Polycondensation Kinetics: 4. Growth of Acyclic Randomly Branched Chains

Master equations for concentrations of nb -mers ( n is the number of units, b is the number of branch points randomly located among the units) in the polycondensation of trifunctional monomers (PC-3) take into account the set of irreversible consecutive–parallel reactions between functional groups ( n , b ) and ( n ′, b ′)-mers with rate constants χ( b , b ′). Stoichiometric coefficients are equal to the number of permutations of bond-forming groups at ∆( b + b ′) = 0, 1, 2. Reaction coordinates are combined into a network of an inhomogeneous Markov process. It is shown that the Flory hypothesis (all χ( b , b ′) values are identical) leads to an explicitly time-independent Gaussian distribution W n ( b ) with a maximum b max that grows linearly with the chain length n .