CONTINUOUS-MIXTURE KINETICS AND EQUILIBRIUM FOR REVERSIBLE OLIGOMERIZATION REACTIONS

Reversible oligomerization of distributions of molecules yields distributions of monomers, dimers, trimers, tetramers and higher-order oligomers. The distributions can be functions of molecular weight, carbon number, or other variables that may be considered continuous. Rate expressions are formulated for the rates of generation of oligomers and loss of reactants due to combination (fusion) reactions and for the generation of fragments and loss of oligomers due to cracking (fission) reactions. Two types of cracking reactions are proposed: proportioned fission where products are precisely proportioned to yield monomers, dimers or trimers of given molecular weight; random fission where the fission products are distributed over all molecular weights up to that of the reactant. The zero moment of a distribution is the species concentration, which satisfies molar equilibrium and kinetics relationships. The temporal evolution of molecular-weight moments is expressed in terms of differential equations for continuous-flow and batch stirred reactors. By setting forward and reverse rates equal, equilibrium relations are developed for zero- and higher-order moments, thus generalizing the mass-action equilibrium concept. Equilibrium states for proportioned and random fission manifest infinitesimally narrow and infinitely broad distributions.