The degradation of polystyrene was modeled at the mechanistic level by developing differential equations describing the evolution of the moments of structurally distinct polymer species. This work extends our previous modeling work by incorporating chain-length-dependent rate parameters, tracking branched species more explicitly, using rate parameters primarily from the literature, and comparing the model results to extensive experimental data on the degradation of polymers of different molecular weights and at different temperatures. Unique polymer groups were devised that allowed the necessary polymeric features for capturing the degradation chemistry to be tracked, while maintaining a manageable model size. The conversion among the species was described using typical free radical reaction types, including hydrogen abstraction, midchain β-scission, end-chain β-scission, 1,5-hydrogen transfer, 1,3-hydrogen transfer, radical addition, bond fission, radical recombination, and disproportionation. The model included over 2700 reactions and tracked 64 species. Programs were developed using the programming language Perl to assemble moment equations from input of the polymeric features to be tracked. The intrinsic kinetic parameters (a frequency factor and activation energy for each reaction) were obtained from data in the literature and previous modeling work in our laboratory. − The model predictions for the evolution of M n and M w and the yields of styrene, dimer, and trimer compare very well with experimental data obtained in our laboratory for the degradation of polystyrene over a large temperature range and with different initial molecular weights. Evolution of low molecular weight products from experiments reported in the literature is also captured.

The pyrolysis of polypropylene was modeled at the mechanistic level to predict the formation of low molecular weight products. Differential equations were developed that describe the evolution of the moments of structurally distinct polymer species. Unique polymer groups were devised that allowed the necessary polymeric features for capturing the pyrolysis chemistry to be tracked, while maintaining a manageable model size. The conversion among the species was described using typical free radical reaction types, including intermolecular hydrogen abstraction, midchain β-scission, end-chain β-scission, intramolecular hydrogen transfer, radical addition, bond fission, radical recombination, and disproportionation. The model included over 24 000 reactions and tracked 213 species (27 products tracked with molecular weights below 215 amu). The intrinsic kinetic parameters (a frequency factor and activation energy for each reaction) were obtained from data in the literature and previous modeling work in our laboratory. , The model predictions for the evolution of the yields of five major alkenes and five major alkanes compare well with experimental data obtained in our laboratory for the pyrolysis of polypropylene over a temperature range of 350−420 °C. In addition, literature data for the evolution of the polypropylene molecular weight was captured by incorporating weak backbone links modeled as peroxide bonds.

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The nitroxide-mediated controlled radical polymerization (NM-CRP) of styrene was modeled at the mechanistic level using the method of moments. The mechanistic models developed described the kinetics and the molecular weight development of the living free-radical polymerization process. A base model was constructed which included initiator decomposition, propagation, end-chain coupling, and termination by recombination and disproportionation. Using an Evans-Polanyi description of the activation energy (E ) E 0 + R∆HR), the base model was fit to a set of experimental data for the living free radical polymerization of styrene at 87 °C1 to obtain the heat of reaction for decoupling (∆HR for the di-tert-butyl nitroxide coupling agent) and to fit the intrinsic barrier (E0) for propagation/depropagation. The remaining rate parameters were primarily obtained from the literature, while some were taken from previous modeling work in our laboratory. 2,3 The fit of the base model to the experimental data was then compared to the fit obtained when chain transfer to monomer and both chain transfer to monomer and styrene thermal initiation were included in the mechanism. It was found that including styrene thermal initiation was critical to being able to obtain good agreement between the model and the experimental data. The fitted parameters obtained after including styrene thermal initiation were E 0 for propagation/ depropagation ) 10.78 ( 0.08 kcal/mol and ∆HR for the decoupling reaction ) 22.70 ( 0.40 kcal/mol. Using these fitted parameters, the model was used to predict the evolution of Mn and Mw of the polymer product at different times and temperatures and with a macroinitiator. The importance of reactions such as chain transfer to polymer and the reaction between a nitroxide radical and a polymeric radical to form a hydroxy amine was also investigated, and it was found that these reactions were negligible.

Limitations associated with preparing high molecular weight polystyrene (PS) by nitroxide-mediated controlled radical polymerization have been tested by considering the role of unimolecular initiator concentration on active polymer radical concentration and thus degree of polymerization. Recent theories ignoring autopolymerization effects lead to the conclusion that, at low monomer conversion, the number-average molecular weight, M n, scales with the −2/3 power of unimolecular initiator concentration. Bulk polymerizations were done using either α-methylstyryl di-tert-butyl nitroxide (A−T) as unimolecular initiator or PS macroinitiator made from A−T. These initiators allow relatively low reaction temperature (77, 87, or 97 °C) and moderate, but not eliminate, the contribution of autopolymerization or thermal initiation of polymerization. By varying unimolecular initiator concentration over nearly 4 orders of magnitude, well-controlled PS, with polydispersity index ≤ 1.4, can be made with M n values in the range 114 000−238 000 g/mol using either A−T as initiator or a PS macroinitiator. For conditions yielding controlled PS, in general the experimental M n−initiator concentration data afforded good agreement with the −2/3 power-law expression and allowed estimation of the equilibrium constant for the capping−uncapping reaction. However, attempts to make controlled, higher molecular weight PS by further reducing initiator concentration resulted in loss of control due to autopolymerization effects. The impact of autopolymerization in producing well-controlled PS was evident from studies yielding a nearly constant conversion as a function of macroinitiator concentration.