Ultrasmall amorphous zirconia nanoparticles catalyse polyolefin hydrogenolysis

Abstract

Carbon–carbon bond cleavage reactions, adapted to deconstruct aliphatic hydrocarbon polymers and recover the intrinsic energy and carbon value in plastic waste, have typically been catalysed by metal nanoparticles or air-sensitive organometallics. Metal oxides that serve as supports for these catalysts are typically considered to be inert. Here we show that Earth-abundant, non-reducible zirconia catalyses the hydrogenolysis of polyolefins with activity rivalling that of precious metal nanoparticles. To harness this unusual reactivity, our catalytic architecture localizes ultrasmall amorphous zirconia nanoparticles between two fused platelets of mesoporous silica. Macromolecules translocate from bulk through radial mesopores to the highly active zirconia particles, where the chains undergo selective hydrogenolytic cleavage into a narrow, C₁₈-centred distribution. Calculations indicated that C–H bond heterolysis across a Zr–O bond of a Zr(O)₂ adatom model for unsaturated surface sites gives a zirconium hydrocarbyl, which cleaves a C–C bond via β-alkyl elimination.

Main

Metal oxides are ubiquitous in catalysis as supports for active species or as catalysts themselves. Active oxides, such as those of molybdenum, tungsten or rhenium, can react with unsaturated hydrocarbons in situ to generate surface alkylidene (M = CR₂) sites for olefin metathesis¹. In contrast, the robust metal oxygen bonds of non-reducible oxides are used to create three-dimensional (3D) architectures, such as in zeolites and mesoporous materials. In catalytic reactions, such materials either make use of acidic or basic surface sites or act as supports for reduced metal nanoparticles, single-atom catalysts or surface organometallic chemistry (SOMC) species, rather than forming metal–carbon bonds themselves. In principle, in situ conversion of non-reducible metal oxides into metal hydride and metal alkyl species, especially in materials with co-localized surface acid sites, could lead to unique multifunctional reaction mechanisms. Such organometalloxide catalysts could be particularly interesting for the selective cleavage of carbon–carbon bonds in hydrocarbons, which has traditionally relied on precious metal-catalysed hydrogenolysis^2,3,4 or acid-catalysed hydrocracking⁵. Moreover, developing more effective processes for conversions of hydrocarbon plastics, which are currently used and discarded on a scale of hundreds of megatons⁶, would also benefit from Earth-abundant oxide-based catalysts.

The growing global plastic waste crisis⁷ has motivated recent studies of supported precious metal nanoparticles as catalysts for hydrogenolysis of polyolefins^8,9,10,11,12. Carbon–carbon bond cleavage via organozirconium-mediated β-alkyl elimination¹³ has received less attention¹⁴, despite the Earth abundance of Zr and attractive mild conditions (<150 °C and atmospheric pressure) used for the hydrogenolysis of polyolefins in pioneering work by Dufaud and Basset¹⁵. The combination of a few of the advantageous features of these distinct classes of catalysts may provide an appropriate strategy for designing organozirconia-mediated hydrogenolysis of hydrocarbons.

The conventional strategy to achieve high catalytic activity involving evenly dispersed sites over high-surface-area materials has not yet enabled the activation of metal oxides for hydrogenolysis. An alternative catalyst design instead positions active sites at specific isolated locations within a 3D nanosized architecture. In support of this idea, a mesoporous silica shell/platinum catalyst/silica core (mSiO₂/Pt/SiO₂) 3D architecture that isolates small Pt nanoparticles at the bottom of mesoporous wells provides high activity and long catalyst lifetimes in polyolefin hydrogenolysis^16,17. In contrast, external-facing platinum in Pt/SiO₂ materials readily deactivates by leaching and sintering. The synthetic methods that localize metal nanoparticles in a 3D architecture, however, are not readily adapted to SOMC zirconium complexes due to their unwanted reactivity with air and moisture, which forces the final synthetic step to be organometallic site installation. In that covalent grafting reaction, the placement of sites is governed by the locations of surface hydroxy groups, which are notoriously difficult to control on metal oxide surfaces¹⁸. Instead, we sought to advance the construction of mixed metal oxide–silica architectures by localizing zirconia particles in a narrow zone within mesoporous silica nanoparticles.

Metal nanoparticle and SOMC catalysts both benefit from coordinatively unsaturated sites, achieved in metal nanoparticle catalysts through high proportions of edge and corner atoms in small nanoparticles and in SOMC catalysts by immobilization onto inert supports. Although zirconia-catalysed polyolefin hydrogenolysis had not previously been demonstrated, zirconia was shown to catalyse the hydrogenation of alkenes¹⁹, and hexane was cracked over zirconia to give similar products and selectivity to the protonated Zeolite Socony Mobil-5 (HZSM-5) acid catalyst²⁰. Moreover, tests of zirconia as a support for noble metals in hydrogenolysis also suggested its possible activity²¹. Smaller nanoparticles²², the presence of oxygen vacancies²⁰ and undercoordinated sites²³ have also been proposed to enhance the reactivity of zirconia by creating either reducible surface sites or Lewis acid sites²⁴. Thus, metal oxides with coordinatively unsaturated surface sites in small nanoparticles that are isolated and stabilized by an inert 3D architecture could be promising for carbon–carbon bond hydrogenolysis.

Herein, we demonstrate that ultrasmall amorphous localized zirconia nanoparticles (L-ZrO₂), covalently embedded in silica and clamped in a void between two mesoporous platelets (L-ZrO₂@mSiO₂), are highly active in the hydrogenolysis of polyethylene. The architecture enhances the catalytic activity of zirconia to become comparable to that of Pt/C and improves its selectivity towards liquid products. Spectroscopic and computational studies implicate heterolytic H–H and C–H bond cleavage steps that generate Zr–H, Zr–C and O–H bonds, indicating that organometallic elementary steps are involved in polymer deconstruction and product formation. From a practical perspective, the catalyst can be handled under ambient conditions and provides a competitive, Earth-abundant and low-cost alternative to precious metal hydrogenolysis catalysts for polyolefin deconstruction.

Results

Synthesis and catalyst structure

L-ZrO₂@mSiO₂ was designed for zirconium-catalysed polyolefin deconstruction (Figs. 1 and 2). Ultrasmall ZrO_x(OH)_4–2x nanoparticles were dispersed on graphene oxide sheets (Supplementary Fig. 1), mSiO₂ layers were grown on the ZrO_x(OH)_4–2x/graphene oxide and the resulting material was washed and calcined to remove structure-directing agents. Inductively coupled plasma mass spectrometry (ICP-MS) analysis of L-ZrO₂@mSiO₂ revealed a ZrO₂ loading of 4.7 wt% (Supplementary Table 1). ICP-MS analyses of three batches of as-synthesized L-ZrO₂@mSiO₂ catalysts (Supplementary Table 2) ruled out the presence of any other transition metals in the catalyst, including Ru, Rh, Pt, Pd, Au, Re, Os, Ir, Ni, Fe, Co, Cu, Zn, Mo, W, Cd, Ce, Hf, Ti and V. The elemental purity of L-ZrO₂@mSiO₂ was further supported by X-ray photoelectron spectroscopy (Supplementary Fig. 2) and energy dispersive X-ray spectroscopy (Supplementary Fig. 3).

