Condensation in capillaries

Water molecules have polar ends, and readily form hydrogen bonding. As a result, several compounds interact with water molecules by surface adsorption, condensation in capillaries, bulk retention, and chemical interaction, and are called hygroscopic. At times, the interaction between the compounds and water is so strong that the interacting water vapors result in dissolving the compound. This process is called deliquescence, wherein a saturated layer of solution is formed around the... 

Fig. 53. Schematic isotherms (density p versus chemical potential pi) corresponding to the gas-liquid condensation in capillaries of thickness D, for the case without (a) and with (b) prewetting, and adsorption isotherm (c) for a semi-infinite system, where the surface excess density pjs is plotted vs. pi. Full curves in (a) and (b) plot the density p vs. pi for a bulk system, phase coexistence occurs there between p,p, (bulk gas) and pn, (bulk liquid), while in the capillary due to the adsorption of fluid at the walls the transition is shifted from paKX to a smaller value rc(D, 7) (with pic(7>, T) 1 /D, the Kelvin equation ), and the density jump (from ps D) to pt D)) is reduced. Note also that in the ease where a semi-infinite system exhibits a first-order wetting transition 7W, for 7 > 7W one may cross a line of (first-order) prewetting transitions (fig. 54) where the density in the capillary jumps from p to p>+ or in the semi-infinite geometry, the surface excess density jumps from p to p +, cf. (c), which means that a transition occurs from a thin adsorbed liquid film to a thick adsorbed film. As pi the thickness of the adsorhed liquid film in the semi-infinite...

Stockhausen et al. [45] differentiated the four types of adsorbed water, condensed in capillaries. The capillaries larger than 100 pm are filled with water only when the sample is in the contact with water. The condensation of water vapour in the pores larger then 10 pm occrrrs at relative humidity higher than 90%. In the capillaries with diameter between 3 and 10 pm the stmctural orientation of water takes place. The condensation is then occurring at 60-80 % RH. This water is frozen at temp, of -43 °C (Fig. 5.24). Finally, the 2.5 molecules thick layer of adsorbed water, belonging to the forrrth type, became frozen at temperature lower than -160 °C. These layers are strongly bound to the surface however, they are movable and behave like a two-dimension van der Waals gas medium. They can also migrate on the surface [46]. 

In particular, Connolly et al. (2005) designed NH capacitive sensor with 500-nm-thick porous SiC film. The response in humidity was very low for RH<50 %, which was attributed to the porous dimensions. The exact sensing mechanism is still not clear, but NH levels as low as-0.5 ppm were detected. Porous alumina (AI2O3) has also been examined as a sensing material for capacitive gas sensors and in particular for humidity measurements (Nahar and Khanna 1982 Timar-Horvath et al. 2008). The Al Og-based humidity sensor was a volume-effect device based on physical adsorption. At low humidity, the walls of the pores are lined with one-molecular-thickness liquid layer. As the humidity increases, after saturating the walls, due to a capillary condensation effect, the water starts condensing in the pores (Boucher 1976 Neimark and Ravikovitch 2001). It was established that the water molecules, even at a partial pressure higher than the saturated vapor pressure tend to condense in capillary pores with a radius below the Kelvin radius r, which is defined as function (1) (Boucher 1976) ... 

The Kelvin equation has numerous applications, e.g. in the stability of colloids (Ostwald ripening, see below), supersaturation of vapours, atmospheric chemistry (fog and rain droplets in the atmosphere), condensation in capillaries, foam stability, enhanced oil recovery and in explaining nucleation phenomena (homo- and heterogeneous). The Kelvin (as well as the Gibbs equations, see Equation 4.7a) are also valid for solids/solid-liquid surfaces, and they can be used for estimating the surface tensions of solids. We discuss hereafter several applications of the Kelvin equation. 

This type of DSC curve is common in samples which exist either as a channel hydrate/solvate structure (i.e. the volatiles are condensed in capillaries or channels within the bulk structure and do not constitute any part of the unit cell of the crystal lattice structure) or as samples which undergo dehydration/desolvation with the resulting desolvated/dehydrated lattice structure remaining thermodynamically stable (i.e. does not undergo spontaneous recrystallisation to a more thermodynamically favourable anhydrous lattice arrangement). Figure 8.15 shows a typical DSC curve obtained for a hydrated compound exhibiting this kind of behaviour. 

The rather low value obtained with the copper phthalocyanine, a low-energy solid (line (v)), is probably explicable by some reversible capillary condensation in the crevices of the aggregate, the effect of which would be to increase the uptake at a given relative pressure the plausibility of this explanation is supported by the fact that very low values of s, 1-47-1-77, were obtained with certain other phthalocyanines known to be meso-porous (cf. Chapter 3). 

Deviation from the standard isotherm in the high-pressure region offers a means of detecting the occurrence of capillary condensation in the crevices l>etween the particles of a solid and in any mesopores present within the particles themselves. A convenient device for detecting deviations from the standard is the t-plot . In the next section the nature and uses of t-plots will be discussed, together with a,-plots, a later development from them. As will l>e shown, both of these plots may l>e used not only for the detection of capillary condensation in mesopores, but also for showing up the presence of micropores and evaluating their volume. 

