Progress in the Solution of the Equations for the Full Molecular Weight Distribution in Addition Polymerization by Direct Techniques

Recently we have shown the feasibility of solving the equations of the full molecular weight distribution (MWD) in addition polymerization by direct integration of the system of ODEs (Ordinary Differential Equations) in a standard personal computer in a matter of seconds or minutes. A few years ago this only was possible in a supercomputer. The dimension of the system of ODEs associated with this problem is in the range of 1000 to several hundreds of thousands of equations, depending on the specific chemistry at hand. In order to efficiently solve these systems, one must exploit their structure and dynamic characteristics and make a proper choice of the algorithms of solution. One of the principles behind the efficient numerical solution of these systems is dynamic decoupling (quasi-steady state for living species) in order to generate an algebraic-differential system, followed by direct solution of the algebraic system without Jacobian inversion, exploiting the structure of the system. In the past we presented simple examples of application of this technique. In this paper we apply the technique to a much more challenging system: the controlled/living RAFT polymerization (Reversible Addition Fragmentation Transfer) and discuss mechanistic details pertaining to this system. We also discuss, with several examples, how to exploit the structure of the equations in order to efficiently solve the full MWD for the steady state CSTR case as opposed to the ODE dynamic case.