Adsorption in porous solids

High-specific-area solids of the type studied by gas adsorption consist of small particles f which the radius of an equivalent sphere is given by Equation (1.2). This figure may be a fail reasonable measure of a characteristic linear dimension even of irregularly shaped partick 

TABLE 9.4 Effect of Traces of Adsorbed Water on the Heat of Immersion of TiOz in Benzene 

Amount of water adsorbed (mmol kg-1) Heat of Immersion (mJ m-2) 

In Chapter 6, Section 6.9, we discussed the pressure required to force a liquid —most commonly mercury —into the pores of a solid. Our emphasis in that section was on the pores between powder particles when the particles are tightly pressed into a plug. In this section we are not concerned with these interstitial pores since powders are not densely packed in adsorption studies instead, our interest is in the pores within the particles themselves. The difference is a matter of emphasis, however, and both liquid intrusion and gas adsorption complement one another for the study of porous solids. 

Adsorption hysteresis is often associated with porous solids, so we must examine porosity for an understanding of the origin of this effect. As a first approximation, we may imagine a pore to be a cylindrical capillary of radius r. As just noted, r will be very small. The surface of any liquid condensed in this capillary will be described by a radius of curvature related to r. According to the Laplace equation (Equation (6.29)), the pressure difference across a curved interface increases as the radius of curvature decreases. This means that vapor will condense 

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Adsorption in porous solids, an important topic in catalysis and other areas, is presented in Section 9.7, in which the adsorption hysteresis and capillary condensation are introduced. 

J. KSrger and D.M. Ruthven, Diffusion and Adsorption in Porous Solids, Ch. 5 in Molecular Sieves Science and Technology, H.G. Karge and J. Weitkamp eds., Wiley-VCH (2002). 

The rest of the book is dedicated to adsorption kinetics. We start with the detailed description of diffusion and adsorption in porous solids, and this is done in Chapter 7. Various simple devices used to measure diffusivity are presented, and the various modes of transport of molecules in porous media are described. The simplest transport is the Knudsen flow, where the transport is dictated by the collision between molecules and surfaces of the pore wall. Other transports are viscous flow, continuum diffusion and surface diffusion. The combination of these transports is possible for a given system, and this chapter will address this in some detail. 

Do, D.D., Adsorption in porous solids having bimodal pore size distribution, Chem. Eng. Common., 23(1). 27-56 (1983). 

When one is asked to describe porosity, using paper and pencil, first attempts are as seen in Chapter 3, as Figures 3.1-3.3. The approach of textbooks when describing adsorption in porous solids is the thermodynamics of adsorption processes. Although high-resolution transmission and scanning electron microscopy (HRTEM and SEM, respectively) have been available for at least 20 years, this facility has probably been under-exploited in analysis of structure in activated carbons. 

M. Jorge, N. A. Seaton, Molecular simulation of phase coexistence in adsorption in porous solids. Mol. Rhys. 100 (2002) 3803-3815. 

Diffusion in porous solids is usually the most important factor con-troUing mass transfer in adsorption, ion exchange, drying, heterogeneous catalysis, leaching, and many other applications. Some of the... 

The adsorption of gas can be of different types. The gas molecule may adsorb as a kind of condensation process it may under other circumstances react with the solid surface (chemical adsorption or chemisorption). In the case of chemiadsorption, a chemical bond formation can almost be expected. On carbon, while oxygen adsorbs (or chemisorbs), one can desorb CO or C02. Experimental data can provide information on the type of adsorption. On porous solid surfaces, the adsorption may give rise to capillary condensation. This indicates that porous solid surfaces will exhibit some specific properties. Catalytic reactions (e.g., formation of NH3 from N2 and Hj) give the most adsorption process in industry. 

Hoinkis E (2004) Small-angle scattering studies of adsorption and of capillary condensation in porous solids. Part Part Syst Charact 21 80-100... 

The effects of physical transport processes on the overall adsorption on porous solids are discussed. Quantitative models are presented by which these effects can be taken into account in designing adsorption equipment or in interpreting observed data. Intraparticle processes are often of major importance in adsorption kinetics, particularly for liquid systems. The diffusivities which describe intraparticle transfer are complex, even for gaseous adsorbates. More than a single rate coefficient is commonly necessary to represent correctly the mass transfer in the interior of the adsorbent. 

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. 

An adsorption equilibrium is quickly established. When lowering the pressure the gas desorbs reversibly (except in porous solids). 

For the measurement of the heat of adsorption, various types of calorimeter have been described, suitable for measurement of the comparatively large amounts of heat given off by the adsorption on porous solids 8 Roberts, however, has been successful in measuring the heat evolved from adsorption on a single tungsten wire, by employing the wire as its own calorimeter. Its temperature is raised by the heat evolution, and the rise of temperature is measured by the resistance of the wire. 

