A two-parameter stretched exponential function for dynamic water vapor sorption of cement-based porous materials

Finding a simple analytical model to represent dynamic water-vapor sorption (DWVS) in cement-based porous materials (CBPMs) is a challenging task because the physical-chemical interactions between water molecules and materials are quite complex. This paper presents a two-parameter stretched exponential function called the fractional kinetic (FK) model to represent the DWVS process in CBPMs. The FK model has a flexible and robust formula that is determined by two key parameters: the kinetic order n and the time index a. With conditioned n and a values, the FK model reduces to the classic exponential model and first-and second-order sorption models. The DWVS data of hardened blended cement-paste samples with different shapes was used to test the applicability of the FK model. The FK model can represent the early sorption data that is generally described by Fick's diffusion law and the late sorption data that matches the classic exponential model. Sorption of water vapor in CBPMs is a complex time-dependent process that is associated with the interactions between water molecules and the contact surfaces, as well as the microstructures of the cement-based materials.