Computing the Trivariate Chain Length/Degree of Branching/Number of Combination Points Distribution for Radical Polymerization with Transfer to Polymer and Recombination Termination

Summary: Polymer molecules made by radical polymerization with transfer to polymer and recombination termination contain branch points (connecting branch arms to backbones) and combination points (connecting various molecular structures). The trivariate chain length/degree of branching/number of combination points distribution (CLD/DBD/CPD) was calculated using a two‐dimensional version of a previously used pseudo‐distribution approach. This yielded the CPD moments for given chain length n and number of branches i. Both DBD and CPD at given chain length resemble a binomial distribution. For the construction of the full DBD and CPD a set of orthogonal polynomials, the Krawtchouk polynomials, in combination with the binomial distribution was employed. A first‐order Krawtchouk approximation enabled to compute the full CLD/DBD/CPD from the three CPD moments as a function of n and i. Results agree well with those from a Monte Carlo (MC) simulation method. However, the large scatter due to the small numbers of molecules collected in the MC method at longer chain lengths prevents comparison in this range.

Solutions of 3D CLD/DBD/CPD: CPD at constant chain length (20 000) and number of branch points (20).