A Monte Carlo simulation procedure has been set up and applied to generate representative ensembles of randomly branched step‐growth polymers based on their reaction recipe. The molecular distributions thus obtained are consistent with those from statistical/analytical approaches. However, because the current method gives access to the complete ensemble of simulated molecules, a very detailed structural analysis is possible. Our procedures are applicable to any ‘AfBg’ system with f + g ≥ 1. We apply this approach to randomly branched polyamides in order to gain insight into their molecular structure and understand the effect of the reaction recipe on the final product.

General step‐growth polymerization systems of order 2 are considered, i.e. systems of type “AfiBgi”. We describe an algorithmic method to calculate the molecular size distribution (MSD). Input to the algorithm is the “recipe”: a list of the monomers involved stating their A and B functionalities and their molar amounts, and the degree of conversion. Output is the MSD and its moments. Three main steps lead from input to output: (i) setting up a polynomial equation for the generating function that generates the MSD, (ii) transforming this polynomial equation to a differential equation, and (iii) transforming the latter one further to a recurrence equation. The recurrence yields the MSD and is of constant order.

General step‐growth polymerization systems of order 2 are considered, i.e., systems of type “AfiBgi”, and a fast algorithmic method is presented to compute, at a given degree of conversion, the MSD and the MWD. The complete distribution is calculated; not just statistical averages of the polymer population such as $\overline {M} _{{\rm n}} $ or $\overline {M} _{{\rm w}} $. For the computation of the low‐ and intermediate size/weight parts of the distribution curves, a set of recurrence relations is used. The high‐molecular size/weight parts of the curves (right tails) are computed using an accurate approximation derived from generating functions. In a previous paper, we applied our method to general order‐1 systems, i.e., systems of type “Afi”. magnified image

A fast method is presented for the calculation of the MSD and the MWD of polymers obtained via step‐growth polymerization of polyfunctional monomers bearing identical reactive groups (i.e., systems of type “Afi”). Using this method, the complete distribution can be calculated rapidly, not just the statistical averages of the polymer population such as $\overline {M} _{{\rm n}} $ or $\overline {M} _{{\rm w}} $. The computed MSD and MWD give more insight than these averages and can be compared to similar data measured on actual polymer systems. The low‐ and intermediate molecular size/weight part of the distribution curves are calculated using a recurrence scheme, while the high‐molecular tail (large and very large polymers) of the distributions is derived from an asymptotic approximation of the associated generating functions.

Step‐growth polymerized systems of general type “AfiBgi” are considered. One or more of the monomer species carries at least three reactive groups and thus can act as a branching point in a polymeric molecule. An algorithmic method is presented to calculate the topology‐averaged square radius of gyration, R 2[s], of the molecules in the class of s‐mers. The degree of polymerization, s, may run through its full range. In addition to R 2[s], the shrinking factor, g[s], is calculated. The method uses integer arithmetic, generating functions, and computer algebra.