When Mayo falls short (Ctr ≫ 1): the use of cumulative chain length distribution data in the determination of chain transfer constants (Ctr) for radical polymerizations†
We report a new method of determining the chain transfer constant in free radical polymerization using molecular weight distribution data. It is specifically designed for systems where its value is substantially greater than 1. In these cases the classical Mayo equation and Gilbert's chain length distribution (CLD) method fall short, in that the concentration ratio of chain transfer agent to monomer can no longer be assumed to be constant. Marked composition drift invalidates the use of both. In our proposed method we use the analytical concentration ratio of chain transfer agent to monomer (t = 0 s) and monomer conversion data, in combination with data for the cumulative molecular weight distributions as input. We determined an analytical solution for the cumulative weight distribution, which is used to calculate the cumulative number and chain length distributions. Chain transfer constants are found either by fitting the natural logarithmic chain length distribution (CLD) data at a given monomer conversion, or by plotting the fitted values for the slopes obtained from the natural logarithmic chain length distribution (CLD) data at a set degree of polymerization, as a function of monomer conversion. Our method is validated by analyses of molecular weight data obtained from Monte Carlo simulations. We used our methodology to determine an experimental value of ca. 223 as a chain transfer constant of n-dodecanethiol in vinyl acetate free radical polymerization at 333.15 K, which we showed was in excellent agreement with the Smith method.