Adsorption gas

The adsorption of a gas to a dry, solid surface can be described by an adsorption isotherm, vdiich is a plot of the amount of adsorbed gas as a function of the relative pressure at a constant tatperature (see Fig. 3). 

The adsorption often yields multilayers of gas molecules and the monolayer edacity may in these cases be calculated from an equation given ty Brunauer, Eiimet and Teller (42), (the BET-equation), v4iich in favourable situations reduces to 

By oembining data of the surface area with data of the pore volune an ete given by 

Nitrogen sorption, (a), and desorption, (b), isotherms of porous silica (Vydac TP 9). Data obtained by courtesy of Ref. 68. 

As seen fnxn Fig. 3, a region exists fdiere the desorption and adsorption isotherms diverge. This hysteresis is attributed to the differences in the mechanians of filling and enptying of mesopores (62). The locaticsi of the hysteresis loop will thus reflect the size distribution of mesopores. The pore size (or more exactly, the core size) may be calculated front the desorption branch with the aid of the Kelvin equation (62) 

Brunauer, Emmet, Teller (BET) analysis of adsorption isotherms allows a surface area to be calculated [17,19]. The BET model is for multilayer adsorption on a flat surface, so when applied to a porous material the surface area obtained is an apparent value. Nevertheless, BET surface area provides a useful comparison between materials. PM-1 shows a higher BET surface area than the activated carbon in Eigure 2.2, a value of 780 m g for PIM-1 as compared to 545 m g for the carbon. 

Further information about the sizes of free volume elements or micropores can be obtained from inverse gas chromatography and positron annihilation lifetime spectroscopy (PALS), as is discussed later. 

The isotherm equations introduced above apply to fluids in general, (liquid or gas), 

For a given adsorbate at a given temperature this relation may be abbreviated as 

Typically, this equation applies to low concentrations of the adsorbate, where k may be predicted or derived from low concentration data. If k is to be determined by a least squares fit of q versus p data, and also ensure the function passes through the origin (p = q = 0), then k can be determined as 

This equation may be converted to a linear form by taking the logarithm on both sides  

A linear representation of this equation can be obtained by rearranging it  

There are two widely used methods for the determination of the specific surface area of particles. One is based on permeability and the other on gas adsorption. 

The determination of the specific surface area of a powder by air permeability methods essentially involves the measurement of the pressure drop across a bed of the powder under carefully controlled flow conditions. The data obtained are substituted in the Kozeny-Carman equation to estimate the specific surface area. Permeability methods have certain advantages, one of them being that the equipment used for carrying out the measurements is cheap and robust. Another advantage is that sample problems are minimized because a large sample of powder is required to be used for analysis. 

Two types of instruments are employed to determine the specific surface area by permea-metry. Those of the first type are called constant pressure systems, and the Fisher subsieve sizer is a typical example that belongs to such systems. Instruments of the second type are known as constant volume permeameters, and the apparatus devised by Blain is an example. 

A commonly used method of determining the specific surface area of a solid is by the adsorption of a gas onto the solid and the determination of the monolayer capacity. Most methods make use of the Brunauer, Emmett, and Teller equation, commonly referred to as the BET equation, for calculating the surface area on the basis of monolayer adsorption. The BET equation can be written as 

Comminution essentially produces a suit of particles in different sizes, and a quantitative description of comminution relates the sizes of particles in the feed with those in the product. Simply stated, comminution modifies only the particle size distribution between the feed and the product. 

Normally adsorption is conducted at or as near ambient temperature as possible and regeneration is at 350-500°F. A new process developed by Union Carbide Corp, the AHR process (adsorption heat recovery), allows the temperature to rise to 200-400 as a result of the heat of adsorption and effects the desorption at comparable temperatures with a stream of inert gas 

A hard water contains 120 ppm of CaCOj, 90% of which is to be removed with a hydrogen exchange resin of capacity 5 meq/g. By the method of Example 15.1 it is ascertained that under these conditions 98% of H ion of the resin will be replaced by the Ca at equilibrium. The minimum amount of resin will correspond to the equilibrium value. That amount will be calculated for treating 100 gpm of water on a 24 hr cycle. The mol wt of CaCOj = 100.06. 

For comparison, the amount of resin needed to remove the Na from a 3.5% solution of NaCl at the rate of 100 gpm in 24 hr will be found  

Moving bed gas adsorbers also have been proposed and used, patterned after moving bed gas oil crackers. In the Hypersorbet of 

Examination of powdered materials with an electron microscope can generally disclose the presence of surface imperfections and pores. However, those imperfections or irregularities smaller than the microscope s resolving power will remain hidden. Also hidden is the internal structure of the pores, their inner shape and dimensions, their volume and volume distribution as well as their contribution to the surface area. However, by enveloping each particle of a powder sample in an adsorbed film, the method of gas adsorption can probe the surface irregularities and pore interiors even at the atomic level. In this manner a very powerful method is available which can generate detailed information about the morphology of surfaces. 

