Catalyst Supports Drive Nonlinear Sub-Arrhenius Kinetics in Levulinic Acid Conversion

Heterogeneous catalytic transformation of biomass-derived levulinic acid into valuable ester products exhibits pronounced deviations from classical linear Arrhenius behavior that are directly governed by the physical properties of the catalyst supports. Lanthanum cobaltite, lanthanum ferrite, and lanthanum manganite perovskites synthesized and immobilized onto silica, alumina, and titania supports revealed that dynamic chemical equilibrium and surface heat dissipation strongly regulate reaction trajectories. The findings demonstrate that thermal conductivity and catalyst-support interactions govern surface restructuring and product back-reactions during organic valorization, showing that non-Arrhenius curvature in biomass transformation is fundamentally linked to overall catalyst architecture and solid-state heat management rather than irreversible thermal degradation alone.

Standard chemical kinetic evaluations of surface-catalyzed systems typically rely on the linearized Arrhenius formulation to calculate apparent activation energies by correlating natural logarithms of rate constants against inverse temperatures. While this foundational relationship presumes uniform linear trajectories across temperature intervals, heterogeneous reaction environments and enzymatic processes frequently display non-Arrhenius curvatures. Whereas super-Arrhenius profiles often reflect interfacial mass transport constraints across solid-liquid boundaries, sub-Arrhenius curvature originates from mechanistic quantum mechanical tunneling phenomena. To evaluate these nonlinear deviations without assuming chemical denaturation or poisoning, a modified Arrhenius mathematical model incorporates a curvature deformation parameter where negative values designate sub-Arrhenius behavior. In catalyzed bio-based transformations, establishing whether apparent rate declines at elevated thermal stages stem from surface fouling or fundamental thermodynamic shifts is essential for designing robust catalytic platforms capable of sustained operational efficiency.

Beyond quantum tunneling considerations, dynamic chemical equilibria significantly shape apparent kinetic rates and observed activation energies over extended reaction periods. Previous investigations into heterogeneous catalytic esterifications and transesterifications observed dramatic drops in apparent activation energy under prolonged operating times, revealing that initial assumptions regarding catalyst deactivation were only valid during early time-on-stream stages. At higher reaction temperatures, opposing thermal influences emerge between kinetic forward rates and surface reactant coverage, while shifts in dynamic equilibrium from products back toward starting reactants can generate apparent negative activation energies. Because the esterification of levulinic acid with alcohols constitutes a reversible transformation in which produced water molecules hydrolyze resulting esters, thermal manipulation influences equilibrium balances. The presence of porous networks within solid catalytic matrices simultaneously introduces transport phenomena and potential tunneling effects, highlighting the necessity of assessing biomass conversions through comprehensive thermodynamic and equilibrium frameworks rather than simplistic forward-rate assumptions.

To rigorously examine these kinetic phenomena, researchers prepared nanostructured lanthanum-based perovskites using a hard-templating methodology based on mesoporous KIT-6 silica. The silica template was synthesized through the controlled cooperative assembly of tetraethyl orthosilicate alongside a triblock copolymer structure-directing agent under acidic aqueous conditions with butanol co-surfactants, followed by thermal aging, filtration, washing, and calcination up to 773.15 Kelvin. Lanthanum nitrate hexahydrate was combined with transition metal nitrate precursors—specifically cobalt(II) nitrate hexahydrate, ferric nitrate nonahydrate, and manganese(II) nitrate hydrate—in ethanolic solutions using citric acid as an anchoring ligand. The precursor mixtures were impregnated into suspensions of KIT-6 in toluene, dried at 353.15 Kelvin, and subsequently calcined in staged thermal profiles culminating at 973.15 Kelvin. Hot aqueous sodium hydroxide was applied to selectively etch and remove the silica template, leaving inverse replica perovskite frameworks that were thoroughly rinsed and dried.

The resulting unsupported perovskite powders were subsequently immobilized onto three distinct carrier materials comprising mesoporous KIT-6 silica, aluminum oxide, and titanium dioxide to systematically vary surface properties and support conductivities. Aqueous suspensions containing precisely weighed quantities of the synthesized perovskite nanoparticles were introduced dropwise into aqueous support slurries under continuous mechanical agitation. After thorough mixing, the composite materials were dried at 378.15 Kelvin and calcined at an elevated temperature of 1173.15 Kelvin for eight hours to ensure robust interfacial bonding. Structural characterization confirmed that the hard-templating synthesis successfully replicated the ordered mesoporous channels of the template into the perovskite phases, generating rough, agglomerated surfaces with uniform elemental distributions and high dispersion across all carrier matrices without introducing detectable chemical impurities.

Catalytic evaluation experiments were conducted in liquid-phase batch systems charging one milliliter of levulinic acid, one milliliter of hexane, seven milliliters of isopropanol, and fifty milligrams of the supported perovskite catalyst. Reaction vessels were operated over eight-hour durations across isothermal regimes spanning 364.15 to 384.15 Kelvin. Product identification and substrate consumption were quantitatively monitored using gas chromatography coupled with mass spectrometry utilizing an automated split injection system, helium carrier gas, and capillary column separation. Quantitative percentage conversions were determined by comparing normalized chromatographic peak areas of levulinic acid prior to reaction initiation against residual concentrations recorded after reaction completion. The chemical esterification pathway proceeds via alcohol-mediated protonation of the carbonyl moiety to enhance electrophilic character, followed by nucleophilic attack by the alcohol oxygen, subsequent expulsion of water, and eventual yield of the corresponding levulinate ester derivative.

