Time evolution of polymer distribution functions from moment equations andmaximum-entropy methods

We use the maximum-entropy method to calculate the chain-length distributio n as a function of time for cooperative polymerization models involving nuc leation and growth. At least the first two moments of the distribution are required for the maximum-entropy method. To obtain the moments we use a gen erating function to give the moment rate equations which in general involve s an infinite set of coupled differential equations which can be truncated to give a finite set by using various closure approximations. In particular we use the maximum-entropy method to treat the reversible growth of chains from a fixed concentration of initiators in which case the initial distrib ution is a sharp Poisson-type one that then evolves slowly to the very broa d equilibrium distribution. For this model we find that there is a scaled t ime that reduces the time dependence of the moments to a universal set of a symptotic curves. (C) 1999 American Institute of Physics. [S0021-9606(99)52 241-1].