To some extent adsorption always occurs when a clean solid surface is exposed to vapor. Invariably the amount adsorbed on a solid surface will depend upon the absolute temperature T, the pressure P, and the interaction potential E between the vapor (adsorbate) and the surface (adsorbent). Therefore, at some equilibrium pressure and temperature the weight W of gas adsorbed on a unit weight of adsorbent is given by 

Usually the quantity adsorbed is measured at constant temperature and equation (2.1) reduces to 

A plot of W versus P, at constant T, is referred to as the adsorption isotherm of a particular vapor-solid interface. Were it not for the fact that E, the interaction potential, varies with the properties of the vapor and the solid and also changes with the extent of adsorption, all adsorption isotherms would be identical. 

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The succeeding material is broadly organized according to the types of experimental quantities measured because much of the literature is so grouped. In the next chapter spread monolayers are discussed, and in later chapters the topics of adsorption from solution and of gas adsorption are considered. Irrespective of the experimental compartmentation, the conclusions as to the nature of mobile adsorbed films, that is, their structure and equations of state, will tend to be of a general validity. Thus, only a limited discussion of Gibbs monolayers has been given here, and none of such related aspects as the contact potentials of solutions or of adsorption at liquid-liquid interfaces, as it is more efficient to treat these topics later. 

An excellent example of work of this type is given by the investigations of Benson and co-workers [127, 128]. They found, for example, a value of = 276 ergs/cm for sodium chloride. Accurate calorimetry is required since there is only a few calories per mole difference between the heats of solution of coarse and finely divided material. The surface area of the latter may be determined by means of the BET gas adsorption method (see Section XVII-5). 

Brunauer and co-workers [129, 130] found values of of 1310, 1180, and 386 ergs/cm for CaO, Ca(OH)2 and tobermorite (a calcium silicate hydrate). Jura and Garland [131] reported a value of 1040 ergs/cm for magnesium oxide. Patterson and coworkers [132] used fractionated sodium chloride particles prepared by a volatilization method to find that the surface contribution to the low-temperature heat capacity varied approximately in proportion to the area determined by gas adsorption. Questions of equilibrium arise in these and adsorption studies on finely divided surfaces as discussed in Section X-3. 

This discussion of gas adsorption applies in similar manner to adsorption from solution, and this topic is taken up in more detail in Chapter XII. 

A logical division is made for the adsorption of nonelectrolytes according to whether they are in dilute or concentrated solution. In dilute solutions, the treatment is very similar to that for gas adsorption, whereas in concentrated binary mixtures the role of the solvent becomes more explicit. An important class of adsorbed materials, self-assembling monolayers, are briefly reviewed along with an overview of the essential features of polymer adsorption. The adsorption of electrolytes is treated briefly, mainly in terms of the exchange of components in an electrical double layer. 

Various functional forms for / have been proposed either as a result of empirical observation or in terms of specific models. A particularly important example of the latter is that known as the Langmuir adsorption equation [2]. By analogy with the derivation for gas adsorption (see Section XVII-3), the Langmuir model assumes the surface to consist of adsorption sites, each having an area a. All adsorbed species interact only with a site and not with each other, and adsorption is thus limited to a monolayer. Related lattice models reduce to the Langmuir model under these assumptions [3,4]. In the case of adsorption from solution, however, it seems more plausible to consider an alternative phrasing of the model. Adsorption is still limited to a monolayer, but this layer is now regarded as an ideal two-dimensional solution of equal-size solute and solvent molecules of area a. Thus lateral interactions, absent in the site picture, cancel out in the ideal solution however, in the first version is a properly of the solid lattice, while in the second it is a properly of the adsorbed species. Both models attribute differences in adsorption behavior entirely to differences in adsorbate-solid interactions. Both present adsorption as a competition between solute and solvent. 

The estimation of surface area from solution adsorption is subject to many of the same considerations as in the case of gas adsorption discussed in Chapter XVII, but with the added complication that larger molecules are involved. 

The subject of gas adsorption is, indeed, a very broad one, and no attempt is made to give complete coverage to the voluminous literature on it. Instead, as in past chapters, the principal models or theories are taken up partly for their own sake and partly as a means of introducing characteristic data. 

The remainder of the chapter is concerned with increasingly specialized developments in the study of gas adsorption, and before proceeding to this material, it seems desirable to consider briefly some of the experimental techniques that are important in obtaining gas adsorption data. See Ref. 22 for a review of traditional methods, and Ref 23 for lUPAC (International Union of Pure and Applied Chemistry) recommendations for symbols and definitions. 