Experimental comparisons revealed that catalytic activity varied substantially across the chosen support materials, demonstrating that chemical conversion is an intrinsic function of the support matrix. Among the evaluated formulations, titanium dioxide supports delivered superior performance relative to alumina and mesoporous silica. When lanthanum manganite was supported on titania, levulinic acid conversion reached 84.1 percent, whereas the same active perovskite on an alumina support attained 81.2 percent conversion. Conversely, on silica supports, lanthanum cobaltite exhibited greater catalytic performance than its manganese counterpart. Increasing reaction temperatures generally enhanced substrate conversion for all lanthanum perovskites supported on titania, a trend attributed to favorable metal-support interactions. However, lanthanum cobaltite immobilized on alumina and silica displayed an unexpected inverse trend, wherein percentage conversion decreased as operating temperatures rose under identical batch conditions, pointing directly toward atypical thermodynamic equilibrium controls.

Thermodynamic analyses of reaction rate constants across operational temperatures confirmed contrasting behavior dictated by carrier thermal properties. While the titania-supported cobalt perovskite exhibited steadily increasing rate constants with elevated temperature, cobalt perovskites hosted on alumina and mesoporous silica displayed decreasing apparent rate constants. Attempting to fit these downward trends to conventional linear Arrhenius models produced negative apparent activation energy values of minus 913.5 kilojoules per mole for the alumina-supported system and minus 2.4 kilojoules per mole for the silica-supported catalyst, accompanied by unsatisfactory regression coefficients. These apparent negative values characterize regimes governed by dynamic chemical equilibrium where elevated thermal input drives the reverse reaction. Because alumina and silica possess low thermal conductivity and retain heat, localized thermal hot spots accumulate on the catalyst surface, injecting thermal energy into converting ester products back into reactants rather than facilitating structural surface optimization.

To accurately capture this nonlinear behavior, experimental rate data were modeled using the modified Arrhenius formulation incorporating the deformation factor. Conventional linear plots failed to achieve acceptable fitting parameters, whereas the nonlinear curvature equations delivered excellent correlation with experimental trajectories. Activation energy values derived from the nonlinear model for supported lanthanum cobaltite spanned from 94.6 to 452.5 kilojoules per mole across the supports, confirming pronounced plot curvature. Crucially, the calculated deformation factor values remained consistently negative across all three supported cobalt systems, demonstrating that the catalytic transformation operates within a concave, sub-Arrhenius kinetic regime. This sub-Arrhenius behavior is directly associated with quantum mechanical tunneling phenomena within the porous architecture, explaining how catalytic conversion of levulinic acid proceeds efficiently at comparatively moderate temperatures relative to harsher baseline catalytic systems.

Recyclability evaluations across three successive eight-hour catalytic runs demonstrated slight catalyst deactivation, manifested as extended operational lag times required to achieve ten percent conversion during second and third cycles. Post-reaction Raman spectroscopy of spent catalysts provided structural explanations for these activity shifts. Low-frequency vibrational bands between 200 and 400 reciprocal centimeters, assigned to perovskite lattice vibrations and metal oxide bending modes, retained strong intensities in titania-supported cobalt and iron systems at higher temperatures, explaining their sustained operational activity. Interfacial perovskite-support interactions involving surface oxygen atoms were identified near 860 reciprocal centimeters. While cobalt and iron perovskites maintained stable interactions, titania-supported lanthanum manganite exhibited weak band intensities around 860 reciprocal centimeters and lost distinct manganese-oxygen bending modes at 364.15 Kelvin, reflecting structural rearrangements and weakened support interactions that correlated with lowered catalytic activity over repeated cycling.

Crystallographic evaluations further confirmed the fundamental stability and phase geometries of the synthesized materials. Theoretical Goldschmidt tolerance factors calculated from constituent ionic radii yielded values of 0.87 for lanthanum cobaltite, 0.89 for lanthanum manganite, and 0.92 for lanthanum ferrite, falling within the established range for stable crystal formation. Powder X-ray diffraction patterns corroborated these geometric predictions, showing that the cobalt and manganese perovskites adopted rhombohedral crystal symmetries within the R-3c space group with elongated unit cell volumes, while lanthanum ferrite formed a cubic lattice consistent with its tolerance factor approaching unity. Nitrogen sorption isotherms revealed type IV profiles characteristic of mesoporous solids with narrow hysteresis loops, where specific surface areas ranged from 7.60 square meters per gram for iron perovskites to 59.96 square meters per gram for cobalt formulations. Collectively, the study demonstrates that rational catalyst design for biomass conversion must integrate support-driven thermodynamics, localized thermal dissipation, and non-Arrhenius kinetics to maintain favorable equilibrium regimes.

Subject of Research: Thermodynamics and nonlinear Arrhenius kinetics of supported perovskite catalysts in levulinic acid valorization

Article Title: Thermodynamic interpretation of catalytic transformation of levulinic acid over supported perovskites catalysts: dynamic equilibrium and nonlinear arrhenius behavior investigation

Article References: Lepedi, T., Maumela, M., Xiao, Q., Ndaba, B., & Bingwa, N. (2025). Thermodynamic interpretation of catalytic transformation of levulinic acid over supported perovskites catalysts: dynamic equilibrium and nonlinear arrhenius behavior investigation. Discover Catalysis, 2(1), Article 17. https://doi.org/10.1007/s44344-025-00023-6

Image Credits: AI Generated

DOI: 10.1007/s44344-025-00023-6

Keywords: Levulinic Acid, Perovskite Catalysts, Heterogeneous Catalysis, Sub-Arrhenius Kinetics, Dynamic Equilibrium, Titanium Dioxide Support, Lanthanum Cobaltite, Lanthanum Manganite, Lanthanum Ferrite, Esterification, Biomass Valorization, Mesoporous Silica KIT-6, Alumina Support, Quantum Tunneling, Raman Spectroscopy, Goldschmidt Tolerance Factor, Thermal Conductivity