Theoretical size distribution in linear step-growth polymerization for a small number of reacting species

The size distributions for the linear step-growth polymerization containing a relatively small number of molecules (in the range of 20-10000) have been calculated using computer simulations. Contrary to the most probable distribution of Flory, which predicts a continuous linear increase of the polydispersity index (PDI) from the value of 1 to 2, it has been found that the PDI increases up to a certain maximum value followed by a decrease to unity as the extent of conversion (p) approaches unity. The maxima of the PDI versus p curves as well as the sharpness of the decrease of these curves to unity have been found to strongly depend on the number of reacting species. In addition, on the basis of a rigorous statistical treatment, the number and the weight-average size distributions have been derived, which are in perfect agreement with those obtained by computer simulation. Furthermore, the derived distributions can also be applied for the description of reaction products of depolymerization reactions.