Fig. 1: Construction of L-ZrO₂@mSiO₂.

The construction of L-ZrO₂@mSiO₂ involves three steps: (1) precipitation–deposition of ZrO_x(OH)_4–2x nanoparticles onto graphene oxide, (2a) coating of mSiO₂ onto ZrO_x(OH)_4–2x/graphene oxide and (2b) calcination at 550 °C.

Fig. 2: Electron microscopy and X-ray absorption spectroscopy for ZrO₂ catalyst characterization.

a,b, Low-magnification (a) and high-magnification (b) high-angle annular dark-field (HAADF) STEM images of L-ZrO₂@mSiO₂. Inset in a, selected area electron diffraction pattern. c,d, Low-magnification (c) and high-resolution (d) HAADF STEM images of the cross-section of an L-ZrO₂@mSiO₂ particle prepared by microtomy. e,f, High-magnification HAADF STEM image (e) and corresponding energy dispersive X-ray spectroscopy elemental (top left, Si and Zr; top right, Si; bottom left, O; bottom right, Zr) maps (f) of the cross-section of an L-ZrO₂@mSiO₂ particle. g,h, Normalized Zr k-edge X-ray absorption near-edge structure spectra (g) and k₂-weighted EXAFS spectra (h) of L-ZrO₂@mSiO₂ and control samples. Inset in g, first derivative spectra.

The performance of L-ZrO₂@SiO₂ is best understood through comparisons with the behaviour of several reference catalysts, whose relevant structures are briefly described here and summarized in Supplementary Table 1. mSiO₂, synthesized by templated silica growth on graphene oxide^25,26, has the same layered platelet morphology and porous structure (Supplementary Fig. 4) as L-ZrO₂@mSiO₂. Imp-ZrO₂/mSiO₂, produced by incipient wetness impregnation of zirconium precursors into mSiO₂, contains randomly dispersed amorphous ZrO₂ nanoparticles (Supplementary Fig. 5). ZrO₂-6/mSiO₂ was prepared by immobilizing pre-synthesized 6 nm monoclinic ZrO₂ nanoparticles (Supplementary Fig. 6) on the external surface of mSiO₂ (Supplementary Fig. 7). ZrO₂-30 and Pt/C are, respectively, commercial monoclinic zirconia (~30 nm in size) and platinum nanoparticles supported on carbon (1.3 ± 0.4 nm in size) (Supplementary Fig. 8). L-Pt@mSiO₂ (Supplementary Fig. 9), synthesized by deposition of PtO_x(OH)_4–2x nanoparticles on graphene oxide (Supplementary Fig. 10) followed by growth of the mSiO₂ shell, creates a comparable architecture to L-ZrO₂@mSiO₂ with 3.5 ± 0.8 nm platinum nanoparticles instead of zirconia. The total surface area and Barrett–Joyner–Halenda pore size for mSiO₂-based samples are ~900–1,000 m² g⁻¹ and 3.4–3.8 nm, respectively (Supplementary Table 1).

The low-magnification scanning transmission electron microscopy (STEM) image (Fig. 2a) of L-ZrO₂@mSiO₂ showed its separated nanoplatelet particle morphology, with lateral dimensions ranging from hundreds of nanometres to a few micrometres. Pore diameters of 3.4 ± 0.4 nm in the mesoporous silica nanoplatelets, as revealed by the higher-magnification image (Fig. 2b), matched the values obtained with N₂ sorption isotherm measurements (Supplementary Table 1 and Supplementary Fig. 11). Notably, the STEM images of cross-sectioned L-ZrO₂@mSiO₂ particles, prepared with an ultramicrotome (Fig. 2c–e), clearly showed a thin (~3 nm) bright band, as was identified by elemental mapping as a region of concentrated zirconium (Fig. 2f), between the two 35-nm-thick sheets of mSiO₂. The mesopores in mSiO₂ are aligned perpendicular to the nanoplate (Fig. 2e)^26,27, and the diameter of the ZrO₂ particles is 3.0 ± 0.5 nm (Supplementary Fig. 12).

The amorphous nature and chemical structure of the ultrasmall ZrO₂ nanoparticles in L-ZrO₂@mSiO₂ were established by electron diffraction, powder X-ray diffraction, X-ray absorption spectroscopy and solid-state nuclear magnetic resonance (NMR) spectroscopy. A diffuse ring in the selected area electron diffraction pattern (inset in Fig. 2a) indicated amorphous characteristics of the material, in contrast with the sharp diffraction spots or rings typical of crystalline substances. The high-resolution image (Fig. 2d) further revealed that both ZrO₂ and mSiO₂ lack long-range order. Diffraction peaks from ZrO₂ were not detected in the powder X-ray diffraction pattern of L-ZrO₂@mSiO₂ (Supplementary Fig. 13). The strong pre-edge peak in X-ray absorption near-edge structure spectra (Fig. 2g) and the same peak intensity in Fourier-transformed extended X-ray absorption fine-structure (EXAFS) spectra (Fig. 2h) for the Zr–O distance in all ZrO₂ samples confirmed that Zr is in the +4 oxidation state. The non-crystalline nature of ZrO₂ in L-ZrO₂@mSiO₂ was distinguished by EXAFS from crystalline ZrO₂-6/mSiO₂ and ZrO₂-30, which contained a Zr–Zr scattering path at 2.9 Å.

The direct (e → ¹⁷O) dynamic nuclear polarization (DNP) surface-enhanced (SENS)²⁸ magic angle spinning (MAS) ¹⁷O Hahn echo NMR spectrum of L-ZrO₂@mSiO₂ (Fig. 3a) contained a broadened, axially symmetric, quadrupolar powder pattern with an isotropic chemical shift of 50 ppm and a quadrupolar coupling constant of 5 MHz, assigned to siloxane linkages. To aid in the assignment of additional broad signals at 400 and 150 ppm at 9.4 T, probably attributable to the ZrO₂ nanoparticles, we acquired DNP SENS data on pure monoclinic ZrO₂ nanoparticles (Fig. 3b). ZrO₂-30 gave rise to sharp resonances at 325 and 402 ppm from μ⁴-O^2– and μ³-O^2– lattice sites²⁹ and a broad resonance from approximately 425–300 ppm from surface μ³- and μ⁴-O^2– sites. The resonance at 400 ppm in the ¹⁷O Hahn echo spectrum of L-ZrO₂@mSiO₂ was assigned to disordered surface Zr oxide sites. In addition, the sharp signals from the crystalline ZrO₂ phase contrasted the broad resonances from L-ZrO₂@mSiO₂, further supporting the conclusion that the ZrO₂ particles are amorphous. We further performed indirect (e → ¹H → ¹⁷O) DNP SENS experiments to assign the resonance at 150 ppm in L-ZrO₂@mSiO₂, using phase-shifted recoupling effects a smooth transfer of order (PRESTO) experiments to acquire the ¹⁷O MAS NMR spectra of only the hydroxy species³⁰. The PRESTO spectrum of L-ZrO₂@mSiO₂ (Fig. 3c) was dominated by a previously obscured resonance at approximately –50 ppm assigned to surface silanols. Alternatively, the spectrum of ZrO₂-30 contained a signal at approximately 150 ppm at 9.4 T (Fig. 3d), which was unambiguously assigned to Zr–OH sites²⁹.^, The contrast between the spectra of the two samples suggests that a dominant component of the resonance at 150 ppm in the ¹⁷O Hahn echo spectrum of L-ZrO₂@mSiO₂ is not a Zr–OH species but rather Si–O–Zr linkages. We observed such a site in a previous study of a Zr(NMe₂)₃/SiO₂ species where it resonated at 146 ppm at 9.4 T³¹. Importantly, the observation of this resonance confirms that the silica and zirconia phases are covalently linked to one another.

