For three types of linear polycondensing systems, equilibrium molecular size distributions, including rings as allowable species, are derived. Average molecular weights and amounts of ring and chain fractions are calculated therefrom. The fractions of rings are shown to increase with dilution, and with molecular weight. It is shown that beyond a critical dilution it is sometimes possible to obtain 100 percent yield of rings by driving the condensation to completion. Detailed calculations are made for two important cases corresponding to condensations of the decamethylene glycol-adipic acid type: (1) for equimolar amounts of the two monomers, and (2) unequal amounts, with one monomer type completely reacted.

Decamethylene adipate polymers prepared in the absence of solvent undergo a reversible decrease in solution viscosity when heated for long times in chlorobenzene. This phenomenon is shown to be due to ester interchange reactions which establish equilibrium between ring and chain molecules. Quantitative agreement with the equilibrium theory of the previous paper is obtained if the effective length of a chain link is taken as 4.5±0.2A, which is of the order of magnitude to be expected from hindered rotation and steric effects. Measurements of ring-chain equilibrium thus appear to offer a useful method for characterizing the stiffness of relatively short and flexible chains.

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Theory of the author is applied to polymer systems resulting from equilibria between DNA-like monomers with reactive ends with Kuhn segment (KS) length of 1000 Á. Computations are made for monomer sizes containing from 1.5 to 600 KS, corresponding to molecular weights from 3 x 106 to 1.2 X 10® daltons, at concentrations from undiluted polymer to mass dilution of 1:109 and over the entire range of possible extents of reaction. Molecular size distributions, weight and number fractions and molecular weight for chains, rings, and simplest catenanes, and overall MW's are computed. Maximum catenane yields are shown to occur, for given fraction of reaction, at intermediate concentration of monomers, growing larger with extent of reaction. For less general systems, current theory gives higher catenane predictions than previous Monte Carlo and overlap calculations. Gelation due to catenane linking is estimated not to occur for the general system, but in the special case of ring-catenane equilibrium alone may (and does, in topoisomerase experiments).