Capillary condensed vapour

Capillary condensed vapours Porous solid Liquid Vapour... 

As with all thermodynamic relations, the Kelvin equation may be arrived at along several paths. Since the occurrence of capillary condensation is intimately, bound up with the curvature of a liquid meniscus, it is helpful to start out from the Young-Laplace equation, the relationship between the pressures on opposite sides of a liquid-vapour interface. 

Let us now consider the process of capillary condensation. For the pure liquid (a) in equilibrium with its vapour fi), the condition for mechanical equilibrium is given by Equation (3.6) and that for physicochemical equilibrium by... 

From the Kelvin equation it follows that the vapour pressure p over a concave meniscus must be less than the saturation vapour pressure p°. Consequently capillary condensation of a vapour to a liquid should occur within a pore at some pressure p determined by the value of r for the pore, and less than the saturation vapour pressure—always provided that the meniscus is concave (i.e. angle of contact <90°). 

Figure 3.10 is a plot of potential against distance from the wall for a liquid in a capillary of sufficient width for its middle A to be outside the range of forces from the wall. Since the capillary condensate is in equilibrium with the vapour, its chemical potential (=p represented by the horizontal line GF, will be lower than that of the free liquid the difference in chemical potential of the condensate at A, represented by the vertical distance AF, is brought about entirely by the pressure drop, Ap = 2y/r , across the meniscus (cf. Equation (3.6)) but at some point B. say, nearer the wall, the chemical potential receives a contribution represented by the line BC, from the adsorption potential. Consequently, the reduction Ap in pressure across the meniscus must be less at B than at A, so that again... 

Here d/l is the additional wall area exposed when the uptake diminishes by dn moles through evaporation from the capillary p." is the chemical potential of the capillary condensate and p° that of the bulk liquid adsorptive. The negative sign is necessary because the area A exposed increases as the uptake diminishes. If the adsorptive vapour behaves as a perfect gas,... 

Critical relative humidity The primary value of the critical relative humidity denotes that humidity below which no corrosion of the metal in question takes place. However, it is important to know whether this refers to a clean metal surface or one covered with corrosion products. In the latter case a secondary critical humidity is usually found at which the rate of corrosion increases markedly. This is attributed to the hygroscopic nature of the corrosion product (see later). In the case of iron and steel it appears that there may even be a tertiary critical humidity . Thus at about 60% r.h. rusting commences at a very slow rate (primary value) at 75-80% r.h. there is a sharp increase in corrosion rate probably attributable to capillary condensation of moisture within the rust . At 90% r.h. there is a further increase in rusting rate corresponding to the vapour pressure of saturated ferrous sulphate solution , ferrous sulphate being identifiable in rust as crystalline agglomerates. The primary critical r.h. for uncorroded metal surfaces seems to be virtually the same for all metals, but the secondary values vary quite widely. 

Capillary condensation The vapour pressure above a concave meniscus of water is less than that in equilibrium with a plane water surface. It is therefore possible for moisture to condense in narrow capillaries from an atmosphere of less than 100% r.h. 

Other methods of surface area determination depend, in general, on adsorption under well defined conditions of various solute molecules of known dimensions (Sposito, 1984 Davis and Kent, 1990). Some of these are dipole molecules so that dipole interactions with the surface or H-bonding are involved. Water adsorbed at a fixed relative water vapour pressure (e. g. 0.2) to provide a monolayer is one example (Torrent et ah, 1990). An organic dipole frequently used for soils is ethylene glycol monoethylether (EGME) (Carter et al., 1965). The main problem with these dipole molecules lies in their mutual association which may lead to localized adsorption beyond a monolayer (capillary condensation), particularly on porous material. 

If condensation of liquid in the micropores of charcoal when brought into contact with a vapour should occur the equilibrium vapour pressure above these constricted liquid filled capillaries will be much less than above a plane surface of liquid (see Chap. ix). Under these conditions the liquid filling the pores will be included in the amount of vapour adsorbed by the charcoal and give an erroneous impression as to the true extent of adsorption. At the same time for actual condensation to occur it is necessary that a mobile free surface of liquid should first be formed at some point in the capillary, in order that the surface forces of the liquid may promote further condensation. The primary formation of a layer more than one molecule thick is thus an essential preliminary to the process of capillary condensation. 

Figure 2.11 Capillary condensation of water vapour into a crack.

Capillary condensation is said to occur when, in porous solids, multilayer adsorption from a vapour proceeds to the point at which pore spaces are filled with liquid separated from the gas phase by menisci. 

Fig. 3. Different types of the tip-sample contact a rigid tip and rigid surface in vacuum, b capillary condensation of water vapour in the contact area,c interaction in a dielectric medium, d deformation of a soft sample induced by a rigid tip...

Type IV isotherms (e.g. benzene on iron(III) oxide gel at 320 K) level off near the saturation vapour pressure and are considered to reflect capillary condensation in porous solids, the effective pore... 

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. 