Fig. 3: Solid-state NMR spectra of ZrO₂ catalysts.

a,b, Direct DNP-enhanced ¹⁷O Hahn echo spectra of L-ZrO₂@mSiO₂ (a) and monoclinic ZrO₂-30 nanoparticles (b). c,d, Indirect DNP-enhanced ¹⁷O{¹H} PRESTO NMR spectra of L-ZrO₂@mSiO₂ (c) and ZrO₂-30 nanoparticles (d). All of the data were acquired at a MAS rate of 14 kHz. Spinning sidebands are indicated by asterisks. Crystalline sites are further labelled by daggers.

The thermochemical stability of ZrO₂ is affected by the mSiO₂ shell. Calcination of ZrO_x(OH)_4–2x/graphene oxide at 550 °C formed a mixture of tetragonal and monoclinic ZrO₂ nanocrystals (Scherrer size = 5.5 and 9.3 nm, respectively; Supplementary Fig. 14). Similar calcination of L-ZrO₂@mSiO₂ did not provide detectable signals of crystalline domains (Supplementary Fig. 13). It is likely that the confinement of ultrasmall ZrO₂ nanoparticles within the mesopores, along with the covalent Si–O–Zr bonding, limits their growth and crystallization.

Polymer deconstruction catalysis

Polyethylene hydrogenolysis was performed with ~3 g melted polyethylene (number-averaged molecular mass (M_n) = 20 kDa and weight-averaged molecular mass (M_w) = 91 kDa; Supplementary Fig. 16) and 5.5 mg catalyst under 0.992 MPa of H₂ at 300 °C as the standard conditions. The high mass-specific catalytic activity of L-ZrO₂@mSiO₂ was established by the rate of C–C bonds cleaved per metal mass (2.3 ± 0.4 mol H₂ (g Zr)^–1 h^–1). The number of C–C bonds that were broken in each experiment was determined by measuring the consumption of H₂ (each H₂ molecule consumed corresponds to one hydrogenolysed C–C bond) and comparing starting and final total molecular weight distributions (M_n) of the entire sample, including the C₁–C₉ species in the reactor headspace, the C₈–C₅₀ liquid and wax fraction extracted with dichloromethane and the >C₅₀ polymeric solid residue (Fig. 4a,b and Supplementary Tables 3 and 6). The M_n versus time curve followed the generally expected decay (Supplementary Fig. 15).

Fig. 4: Hydrogenolysis results from L-ZrO₂@mSiO₂ and control catalysts.

a, Time-dependent conversion of polyethylene (M_n = 20 kDa; M_w = 90 kDa; Ð = 4.8), liquid yield and volatile yield, in mass percentage, catalysed by L-ZrO₂@mSiO₂ under H₂ at 300 °C. The data are presented as H₂ quantification (means ± 1σ), as determined from three or more gas chromatography measurements. b, Carbon number distribution of liquid products from the hydrogenolysis of polyethylene catalysed by L-ZrO₂@mSiO₂ after 2, 4, 6, 8, 12 and 20 h. c, Comparison of C–C bond cleavage activity (left axis, hashed bars, mean ± 1σ, as determined from three H₂ quantification measurements and the mass of metal loading) and conversion of polyethylene (PE; right axis, open bars, mean ± 1σ, as determined from two experiments of isolated material) at 300 °C for 6 h. d, Comparison of C–C bond cleavage reactivity for short, long, and ultra-high-molecular-weight high-density polyethylene (UHMWPE), as well as linear and branched polymers in L-ZrO₂@mSiO₂-catalysed hydrogenolysisσ (mean ± 1σ). e, Carbon number distribution of liquid products catalysed by L-ZrO₂@mSiO₂, ZrO₂-30, Imp-ZrO₂/mSiO₂ and ZrO₂-6/mSiO₂, obtained from reactions that consumed similar moles of H₂.

Source data

A few zirconia materials show catalytic activity in polyethylene hydrogenolysis, with L-ZrO₂@mSiO₂ providing the highest conversion of polyethylene and high mass-specific activity for C–C bond breakage (Fig. 4c). Its activity for C–C bond cleavage is ~23 ± 2× and 2.4 ± 0.3× higher than the activities of ZrO₂-30 and ZrO₂-6/mSiO₂, and comparable to that of Imp-ZrO₂/mSiO₂ (Supplementary Table 6). Remarkably, the activity of L-ZrO₂@mSiO₂ for C–C cleavage is even competitive with that of Pt-based catalysts following the trend L-ZrO₂@mSiO₂ ~ Pt/C < L-Pt@mSiO₂. The similar activity of Pt and confined Zr, along with the <0.001 wt% concentration of other transition metals measured by ICP-MS of as-synthesized and post-reaction zirconia catalysts, as well as catalyst-free control experiments, also ruled out trace contaminants as being catalytically important species.

The L-ZrO₂@mSiO₂-catalysed polyethylene hydrogenolysis produced a narrow, Gaussian-type C₁₈-centred distribution of liquid hydrocarbons, with C₉–C₂₇ representing >90% of the chains. This characteristic distribution was formed at the initial stage of the reaction and increased in yield in a roughly linear fashion until ~75% polyethylene conversion (Fig. 4a,b and Supplementary Table 3). The volatile species, which represented the low-end tail of the product distribution, similarly increased in yield as the reaction progressed (Supplementary Figs. 20–44). After >80% conversion of the polyethylene, the average chain length in the liquid products decreased to C₁₆ after 15 h (Supplementary Figs. 47 and 48) and sharpened after 20 h (Fig. 4b), and the weight fraction of volatile products, mostly composed of methane and ethane, further increased (Supplementary Figs. 45–53). We attribute these observations to the secondary hydrogenolysis of the C₁₈-centred distribution that occurred primarily at the ends of the chains. These results further indicate that L-ZrO₂@mSiO₂-catalysed hydrogenolysis is selective for the long hydrocarbon chains of polyethylene rather than the shorter chains of the primary products. This remarkable behaviour resembles mSiO₂/Pt/SiO₂-catalysed hydrogenolysis of polyethylene^16,17 and contrasts with the performance of the other ZrO₂ catalysts, which give broader, non-Gaussian or multimodal distributions (Fig. 4e), which also vary throughout the polyethylene conversion (Supplementary Tables 4 and 6 and Supplementary Figs. 54–87).

