First Shell Substitution Effects in Hyperbranched Polymers: Kinetic−Recursive Probability Analysis

Abstract

The kinetic−probability approach taking into account first shell substitution effects (FSSE) is applied to hyperbranched condensation polymerizations. Simple explicit relationships giving the mass-average molar mass ( ) and mass-average degree of polymerization ( ) as a function of conversion, of initial monomer mixture composition and of polymer architecture at a given reaction time are derived using the “in−out” recursive probability approach. Three experimentally available parameters, the A-, B-, and AB-branching factors (δA, δB, and δAB) are introduced to describe polymer branching. δB generalizes Frey's degree of branching to polymerizations involving any type of monomer mixture and can directly be used to calculate polymer . δAB characterizes the substitution effects induced on A-group reactivity by the reaction of B-groups (and vice versa). This effect, generally neglected in hyperbranched polymerization studies, may exert a dramatic influence on hyperbranched polymer dispersity ( / ). Two systems,...