Models of Sigmoid Equilibrium Moisture Sorption Isotherms With and Without the Monolayer Hypothesis

Abstract

Among the numerous moisture sorption models, the GAB, an expanded version of the BET equation originally derived for inert gases adsorption on solid surfaces, is the most prominent. Both models are based on distinction between the adsorbate molecules settling on the bare surface in a monolayer (Langmuir adsorption) and those settling on already absorbed molecules forming multilayers. The BET theory has been successfully used to determine porous catalysts’ and fine powders’ specific surface area to this day. In contrast, applying the BET and GAB equations to water vapor sorption by solid foods (and non-foods) has at least three major problems: The calculated food powders’ specific surface area is independent of their particle size; the expected shoulder in foods’ enthalpy vs. moisture plot is absent; and there is a huge discrepancy between the specific surface areas calculated from moisture sorption isotherms and those of nitrogen. An alternative modeling approach posits the non-existence of a water monolayer, and suggests that moisture sorption is governed by at least two simultaneous mechanisms having different scaling exponents. Mathematical analysis and comparison of the resulting sorption models with the GAB equation show that they produce practically indistinguishable moisture sorption isotherms even with the same number of adjustable parameters. They also demonstrate that the sigmoid shape of a moisture sorption isotherm does not contain enough information to identify and quantify the underlying sorption mechanisms, and that a model’s good fit by statistical criteria in itself does not validate mechanistic assumptions.