We take up here some aspects of the thermodynamics of adsorption that are of special relevance to gas adsorption. Two types of processes are of interest ... 

Section 3.7, the gas adsorption method breaks down for practical reasons. Since the angle of contact of mercury with solids is 140° (see later), and therefore more than 90°, an excess pressure Ap is required to force liquid mercury into the pores of a soh d. The idea of using mercury intrusion to measure pore size appears to have been first suggested by Washburn who put forward the basic equation... 

Since in practice the lower limit of mercury porosimetry is around 35 A, and the upper limit of the gas adsorption method is in the region 100-200 A (cf. p. 133) the two methods need to be used in conjunction if the complete curve of total pore volume against pore radius is to be obtained. 

Whereas at the lower end of its range mercury porosimetry overlaps with the gas adsorption method, at its upper end it overlaps with photomicrography. An instructive example is provided by the work of Dullien and his associates on samples of sandstone. By stereological measurements they were able to arrive at a curve of pore size distribution, which was extremely broad and extended to very coarse macropores the size distribution from mercury porosimetry on the other hand was quite narrow and showed a sharp peak at a much lower figure, 10nm (Fig. 3.31). The apparent contradiction is readily explained in terms of wide cavities which are revealed by photomicrography, and are entered through narrower constrictions which are shown up by mercury porosimetry. 

Mercury porosimetry is generally regarded as the best method available for the routine determination of pore size in the macropore and upper mesopore range. The apparatus is relatively simple in principle (though not inexpensive) and the experimental procedure is less demanding than gas adsorption measurements, in either time or skill. Perhaps on account of the simplicity of the method there is some temptation to overlook the assumptions, often tacit, that are involved, and also the potential sources of error. 

The Use of Gas Adsorption for the Determination of Surface Area and Pore Size Distribution... 

A vast amount of research has been undertaken on adsorption phenomena and the nature of solid surfaces over the fifteen years since the first edition was published, but for the most part this work has resulted in the refinement of existing theoretical principles and experimental procedures rather than in the formulation of entirely new concepts. In spite of the acknowledged weakness of its theoretical foundations, the Brunauer-Emmett-Teller (BET) method still remains the most widely used procedure for the determination of surface area similarly, methods based on the Kelvin equation are still generally applied for the computation of mesopore size distribution from gas adsorption data. However, the more recent studies, especially those carried out on well defined surfaces, have led to a clearer understanding of the scope and limitations of these methods furthermore, the growing awareness of the importance of molecular sieve carbons and zeolites has generated considerable interest in the properties of microporous solids and the mechanism of micropore filling. 

The second edition, like the first, is addressed to those workers in academic laboratories or industrial laboratories who are not necessarily specialists in the field of gas adsorption, but whose work is concerned either directly or indirectly with the characterization of finely divided or porous solids. 

Figure 9,16 Comparison of theory with experiment for rg/a versus K. The solid line is drawn according to the theory for flexible chains in a cylindrical pore. Experimental points show some data, with pore dimensions determined by mercury penetration (circles, a = 21 nm) and gas adsorption (squares, a= 41 nm). [From W. W. Yau and C. P. yidXont, Polym. Prepr. 12 797 (1971), used with permission.]...

Characterization. Ceramic bodies are characterized by density, mass, and physical dimensions. Other common techniques employed in characterizing include x-ray diffraction (XRD) and electron or petrographic microscopy to determine crystal species, stmcture, and size (100). Microscopy (qv) can be used to determine chemical constitution, crystal morphology, and pore size and morphology as well. Mercury porosknetry and gas adsorption are used to characterize pore size, pore size distribution, and surface area (100). A variety of techniques can be employed to characterize bulk chemical composition and the physical characteristics of a powder (100,101). 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Surface Area Determination The surface-to-volume ratio is an important powder property since it governs the rate at which a powder interacts with its surroundings. Surface area may be determined from size-distribution data or measured directly by flow through a powder bed or the adsorption of gas molecules on the powder surface. Other methods such as gas diffusion, dye adsorption from solution, and heats of adsorption have also been used. It is emphasized that a powder does not have a unique surface, unless the surface is considered to be absolutely smooth, and the magnitude of the measured surface depends upon the level of scrutiny (e.g., the smaller the gas molecules used for gas adsorption measurement the larger the measured surface). 

Agglomerate porosity can be measured by gas adsorption or mercuiy porosimetiy. However, any breakage or compression of the granules under high pressure during porosimetiy can invahdate the results. 

Adsorption The design of gas-adsorption equipment is in many ways analogous to the design of gas-absorption equipment, with a solid adsorbent replacing the liqiiid solvent (see Secs. 16 and 19). Similarity is evident in the material- and energy-balance equations as well as in the methods employed to determine the column height. The final choice, as one would expect, rests with the overall process economics. 

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