Macromolecules, Vol.45, No.17, 7186-7196, 2012
Interpretation of Gel Points of an Epoxy-Amine System Including Ring Formation and Unequal Reactivity: Reaction Scheme and Gel-Point Prediction
First, the kinetics of the reaction of a polyoxypropylene (POP) diamine and the diglycidyl ether of Bisphenol A (DGEBA), taking account of the induced unequal reactivity (substitution effect) of the hydrogen atoms of the amine groups, are analyzed. It is shown that a larger reduction int he reactivity of the second hydrogen atom of an amine group to react leads to a higherproportion of semireacted amine groups at a given overall extent of reaction. Second, the statistics of gelation of the diamine epoxy polymerization in the absence of intramolecular reaction but accounting for the aforementioned unequal reactivity are investigated. The description is cast in terms of an RA(4) + R'B-2 polymerization, where A represents a hydrogen atom of an amine group and B represents an epoxide group. It is shown that the induced unequal reactivity has only a very small effect on the gel point. For example, a decrease by a factor of 10 in the reactivity of the second hydrogen atom of an amine group to react leads to an increase in an extent of reaction at the gel point (pc) of only 0.022 over the Flory-Stockmayer value of 0.577. Third, a theory for predicting the gel point in RA(4) + R'B-2 type polymerizations accounting for intramolecular reaction is developed. The theory is an extension of Ahmed-Rolfes-Stepto (ARS) theory to include more detail of the molecular structures around pairs of reacting groups. The very small effects of induced unequal reactivity on the gel point mean that the probabilities of intramolecular reaction can be calculated assuming the equal reactivity of like reactive groups. ARS theory leads to a quadratic relationship between p(c) and the ring-forming parameter, lambda(0). The present, more comprehensive theory does not lead to an analytical relationship between p(c) and lambda(0), but numerical evaluation of p(c) as a function of lambda(0) shows that many more ring structures are accounted for than by ARS theory, even at small values of lambda(0). The present theory is applied to the experimental data in the following paper.