Processive Depolymerization Catalysts: A Population Balance Model for Chemistry’s “While” Loop

Abstract

A processive catalyst associates with a substrate and performs multiple reactions before dissociation, a mechanism used by enzymes to increase efficiency. Recent work [Tennakoon et al. Nature Catalysis 2020, 3, 893–901] reported a synthetic processive catalyst for polyethylene upcycling. In this paper, we embed a microkinetic model for processive depolymerization within coupled population balance models for the bulk and adsorbed polymer molecular weight distributions. Nondimensionalization reveals a small parameter that enables a reduction to one bulk population balance equation coupled to a pseudo-steady-state distribution for the distribution of adsorbed chains. We develop solutions to the model, with varying degrees of processivity, and starting from experimental molecular weight distributions taken from recent publications. The model predicts identifiable signatures of processivity in the evolving molecular weight distribution. The model also provides a framework for analysis of experimental data to obtain the underlying catalytic rate parameters.

Mechanistic Insights into Processive Polyethylene Hydrogenolysis throughIn SituNMR

“…The likelihood of hydrogenolysis relative to rehydrogenation depends on several apparent rate constants, including the rate of rehydrogenation k R , the rate of hydrogenolysis k H , and the rate of polymer exfiltration from the pore k E . When hydrogenolysis is rate-limiting (202−352 °C), 53 the extent of processivity, or average number of cuts per residence, 32 is equal to k H /k E . 54 However, while k H can be measured directly via the time-dependent signal intensity of the hydrogenolysis products, the NMR spectra do not provide information about the rate of exfiltration.…”

“…Instead, the reactant macromolecule repeatedly repositions itself in quasi-equilibrated conformations within the catalytic channel to undergo successive chemical cleavages, so that ideally the chain is converted in its entirety before the next reactant molecule is processed. Processive mechanisms have the desirable property that product MW distributions are independent of the degree of conversion and that a reaction mixture contains only high-MW reactants and small molecule products, with intermediate-length chains only existing as catalyst-bound transients …”

“…the desirable property that product MW distributions are independent of the degree of conversion and that a reaction mixture contains only high-MW reactants and small molecule products, with intermediate-length chains only existing as catalyst-bound transients. 32 The aforementioned catalyst was constructed through a stepwise growth process in which Pt nanoparticles were deposited onto a silica sphere (Pt/SiO 2 ), and a mesoporous shell was grown around the particle (mSiO 2 /Pt/SiO 2 ), so that the catalytic sites were located at the base of mesopores with tunable pore length and diameter. 23,33 This catalyst produced a time-independent and narrow product distribution, while the nonporous variant, Pt/SiO 2 , yielded a wider distribution of hydrocarbon chains with a conversion-dependent numberaveraged molecular weight (M n ).…”

Competing Time Scales in Surface-Driven Solution Depolymerization

“…Other variations on this depolymerization scheme have also been considered, including effects such as recombination (where polymers of any length can combine together) and Gaussian or central-chain scission, where chains break in a nonuniform way along the backbone . More recently, progress has been made in developing models that account for catalyst-driven depolymerization, − where features related to chemistry or substrate can play an important role. Indeed, clever design of the catalyst substrate can promote the linear depolymerization of polymers in upcycling processes so that the kinetic pathways resemble the “unzipping” behaviors seen in self-immolative polymers. ,− This has the advantage of yielding almost exclusively small molecular weight components desired for chemical upcycling, contrasting with the broad molecular weight distributions seen in random scission. , …”

“…8,68−70 This has the advantage of yielding almost exclusively small molecular weight components desired for chemical upcycling, contrasting with the broad molecular weight distributions seen in random scission. 67,68 Substrate geometry can also play an important role in polymers designed to undergo depolymerization in response to a stimulus. Recently, a strategy of depolymerization has been considered as a way to address surface fouling in redox polymer flow batteries.…”