The binary degradation of polystyrene (PS) and polypropylene (PP) was modeled at the mechanistic level by combining the individual component models developed in previous modeling work [T.M. Kruse, O.S. Woo, H.-W. Wong, S.S. Khan, L.J. Broadbelt, Macromolecules 35 (2002) 7830; T.M. Kruse, H.-W. Wong, L.J. Broadbelt, Macromolecules 36 (2003) 9594] and adding interactions between PS- and PP-derived species. The full binary model developed for the pyrolysis of PS/PP mixtures consisted of over 37,000 reactions and tracked 277 species. Within the binary model, interactions between polymeric species of different polymer types were not allowed since PS and PP are immiscible. However, a fraction of low molecular weight radicals (LMWR) of each polymer type was allowed to diffuse into the other polymer type. This was the only adjustable parameter in the model. Based on experimental data for a 50/50 wt% PS/PP mixture at 380 °C, we found that allowing 0.037% of the LMWR derived from PS to diffuse into PP captured the enhancement of nearly a factor of four in the PP degradation rate that was observed experimentally at these conditions. To increase the enhancement in the PP degradation rate, solid-state shear pulverization (SSSP) and changes in the PS/PP weight ratio were used to manipulate the interfacial area between PS and PP during binary pyrolysis (no premixing was performed during the conventional binary experiments). Using SSSP to blend PS and PP resulted in a 25% increase in the enhancement in the PP degradation rate compared to no premixing. In order to model this enhancement, the fraction of low molecular weight PS radicals that could diffuse into PP was increased to 0.10%.

The degradation of polystyrene was modeled at the mechanistic level using the method of moments to track structurally distinct polymer species. To keep the model size manageable, polymer species were lumped into groups, and within these groups, the necessary polymeric features for capturing the degradation chemistry were tracked. The pyrolysis reactions incorporated into the model included hydrogen abstraction, midehain beta-scission, end-chain beta-scission, 1,5-hydrogen transfer, 1,3-hydrogen transfer, radical addition, bond fission, radical recombination, and disproportionation. From the evolution of the zeroth, first, and second moments tracked for each dead species, polymer molecular weight distributions were constructed by summing the Schultz (Teymour, F.; Campbell, J. Macromolecules 1994,27, 2460) and Wesslau. (Pladis, P.; Kiparissides, C. Chem. Eng. Sci. 1998, 53 (18), 3315) distributions for the polymer groups. Model results were compared to experimental data collected in our laboratory, where polystyrene samples that differed in the shape and breadth of their initial distributions were pyrolyzed. The model was able to predict the formation of a bimodal distribution during the pyrolysis of polystyrene samples (molecular weight range of 10000-500000 g/mol) with narrow unimodal molecular weight distributions (polydispersity index < 1.1). This was accomplished by distinguishing the initial polymer from the polymer formed from midchain beta-scission reactions within the model. At high conversions, all of the polystyrene samples investigated evolved to unimodal distributions, and these distributions were best captured by the Schultz distribution.

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 beta-scission, end-chain beta-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. 1,2 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 degreesC. In addition, literature data(3) for the evolution of the polypropylene molecular weight was captured by incorporating weak backbone links modeled as peroxide bonds.

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 + alphaDeltaH(R)), the base model was fit to a set of experimental data for the living free radical polymerization of styrene at 87 degreesC(1) to obtain the heat of reaction for decoupling (DeltaH(R) for the di-tert-butyl nitroxide coupling agent) and to fit the intrinsic barrier (E-0) 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 DeltaH(R) for the decoupling reaction = 22.70 +/- 0.40 kcal/mol. Using these fitted parameters, the model was used to predict the evolution of M-n and M-w 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.

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(1) 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 beta-scission, end-chain beta-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.(2-4) 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 degradation of polystyrene was modeled at the mechanistic level using population balance equations formulated via the method of moments. Five degradation models of varying complexity were developed. For all models, the conversion among the species was described using typical free radical reaction types, including hydrogen abstraction, mid-chain β-scission, end-chain β-scission, 1,5-hydrogen transfer, radical addition, bond fission, radical recombination, and disproportionation. The five models differed in their resolution of the structural characteristics of the “dead” and “live” polymeric species and whether they explicitly tracked low molecular weight species. The most complex model included over 4500 reactions and tracked 93 polymeric and low molecular weight species, both dead and live species. To facilitate model construction, programs were developed using the programming language Perl to assemble population balance equations from specific reaction mechanism input. The intrinsic kinetic parameters (a frequency factor and activation energy for each reaction) were obtained from previous modeling work in which the decomposition of a polystyrene mimic was described at the mechanistic level (Woo, Ph.D. dissertion, Northwestern University, 1999; Woo and Broadbelt, 1998, Catal. Today 40, 121) to link reactivity directly to structure. As the complexity of the models increased to include branching reactions and branched species, the model predictions improved. The separation between Mn and Mw observed experimentally was reproduced well for the three most complex models. The general modeling framework established may be easily extended to other single-component and multicomponent polymeric systems.

The batch pyrolysis of polystyrene (PS) in the presence of poly(α-methylstyrene) (PAMS) was investigated to determine the effect of the second polymer on the decomposition of polystyrene. Experimental parameters that were varied included the molecular weight and the concentration of each polymeric reactant. It was observed that the decomposition of polystyrene was dependent on the molecular weight of poly(α-methylstyrene). An enhancement in the polystyrene degradation rate was achieved during binary mixture pyrolysis of low molecular weight polymers, but a rate inhibition was observed during degradation in the presence of higher molecular weight PAMS. It is proposed that the divergence arises from differences in the relative magnitude of the enhancement caused by the production of PAMS-derived radicals and the inhibition due to incorporation of α-methylstyrene monomer into depolymerizing polystyrene chains. Variations in the initial concentration of the reactants had little effect on the yields of polystyrene degradation products.