Fig. 3.11 Capillary condensation in cylindrical pores, (a) Cylinder closed at one end, B. The meniscus is hemispherical during both capillary condensation and capillary evaporation, (h) and (c) Cylinder open at both ends. The meniscus is cylindrical during capillary condensation and hemispherical during capillary evaporation. Dotted lines denote the...

Occasionally the DR plot falls into two straight lines (cf. Fig. 4.20), and the question again arises as to the significance of the different values of the uptake at p°jp = 1, derived by extrapolation of the respective branches, ( te often, the DR plot displays an upward turn as saturation pressure is approached (Fig. 4.18 and 4.21), a feature which can readily be understood in terms of multilayer adsorption and capillary condensation in mesopores. 

The limits of pore size corresponding to each process will, of course, depend both on the pore geometry and the size of the adsorbate molecule. For slit-shaped pores the primary process will be expected to be limited to widths below la, and the secondary to widths between 2a and 5ff. For more complicated shapes such as interstices between small spheres, the equivalent diameter will be somewhat higher, because of the more effective overlap of adsorption fields from neighbouring parts of the pore walls. The tertiary process—the reversible capillary condensation—will not be able to occur at all in slits if the walls are exactly parallel in other pores, this condensation will take place in the region between 5hysteresis loop and in a pore system containing a variety of pore shapes, reversible capillary condensation occurs in such pores as have a suitable shape alongside the irreversible condensation in the main body of pores. 

This principle is illustrated in Figure 10 (45). Water adsorption at low pressures is markedly reduced on a poly(vinyhdene chloride)-based activated carbon after removal of surface oxygenated groups by degassing at 1000°C. Following this treatment, water adsorption is dominated by capillary condensation in mesopores, and the si2e of the adsorption-desorption hysteresis loop increases, because the pore volume previously occupied by water at the lower pressures now remains empty until the water pressure reaches pressures 0.3 to 0.4 times the vapor pressure) at which capillary condensation can occur. 

In diying solids it is important to distinguish between hygroscopic and nonhygroscopic materials. If a hygroscopic material is maintained in contact with air at constant temperature and humidity until equilibrium is reached, the material will attain a definite moisture content. This moisture is termed the equilibrium moisture content for the specified conditions. Equilibrium moisture may be adsorbed as a surface film or condensed in the fine capillaries of the solid at reduced pressure, and its concentration will vaiy with the temperature and humidity of the surrounding air. However, at low temperatures, e.g., 15 to 50°C, a plot of equilibrium moisture content versus percent relative humidity is essentially independent of temperature. At zero humidity the equilibrium moisture content of all materials is zero. 

Sec. Ill is concerned with the description of models with directional associative forces, introduced by Wertheim. Singlet and pair theories for these models are presented. However, the main part of this section describes the density functional methodology and shows its application in the studies of adsorption of associating fluids on partially permeable walls. In addition, the application of the density functional method in investigations of wettability of associating fluids on solid surfaces and of capillary condensation in slit-like pores is presented. 

The density functional approach has also been used to study capillary condensation in slit-like pores [148,149]. As in the previous section, a simple model of the Lennard-Jones associating fluid with a single associative site is considered. All the parameters of the interparticle potentials are chosen the same as in the previous section. Our attention has been focused on the influence of association on capillary condensation and the evaluation of the phase diagram [42]. 

In Fig. 15 we show similar results, but for = 10. Part (a) displays some examples of the adsorption isotherms at three temperatures. The highest temperature, T = 1.27, is the critical temperature for this system. At any T > 0.7 the layering transition is not observed, always the condensation in the pore is via an instantaneous filling of the entire pore. Part (b) shows the density profiles at T = 1. The transition from gas to hquid occurs at p/, = 0.004 15. Before the capillary condensation point, only a thin film adjacent to a pore wall is formed. The capillary condensation is now competing with wetting. 

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. 

Sample 5 is close to an H2-type hysteresis, whereas 6 and 7 can be tentatively assigned to H3- and Hi-type hystereses, respectively [27]. The hystereses are caused by capillary condensation in interparticle pores and the shape is an indication of a particular particle morphology. Sample 7 has a more regular narrow mesopore size distribution, whereas sample 5 is more complex with pores of... 

Including capillary condensation with the Hertz approximation, as considered by Fogden and White [20], introduces pressure outside the contact area i.e., adhesion enters the problem nonenergetically through the tensile normal stress exerted by the condensate in an annulus around the contact circle. The resulting equations cannot be solved analytically however, their asymptotic analysis may be summarized as follows. 

FHH (Frenkel-Halsey-Hill) theory is valid for multi molecules adsorption model of the flat surfrtce material. When this model is applied for the surface fractal in the range of capillary condensation, in other words, in the state of interface which was controlled by the surface tension between liquid and gas, the modified FHH equation can be expressed as Eq. (3). 

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. 

Capillary forces increase in relationship to the relative humidity (RH) of the ambient air. At greater than 65% RH, fluid condenses in the space between adjacent particles. This leads to liquid bridges causing attractive forces due to the surface tension of the water. 

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