The sorption behavior in mesopores (2- 50 run) depends not only on the fluid-wall attraction, but also on the attractive interactions between fluid molecules. This leads to the occurrence of multilayer adsorption and capillary (pore) condensation. Pore condensation is the phenomenon whereby a gas condenses to a liquid-like phase in a pore at a pressure Pless than the saturation pressure Po of the bulk liquid. Typically, type IV and V sorption isotherms according to the IUPAC classification can be observed. Significant progress was achieved during the last decade with regard to the understanding of sorption phenomena in narrow pores and the subsequent improvement in the pore size analysis of porous materials. This progress can be primarily attributed to: (i) the discovery of novel ordered mesoporous materials, such as MCM-41, MCM-48, SBA-15, which exhibit a uniform pore structure and morphology and could therefore be used as model adsorbents to test theories of gas adsorption; (ii) carefully performed adsorption experiments and (iii) the development of microscopic methods, such as the Non-LocalDensity Functional Theory (NLDFT) or computer simulation methods (e.g. Monte-Carlo - and Molecular-Dynamic simulations), which allow to describe the configuration of adsorbed molecules in pores on a molecular level. In the following chapter we discuss the most important phenomena occurring in mesopores, i.e. multilayer adsorption, phase transition (e.g., pore condensation) and sorption hysteresis in the context of classical approaches and the most recent developments.

For fluids in contact with a planar surface the thickness l of the adsorbed film is expected to increase without limit i.e., 

where  is the fluid-wall interaction parameter, and the  law results from the long-range van der Waals' interactions between a fluid molecule and a semi-infinite planar wall. In the case of non-retarded van der Waals' fluidwall interactions, the exponent m has a theoretical value of 3. However, experimental values for m are often significantly smaller than the theoretical value, even for strongly attractive adsorbents like graphite, i.e., m = 2.5 - 2.7.

In pores, however, the film thickness cannot grow unlimited. The stability of this film is determined by the attractive fluid-wall interactions, the surface tension and curvature of the liquid-vapor interface. In this case the difference in chemical potential  between the adsorbed liquid-like film (u) and the value at gas-liquid coexistence (u0) of the bulk fluid is given by

For small film thickness the first term  associated with multilayer adsorption dominates:

When the adsorbed film becomes thicker, the adsorption potential will become less important, and  will be dominated almost entirely by the curvature contribution  (i.e., the Laplace term), which is given for cylindrical pores by

where a is the core radius (a = r - l; r is the pore radius), Y is the surface tension of the adsorbed liquid-like film (which is assumed to be identical with the liquid),  describes the density difference between the liquid like film and the vapor phase. At a critical thickness, lc pore condensation occurs in the core of the pore, controlled by intermolecular forces in the core fluid. Pore condensation represents a first-order phase transition from a gas-like state to a liquid-like state of the pore fluid, occurring at a chemical potential 11 less than the value of 110 at gas-liquid coexistence of the bulk fluid.

These phenomena are illustrated in below figure, which depicts a sorption isotherm as it is expected for adsorption/desorption of a pure fluid in a single mesopore of cylindrical shape in combination together with a schematic representation of the appropriate sorption and phase phenomena occurring in the pore. Please note, that the schematic isotherm reveals a vertical pore condensation step; however, a truly vertical step in the adsorption isotherm is not to be expected for any real porous material with a non-vanishing pore-size distribution, i.e. the wider the pore size distribution, the less sharp is the pore condensation step. At lower relative pressures the adsorption mechanism in mesopores is comparable to that on planar surfaces. After completion of the monolayer formation (A), multilayer adsorption commences (B). After reaching a critical film thickness (C), capillary condensation occurs essentially in the core of the pore (transition from configuration C to D). The plateau region of the isotherm reflects the situation where the pore is completely filled with liquid and separated from the bulk gas phase by a hemispherical meniscus. Pore evaporation therefore occurs by a receding meniscus (E) at a pressure, which is less than the pore condensation pressure. The pressure where the hysteresis closes corresponds again to the situation of an adsorbed multilayer film which is in equilibrium with a vapor in the core of the pore and the bulk gas phase. In the relative pressure range between (F) and (A) adsorption and desorption are reversible.

Schematic representation of multilayer adsorption, pore condensation and hysteresis in a single cylindrical pore.