First shell substitution effects in hyperbranched polymers: Kinetic-recursive probability analysis

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 ((X) over bar (w)) 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 (delta(A), delta(B), and delta(AB)) are introduced to describe polymer branching. delta(B) generalizes Frey's degree of branching to polymerizations involving any type of monomer mixture and can directly be used to calculate polymer (M) over bar (w) delta(AB) 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 ((M) over bar (w)/(M) over bar (n)). Two systems, AB(f) polymerizations and AB(f) + B-g polymerizations, are taken as examples and discussed to illustrate the method. The polymerizations of 2,2-bis(hydroxymethyl)propanoic acid (BMPA) (AB(2) polymerization) and of BMPA with Pentaerythritol (AB(2) + B-4 polymerization) are more specifically studied. The results are compared to experimental data, showing that negative FSSE involving both OH and COOH groups take place, leading to much lower dispersities and branching factors than expected for ideal (random) polymerizations. The method can be extended to any type of condensation polymerizations.