Capillary phenomena condensation

The principle underlying surface area measurements is simple physisorb an inert gas such as argon or nitrogen and determine how many molecules are needed to form a complete monolayer. As, for example, the N2 molecule occupies 0.162 nm at 77 K, the total surface area follows directly. Although this sounds straightforward, in practice molecules may adsorb beyond the monolayer to form multilayers. In addition, the molecules may condense in small pores. In fact, the narrower the pores, the easier N2 will condense in them. This phenomenon of capillary pore condensation, as described by the Kelvin equation, can be used to determine the types of pores and their size distribution inside a system. But first we need to know more about adsorption isotherms of physisorbed species. Thus, we will derive the isotherm of Brunauer Emmett and Teller, usually called BET isotherm. 

Here the phenomenon of capillary pore condensation comes into play. The adsorption on an infinitely extended, microporous material is described by the Type I isotherm of Fig. 5.20. Here the plateau measures the internal volume of the micropores. For mesoporous materials, one will first observe the filling of a monolayer at relatively low pressures, as in a Type II isotherm, followed by build up of multilayers until capillary condensation sets in and puts a limit to the amount of gas that can be accommodated in the material. Removal of the gas from the pores will show a hysteresis effect the gas leaves the pores at lower equilibrium pressures than at which it entered, because capillary forces have to be overcome. This Type IV isotherm. 

There are two approaches to explain physical mechanism of the phenomenon. The first model is based on the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. 

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

Adsorbents such as some silica gels and types of carbons and zeolites have pores of the order of molecular dimensions, that is, from several up to 10-15 A in diameter. Adsorption in such pores is not readily treated as a capillary condensation phenomenon—in fact, there is typically no hysteresis loop. What happens physically is that as multilayer adsorption develops, the pore becomes filled by a meeting of the adsorbed films from opposing walls. Pores showing this type of adsorption behavior have come to be called micropores—a conventional definition is that micropore diameters are of width not exceeding 20 A (larger pores are called mesopores), see Ref. 221a. 

This is the capillary condensation phenomenon, which partiy accounts for the hysteresis observed in adsorption profiles of porous materials. 

Vapor sorption onto porous solids differs from vapor uptake onto the surfaces of flat materials in that a vapor (in the case of interest, water) will condense to a liquid in a pore structure at a vapor pressure, Pt, below the vapor pressure, P°, where condensation occurs on flat surfaces. This is generally attributed to the increased attractive forces between adsorbate molecules that occur as surfaces become highly curved, such as in a pore or capillary. This phenomenon is referred to as capillary condensation and is described by the Kelvin equation [19] ... 

Juza and Blanke (125) investigated the reaction of carbon and sulfur between 100 and 1000° at various pressures. They thought it unlikely that there was genuine chemical bonding. The phenomenon of sulfur fixation was ascribed to capillary condensation, adsorption, chemisorption, and solution in the carbon structure. 

The BET equation describes the phenomenon of multilayer adsorption, which is characteristic of physical or van der Waals interactions. In the case of gas adsorption, for example, multilayer adsorption merges directly into capillary condensation... 

The concept of a pore potential is generally accepted in gas adsorption theory to account for capillary condensation at pressures well below the expected values. Gregg and Sing ° described the intensification of the attractive forces acting on adsorbate molecules by overlapping fields from the pore wall. Adamson has pointed out that evidence exists for changes induced in liquids by capillary walls over distances in the order of a micron. The Polanyi potential theory postulates that molecules can fall into the potential field at the surface of a solid, a phenomenon which would be greatly enhanced in a narrow pore. 

For porous adsorbents capillary condensation is a common phenomenon. It leads to hysteresis in the adsorption curve. 

Condensation can, therefore, take place in narrow capillaries at pressures which are lower than the normal saturation vapour pressure. Zsigmondy (1911) suggested that this phenomenon might also apply to porous solids. Capillary rise in the pores of a solid will usually be so large that the pores will tend to be either completely full of capillary condensed liquid or completely empty. Ideally, at a certain pressure below the normal condensation pressure all the pores of a certain size and below will be filled with liquid and the rest will be empty. It is probably more realistic to assume that an adsorbed monomolecular film exists on the pore walls before capillary condensation takes place. By a corresponding modification of the pore diameter, an estimate of pore size distribution (which will only be of statistical significance because of the complex shape of the pores) can be obtained from the adsorption isotherm. 

