Comprehensive Analytical Sorption Thermodynamic (CAST) model for water vapor sorption in cellulosic materials

Water vapor sorption is a fundamental property of cellulosic materials. Numerous theoretical and empirical models have been developed to describe the relationship between water activity, temperature, and equilibrium moisture content (EMC). However, a meaningful connection between model parameters and thermodynamic properties related to the sorption process is often lacking. In cases where models yield thermodynamic properties, such as through use of the Clausius-Clapeyron equation, these are limited to temperatures where the ideal gas equation is applicable. In this paper we advance a thermodynamic framework and formulate a new semi-empirical sorption model based on the differential Gibbs energy of sorption as a function of EMC and temperature, intended for high temperature applications such as steam drying or fire modeling. We refer to this as the Comprehensive Analytical Sorption Thermodynamic (CAST) model. It has six parameters, includes temperature explicitly, and is invertible. The CAST model includes analytical equations for the differential enthalpy of sorption, the differential entropy of sorption, and the integral heat of wetting. The model is evaluated using sorption data and calorimetric data over a range of temperatures from the wood science literature and compared with several existing models. Overall, the CAST model fits the experimental sorption and calorimetric data with higher accuracy than existing models.