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, <<i>k</i>_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, <i>E</i>_a(<<i>k</i>_t>), which we subject to detailed mechanistic investigation for the first time. The experimental side of this work measures <i>E</i>_a(<<i>k</i>_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 <i>E</i>_a(<<i>k</i>_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 <i>E</i>_a(<<i>k</i>_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 <i>E</i>_a(<<i>k</i>_t>) is determined by far more than just the <i>E</i>_a of radical diffusion. This framework is extended to activation energy for the number-average degree of polymerization, <i>E</i>_a(<i>DP</i>_n), which we measure and successfully scrutinize via our CLDT model. In the final section of this work, we make interesting, testable predictions about <i>E</i>_a(<<i>k</i>_t>) and/or <i>E</i>_a(<i>DP</i>_n) in various RP systems of different natures to those studied here, most notably, systems involving acrylates, continuous photoinitiation, or dominant chain transfer.