Mathematical model for predicting gel point in the process of manufacturing alkyd resins

Abstract

A mathematical model for the prediction of gel formation in the synthesis of alkyd resins is developed. The probability of developing linear polymer molecules is related to the average functionality, F-av. A statistical factor phi is introduced to represent the probability of having free OH groups in the backbone of a linear alkyd molecule. Factor phi increases from 0 to a maximum of phi(max) when the acid value decreases from AV(initial) to AV(max) during the polymerization. Branch generation in alkyd molecules becomes significant only after the acid value is reached, AV(max), and it continues until a gel is formed. At phi(max), the average functionality (F-av(max)) and the acid value (AV(max)) are calculated in terms of the number of moles of OH groups, number of moles of COOH groups, and total number of molecules per unit mass at the beginning of polymerization. The acid value at the gel point, AV(gel), is then calculated using the values of F-av(max) and AV(max). The predicted acid values using the new model are in good agreement with the actual data reported for polyesterification in the synthesis of alkyd resins.