The gas adsorption isotherm requires accurate measurement for the analysis of porous materials and is used as an index of surface area, pore distribution, and adsorption amount of gas. Basically, adsorption isotherms of porous materials are measured conventionally at 77K and 87K using liquid nitrogen and liquid argon. The cold volume calibration in this conventional method is done simply by splitting a sample cell into two zones (cold and warm volumes) by controlling the level sensor in a Dewar filled with liquid nitrogen or argon. As a result, BET measurement for textural properties is mainly limited to liquefied gases (i.e. N2 or Ar) at atmospheric pressure. In order to independently investigate other gases (e.g. hydrogen isotopes) at cryogenic temperature, a novel temperature control system in the sample cell is required, and consequently cold volume calibration at various temperatures becomes more important. In this study, a cryocooler system is installed in a commercially available BET device to control the sample cell temperature, and the automated cold volume calibration method of temperature variation is introduced. This developed calibration method presents a reliable and reproducible method of cryogenic measurement for hydrogen isotope separation in porous materials, and also provides large flexibility for evaluating various other gases at various temperature.

We study and describe-from the point of view of the interactions of the adsorbed particles-three types of the adsorption isotherms, namely, Langmuir type adsorption isotherms, phase transition type adsorption isotherms, and adsorption limited type adsorption isotherms, which are observed by experiments. By introducing and using a one dimensional statistical occupancy model, we derived analytical adsorption isotherms for the no force, the attractive force, and the repulsive force exerted on the other adsorbed particles. Our derived adsorption isotherms qualitatively pretty well agree with the experimental results of the adsorption isotherms. To specify each adsorption type, Langmuir type adsorption is a phenomenon that occurs with no forces between the adsorbed particles, phase transition type adsorption is a phenomenon that occurs with the strong attractive forces between the adsorbed particles, and adsorption limited type adsorption is a phenomenon that occurs with the repulsive forces between the adsorbed particles. The theoretical analysis-only using fundamental thermodynamics and occupancy statistics though-qualitatively quite well explains the experimental results.