature, the POISSON polymer is produced in a few seconds, but the final equilibration requires of the order of 100 years, although the unreacted monomer concentration very early reaches its equilibrium value. Thus the equilibrium constant for polymerization can be accurately measured long before complete equilibrium is attained in the system.