Population Balance Equations for Reactive Separation in Polymer Upcycling.

Many polymer upcycling efforts aim to convert plastic waste into high-value liquid hydrocarbons. However, the subsequent cleavage of middle distillates to light gases can be problematic. The reactor often contains a vapor phase (light gases and middle distillates) and a liquid phase (molten polymers and waxes with a suspended or dissolved catalyst). Because the catalyst resides in the liquid phase, middle distillates that partition into the vapor phase are protected against further cleavage into light gases. In this paper, we consider a simple reactive separation strategy, in which a gas outflow removes the volatile products as they form. We combine vapor-liquid equilibrium models and population balance equations (PBEs) to describe polymer upcycling in a two-phase semibatch reactor. The results suggest that the temperature, headspace volume, and flow rate of the reactor can be used to tune selectivity toward the middle distillates, in addition to the molecular mechanism of catalysis. We anticipate that two-phase reactor models will be important in many polymer upcycling processes and that reactive separation strategies will provide ways to boost the yield of the desired products in these cases.

Zirconium-Catalyzed C-H Alumination of Polyolefins, Paraffins, and Methane.

C-H/Et-Al exchange in zirconium-catalyzed reactions of saturated hydrocarbons and AlEt3 affords versatile organoaluminum compounds and ethane. The grafting of commercially available Zr(OtBu)4 on silica/alumina gives monopodal ≡SiO-Zr(OtBu)3 surface pre-catalyst sites that are activated in situ by ligand exchange with AlEt3. The catalytic C-H alumination of dodecane at 150 °C followed by quenching in air affords n-dodecanol as the major product, revealing selectivity for methyl group activation. Shorter hydrocarbon or alcohol products were not detected under these conditions. Catalytic reactions of cyclooctane and AlEt3, however, afford ring-opened products, indicating that C-C bond cleavage occurs readily in methyl group-free reactants. This selectivity for methyl group alumination enables the C-H alumination of polyethylenes, polypropylene, polystyrene, and poly-α-olefin oils without significant chain deconstruction. In addition, the smallest hydrocarbon, methane, undergoes selective mono-alumination under solvent-free catalytic conditions, providing a direct route to Al-Me species.

Size-Controlled Nanoparticles Embedded in a Mesoporous Architecture Leading to Efficient and Selective Hydrogenolysis of Polyolefins.

A catalytic architecture, comprising a mesoporous silica shell surrounding platinum nanoparticles (NPs) supported on a solid silica sphere (mSiO2/Pt-X/SiO2; X is the mean NP diameter), catalyzes hydrogenolysis of melt-phase polyethylene (PE) into a narrow C23-centered distribution of hydrocarbons in high yield using very low Pt loadings (∼10-5 g Pt/g PE). During catalysis, a polymer chain enters a pore and contacts a Pt NP where the C-C bond cleavage occurs and then the smaller fragment exits the pore. mSiO2/Pt/SiO2 resists sintering or leaching of Pt and provides high yields of liquids; however, many structural and chemical effects on catalysis are not yet resolved. Here, we report the effects of Pt NP size on activity and selectivity in PE hydrogenolysis. Time-dependent conversion and yields and a lumped kinetics model based on the competitive adsorption of long vs short chains reveal that the activity of catalytic material is highest with the smallest NPs, consistent with a structure-sensitive reaction. Remarkably, the three mSiO2/Pt-X/SiO2 catalysts give equivalent selectivity. We propose that mesoscale pores in the catalytic architecture template the C23-centered distribution, whereas the active Pt sites influence the carbon-carbon bond cleavage rate. This conclusion provides a framework for catalyst design by separating the C-C bond cleavage activity at catalytic sites from selectivity for chain lengths of the products influenced by the structure of the catalytic architecture. The increased activity, selectivity, efficiency, and lifetime obtained using this architecture highlight the benefits of localized and confined environments for isolated catalytic particles under condensed-phase reaction conditions.

Polyethylene upcycling to long-chain alkylaromatics by tandem hydrogenolysis/aromatization.

The current scale of plastics production and the accompanying waste disposal problems represent a largely untapped opportunity for chemical upcycling. Tandem catalytic conversion by platinum supported on γ-alumina converts various polyethylene grades in high yields (up to 80 weight percent) to low-molecular-weight liquid/wax products, in the absence of added solvent or molecular hydrogen, with little production of light gases. The major components are valuable long-chain alkylaromatics and alkylnaphthenes (average ~C30, dispersity Ð = 1.1). Coupling exothermic hydrogenolysis with endothermic aromatization renders the overall transformation thermodynamically accessible despite the moderate reaction temperature of 280°C. This approach demonstrates how waste polyolefins can be a viable feedstock for the generation of molecular hydrocarbon products.

The overdamped transmission coefficient: Recovering the true mean first passage time from an inaccurate reaction coordinate.

For inertial reaction dynamics, a transition state theory rate constant obtained from an inaccurate reaction coordinate can be a posteriori corrected with reactive flux methods. In contrast, reaction coordinate errors in overdamped mean first passage time calculations cannot be a posteriori corrected. This work develops an overdamped version of the transmission coefficient. The calculation requires information from committor analyses and an estimate of the diffusivity along the committor coordinate. We illustrate the calculation for a simple two-dimensional potential that admits exact solutions.