Condensing phenomenon

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. 

Analytic description of the condensation phenomenon near the limit of infi-... 

As indicated, a single mean-field parameter amf is included as the proportionality factor. It is noteworthy that the numerical value of amf is unimportant to the condensation phenomenon itself, so that even an infinitesimally small value (e.g., of order 10-6 a.u.), is sufficient to reward thermodynamic condensation and yield an alternative phase of greatly reduced V under appropriate conditions of temperature and pressure. 

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... 

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. 

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. ... 

During shutdowns, water can also condense on the fireside of the boiler. Each shutdown results in a recurrence of this condensation phenomenon. The moisture can combine with acidic residue on the tubes and cause severe corrosion. If allowed to continue, tube failures can occur. The problem is most pronounced in boilers burning sulfur-laden fuels, even when such fuels are burned only occasionally. 

Fig. 10.11. The effect of osmolarity on the apparent number of GDP binding sites in brown adipose tissue mitochondria. The number of GDP-binding sites was measured in mitochondria from control and cold-exposed (24 h at 4°C) rats as earlier described (Sundin and Cannon [37]), but in media with the indicated concentrations of sucrose. Note that, if iso-osmotic sucrose is used (250 mM), a low GDP binding can be observed, especially in control rats. This may be related to the condensation phenomenon discussed in section 2.4. However, if 100 mM sucrose is used, the mitochondria swell, and the full number of binding sites is determined. (Our unpublished observations.)...

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-... 

In the case of nitrogen physisoiption at 77 K, the pore condensation phenomenon takes place in materials exhibiting pores larger than 2nm (mesopores). At a given temperature, the condensation pressure is a function of pore size. Considering three mesoporous solids having the same pore size but with different pore shapes, such as cylindrical, spherical, and slit-like, indicate whether pore condensation pressure would also be a function of pore shape. Justify your answer. 

The pre-smectic interaction is therefore observable already in the isotropic phase, although there is no direct phase transition from the isotropic to the smectic-A phase in 8CB. This makes the capillary condensation of the smectic-A phai in the gap between the surfaces impossible and consequently enables more detailed observation of the presmectic interaction. In the case when there is a direct isotropic-smectic-A phase transition, like for example in 12CB, a condensation phenomenon similar to nematic capillary condensation is observable. 

The capillary condensation phenomenon is of course not exclusive to water. It can be found in any confined system, where the surfaces prefer one phase over another and there is a first order phase transition between the phases of the material between the surfaces. A nematic liquid crystal is an example of such a system exhibiting a first order phase transition between the isotropic and the nematic phase. For this system, the nematic capillary condensation has been predicted by P. Sheng in 1976 [17]. Since the isotropic-nematic phase transition is only weakly first order, the phenomenon is not easy to observe. One has to be able to control the distance between the surfaces with a nanometer precision and the temperature within 10 K, which is unachievable to methods like NMR, SEA, DSC, etc., and very difficnlt to achieve in dynamic light scattering experiments [18,19]... 

M. Wajima, Y. Hosotani, J. Shibata, H. Souma and K. Tashiro, Condensing Phenomenon of Moisture in Sintering Bed and Its Effect on Bed Permeability, Tetsu-to-Hagane. Vol. 68,1982,1719-1727. 

In the presence of only one phase, rarefied DPD gas with attractive tail in interparticle interaction forces, we can simulate condensation phenomenon. As shown in Figure 26.27, the microstructures appearing are different than those for binary fluids. The average cluster size S(f) R t) increases much slower than in binary systems. Condensation patterns are more regular and resemble separate droplets rather than shapeless cluster structures. Therefore one can suppose that the mechanisms of growth in condensing gas must also be different than in separation of binary mixture. 

Fowler-Guggenheim equation (2.3-29) is one of the simplest equations allowing for the lateral interaction. Before discussing the two dimensional condensation phenomenon, we first investigate the isosteric heat behaviour. 

A typical adsorption-desorption isotherm of a practical porous solid usually exhibits a hysteresis (Figure 3.9-1) over the pressure range where the capillary condensation phenomenon is operating. 

The capillary condensation phenomenon was discovered by Zsigismody [139], who investigated the uptake of water vapour by silica materials. Zsigismody proved that the condensation of physicosorbed vapours can occur in narrow pores below the standard saturated vapour pressure. The main condition for the capillary condensation existence is the presence of liquid meniscus in the adsorbent capillaries. As it is known, the decrease of saturated vapour pressure takes place over the concave meniscus. For cylindrical pores, with the pore width in the range 2-50 nm, i.e., for the mesopores, this phenomenon is relatively well described by the Kelvin equation [14]. This equation is still widely applied for the pore size analysis, but its main limitations remain unresolved. Capillary condensation is always preceded by mono- and/or multilayer adsorption on the pore walls. It means that this phenomenon plays an important, but secondary role in comparison with the physical adsorption of gases by porous solids. Consequently, the true pore width can be assessed if the adsorbed layer thickness is known. 

A very important characteristics of capillary condensation is the so-called hysteresis loop occurring on many experimental adsorption isotherms. According to Foster [141] and Cohan [142] the adsorption branch of hysteresis loop is caused by the polymolecular adsorption and capillary condensation but the desorption branch appears only by the condensation phenomenon. 

The capillary condensation phenomenon often involves vapor and liquid phases in equilibrium. Hence, vapor-liquid and liquid-liquid equilibrium studies become extremely important and essential not only from a scientific point of view but also for the efficient design and improved operation of various industrial processes (Altwasser et al. 2005 Bhatia 1998 Gupta et al. 1997 Jackson and McKenn 1990 Matranga et al. 1992). Several studies done over the last decade using theoretical approaches such as density functional theory (Evans 1992) and molecular simulation (Evans 1990 Koga and Tanaka 2005 Rivera et al. 2002 Zangi 2004), as well as experimental... 

The practical implementation of BEC and of its mean field approximation usually makes use of thermodynamically limit constraint which enables the usage of the so called Thomas-Fermi approximation of DFT (Parr and Yang, 1989) for systems with many-to-infinite number of particles (V- oo), since in condensation phenomenon infinite more is the same (Kadanoff, 2009). 

The main problem was attributed to capillary condensation phenomenon in the mesoporous solids and the formation of a layer thickness on the surface. These cases were solved using Kelvin s equation, as proposed by Barret, Jayner, and Halenda [8], by developing the BJH method. It allows determining volumes and areas of mesoporous materials, through the distribution of pore radii with increasing pressure. However, Lippens de Boer [9] developed the f-plot method that allows determining the volume of micropores and mesoporous and the outside area. 

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