Controlling thermal energy transport (thermal diode) for the desired direction is crucial to improve the efficiency of thermal energy transport, conversion, and storage systems as electrical diodes significantly impact on modern electronic systems. The degree of thermal rectification is measured by the difference between the heat transfer rate in favorable and unfavorable directions to the heat transfer rate in the unfavorable direction. A gas-filled, nano-gap structure with two different surface coatings is considered to design the thermal rectifier. In such a structure where the characteristic length scale is similar to the order of the mean free path of the fluid particles (Knudsen flow regime), the effective thermal conductivity is dominantly controlled by the gas-surface interaction, i.e., thermal accommodation coefficient. For the thermal rectification, the adsorption-based, nonlinear thermal accommodation coefficient change is a key design parameter. Here, these are examined using the kinetic theory for various pressure and temperature ranges. Optimal material selections are also discussed.