Sorption isotherm restricted by multilayer hindered adsorption and its relation to nanopore size distribution

Hindered adsorbed layers completely filling the nanopores cause significant deviations from the classical BET isotherms for multimolecular adsorption of vapor in porous solids. Since the point of transition from free to hindered adsorption moves into wider nanopores as vapor pressure increases, the surface area exposed to vapor is decreased by an area reduction factor that decreases with increasing adsorbed volume, and thus also with increasing vapor pressure (or humidity). The area reduction factor does not affect the rates of the local process of direct adsorption or condensation of individual vapor or gas molecules, but it imposes a lateral constraint on the total area and volume of the free portion of the adsorption layer that is in direct contact with vapor. A reasonable assumption for the dependence of the area reduction factor on the number of molecular layers is a selfsimilar function, i.e., a power law. This leads to a sorption isotherm expressed in terms of polylogarithms (aka Jonquière functions). The power-law exponent is a property that serves as an additional data fitting parameter, which is related to the pore size distribution. Compared to BET isotherm with the same initial slope, the proposed isotherm reduces the growth of the BET isotherm at low and intermediate humidity and the deviation increases with the exponent. The fitting of isotherm data is reduced to either a series of linear regressions or the minimization of a quadratic expression with respect to one parameter only. It is shown how to use the optimum fit to calculate the size (or width) distribution of nanopores < 6 nm. Comparisons with several published isotherms and pore size data measured on hardened cement pastes show that the present theory gives excellent fits. Finally, the semi-empirical GAB adsorption model is considered, but its additional parameters are not adopted because they weaken the physical foundation and are not constants as they need to be varied empirically with temperature and, for cements, with the degree of hydration.