Uncertainty in pore size distribution derived from adsorption isotherms: II. Adsorption integral approach

Abstract

Uncertainty in the amount adsorbed in manometric adsorption isotherm measurements is well established. Here, we extend uncertainty methodologies from adsorption isotherm data uncertainty and apply them to calculate pore size distributions based on adsorption integral methods. The analyses consider as variables: uncertainty in adsorption isotherm data, regularization parameter, molecular potential model, and the number of single pore isotherms calculated with an associated quadrature interval. We demonstrate how the calculated pore size distribution is quite insensitive to the uncertainty in experimental data, but in contrast, the uncertainty in the experimental data affects the calculated value of the optimized regularization parameter which, in turn, leads to considerable variation in the calculated pore size distribution. The calculated pore size distribution is also shown to be highly dependent on the potential model selected and on the number of single pore isotherms applied to the inversion process. We conclude and suggest a quantitative comparison between calculated pore size distributions should be discouraged unless the uncertainty in the experimental data is relatively small and, default values for regularization parameters, potential models, the number of single pore isotherms and their distribution are exactly the same for each pore size distribution evaluation.

Analysis of Adsorbate–Adsorbate and Adsorbate–Adsorbent Interactions to Decode Isosteric Heats of Gas Adsorption

“…Previous analyses of QSDFT‐derived PSD suggest the uncertainty in this mean width is negligible. The apparent widths equivalent to the maxima at 0.8 nm and 0.11 nm may be real, but their presence may also be due to the value of the regularization parameter selected and/or the number of single pore isotherms employed; both variables have been shown to introduce such observations …”

Immersion Calorimetry: Molecular Packing Effects in Micropores

“…This ambiguity is due to disagreements in the validity of calculated specific surface areas and disagreements in the applicability of the models used for PSD reduction from adsorption isotherm data. This latter characterization method typically results from complex models containing several simplifying, model‐dependent assumptions . Several model‐independent techniques including adsorption calorimetry, immersion calorimetry, TEM, XRD, SANS, TPD, and XPS are often used as supporting characterization techniques.…”

“…Thisl atter characterization method typically results from complex modelsc ontaining severals implifying, modeldependent assumptions. [2,3] Several model-independent techniques includinga dsorption calorimetry,i mmersion calorime-try,T EM, XRD, SANS, TPD, and XPS [4] are often used as supporting characterization techniques. Of these,i mmersion calorimetry provides the option to evaluateb oth specific surface area and PSD.…”

Uncertainty in pore size distribution derived from adsorption isotherms: I. Classical methods

“…No effort is made to interpret or understand any differences between the PSD for mesopores and micropores in the transition range other than attribute them to differences between their foundation assumptions and pore geometry. Uncertainty propagation in adsorption integral equation methods is presented and discussed elsewhere [19].…”

“…For a detailed analysis see [19]. Over the last three decades a vast number of papers have been published describing the development, modification, and application of adsorption integral equation methods for PSD determination (For a review see [20] or [21]).…”