Application of numerical methods for the calculation of size distribution functions of polymers produced by ionic polymerizations

The application of numerical methods for the calculation of the molecular weight distribution of living ionic polymerization, carried out in the presence of monofunctional and polyfunctional transfer agents, is described. The methods used include the numerical solution of a system of differential equations by the Runge‐Kutta‐Merson procedure and the statistical Monte‐Carlo approach. When a monofunctional transfer agent is used, the Runge‐Kutta‐Merson procedure is quite useful for the calculation of the molecular weight distribution for various polymerization systems. When a polymerization is carried out in the presence of a polyfunctional transfer agent, the mechanism includes the coupling of polymer chains. Due to the complexity of the system, the Runge‐Kutta‐Merson procedure is hardly applicable and problems of this type should be solved by a Monte Carlo simulation procedure. Once a computer program has been written, both methods allow the chemist to calculate the molecular weight distribution of a polymer as a function of the different kinetic parameters of the polymerization.