This highly disperse polyethylene (M_n = 20 kDa) represents the typical range used for flexible packaging applications. Accordingly, L-ZrO₂@mSiO₂-catalysed hydrogenolysis of a post-consumer low-density polyethylene (LDPE) grocery bag (M_n = 10.6 kDa and M_w = 150 kDa; dried under vacuum; Supplementary Fig. 18) resulted in equivalent reactivity (Fig. 4d; 2.3 ± 0.4 mol H₂(g Zr)^–1 h^–1). The catalytic activity was also similar for hexatriacontane (n-C₃₆H₇₄), LDPE (M_n = 2.8 kDa and M_w = 5.3 kDa; Supplementary Fig. 17) and ultra-high-molecular-weight high-density polyethylene (M_w = ~3,000–5,000 kDa). These results suggest that rates of threading of chains into pores and translocation to the active sites at the ends of the pores are not limiting the rates of C–C bond cleavage for short and long chains as well as branched and linear polymers, and the distribution is independent of the C–C bond cleavage rate; however, the conformations of long and short chains probably vary to influence the distributions. Specifically, hydrogenolysis of hexatriacontane provided a distribution of chain end-cleaved hydrocarbons, similar to the process observed for secondary hydrogenolysis of C₁₈ primary products noted above. In contrast, ultra-high-molecular-weight high-density polyethylene or post-consumer LDPE gave broad distributions, respectively (Supplementary Figs. 88–103). In addition, L-ZrO₂@mSiO₂ produced a narrower distribution of chain lengths of extractable species compared with the other ZrO₂-based catalysts at a similar polyethylene conversion (39–54%; Fig. 4e).

Mechanistic analysis

The amorphous ZrO₂ nanoparticles in L-ZrO₂@mSiO₂, leading to low-coordinated metal ions^32,33,34,35, were modelled by a Zr adatom supported on a (–111) surface of monoclinic ZrO₂ (Zr/ZrO₂). A constrained ab initio thermodynamic analysis of 21 structures (Supplementary Fig. 106 and Supplementary Table 9) with varying numbers of H, O and OH groups adsorbed on the Zr atom identified Zr(O)₂/ZrO₂ as the lowest energy of a possible adatom species with reference to Zr/m-ZrO₂, gas-phase H₂ and trace H₂O (a0 in Fig. 5; ΔG = –3.41 eV; T = 300 °C; $P_{{\rm{H}}_{2}}$ = 0.90 MPa; $P_{{\rm{H}}_{2}{\rm{O}}}$ = 6.89 × 10⁻¹⁵ MPa). In Zr(O)₂/ZrO₂, the Zr adatom is bonded to two oxo species with short Zr–O interatomic distances (1.92 and 1.97 Å) and coordinated by surface oxygen donors with longer Zr–O distances. The oxo species are also bridged to the Zr of the support. The resulting electron-deficient, low-coordinate Zr species are representative of adatom, corner and edge sites that are expected to be widely present in the amorphous ZrO₂ nanoparticles. The Zr(O)₂/ZrO₂ species reacts with H₂ via heterolytic dissociation, leading to HZr(OH)(O)/ZrO₂ (ΔG = –3.34 eV; b0 in Fig. 5 and Supplementary Table 9).

Fig. 5: Calculated bond activation by ZrO₂.

Side views of the optimized structures of intermediates and transition states (TS) corresponding to the initial C–H bond activation of hexane over Zr(O)₂/ZrO₂ (a0) and HZr(OH)(O)/ZrO₂ (b0) adatom models, both forming H₁₃C₆Zr(OH)(O)/ZrO₂ (a2). Distances are given in Å.

This heterolytic dissociation of H₂ on L-ZrO₂@mSiO₂ was supported by in situ diffuse reflectance infrared Fourier transform spectroscopy experiments under flowing H₂ at 300 °C, which revealed a small peak at 1,547 cm⁻¹, bands at 3,731 and 1,613 cm⁻¹ and a broad feature at 3,600–3,100 cm⁻¹ (Supplementary Fig. 104). The signal at 1,547 cm⁻¹ disappeared upon flowing D₂; however, the expected band at ~1,100 cm^–1 was not detected above the strong silica absorption (Supplementary Fig. 105). The peak intensities at 3,730 and 3,600–3,100 cm⁻¹ also diminished under D₂, and signals appeared at 2,700 and 2,600–2,300 cm⁻¹. These signals disappeared and the original features reappeared upon flowing H₂. On the basis of this H/D exchange behaviour and reported assignments^36,37, the band at 1,547 cm⁻¹ was assigned to ν_ZrH and the other signals were attributed to ν_OH from SiOH and ZrOH, providing experimental support for the idea of heterolytic dissociative adsorption of H₂ and D₂ in L-ZrO₂@mSiO₂.

Low-energy pathways were investigated computationally using density functional theory (DFT), and several plausible models for hydrogenolysis of n-hexane by the Zr(O)₂/ZrO₂ species at 300 °C under 0.1 MPa of H₂ are presented here (Fig. 6). Although the experimental study focused primarily on polyethylene, the secondary cleavage of the C₁₈-centred primary products and hydrogenolysis of hexatriacontane indicate that L-ZrO₂@mSiO₂ is also a catalyst for small-molecule hydrogenolysis. Hexane and the low-coordinated Zr(O)₂ react through an initial C–H bond activation to form H₁₃C₆-Zr(O)(OH)/ZrO₂ (a1 → a2), involving transfer of a hexane H atom to one of the O atoms and the hexyl group to the Zr atom. This step, as well as the heterolytic H₂ cleavage above, is reminiscent of 1,2-addition of a C–H or H–H bond across Zr=NR to give C–Zr–NHR or H–Zr–NHR^38,39. Hexane metalation by HZr(OH)(O)/ZrO₂ to give H₁₃C₆-Zr(O)(OH)/ZrO₂ with liberation of H₂ (b1 → a2), similar to the σ-bond metathesis reaction of (SiO)₃ZrH and hydrocarbons¹⁵, is ruled out by its 0.5 eV higher barrier than that of hexane dissociative adsorption on Zr(O)₂/ZrO₂.

