Statistical identification of isotherm models from vacuum pump-down data

Pump-down pressure–time data are routinely fitted to infer the surface physics of adsorption, yet models built on different assumptions produce near-indistinguishable fits, so the inferred physics can be an artifact of the fitting choice rather than a property of the surface. This work provides two tools to close that gap: a model-selection criterion suited to autocorrelated pump-down data (a corrected Akaike information criterion with a generalized-least-squares first-order autocorrelation correction, AICcGLS), and an identifiability diagnostic that determines whether a given experimental protocol can constrain an adsorption isotherm at all. Applying both to 20 datasets from AISI 1020 low-carbon steel and 316L stainless steel chambers, under three protocols (isothermal pump-down, nonisothermal throughput with a bake, and N2 vent/repump at 25 °C), shows that the protocol, the combination of thermal regime, pumping speed, and surface-area-to-pump-speed (A/S0) ratio, is the primary factor controlling identifiability. Only the isothermal, high-pumping-speed protocol resolves the isotherm; even there the five candidates fit statistically indistinguishably (all R2 ≥ 0.96), so goodness-of-fit cannot select among them and the apparent preference reduces to parsimony under the information criterion: the two-parameter Dubinin–Radushkevich model on most datasets, with the single-energy Langmuir model most parsimonious at 75 °C. The chamber-bake protocol is confounded by the thermal ramp and the N2-vent protocol by the H2 background, leaving the isotherm unidentifiable in both. The diagnostic identifies when isotherm parameters from pump-down data are physically meaningful rather than fitting artifacts.