(42e) A Macrothermodynamical Approach to the Limit of Reversible Capillary Condensation

A hysteresis loop is such a common occurrence in the adsorption-desorption cycles on mesoporous adsorbents that its presence has been included in the IUPAC definition of the type IV isotherm. It was early observed that no hysteresis loop can extend below a given relative pressure threshold, p/p° = 0.42 in the case of N2 at 77 K. Any desorption loop begun at higher pressure is terminated by a sudden evaporation when this threshold of relative pressure is reached. This effect, suggestively defined as catastrophic desorption, is at the basis of a frequent artefact in the evaluation of pore size: the sudden desorption is attributed to a narrow distribution of pores around 4 nm diameter, albeit the actual porosity has smaller size and is more broadly distributed. For smaller mesopores, in which capillary condensation takes place below the lowest possible closure point of the hysteresis loop, pores are filled and emptied following the same reversible path. For each pore size and shape, the pressure of the hysteresis closure point depends both on the nature of the adsorbate and on the temperature. The absence of hysteresis in the adsorption-desorption cycle for small mesopores was attributed to a tensional instability of the meniscus at low curvature radius. The smaller the mesopores are, the larger the capillary tension experienced by the liquid is. For very small mesopores, the tension can exceed the tensile strength of the liquid, which cannot help to evaporate. Conditions in which a liquid-gas interface is unstable are strongly reminiscent of the definition of the critical point of a fluid. Since the beginning of the eighties, a large research effort has been devoted to the evaluation of the critical properties of confined fluids. NLDFT calculations allowed to simulate the adsorption and desorption branches of the isotherm in porous systems. It was calculated that a mesopore is filled and emptied along the same path above a threshold of temperature and pressure defined as a capillary critical point. The threshold of reversible capillary condensation is a well-defined thermodynamical property, as evidenced by corresponding states treatment of literature and experimental data on the lowest closure point of the hysteresis loop in capillary condensation-evaporation cycles for several adsorbates. The non-hysteretical filling of small mesopores presents the properties of a first-order phase transition, confirming that the condensation reversibility does not depend on the capillary shift of the critical point. The enthalpy of reversible capillary condensation can be calculated by a Clausius- Clapeyron approach and is consistently larger than the condensation heat in unconfined conditions. The limit of reversible pore filling (rpf limit) has been empirically defined as the relative pressure level below which adsorption and desorption in a mesoporous system follow the same path. The attempts to identify the rpf limit with the critical point of the confined fluid have failed. Nevertheless, the rpf limit can be defined on the basis of macro-thermodynamical properties. Its dependence on temperature follows corresponding states relations and strongly suggests that it has to be considered as a first-order gas-liquid transition in the confined environment of the mesopores. The data on which this paper is drawn seem quite general, applying to adsorbates as different as argon and dimethylbenzene. The nature of the adsorbent seems not to be a determining factor, experimental data on several adsorbents (silica, zirconia, magnesia, and carbon) having been used. An important property of the rpf limit is a value of transition enthalpy significantly higher than the condensation enthalpy on a flat liquid surface. It seems to correspond to a given threshold in the continuous evolution of adsorption enthalpy with confinement. The rpf limit can likely be defined as the threshold of confinement beyond which the properties of the adsorbed layer create an infinite probability of formation of bridges between the layers adsorbed on the opposite walls of the pore. In this way, adsorption behaves no more as an activated process and is superposed to the equilibrium desorption curve. It is also significant that a macrothermodynamical treatment can provide useful information on the condensation in pores not larger than 10 molecular sizes, a domain usually reserved to statistical thermodynamics. Calorimetric data on the capillary condensation of tert-butanol in MCM-41 silica confirm a 20 % increase of condensation heat in small mesopores. This enthalpic advantage makes easier the overcoming of the adhesion forces by the capillary forces and justify the disappearing of the hysteresis loop.