Time Dependent Aspects of Adsorption: Evaluating the Lifetimes within the Hysteresis Loop

The phenomenon of hysteresis occurs frequently when fluids adsorb in mesoporous material in contact with a vapour reservoir. It piques interest because it seems to go against thermodynamics, which states that a system's response to a collection of boundary conditions is unique, irrespective of the systems’s history. It is, on the other hand, reproducible in experiments and by all computer simulation approaches. Many authors have attempted to address this problem by postulating that either or both branches of a double valued adsorption isotherm must be metastable. A finite lifetime against decay into the ground state distinguishes a metastable condition. However, there is no experimental evidence that the adsorption isotherm within the hysteresis loop is time dependent, and we are ignorant of any attempt in the literature to use computer simulation to estimate the lifetime of either of the adsorption isotherm branches. In the present contribution we evaluate a reliable estimate for the lifetime of the states within the hysteresis loop. We find that even the shortest lived states display lifetimes that are several times the age of the universe and, thus, are practically to be considered as stable states. Accordingly, the concept of bistability (in some cases even multistability) appears appropriate to describe the hysteresis loop of adsorption isotherms. Clearly, certain thermodynamic laws do not apply to confined systems. The current work is the first to attempt to formulate a time dependent theory for confined thermodynamics, allowing access to the lifetime of states within the hysteresis loop for the first time.