Obtaining the kinetic function of depolymerization from evolving molecular weight distribution data-an inverse problem

Depolymerization of macromolecules is generally regarded as a first order process with a kinetic function that depends on the molecular weights of the fragmenting molecule and fragmentation products. This article describes a computation scheme for obtaining the kinetic function from observed molecular weight distribution (MWD) data. The integro-differential equation used by most investigators to compute MWD with some assumed kinetic function is reformulated as an inverse problem in which the kinetic function is treated as the unknown to be extracted from evolving MWD data. A numerical procedure based on two consecutive applications of Tikhonov regularization is developed to solve this inverse problem. It gives the kinetic function as the solution of a set of linear algebraic equations. Implementation of this procedure is described in full and its performance is assessed by applying it to simulated MWD data. A number of issues associated with discretization and regularization are discussed. © 2012 American Institute of Chemical Engineers (AIChE).