Improvements of the DA equation for application in hydrogen adsorption at supercritical conditions

The Dubinin and Astakhov's equation (DA equation) is a privileged model for describing the behaviors of gas adsorption in microporous adsorbents. However, the behaviors of hydrogen adsorption at supercritical conditions reported are quite different from the normal gas adsorption. For example, the saturation vapor pressure P_S of hydrogen does not exit above its critical temperature T_C (33.2 K), and the specific amount of saturated adsorbed molecules n₀ and the characteristic energy of adsorption system E vary with equilibrium temperature. Whether the DA equation is adequate for hydrogen adsorption at supercritical conditions or not is well worth discussing. The authors have measured systematically the adsorption isotherms of hydrogen over a wide range of temperatures and pressures. In present works, an interesting phenomenon was reported that hydrogen adsorption exists an utmost value at supercritical conditions. Based on the new adsorption phenomenon, the parameters of the DA equation are analyzed and further modified for application in hydrogen adsorption. The results show that the DA equation can be applied to describe the behaviors of hydrogen adsorption at supercritical conditions, if it is modified as the following, n = f(T _C) [RTln(Ps/P)/g(T_C)]², (I) in which, In P _s = -134.5/T - 4.3362, (II) f(T_C) = α + βT _C, (III) g(T_C) = λ + γT_C. (IV).