The relationship between "BET" and "free volume"-derived parameters for water vapor absorption into amorphous solids

Water vapor absorption isotherms for amorphous solids with the same chemical composition but differing in molecular weight (i.e., PVP-90, PVP-30, and PVP-12), and for glucose, trehalose, and two molecular weight grades of dextran were obtained at 30 degrees C and analyzed using the Brunauer-Emmett-Teller (BET) equation to obtain the parameters, W(m) and C(B). Similar analyses were carried out for the same molecule (e.g., glucose or fructose) at -10 and 40 degrees C. Within each chemical group, W(m), the apparent BET-like parameter that is generally referred to as the "monolayer-limit of absorption", changed very little. In contrast, C(B), a measure of the free energy of absorption, significantly increased with increasing molecular weight or decreasing temperature, leading to a shift from a Type III to a Type II isotherm. The shift in isotherm shape correlates directly with the glass transition temperature, T(g), of the dry sample relative to the operating temperature, T (i.e., Type III when T > T(g) and Type II when T < T(g). These results are shown to be consistent with the combined Flory-Huggins solution model and Vrentas structural relaxation model; wherein Type II isotherm behavior, observed for T < T(g), reflects nonideal volumetric contributions to the overall free energy of absorption due to plasticization by water, as described by Vrentas, whereas Type III behavior only reflects the Flory-Huggins solution model. These volumetric free energy changes within each chemical group are shown to be correlated to the values of the "BET" parameter C(B).