Fig. 6: Calculated mechanistic model for hydrocarbon hydrogenolysis.

a, Schematic of the reaction pathways considered for n-hexane hydrogenolysis on the Zr(O)₂/m-ZrO₂ and H–Zr(O)(OH)/m-ZrO₂ models. b, Corresponding free energy profiles (T = 300 °C; P_gas = 0.1 MPa). All free energies are with reference to the sum of the energies of the Zr(O)₂/m-ZrO₂ catalyst model and the reactant gas molecules. c, Transition state calculated for C–C bond dissociation.

Kinetically favourable cleavage of the β-C–H bond in H₁₃C₆-Zr(O)(OH)/ZrO₂ produces cis-2-hexene (a2 → c1; G^act = 0.94 eV), 1-hexene or trans-2-hexene (via a <0.3 eV higher barrier compared with cis-2-hexene). Alternatively, the 1.26 eV barrier for β-C–C bond cleavage in H₁₃C₆-Zr(O)(OH)/ZrO₂ to give a3 is slightly higher. After hydrogenation of the propene product to propane, this pathway is thermodynamically more favourable than the endergonic formation of cis-2-hexene. Our calculations predicted a free energy of 1.8 eV for the C–C bond cleavage transition state over the Zr(O)₂ model, which is the highest-energy state in the free energy profiles of Zr(O)₂ active site models (Fig. 6). Thus, this process could be rate limiting for n-hexane and possibly also polyethylene hydrogenolysis. In addition, C–H or C–C bond cleavage steps solely based on acidic Zr(OH) have much higher activation barriers (G^act = 2.05 and 2.30 eV, respectively) than 1,2-addition and β-elimination. A bona fide acid catalyst, beta zeolite, under the standard hydrogenolysis condition gave coke and branched products in experiments using polyethylene. The differences between acid- and L-ZrO₂@mSiO₂-catalysed deconstructions further support the organozirconia-catalysed computational mechanism.

Propane is eliminated by a proton transfer from the proximal hydroxy to the propylzirconium species to regenerate the Zr(O)₂ species; the protonolytic propane elimination distinguishes this pathway from the σ-bond metathesis mechanism typically proposed for reactions of H₂ and molecular organozirconium compounds in solution. The activation barrier for an alternative mechanism involving the σ-bond metathesis-type reaction of H₇C₃–Zr(O)(OH) and H₂, as established for catalytic alkene hydrogenation or alkane hydrogenolysis by seemingly related SOMC species (≡SiO)₃ZrH⁴⁰, is ~0.4 eV higher than protonolytic elimination and appears less likely. In support of this idea, the reaction of grafted ≡Si–O–Zr(CH₂CMe₃)₃ and H₂ requires several hours at 150 °C. Although the hydridozirconium species H–Zr(O)OH is neither involved in C–H bond metalation nor formed from H₇C₃–Zr(O)(OH) and H₂, it is nonetheless essential for hydrogenation of propene (a5 → a7).

These reaction steps were confirmed by parahydrogen (pH₂)-induced polarization (PHIP) NMR spectroscopy, a technique that produces NMR signal enhancements only when the hydrogenation with pH₂ occurs by pairwise addition. The ¹H PHIP NMR spectrum for L-ZrO₂@mSiO₂-catalysed propene hydrogenation under ALTADENA (adiabatic longitudinal transport after dissociation engenders net alignment)⁴¹ conditions using 99% pH₂ (Supplementary Fig. 108) showed net alignment multiplet patterns of the CH₂ and CH₃ peaks with integral ratios close to 1:−1. Thus, the propane product had received both protons from the same pH₂ molecule with retention of spin–spin coupling⁴², in accordance with the steps a5 → a7. The σ-bond metathesis reaction of H₂ and propylzirconium transfers only a single proton from a pH₂ molecule and cannot produce the NMR signal enhancements in accordance with the above calculations. Moreover, 1,2-addition of the hydrocarbon CH bond (for example, a1 → a2) is the reverse reaction of propane elimination, by H transfer from OH to propylzirconium (a6 → a7). The principle of microscopic reversibility and the PHIP results together indicate that hydrocarbon metalation on L-ZrO₂@mSiO₂ is more consistent with 1,2-addition than dehydrogenative metalation by σ-bond metathesis, again in line with the calculations.

A microkinetic model was used to further examine the n-hexane hydrogenolysis over the Zr(O)₂/m-ZrO₂ active site, employing a continuous stirred-tank reactor (CSTR; T = 300 °C; $P_{{\rm{H}}_{2}}$ = 1 MPa; P_hexane = 0.1 MPa; Table 1). The model revealed that as hexane conversion increases with increased residence time, selectivity for the C–C bond cleavage product, propane, increases to 100% at sufficiently high residence times. These results suggest that the C–C bond cleavage is favoured in the presence of H₂, which shifts the equilibria towards the propane formation. The microkinetic model also predicted a high steady-state surface coverage of H–Zr(O)OH (θ = 0.63) under H₂ (1 MPa), which further promoted the conversion of propene to propane. Reasonable turnover frequencies, on the order of 10^–4 s^–1, were observed in the microkinetic model when hexane conversion to propane was between 0.1 and 12.4%.

Table 1 Conversion, selectivity and turnover frequencies of n-hexane hydrogenolysis predicted by the microkinetic CSTR model for the Zr(O)₂/m-ZrO₂ active site with respect to the effective residence time^a

The activation barriers of H₂ dissociation and the rate-limiting C–C bond cleavage calculated from the Zr(O)₂/m-ZrO₂ model were compared with those from the most stable flat surfaces of monoclinic ZrO₂ (–111) and tetragonal ZrO₂ (101) surface sites (Supplementary Fig. 107). H₂ activation was found to be thermodynamically less favourable on the flat surfaces compared with the Zr(O)₂/m-ZrO₂ model. The C–C bond cleavage barriers on the flat surfaces are in the range of 2.1–2.4 eV, in contrast with 1.26 eV for low-coordinated Zr sites, indicating that flat crystal surfaces of ZrO₂ are less active for breaking the C–C bonds of hydrocarbons. Thus, these results are consistent with the experimental observation that ultrasmall amorphous ZrO₂ nanoparticles are more active in polyethylene hydrogenolysis than larger crystalline ZrO₂ nanoparticles dominated by more stable flat surfaces.

Conclusions

Our synthetic, spectroscopic and mechanistic investigations of L-ZrO₂@mSiO₂ reveal the combined architectural and chemical features that enable Earth-abundant, non-reducible metal oxides (Zr, Si and O) to catalyse the selective hydrogenolysis of hydrocarbon polymers. The synthesis of L-ZrO₂@mSiO₂ shows, remarkably, that ZrO_x(OH)_4–x nanoparticles are stable under the hydrolytic conditions necessary for the growth of mesoporous silica and creation of the catalytic architecture with core-localized nanoparticles. Moreover, the coordinatively unsaturated surface sites needed for catalysis are stabilized by covalently embedding the amorphous zirconium nanoparticles in the walls of mesoporous silica. These sites, modelled as Zr(O)₂ surface species in DFT calculations, mediate C–C bond hydrogenolysis with comparable activity to Pt/C. The quantitative comparison of activity across a series of catalysts is based on H₂ consumption or the relationship between the number of C–C bonds that are cleaved and the change in M_n of the entire hydrocarbon population, as determined from the detailed characterization of gas, liquid and solid compositions. This quantitative comparison reveals that the catalytic enhancement observed with L-ZrO₂@mSiO₂ is more than simply the combination of small crystalline ZrO₂ with mSiO₂, as shown by the poorer activity of ZrO₂–6/mSiO₂.

