Molecular Weight Distribution Modeling of Radical Polymerization in a CSTR with Long Chain Branching through Transfer to Polymer and Terminal Double Bond (TDB) Propagation

Abstract

The modeling of free radical polymerization with long chain branching in a CSTR is addressed. Long branches are assumed to be created by transfer to polymer and by insertion of active terminal double bonds (TDBs). Such TDBs may be produced by transfer to monomer and termination by disproportionation. The modeling approach is based on population balances being solved using a Galerkin finite element method (FEM). Two different models have been derived. The “TDB classes” model employs different equations for each class of chains with a certain number of TDBs. The “TDB moment distribution” uses the pseudodistribution method developed by us before22 for simultaneous molecular weight/degree of branching distribution modeling. Model calculations have been performed for the case of poly(vinyl acetate) (PVAc). In the case of the maximum one TDB per chain, the two models prove to be mathematically equivalent. An increase of TDB propagation rate leads to a broadening of chain length distribution (CLD) and sometimes to a more pronounced “shoulder” at long chain lengths. The significant concentration range extends to extremely long chain lengths (1010)well within a gel regimebut the model could fully cover this. Quite remarkably, concentrations of living chains are higher than those of dead chains in this region. The average number of TDBs per chain could be calculated and turns out to be constant at shorter chain lengths, but becomes lower for longer chains. This is explained by the combined action of chain growth by TDB propagation, which implies TDB consumption as well, and transfer to polymer. For the case of more than one TDB per chain, the two models yield different results depending on closure relationships. The TDB moment distribution model revealed that the longest chains carry tens of thousands of TDBs. The classes model strongly underestimates the number of TDBs and hence the reactivity of the dead chains to TDB propagation. The results show the effect of dead chains with many TDBs acting as cross-linkers for living chains. As an interesting trend, it was observed that with increasing TDB propagation rate an increasing fraction of monomer units existing in polymer chains is present in fewer, but extremely long living, chains.