On the Activation Energy of Termination in Radical Polymerization, as Studied at Low Conversion

The chain-length-dependent nature of the termination reaction in radical polymerization (RP) renders the overall termination rate coefficient, <k_t>, a complex parameter in the usual situation where the radical chain-length distribution is non-uniform. This applies also for the activation energy of termination, E_a(<k_t>), which we subject to detailed mechanistic investigation for the first time. The experimental side of this work measures E_a(<k_t>) for the dilute-solution, low-conversion, chemically initiated homopolymerization of styrene (ST), methyl methacrylate (MMA), butyl methacrylate, and dodecyl methacrylate. Values of 25-39 kJ mol^-1 are obtained, consistent with strong chain-length-dependent termination (CLDT) for short chains. On other hand, the reanalysis of analogous bulk polymerization data for ST and MMA finds E_a(<k_t>) values of 18-24 kJ mol^-1, consistent with weak CLDT for long chains. Both these results are as expected from the so-called composite model for CLDT. A simple analytic framework for understanding and predicting E_a(<k_t>) values is presented for the standard RP situation of continuous initiation. All the results of this work can be rationalized via this framework, which clearly establishes that E_a(<k_t>) is determined by far more than just the E_a of radical diffusion. This framework is extended to activation energy for the number-average degree of polymerization, E_a(DP_n), which we measure and successfully scrutinize via our CLDT model. In the final section of this work, we make interesting, testable predictions about E_a(<k_t>) and/or E_a(DP_n) in various RP systems of different natures to those studied here, most notably, systems involving acrylates, continuous photoinitiation, or dominant chain transfer.