In addition, L-ZrO₂@mSiO₂ provides advantageous selectivity over the other zirconia-based catalysts investigated in this study. Alignment of long chains in the pores¹⁶, non-dissociative adsorption of polymer onto the walls of silica and escape of smaller products through the void space between the two mesoporous silica plates may all contribute to higher selectivity. In fact, both L-ZrO₂@mSiO₂ and L-Pt@mSiO₂ have sites localized at the ends of mesopores and are both more selective than their non-pore-confined analogues. The mechanisms of zirconia- and platinum-catalysed reactions, however, are distinct. In fact, the energetically favourable heterolytic mechanism for H–H and C–H bond cleavage on Zr(O)₂/ZrO₂ is different from those proposed for reducible oxides or metal nanoparticles, or even the SOMC zirconium hydride, instead resembling 1,2-addition to zirconium imido compounds. This heterolytic cleavage generates O–H and Zr–H or Zr–CH₂CH₂R species, which subsequently engage in protonolytic elimination, insertion and β-alkyl elimination. Thus, the proposed active species is a bifunctional (hydroxy)organozirconium oxide species. Access to such species directly from ZrO₂, rather than by grafting neopentylzirconium onto silica, allows the catalytic architecture to be constructed under aqueous conditions and enables the catalytic chemistry to be accessed with air-stable precursors. In this sense, hydrogenolysis with L-ZrO₂@mSiO₂ is a previously unrecognized heterogeneous analogue of the SOMC-catalysed C–C cleavage processes.

Methods

Synthesis of L-ZrO₂@mSiO₂

L-ZrO₂@mSiO₂ was prepared via a two-step synthesis method. In the first step, precipitated zirconium oxyhydroxide nanoparticles were deposited onto graphene oxide in an aqueous solution to give ZrO_2–x(OH)_2x/graphene oxide. That material was prepared as follows. Urea (0.150 g) was dissolved in deionized H₂O (100 ml), graphene oxide (10 mg) was added and the mixture was treated in an ultrasonication bath for 30 min. An aqueous solution of ZrCl₄ (0.024 g in 1.25 ml H₂O) was added dropwise to the graphene oxide suspension and the mixture was stirred for 3 h at room temperature. The mixture was subsequently stirred and heated at 90 °C for 12 h. The solid ZrO_x(OH)_4–2x/graphene oxide product was collected by centrifugation, washed with deionized H₂O (3 × 50 ml) and then dispersed into H₂O (10 ml). In the second step, mesoporous silica (mSiO₂) layers were grown onto ZrO_x(OH)_4–2x/graphene oxide following the procedure described in Supplementary Information for the synthesis of mSiO₂ platelets. The final product was characterized and displayed a double-layered platelet structure with ultrasmall ZrO₂ nanoparticles in the narrow core.

Catalytic hydrogenolysis

The catalytic hydrogenolysis of polyolefins was performed in a glass-lined high-pressure autoclave reactor (250 ml; Parr Instruments) equipped with a mechanical impeller-style stirrer and a thermocouple that extended into the melted polymer¹⁶. Polyethylene (3.0 g; M_n = 20,000; Đ = 4.8) and a catalyst (5.5 mg) were placed into the glass-lined reaction vessel. The reactor was assembled and the system was evacuated under reduced pressure (100 Pa) and then refilled with Ar (3×). H₂ was introduced to the desired pressure (0.482 MPa) at room temperature and the reactor was sealed. The reactor was heated to 300 °C and the gauge pressure was increased to 0.896 MPa for experiments running for 2–20 h. All pressure values are reported as the absolute pressure at the reaction temperature (0.992 MPa = 0.896 MPa on the pressure gauge). At the end of the designated time, the reactor was allowed to cool to room temperature. The volatile products were sampled by connecting the cooled reactor to a gas chromatography sampling loop and analysed using a gas chromatography flame ionized detector (FID) and gas chromatography thermal conductivity detector. The mass yield of gas-phase products was obtained from direct gas chromatography-calibrated quantitative analysis of C₁–C₉ hydrocarbons separated on an Agilent Technologies 5890 gas chromatograph using an Agilent J&W GS-GasPro (0.32 mm × 15 m) capillary column (gas chromatography FID). H₂ was quantified with respect to a He internal standard using a Supelco Carboxen 1000 (4.6 m × 3.175 mm × 2.1 mm stainless steel) packed column (gas chromatography thermal conductivity detector). Dichloromethane was added to the reactor, which was resealed and heated to 100 °C. The reactor was cooled and the mixture was filtered on a Büchner funnel to separate residual insoluble polymer from the dichloromethane-soluble liquid products. The volatile components were evaporated in a rotary evaporator and the yields of extracted liquid species and solid materials were measured. The soluble materials were analysed by calibrated gas chromatography mass spectrometry using an Agilent Technologies 7890A GC system equipped with a FID or an Agilent Technologies 5975C inert MSD mass spectrometer on an Agilent J&W DB-5ht ((5%-phenyl)-methylpolysiloxane; 0.25 mm × 30 m × 0.1 μm) capillary column (see the section ‘Quantification of liquid products’ for details). The solid portion was dissolved in 1,2,4-trichlorobenzene (TCB) at 150 °C and analysed by high-temperature gel permeation chromatography (HT-GPC).

Analysis of the reaction products

The solid polymeric residue was analysed by HT-GPC (Agilent-Polymer Laboratories 220) to determine the molecular weights (M_n and M_w) and molecular weight distributions (Ð = M_w/M_n). The HT-GPC was equipped with refractive index and viscometry detectors. Monodisperse polyethylene standards (PSS Polymer Standards Service) were used for calibration ranging from ~330 Da to ~120 kDa. The column set included three Agilent PLgel MIXED-B columns and one PLgel Mixed-B Guard column. TCB containing 0.01 wt% 3,5-di-tert-butyl-4-hydroxytoluene was used as the eluent at a flow rate of 1.0 ml min⁻¹ at 160 °C. The lubricant samples were prepared in TCB at a concentration of ~5.0 mg ml⁻¹ and heated at 150 °C for 24 h before injection.

Quantification of liquid products

The composition of the dichloromethane-extracted liquid products, in terms of amounts of each chain length in the samples, was estimated using our previously reported approach¹⁶, summarized here briefly for convenience. Gas chromatography mass spectrometry of the ASTM standard was integrated. A plot of the integrated area versus the carbon number allowed determination of the response of all C_n values (since the ASTM standard does not include C₁₃, C₁₉, C₂₁ and so on) by interpolation. The regions of C₆–C₂₀ and C₂₀–C₄₀ are linear, but with inequivalent slopes. Therefore, these two regions were fit separately and used as calibration curves for liquid products.

