Development of a statistical model for the formation of poly [acryloyl hydroxyethyl starch] microspheres

To develop a mathematical model for predicting the molecular weight between crosslinks, Mc, of poly[Acryloyl Hydroxyethyl Starch] (Ac-HES) microspheres system and to identify and evaluate the key microsphere preparation parameters which affect the Mc of the formed microsphere structure based on the developed model.

Link probability generating functions (LPGFs) based on the classical branching theory were used to derive a model for the calculation of Mc for the Ac-HES system. Based on the developed model, simulation was made to study the effects of the microsphere preparation variables on Mc of the formed microspheres. The process variables were the degree of derivatization (DD) of the Ac-HES, the molar ratio (MR) of the Ac-HES to acrylamide monomer, the fractional conversion of the unsaturation (alpha), the initiator efficiency (f), the molar concentration of initiator (I), the fraction of intramolecular cyclization (c), and the total weight of the reactable monomer and polymer (s).

A model to describe the crosslinking reaction of Ac-HES system and predict Mc was developed. Simulation based on the model showed that Mc decreased as alpha increased and reached a limiting value before total conversion. At constant alpha, Mc initially decreased with MR to a minimum and then increased with MR; while Mc decreased monotonically with DD. I and c affected Mc only at very low alpha and changes in s and f had no effect on Mc.

Simulation based on the model suggested that the most important microsphere preparation parameters influencing Mc of the Ac-HES system are the number of functional groups on the Ac-HES (DD) and the stoichiometry (MR) of the crosslinking reaction.