Pre- and post-gel size distributions in (ir)reversible polymerisation

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Abstract
A class of irreversible coagulation processes can be modelled by Smoluchowski's coagulation equation with rate constants Kij=A+B(i+j)+Cij (non-negative A, B and C). For C not=0 a gelation transition occurs. The authors obtain explicit solutions for the size distribution ck(t) with ck(0)= delta k1. Next, they construct and solve the equations for reversible polymerisation by incorporating break-up processes in the kinetic equation with a unimolecular fragmentation rate Fij= lambda NiNjKij/Ni+j. The degeneracy factors Nk obey (k-1)Nk=1/2 Sigma KijNiNj with i+j=k and N1=1, and the strength parameter lambda =exp(g/kBT), where the binding energy g to - infinity for irreversible coagulation. Explicit results are only given for Flory's polymerisation models RAf and BRAf-1. In the vicinity of the gel point the authors verify the scaling hypothesis and calculate critical exponents.

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