Kinetics of Nonideal Hyperbranched Polymerizations. 1. Numeric Modeling of the Structural Units and the Diads

Abstract

The kinetics of reactions with nonuniform reaction rate constants leading to hyperbranched polymers has been examined and discussed. A matrix notation was developed, which has then been applied to the analysis of the kinetics of AB2, AB3, AB n , and ABB‘ systems. All differential equations have been integrated numerically in order to obtain plots of the ratios of structural units as functions of the conversion. Three general situations for AB2 systems and the kinetics of self-condensing vinyl polymerization as one example of an ABB‘ system are discussed. It was found that the influence of the first B group on the reactivity of the second B group has the largest effect on ratio of structural units and final composition. Thus, by varying the rate constants of these reaction steps in the model the resulting degree of branching ranges between 15 and 89%. Furthermore, the diad formation of the AB2 system is analyzed.

Kinetic Evaluation of Hyperbranched A2 + B3 Polycondensation Reactions

“…We studied the kinetics of AB 2 systems and discussed influences of the reaction rate constants on the final structure of the polymer both for an ideal and a non-ideal polycondensation. [36][37][38] The comparison to experimental data proved our theoretical discussion. We also introduced a matrix notation, which was useful to distinguish and separate different effects on the kinetics.…”

“…More details can be found in ref. [37] and ref. [38] The structural units and the degree of branching were calculated as a function of the conversion of A-groups p A from p A ¼ 0 up to the critical conversion of gelation p c,A .…”

“…In contrast, an AB 2 systems would span a two-dimensional set of reaction pathways, because both A-and B-functions are joined in one monomer and they can react independently from each other leading to different intermediate products. [37] As already mentioned in earlier publications, the matrix notation is useful to indicate all possible reactions and the corresponding reaction rate constants. Furthermore, it simplifies deriving the set of differential equations and its calculations.…”

“…A detailed discussion of the matrix notation is given elsewhere. [37] We will only discuss relative changes, whereas the absolute values of the reaction rate constants are of no interest within this context. As long as it is not indicated otherwise, we will discuss the situation, where each elementary reaction has the same reaction rate constant (K n , [Equation (9)]).…”

Polyesters

“…For most hyperbranched polymers, nuclear magnetic resonance (NMR) spectroscopy determinations lead to DB values close to 0.5, that is, close to the theoretical value for randomly branched polymers. Slow monomer addition 193,194 or polycondensations with nonequal reactivity of functional groups 195 have been reported to yield polymers with higher DBs (0.6-0.66 range).…”