Acid Hydrolysis of K‐Carrageenan in a Batch Reactor: Stochastic Simulation of Change of Molecular Weight Distribution with Time

Abstract

AbstractThe degradation of K‐carrageenan by acid hydrolysis in a LiCl/HCl (pH 2) buffer solution has been studied at various temperatures in a batch reactor. The reduction in the weight‐average molecular weight and the variation in the molecular weight distribution (MWD) have been followed over time by an SEC‐MALLS‐RI chromatography system. While a deterministic rate equation can be fit to the average molecular weight‐time data, this is not the case for the MWD‐time data. Since depolymerization by hydrolysis usually proceeds via nonspecific (random) bond cleavage, a stochastic approach can be appropriate for the resultant MWD‐time data. In the present work, the master equation has been derived from the stochastic population balance for this batch hydrolysis system characterized by a set of discrete states, each representing a particular molecular weight range. The governing equations for the means, variances, and covariances of the random variables, each representing the number of carrageenan molecules in an individual state, have been extracted from the master equation. The equations for the means have been applied to the MWD‐reaction time data, and the unknown reaction rate parameters have been estimated. These parameters can be used to generate the MWD at any hydrolysis reaction time from any initial MWD. The applicability, limitations, advantages, and sources of error of the derived model have been discussed.