The capillary condensation theory provides a satisfactory explanation of the phenomenon of adsorption hysteresis, which is frequently observed for porous solids. Adsorption hysteresis is a term which is used when the desorption isotherm curve does not coincide with the adsorption isotherm curve (Figure 5.8). 

The phenomenon of capillary condensation provides a method for measuring pore-size distribution. Nitrogen vapor at the temperature of liquid nitrogen for which cos(0) = 1 is universally used. To determine the pore size distribution, the variation in the amount of nitrogen inside the porous particle is measured when the pressure is slightly increased or decreased. This variation is divided into two parts one part is due to true adsorption and the other to capillary condensation. The variation due to adsorption is known from adsorption experiments with nonporous substances of known surface area, so the variation due to condensation can be calculated. The volume of this amount of nitrogen is equal to the volume of pores with the size as determined by the Kelvin equation. Once a certain model has been selected for the complicated pore geometry, the size of the pores can be calculated. Usually it is assumed that an array of cylindrical capillaries of uniform but different radii, and randomly oriented represents the porous medium. So the Kelvin equation in the form of Equation 3.9 is used. Since condensation is combined with adsorption, the thickness of the adsorption layer... 

It is generally accepted that the phenomenon of adsorption hysteresis has its origin in capillary condensation, i.e. condensation of vapour in capillaries under conditions differing from those for bulk phases. The steep rise in the amount adsorbed, that is observed at certain p(sat) below unity, indicates that pores... 

Regarding the mechanism, of capillary condensation, it is possible that more than one is viable, depending on the nature of the pores. As long ago as 1911 Zslgmundi J recognized the phenomenon he attributed it to contact angle hysteresis. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

Confinement in porous materials is known to modify the thermodynamical properties of fluids. Capillary condensation is an example where a dense phase appears before saturating pressure is reached. Such phenomenon is not yet well understood in disordered mesoporous materials presenting highly interconnected pores. 

Mesopore size analysis is usually based on the application of Kelvin s relation between vapor pressure of a capillary condensed phase and pore size. It is conventionally admitted that mesopores are pores whose width lies between 2 and 50 run. For narrower pores, the capillary condensation phenomenon does not take place and Kelvin s relation is irrelevant. These methods are thus strictly limited to pores in which the capillary condensation phenomenon occurs, as can be visualized by the hysteresis loop. 

Permporometry. Permporometry is based on the well known phenomenon of capillary condensation of liquids in mesopores. It is a collection of techniques that characterize the interconnecting active pores of a mesoporous membrane as-is and nondestiuctively using a gas and a liquid or using two liquids. The former is called gas-liquid permporometry [Eyraud, 1986 Cuperus et al., 1992b] and the latter liquid-liquid permporometry [Capanneli et al., 1983 Munari et al., 1989]. The "active" pores are those pores that actually determine the membrane performance. 

Thermoporometry. Thermoporometry is the calorimetric study of the liquid-solid transformation of a capillary condensate that saturates a porous material such as a membrane. The basic principle involved is the freezing (or melting) point depression as a result of the strong curvature of the liquid-solid interface present in small pores. The thermodynamic basis of this phenomenon has been described by Brun et al. [1973] who introduced thermoporometry as a new pore structure analysis technique. It is capable of characterizing the pore size and shape. Unlike many other methods, this technique gives the actual size of the cavities instead of the size of the openings [Eyraud. 1984]. 

During desorption, as the relative vapor pressure is reduced, pore solids in which capillary condensation occurs often show a hysteresis loop. The simplest interpretation of this phenomenon is given by the ink-bottle model (6). In the framework of this model (Fig. 12) the adsorption and desorption processes are controlled, respectively, by the void and neck sizes. Thus, desorption from a given pore occurs at a lower pressure than adsorption. 

