Gas-solid adsorption isotherm

However, technological advances have led to the appearance of prototype sorptometers potentially capable of providing gas-solid adsorption isotherms of far superior quality and with a very high pressure resolution. At the same time, modem molecular modelling techniques have recently achieved significant successes in the description of the properties of heterogeneous fluids, as are found specifically in the adsorbed phase in micropores. Two complementary approaches have been developed ... 

Equations 4.17 to 4.20 employ the component partial pressure and can therefore be applied to calculate the gas-solid adsorption isotherm. 

FIG. 3 Model calculations prove that in a high equilibrium pressure range, the gas/solid adsorption isotherms have maximum values. 

The procedures for obtaining the gas-solid adsorption isotherms briefly outlined above are based on a solution thermodynamic Gibbs approach. There are two other approaches the potential theory and the Langmuir approach. The latter approach is based on a dynamic equilibrium between the rates of adsorption and desorption of any species from adsorption sites on the solid surface. Since most data correlation in separation processes employs the Langmuir approach (Yang, 1987), with the adsorbate amount expressed as a function of species partial pressure, such isotherm types will be briefly identified here. For a comprehensive introduction to adsorption isotherms and phenomena, consult Ruthven (1984) and Yang (1987). 

Figure 3.3.8B. Typical gas-solid adsorption isotherms. For a mixture of n species.

In the early experiments, when gas-solid adsorption was studied by some 200 years ago, charcoal was the most widely used adsorbent [12]. These investigations, generally limited to adsorption from dilute solutions, gave adsorption isotherms of the form shown in Figure 10.4. These isotherms could be fitted by the equation ... 

The Adsorption isotherm . The relation between the amount adsorbed and the pressure in the gas, the adsorption isotherm is a complicated one, and depends on the nature of the solid surface, on its homogeneity or otherwise (and few, if any, solid surfaces are homogeneous), and of course on the forces between gas molecules and solid, which depend on the chemical nature of the gas. For many porous, and some other, solids, a first approximation is given by Freundlich s well-known equation if x is the amount of gas adsorbed, and p the pressure of the gas,... 

The fundamental references in gas-solid adsorption are the works by Fowler and Guggenheim [12], Everett [13], and Hill [14,15], and the books by Young and Crowell [16], de Boer [17], Kiselev [4], and more recently by Ruthven [18] and T6th [19], who gives a clear, logical, and simple presentation of this topic. We present first a few theoretical results obtained in the study of gas-sohd adsorption, results that have been extended semiempirically to liquid-solid adsorption [18]. Then, we describe the various isotherm models that have been used in the study of retention mechanisms in liquid chromatography. 

As we have explained in the previous sections, the Langmuir model has been established on firm theoretical groimd for gas-solid adsorption, a case where there is no competition between the adsorbate and the mobile gas phase. On the contrary, in liquid-solid adsorption, there is competition for adsorption between the molecules of any component and those of the solvent. Although we can choose a convention canceling the apparent effect of this competition on the isotherm [30,36], the conditions of validity of Eq. 3.47 are not met. These conditions are (i) the solution is ideal (ii) the solute gives monolayer coverage (iii) the adsorption layer is ideal (iv) there are no solute-solute interactions in the monolayer (v) there are no solvent-solute interactions. These conditions cannot be valid in liquid-solid adsorption, especially at high concentrations. 

This isotherm is similar to the Langmuir model, to which it becomes identical for t = 1. The parameters b and t permit independent adjustment of the initial slope and curvature of the isotherm. This model has been used successfully to account for experimental isotherm data regarding gas-solid adsorption [33]. It was used to account for the adsorption behavior of theophylline on a Kromasil Cig column eluted with an aqueous solution of methanol [11]. It is frequently used to account... 

The isotherm of Radke-Prausnitz is somewhat similar, with q = KC/[1 + (fCC)Pj. It has been used essentially in gas-solid adsorption. 

Equation (608) is exactly equal to Equation (433), given in Section 5.5.3 for the two-dimensional perfect gas for liquid solution surfaces. Equation (608) relates 7Tto the surface excess and is called the surface equation of state. Similarly to Equation (436), we can write [ Amoiecuie = kT] for gas-solid adsorption, where A oWe is the area available per adsorbate molecule in the monolayer, and k is the Boltzmann constant (R = kNA). The adsorption isotherm given by Equations (607) and (608) corresponds to the so-called Henry s law limit, in analogy with the Henry s law equations that describe the vapor pressures of dilute solutions. Equation (606) predicts a linear relation between m (or fractional surface coverage, 0f, and adsorbate gas pressure, P2, as shown in the linear plot in Figure 8.1. 

Interactions between adjacent adsorbed molecules (3) exist for almost all real adsorption systems. For gas-solid adsorption these interactions make an important contribution to isotherm shape and in systems where adsorbent-adsorbate interactions are comparatively the interactions between adjacent adsorbed molecules may play a dottunant role (e.g., type 111 isotherm of Fig. 3-6)1 In liquid-solid adsorptidh the interactions between adsorbed molecules are generally much leSS ihiportant than in gas-solid adsorption, insofar as their influence oh. isotherm shape is concerned. Similar interactions exist in the nonadsorbed phase and largely cancel the net contribution to adsorption energy of interactions between adsorbed molecules. Occasionally, this cancellation may be incomplete, and interactions between adsorbate molecules can then make an important contribution to adsorption in liquid-solid systems (e.g. basic eluent effect in Section 8-3B). 

