Theory of Step-Growth Ring Expansion Polymerization

The power law describing the distribution X n of molecular weights for polymerizations that proceed via step-growth ring expansion is shown to be X n ∼ n –3/2. This differs from ring-chain equilibria that are described by Jacobson–Stockmayer theory with its X n ∼ n –5/2 law. This difference in the power law for formation of rings has a profound effect on the distribution of macrocycle molecular weights. At high conversions, the number average degree of polymerization (DP) for a ring expansion polymerization is approximately the square root of that for an equivalent linear step-growth polymerization and is not increased by dilution. The weight average DP at high conversions is approximately one-half that of the number average DP for a linear polymerization at the same conversion.