The most widely used unsteady state method for determining diffusivities in porous solids involves measuring the rate of adsorption or desorption when the sample is subjected to a well defined change in the concentration or pressure of sorbate. The experimental methods differ mainly in the choice of the initial and boundary conditions and the means by which progress towards the new position of equilibrium is followed. The diffusivities are found by matching the experimental transient sorption curve to the solution of Fick s second law. Detailed presentations of the relevant formulae may be found in the literature [1, 2, 12, 15-17]. For spherical particles of radius R, for example, the fractional uptake after a pressure step obeys the relation... 

For physisorption on/in porous solids, transport into mesopores and micropores often limits the rate of adsorption. Two-stage equilibria are frequently observed the more accessible outer surfaces equilibrate rapidly and remain in equilibrium with the ambient phase, acting as a source for slower transport of the adsorbate into the interior of the solid. Establishment of cmnplete equilibrium can be a slow process. 

The type IV isotherm corresponds to adsorption and desorption in porous solids. In particular, the mesoporous range of pore sizes usually gives rise to this type of isotherm (6). In the low-pressure region, the type IV... 

It is of interest to note that in the case under consideration (i.e., when the pore volume is concentrated in necks) the desorption process is described [Eqs. (38) or (39)] by employing only the neck-size distribution and the mean coordination number for voids. The neck-size distribution can be calculated from the adsorption branch of the isotherm. Thus, the analysis of the desorption branch of the isotherm allows one to obtain the mean coordination number. In fact, Zo can be obtained from the position of the desorption knee. In addition, using Eq. (39) and the scaling expression for 9 b2 [Eq. (12)], it is possible to estimate the average linear dimension L of the microparticles in porous solids 34). 

As an example of the above statement. Fig. 17.3 contains the Nj adsorption isotherms for powder AC vidth different adsorption capacities [3]. These isotherms, compared with those in Figs. 17.1 and 17.2, clearly demonstrate that the adsorption isotherms do not permit neither to distinguish the ACF from the AC nor to deduce differences in the pore size distribution. However, the unique fiber shape and porous structure of the ACF are advantages that permit to deepen into the fundamentals of adsorption in microporous solids [31]. ACFs are essentially microporous materials [13, 31], with sht-shaped pores and a quite uniform pore size distribution [42, 43]. Thus, they have simpler structures than ordinary granulated ACs [31] and can be considered as model microporous carbon materials. For this reason, important contributions to the understanding of adsorption in microporous solids for the assessment of pore size distribution have been made using ACF [31, 33, 34, 39, 42-46], which merit to be reviewed. 

On the other hand, the Kelvin equation has been extensively used in research on gas adsorption onto porous solids (see Sections 8.4 and 8.5) and capillary condensation. 

Lord Kelvin realized that, instead of completely drying out, moisture is retained within porous materials such as plants and vegetables or biscuits at temperatures far above the dew point of the surrounding atmosphere, because of capillary forces. This process was later termed capillary condensation, which is the condensation of any vapor into capillaries or fine pores of solids, even at pressures below the equilibrium vapor pressure, Pv. Capillary condensation is said to occur when, in porous solids, multilayer adsorption from a vapor proceeds to the point at which pore spaces are filled with liquid separated from the gas phase by menisci. If a vapor or liquid wets a solid completely, that is the contact angle, 0= 0°, then this vapor will immediately condense in the tip of a conical pore, as seen in Figure 4.8 a. The formation of the liquid in the tip of the cone by condensation continues until the cone radius, r, reaches a critical value, rc, where the radius of curvature of the vapor bubble reaches the value given by the Kelvin equation (r = rc). Then, for a spherical vapor bubble, we can write... 

Retention in Porous Media. Anionic surfactants can be lost in porous media in a number of ways adsorption at the solid—liquid interface, adsorption at the gas—liquid interface, precipitation or phase-separation due to incompatibility of the surfactant and the reservoir brine (especially divalent ions), partitioning or solubilization of the surfactant into the oil phase, and emulsification of the aqueous phase (containing surfactant) into the oil. The adsorption of surfactant on reservoir rock has a major effect on foam propagation and is described in detail in Chapter 7 by Mannhardt and Novosad. Fortunately, adsorption in porous media tends to be, in general, less important at elevated temperatures 10, 11). The presence of ionic materials, however, lowers the solubility of the surfactant in the aqueous phase and tends to increase adsorption. The ability of cosurfactants to reduce the adsorption on reservoir materials by lowering the critical micelle concentration (CMC), and thus the monomer concentration, has been demonstrated (72,13). 

Porous silicas are usually mesoporous materials and they can be made with a variety of pore dimensions. In particular, silica glasses can be made with well-defined pore diameters, typically in the range 30-250 A, using sol-gel methods. Such a system provides a good model for testing the models of relaxation behaviour of fluids in porous solids. It is normally found that the two-site fast-exchange model for relaxation described above for macroporous systems is still valid. For instance, H and relaxation times have been measured during both adsorption and desorption of water in a porous silica. Despite hysteresis in the observed adsorption isotherms, it was found that the relaxation times depended solely on water content.For deuterated water in some porous silicas, multicomponent relaxation behaviour for T2 and Tip has been observed, and this has been attributed to the fractal nature of the pore structure. 

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