It is also convenient to combine studies of polymer interactions with solid substrates with studies of the adsorption characteristics of the organic components themselves. Such an approach has much to offer in adhesion research and the basis of studies of adsorption from a liquid phase and its applicability in adhesion has been discussed in detail elsewhere [7] so it will not be treated in depth here. A brief overview will, however, provide a background to this approach. The determination of gas-phase adsorption isotherms is a well-known methodology in surface chemistry in this manner it is possible to describe adsorption as following Langmuir or other characteristic adsorption types. The conventional method of studying the adsorption of molecules from the liquid phase is to establish the depletion of the adsorbate molecule from the liquid phase. However, as first pointed out by Castle and Bailey [8], with the advent of surface analysis methods it is now... 

Recall from our previous section on incomplete reaction processes that the ratio of the rate constants for the forward and reverse reaction processes yields the equilibrium constant K for the reaction. Thus, in the case of an incomplete reaction, this equilibrium constant, in concert with the gas-phase CO concentration, would determine the equilibrium surface coverage of CO. This equation is known as the Langmuir isotherm and it is one of a number of physical models that is Irequently encomitered when describing gas-solid adsorption processes. 

The gas-solid adsorption equilibrium is represented with a loading ratio correlation or Nitta et al. model isotherms. 

The relation between the amount of substance adsorbed by an adsorbent and the equilibrium partial pressure or concentration at constant temperature is called an adsorption isotherm. The adsorption isotherm is the most important and by far the most often used of the various equilibria data that can be measured. Five general types of isotherms have been observed in the adsorption of gases on solids. These are shown in Figure 17.2. In cases of chemisorption, only isotherms of type I are encountered, while in physical adsorption, all five types occur. Also note that the development to follow will primarily be concerned with gas-solid adsorption. 

It is well known that in the hterature there are more than 100 isotherm equations derived based on various physical, mathematical, and experimental considerations. These variances are justified by the fact that the different types of adsorption, solid/gas (S/G), solid/liquid (S/L), and liquid/gas (L/G), have, apparently, various properties and, therefore, these different phenomena should be discussed and explained with different physical pictures and mathematical treatments. For example, the gas/solid adsorption on heterogeneous surfaces have been discussed with different surface topographies such are arbitrary, patchwise, and random ones. These models are very useful and important for the calculation of the energy distribution functions (Gaussian, multi-Gaussian, quasi-Gaussian, exponential) and so we are able to characterize the solid adsorbents. Evidently, for these calculations, one must apply different isotherm equations based on various theoretical and mathematical treatments. However, as far as we know, nobody had taken into account that aU of these different isotherm equations have a common thermodynamical base which makes possible a common mathematical treatment of physical adsorption. Thus, the main aim of the following parts of this chapter is to prove these common features of adsorption isotherms. 

In the frame of the uniform interpretation of gas/solid adsorption it is necessary to calculate the function /(pj.) of the BET equation for comparison with those of the monolayer isotherm equations. After application of Eqs (39) and (51) we have... 

The calculation of the specific surface area should be taken in three steps (1) determination of the gas (vapor) adsorption isotherm on the solid materials to be investigated, (2) calculation of the function v /(p) from the measured isotherm, and (3) based on the function y(p) selection of the appropriate isotherm equation and the calculation of the specific surface area from this equation which has to include the value of the total monolayer capacity ( ). 

Solution The data is for gas solid adsorption so we will concentrate on Langmuir, BET, and Gibbs isotherms for this purpose. 

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

The present discussion is restricted to an introductory demonstration of how, in principle, adsorption data may be employed to determine changes in the solid-gas interfacial free energy. A typical adsorption isotherm (of the physical adsorption type) is shown in Fig. X-1. In this figure, the amount adsorbed per gram of powdered quartz is plotted against P/F, where P is the pressure of the adsorbate vapor and P is the vapor pressure of the pure liquid adsorbate. 

Characterization. When siHca gel is used as an adsorbent, the pore stmcture determines the gel adsorption capacity. Pores are characterized by specific surface area, specific pore volume (total volume of pores per gram of solid), average pore diameter, pore size distribution, and the degree to which entrance to larger pores is restricted by smaller pores. These parameters are derived from measuring vapor adsorption isotherms, mercury intmsion, low angle x-ray scattering, electron microscopy, gas permeabiHty, ion or molecule exclusion, or the volume of imbibed Hquid (1). 

In the first step, in which the molecules of the fluid come in contact with the adsorbent, an equihbrium is established between the adsorbed fluid and the fluid remaining in the fluid phase. Figures 25-7 through 25-9 show several experimental equihbrium adsorption isotherms for a number of components adsorbed on various adsorbents. Consider Fig. 25-7, in which the concentration of adsorbed gas on the solid is plotted against the equilibrium partial pressure p of the vapor or gas at constant temperature. At 40° C, for example, pure propane vapor at a pressure of 550 mm Hg is in equilibrium with an adsorbate concentration at point P of 0.04 lb adsorbed propane per pound of silica gel. Increasing the pressure of the propane will cause... 

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