Estimation of C–C bond cleavage from mass balance

M_n can be calculated as the total weight of polymer W divided by the total number of chains N. Under reaction, the number of chains grows over time, with each cleavage reaction producing one new chain. The number of chains may then be expressed as

$$N(t) = N\left( 0 \right) + \mathop {\int}\limits_0^t {r_{{\rm{cut}}}} {\rm{d}}t$$

(1)

where r_cut is the rate of cleavage in cuts per unit time. This may be substituted into the expression for M_n:

$$M_{\rm{n}}\left( t \right) = \frac{W}{{N(t)}} = \frac{{M_{\rm{n}}\left( 0 \right)W}}{{W + M_{\rm{n}}(0){\int}_0^t {r_{{\rm{cut}}}} {\rm{d}}t}}$$

(2)

Assuming the cleavage rate is constant and rearranging for r_cut:

$$r_{{\rm{cut}}} = \frac{W}{t}\left( {\frac{1}{{M_{\rm{n}}(t)}} - \frac{1}{{M_{\rm{n}}\left( 0 \right)}}} \right)$$

(3)

For this relationship to be accurate, the M_n used must be that of the entire population. As the polymer in this work was analysed in separate groups depending on the molecular weight, these analyses must be combined to determine the overall M_n. As the number average is the first moment of the distribution, the M_n of the entire population is the weighted average of the groups:

$$M_{{\rm{n}},{\rm{total}}} = \frac{{{\sum} {W_i} M_{{\rm{n}},i}}}{{{\sum} {W_i} }}$$

(4)

where the W_i is the mass of an analysed group, M_n,i is its number-averaged molecular weight and the summations are over all analysed groups. This result is valid for any number of groups and is true even when polymers of the same size may exist in multiple groups. M_n,total may then be used to estimate the C–C bond cleavage rate, per equation (3).

DFT calculations

DFT calculations related to the reaction network of hexane activation over the ZrO_xH_y models supported on the (−111) surface of monoclinic ZrO₂ were performed using the periodic plane-wave code Vienna ab initio simulation package (VASP 5.4)^43,44. The ion–electron interaction was described by pseudopotentials constructed within the projector augmented wave framework⁴⁵. The Perdew–Burke–Ernzerhof⁴⁶ functional form of the generalized gradient approximation was used to treat electron exchange–correlation effects and Grimme’s DFT-D3⁴⁷ method was used to semiempirically describe the van der Waals interactions. To partially account for the self-interaction errors associated with the generalized gradient approximation Perdew–Burke–Ernzerhof functional, we used the DFT+U methodology by setting the U–J value for the 4d states of Zr to 4 eV²². For the structure relaxation, we sampled the Brillouin zone by a 2 × 2 × 1 Monkhorst–Pack k-mesh applying a Gaussian smearing approach (σ = 0.05 eV) with a plane-wave kinetic energy cut-off of 500 eV. All of the calculations included dipole and quadrupole corrections for the energies as implemented in VASP using a modified version of the Makov and Payne method⁴⁸, and Harris–Foulke-type corrections⁴⁹ were applied for the forces. The transition state structures were determined using the climbing image nudged elastic band⁵⁰ and dimer methods⁵¹.

Microkinetic CSTR model for hexane hydrogenolysis over the ZrO_xH_y/m-ZrO₂ model

The rate constants for elementary surface reactions and adsorption processes were calculated using classical harmonic transition state theory and collision theory, respectively. A detailed description of the methodology can be found in our recent report⁵². Vibrational frequencies (ν_i) obtained from DFT calculations were used to calculate the zero-point energy and vibrational partition functions of the intermediate and transition states. Small computed vibrational frequencies (<50 cm^–1) for surface species were shifted to 50 cm^–1 since the harmonic approximation cannot accurately predict these small frequencies (these frequencies in effect cancel out). The number of active sites per surface area used to calculate adsorption rate constants was 2.5 × 10¹⁹ m⁻². The entropy term for hexane adsorption was calculated using the empirical formula S_ad⁰ (T) = 0.70 × S_gas⁰ (T) − 3.3R, derived by Campbell and Sellers⁵³.

The CSTR model was constructed under the assumption of an isobaric and isothermal reactor. The species balance for the ideal gas-phase reactants and products was described as:

$$\frac{{\partial {{{\mathrm{y}}}}_{i,{\rm{gas}}}}}{{\partial \left( {\frac{{{{\it{t}}}}}{\tau }} \right)}} = y_{i,{\rm{gas}},0} - y_{i,{\rm{gas}}}\left( {1 + \tau \times \alpha \mathop {\sum}\limits_i {r_{i,{\rm{gas}}}} } \right) + \tau \times \alpha \times r_{i,{\rm{gas}}}$$

(5)

where y_i,gas,0 and y_i,gas correspond to the inlet and outlet mole fractions of gas species i, respectively, t is the time, τ represents a residence time defined as the ratio of the total mole number of gas molecules in the reactor over the total feed flow rate at reactor entrance conditions τ = N_tot,0/F_tot,0, α is the total number of active sites in the reactor over the total mole number of gas molecules in the reactor N_cat/N_tot,0 and r_i,gas designates a generation rate of gas species i per active site. With the assumption of a constant surface density for the catalyst under various reaction conditions, the value of α was fixed at 1 × 10^–3 and y_i,gas was calculated by varying τ at a fixed temperature. The steady-state reactor outlet composition, y_i,gas, and overall conversion only depend on the product of α × τ = N_cat/F_tot,0. Thus, meaningful values of α × τ can be obtained from the conversion, and predicting the reactor outlet composition for different τ values is equivalent to predicting the outlet composition for different conversion levels.

