A Molecular Weight Distribution Polydispersity Equation for the ATRP System: Quantifying the Effect of Radical Termination

Polydispersity quantifies the breadth of polymer molecular weight distribution, making it an important and frequently quoted chain microstructural property for characterization. An explicit expression of such an important variable is desirable for ease of calculation, correlation with experiment data, and/or parameter estimation. A review of published literatures shows that great efforts have been put forth by many researchers to derive these equations for various polymerization mechanisms. In atom transfer radical polymerization (ATRP), polydispersity depends on three factors: monomer conversion, number of monomer addition per activation/deactivation cycle, and amount of dead chains. The existing expressions available in the literature only account for, at most, two of these three factors, with the contribution from dead chains commonly neglected. This assumption results in polydispersity monotonically decreasing with conversion, which is often not observed in experiments. In this work, a new equation for polydispersity, which accounts for contributions of all the three aforementioned factors, is proposed. The validity of assumptions involved in the derivation is evaluated by comparing the polydispersity profiles to those simulated by the method of moments. In addition, this new equation is used to correlate several experiment data sets for verification, namely from ATRP of 2-hydroxyethyl methacrylate, methyl methacrylate, and <i>N</i>-isopropylacrylamide, showing better agreement than the existing equation. Although the equation derived here is strictly applicable to homogeneous (bulk and solution) normal ATRP, with further effort it may be extended to other types of ATRP as well as NMP and RAFT systems