Size distribution in the polymerisation model AfRBg

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Abstract
The polymer size distribution in Flory's polymerisation model, AfRBg is in equilibrium and non-equilibrium of the general form ck=ANk xi k both below and above the gelation transition. Here explicit expressions are derived for A( alpha ) and xi ( alpha ) as a function of the extent of reaction alpha . The combinatorial factors Nk are calculated from the recursion relation 2(k-1)Nk= Sigma i+j=kKijNiNj with Kij=si(f)sj(g)+si(g)sj(f) and sk(f)=(f-1)k+1. Using a generating function technique the authors express Nk in terms of Laguerre polynomials (g to infinity ) and Jacobi polynomials (g finite), whose large-k behaviour is of the form Nk approximately=Bk- tau xi c-k with tau =3/2 (no gelation occurs) if f or g equals 1, and with tau =5/2 (gelation occurs) if f>1 and g>1.

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