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

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.