The type II isotherm is associated with solids with no apparent porosity or macropores (pore size > 50 nm). The adsorption phenomenon involved is interpreted in terms of single-layer adsorption up to an inversion point B, followed by a multi-layer type adsorption. The type IV isotherm is characteristic of solids with mesopores (2 nm < pore size < 50 nm). It has a hysteresis loop reflecting a capillary condensation type phenomenon. A phase transition occurs during which, under the eflcct of interactions with the surface of the solid, the gas phase abruptly condenses in the pore, accompanied by the formation of a meniscus at the liquid-gas interface. Modelling of this phenomenon, in the form of semi-empirical equations (BJH, Kelvin), can be used to ascertain the pore size distribution (cf. Paragr. 1.1.3.2). 

For macroporous samples (pore size greater than 50 nm), the absence of any capillary condensation phenomenon means that only the specific surface area can be obtained from the adsorption isotherm using the BET equation. Mercury porosimetry (Paragr. 1.2) will then be necessary to obtain the pore size distribution. 

The study of this type of solid is based on the capillary condensation phenomenon and its quantitative expression is given by Kelvin s equation relating the adsorbate condensation pressure P to the radius of the pore r. ... 

For adsorbents with sufficiently laig e porosities (often referred to as mesoporous systems) isotherms can exhibit hysteresis between the adsorption and desorption branches as illustrated schematically in figure 1. A classification of the kinds of hysteresis loops has also been made. It is generally accepted that such behavior is related to the occurrence of capillary condensation - a phenomenon whereby the low density adsorbate condenses to a liquid like phase at a chemical potential (or bulk pressure) lower than that corresponding to bulk saturation. However, the exact relationship between the hysteresis loops and the capillary phase transition is not fully understood - especially for materials where adsorption cannot be described in terms of single pore behavior. 

The problem of adsorption hysteresis remains enigmatic after more than fifty years of active use of adsorption method for pore size characterization in mesoporous solids [1-3]. Which branch of the hysteresis loop, adsorption or desorption, should be used for calculations This problem has two aspects. The first is practical pore size distributions calculated from the adsorption and desorption branches are substantially diflferent, and the users of adsorption instruments want to have clear instructions in which situations this or that branch of the isotherm must be employed. The second is fundamental as for now, no theory exists, which can provide a quantitatively accurate description of capillary condensation hysteresis in nanopores. A better understanding of this phenomenon would shed light on peculiarities of phase transitions in confined fluids. 

MCM-41 material synthesized in 1992 by the Mobil Oil Company [1, 2] is up to now the first model mesoporous material as a consequence of its well defined porosity, composed of an hexagonal structure of cylindrical mesopores (whose diameter can be monitored in the range 20 - 100 A). MCM-41 samples are very suited to analyze the capillary condensation phenomenon. In particular the phase diagram of the confined capillary phase can be determined. Such a "capillary phase diagram" is characterized by the capillary critical temperature Tcc and the capillary triple point temperature T. Recent studies of the thermodynamic properties of confined phases (Ar, N2, O2, C2H4 and CO2) in MCM-41 have pointed out that their critical temperatures T are strongly displaced to-... 

The flow of a condensable vapor through a mesoporous membrane is a phenomenon of great complexity [18,14]. As the membrane is exposed to a certain vapor pressure gradient, adsorption, capillary condensation and surface flow phenomena occur at the same time, during the initial stages of the experiment [15]. As the system reaches a steady state, a film of adsorbate has been formed on the pore walls, while at the same time capillary condensation occurs in the subcritical pores according to the modified for the case of adsorption, Kelvin equation (eq. 3). 

These results, and particularly the existence of a negative temperature coefficient beyond 90°C., may be explained if again ethylene polymerization in the presencie of microporous solids is thought of as a surface phenomenon at the expense of adsorbed molecules. Indeed, at temperatures beyond 9°C., no capillary condensation can take place, and a temperature increase simply results in a concentration decrease of the adsorbed ethylene. Below 9°C. practically all the ethylene can be shown to be condensed within the solid micropores. This, to a certain extent at least, allows for the fact of the small influence of the temperature upon ethylene polymerization rate. 

---