Most models to calculate the pore size distributions of mesoporous solids, are based on the Kelvin equation, based on Thomson s23 (later Lord Kelvin) thermodynamical statement that the equilibrium vapour pressure (p), over a concave meniscus of liquid, must be less than the saturation vapour pressure (p0) at the same temperature . This implies that a vapour will be able to condense to a liquid in the pore of a solid, even when the relative pressure is less than unity. This process is commonly called the capillary condensation. 

For vapours whose critical temperature is higher than room temperature, however, Vp will be almost equal to the molar volume in the liquid state (capillary condensation) and... 

The ratio dA/dN is a geometric quantity, determined by the curvature of the adsorbate/vapour interface. When dealing with a concave hemispherical meniscus of the capillary condensed liquid in a cylindrical tube, it can easily be calculated that... 

Types TV and V They are considered to reflect capillary condensation phenomena, i.e., possibility of condensation of gases in minute pores of the adsorbent at pressures even below the saturation pressures of p0 of the gas and may show hysteresis effect. An example of type IV is furnished by adsorption of benzene on silica gel at 50 C and that of type V by adsorption of water vapour on activated charcoal at 100 C. 

In 1911 Zsigmondy pointed out that the condensation of a vapour can occur in very narrow pores at pressures well below the normal vapour pressure of the bulk liquid. This explanation was given for the large uptake of water vapour by silica gel and was based on an extension of a concept originally put forward by Thomson (Lord Kelvin) in 1871. It is now generally accepted that capillary condensation does play an important role in the physisorption by porous solids, but that the original theory of Zsigmondy cannot be applied to pores of molecular dimensions. 

The few investigators who have attempted to use the original Harkins-Junt method have encountered a number of inherent difficulties. A major problem is that it is virtually impossible to avoid some interparticle capillary condensation as p/p° —+ 1. This inevitably reduces the extent of the available liquid-vapour interface (Wade and Hackerman, 1960), Moreover, the thickness of a pre-adsorbed film as p/p° — 1 is highly dependent on the shape, size and roughness of the particles. 

Since the capillary condensate in a particular mesopore is in thermodynamic equilibrium with the vapour, its chemical potential, p°, must be equal to that of the gas (under the given conditions of T and p). As we have seen, the difference between p° and p1 (the chemical potential of the free liquid) is normally assumed to be entirely due to the Laplace pressure drop, Ap, across the meniscus. However, in the vicinity of the pore wall a contribution from the adsorption potential, 0(z), should be taken into account. Thus, if the chemical potential is to be maintained constant throughout the adsorbed phase, the capillary condensation contribution must be reduced. 

The question of the constancy of the surface tension in porous media has been under consideration for many years and has been taken up again recently by Grown et al. (1997). Formerly, it was thought that for a concave liquid-vapour interface the surface tension should increase with increased curvature. The experimental findings that the hysteresis critical temperature is generally appreciably lower that the bulk critical temperature (see Section 7.5) is considered to be a strong indication that the surface tension of a capillary-condensate is reduced below the bulk value. More work on model pore structures is evidently required to settle this question. 

On the basis of the Saam-Cole-Findenegg approach, we are now able to revise the ideal isotherm for capillary condensation. A more realistic isotherm for the physisorption of a vapour in an assemblage of uniform cylindrical mesopores is shown in Figure 7.5. Here, C represents the limit of metastability of the multilayer (of thickness fc) and M the point at which the three phases (multilayer, condensate and gas) all coexist. Along MC the multilayer and gas are in metastable equilibrium. 

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... 

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... 

Langmuir isotherm assumes a monolayer coverage while the Type II isotherm deals with multilayer adsorption followed by capillary condensation. Types II and III are closely related to Types IV and V. The only significant difference between Types II, III and Types IV, V is that a maximum adsorption is reached for the latter case while for the former case, the adsorption increases as the adsorbate gas approaches its vapour pressure. 

This technique, developed by Eyraud [140] modified by Katz et al. [143] and recently by Cuperus et al. [141], is based on the controlled blocking of pores by capillary condensation of a vapour (e.g. CCli, methanol, ethanol, cyclohexane), present as a component of a gas mixture, and the simultaneous measurement of the gas flux through the remaining open pores of the membrane. The capillary condensation process is related to the relative vapour pressure by the Kelvin equation. Thus for a cylindrical pore model and during desorption we have... 

When the pore walls strongly absorb gas molecules, surface diffusion and/or capillary condensation accompanied by (surface) flow occurs. Usually this is the case with gases which condense rather easily at moderate temperature-pressure conditions (in any case being below their critical point) and we are dealing with vapour flow. 

In this model also the decrease of the pore radius due to the formation of an adsorbed layer is incorporated. Flow 1 in Fig. 9.9 is the case of combined Knudsen molecular diffusion in the gas phase and multilayer (surface) flow in the adsorbed phase. In case 2, capillary condensation takes place at the upstream end of the pore (high pressure Pi) but not at the downstream end (P2), and in case 3 the entire capillary is filled with condensate. The crucial point in cases 3 and 4 is that the liquid meniscus with a curved surface not only reduces the vapour pressure (Kelvin equation) but also causes a hydrostatic pressure difference across the meniscus and so causes a capillary suction pressure Pc equal to... 

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