Distributions of cyclic oligomers formed by irreversible step-growth polymerisation. Results from kinetic modeling

The distribution of cyclic oligomer concentrations (examined up to the cyclic pentamer) in the process of step-growth polymerisation decreases, in concentrated solution, with i(-2.5) if the chains follow Gaussian statistics (i: degree of polymerization). This picture is analogous to that shown by cyclic oligomer distributions obtained under thermodynamic control and is in contrast with that shown by cyclic oligomer distributions obtained by irreversible chain-growth polymerisation which is characterized by a gradient of -1.5. This result has been initially obtained by numerical integration of the differential rate equations pertinent to a kinetic model relative to the reaction of a bifunctional reactant A-B under batchwise conditions, and then confirmed by analytical integration of the differential rate equations under the condition that propagation is much faster than cyclisation. The case in which the monomeric ring is strained has been also investigated. Also in this case the obtained distribution is analogous to that shown under equilibrium conditions. From an examination of the distributions of the ring yields, the best conditions for the preparation of either the cyclic monomer or the cyclic dimer are suggested.