PHIP study

Hydrogenation of propene over L-ZrO₂@mSiO₂ was examined by adiabatic longitudinal transport after dissociation engenders net alignment (ALTADENA)⁴¹ NMR experiments using 99% enriched pH₂. The pH₂ gas was produced by flowing H₂ (Airgas; UHP) through a cryocooled pH₂ converter (Advanced Research Systems) with a catalyst compartment packed with 46 g FeO(OH) (Sigma–Aldrich) at 20 K. The pH₂ and propene (Airgas; UHP) were mixed by combining the outlets of the mass flow controllers (Alicat) for each gas with a total flow rate of 60 sccm and a pH₂:propene ratio of 5:1. Experiments were performed using 64.9 mg L-ZrO₂@mSiO₂ packed into a 304 stainless steel reactor tube (McMaster-Carr; 5 cm length; 6.35 mm outer diameter; 3.86 mm internal diameter). The catalyst material was held in place using quartz wool and porous 316 L stainless steel frits (McMaster-Carr; 10 μm pore size) on both ends of the reactor tube. The reactor was mounted in the 4.5 mT fringe field of the 9.4 T Bruker Avance wide bore magnet. The catalyst was pre-treated by flowing an H₂/N₂ mixture (total flow rate = 50 ml min⁻¹; 10% H₂) through the reactor at 550 °C for 6 h. Propene hydrogenation was carried out by flowing the pH₂/propene mixture through the catalyst bed at 300 °C at an inlet pressure of 0.294 MPa. The reactor effluent was then transported to the detection coil of a Varian 400 MHz triple-resonance IFC-flow NMR probe at high field (9.4 T) via flow of the gas through approximately 110 cm of 1.59 mm outer diameter PEEK tubing (0.51 mm internal diameter). The ¹H NMR spectrum of the reactor effluent was collected on a 400 MHz Varian VNMRS spectrometer. The continuous-flow hyperpolarized spectrum was acquired by signal averaging of 32 transients using a recycle delay of 1 s and an acquisition time of 0.2 s. The thermally polarized spectrum was acquired after sealing the gas in the NMR probe and signal averaging of 32 transients using a recycle delay of 5 s and an acquisition time of 0.5 s. The propene hydrogenation with normal (n)H₂ (a thermal equilibrium 3:1 mixture of ortho and pH₂) was also performed under identical conditions. The pure ALTADENA spectrum was obtained by subtracting the continous-flow NMR spectrum acquired using nH₂ from the spectrum acquired with 99% pH₂. To ensure that the ALTADENA signal was due to hydrogenation over the L-ZrO₂@mSiO₂ catalyst and not from any other contaminant or metal in the reactor system, control experiments were performed using 99% pH₂ and a reactor tube packed only with an inert filler material (quartz wool). The experimental conditions were otherwise identical. The empty reactor did not yield any detectable conversion, but it did produce a small propane ALTADENA signal with an intensity of ~5% relative to the signal acquired using the L-ZrO₂@mSiO₂ catalyst at 300 °C. The small background NMR signal appeared to arise from the stainless steel surfaces in the reactor and had been observed in our laboratory previously.

Calculation of conversion

The fractional conversion of propene to propane (PA) was calculated from the thermally polarized (TP) spectrum using the following equations:

$$S_{{\rm{PA}},^{1}{\rm{H}}}^{{\rm{TP}}} = \frac{{S_{{\rm{PA}},{\rm{CH}}_{3}}^{{\rm{TP}}}/6 - X_{{\rm{imp}}} \times S_{{\rm{Propene}},{\rm{CH}}}^{{\rm{TP}}}}}{{1 + X_{{\rm{imp}}}}}$$

(6)

$$\chi = \left( {\frac{{S_{{\rm{PA}},^{1}{\rm{H}}}^{{\rm{TP}}}}}{{S_{{\rm{PA}},^{1}{\rm{H}}}^{{\rm{TP}}} + S_{{\rm{Propene}},{\rm{CH}}}^{{\rm{TP}}}}}} \right) \times 100\%$$

(7)

where $\chi$ is the conversion of propene to propane, $S_{{\rm{PA}},{\rm{CH}}_{3}}^{{\rm{TP}}}$ is the measured integral of the PA CH₃ peak in the thermally polarized spectrum, $S_{{\rm{Propene}},{\rm{CH}}}^{{\rm{TP}}}$ is the measured integral of the propene CH peak in the thermally polarized spectrum, $S_{{\rm{PA}},^{1}{\rm{H}}}^{{\rm{TP}}}$ is the calculated integral per proton of PA after the correction of PA impurity and ${{X}}_{{\rm{imp}}}$ is the percentage impurity of PA in stock propene (0.26%).

Calculation of signal enhancement

The experimental ALTADENA NMR signal enhancement (ε) was evaluated by subtracting the ALTADENA integral of PA CH₃ for the experiment using a stainless steel cartridge with inert fillers from that using L-ZrO₂@mSiO₂, then comparing it with the PA CH₃ peak integral of the thermally polarized spectrum:

$$\varepsilon = \frac{{S_{{\rm{PA}},{\rm{CH}}_{3}}^{{\rm{ZrO}}_{2}} - S_{{\rm{PA}},{\rm{CH}}_{3}}^{{\rm{SS}}}}}{{S_{{\rm{PA}},^{1}{\rm{H}}}^{{\rm{TP}}}}}$$

(8)

where $S_{{\rm{PA}},{\rm{CH}}_{3}}^{{\rm{ZrO}}_{2}}$ is the integral of the PA CH₃ peak in the ALTADENA spectrum of experiments catalysed by L-ZrO₂@mSiO₂ and $S_{{\rm{PA}},{\rm{CH}}_{3}}^{{\rm{SS}}}$ is the integral of the PA CH₃ peak in the ALTADENA spectrum of experiments catalysed by the stainless steel cartridge with inert fillers.

Calculation of pairwise selectivity

The pairwise selectivity (𝜑) was obtained by dividing the experimental ALTADENA NMR signal enhancement (ε) by the theoretical value (ε^theor, assuming 100% pairwise addition), as in equation (9).

$$\varphi = \frac{\varepsilon }{{\varepsilon ^{{\rm{theor}}}}} \times 100\%$$

(9)

For the CH₃ proton of PA, the theoretical ALTADENA signal enhancement was obtained from equation (10)^54,55.

$$\varepsilon _{{\rm{ALTADENA}}}^{{\rm{theor}}} = \frac{{2k_{\rm{B}}T(4\chi _{\rm{p}} - 1)}}{{3\hbar \gamma _{\rm{H}}B_0}}$$

(10)

where T is the temperature, γ_H is the ¹H gyromagnetic ratio (in rad s⁻¹), B₀ is the static magnetic field and χ_p is the para-enrichment. When T = 300 K, B₀ = 9.4 T and χ_p = 99%, $\varepsilon _{{\rm{ALTADENA}}}^{{\rm{theor}}}$ = 31,524.

Due to the back-conversion of pH₂ to nH₂ by the catalyst during propene hydrogenation, the actual para-enrichment of the H₂ gas within the reactor could be lower than 99%. Indeed, the para-enrichment observed under reaction conditions was only χ′_p = 58.7% (Table 2), as estimated from equation (11):

$$\chi _{\rm{p}}^\prime = \left( {1 - \frac{{3S_{{\rm{pH}}_2}}}{{4S_{{\rm{nH}}_2}}}} \right) \times 100{{{\mathrm{\% }}}}$$

(11)

where $S_{{\rm{pH}}_2}$ and $S_{{\rm{nH}}_2}$ represent the integrals of the nH₂ peak in spectra acquired with pH₂ and nH₂, respectively, in the presence of propene, under reaction conditions. The corrected pairwise selectivity (φ′) was then obtained using equations (9)–(11).

Table 2 Hydrogenation of propene over L-ZrO₂@mSiO₂—ALTADENA-PHIP NMR results