Direct Integration of the Equations for the Full Molecular Weight Distribution in Addition Polymerization: A Re-Assessment of the Problem

The increasing computing power of computers makes it possible now to solve for the equations of the full molecular weight distribution (MWD) by direct integration of the system of ODEs (Ordinary Differential Equations) describing this population, in reasonable computing times. Less than two decades before this was unthinkable and required the use of supercomputers. The system of ODEs associated with this problem have a dimension varying from around 1000 to several hundreds of thousands of equations. However, in order to efficiently solve these systems in standard computers one must exploit the structure and the dynamic characteristics of these systems and make a proper choice of the algorithms of solution. In this paper we will show several examples of solution of realistic problems of polymerization in which the full MWD is solved in a matter of seconds or minutes in a standard laptop computer. The principles behind the efficient solution of these systems will be presented and discussed. Some of the examples to be presented include traditional and controlled/living (nitroxide mediated) radical polymerization and free radical polymerization with long chain branching. It will also be shown how the use of these tools provides new insight on the mechanism and dynamics of the systems studied.