Evaluating carbon affinity in catalytic methane decomposition using UBI-QEP energetics and DFT carbon-binding...

Catalytic methane decomposition produces hydrogen and solid carbon, but carbon growth does not necessarily cause catalyst deactivation. This study examines the usefulness and limitations of carbon affinity as a descriptor using UBI-QEP energetics for Fe, Ni, Pt and Cu, supported by published density functional theory (DFT) and experimental evidence. The methane-to-adsorbed-carbon enthalpy, D _C, correlates strongly with the carbon chemisorption energy (r = -0.994) and almost exactly with the combined carbon and hydrogen binding term, Q(C) + 4Q(H). These relationships reveal its algebraic dependence on the underlying adsorption energies, rather than establishing an independent descriptor. Closing the thermochemical cycle to gaseous H₂ eliminates the hydrogen-binding contribution and clarifies the physical meaning of the chosen endpoint. An internally consistent DFT dataset covering 14 transition metals provides an external energetic comparison of carbon-binding order. For the four core metals, carbon-binding magnitudes show strong correlation (r = 0.929), although the Ni-Pt ordering is reversed. Facet-dependent adsorption, carbon migration barriers and experimental comparisons further demonstrate why elemental carbon affinity alone cannot predict activity or catalyst lifetime. Neither the DFT energetic comparison nor the heterogeneous experimental contrasts constitute validation of an out-of-sample model for catalytic activity or catalyst lifetime. Graphite-referenced equilibrium calculations quantify temperature and pressure effects without assuming quasi-equilibrium among the adsorbed CH _x intermediates. The analysis retains D _C as a transparent semi-empirical reaction-energy index while identifying carbon transport, nucleation and catalyst-state evolution as essential to interpreting filament growth, encapsulation and sustained hydrogen production.