Adsorption data, interpretation

The BET equation filled an annoying gap in the interpretation of adsorption isotherms, and at the time of its appearance in 1938 it was also hailed as a general method for obtaining surface areas from adsorption data. The equation can be put in the form... 

Surface areas are deterrnined routinely and exactiy from measurements of the amount of physically adsorbed, physisorbed, nitrogen. Physical adsorption is a process akin to condensation the adsorbed molecules interact weakly with the surface and multilayers form. The standard interpretation of nitrogen adsorption data is based on the BET model (45), which accounts for multilayer adsorption. From a measured adsorption isotherm and the known area of an adsorbed N2 molecule, taken to be 0.162 nm, the surface area of the soHd is calculated (see Adsorption). 

Most surface area measurements are based on the interpretation of the low temperature equilibrium adsorption of nitrogen or of krypton on the solid using the BET theory [33,269,276—278]. There is an extensive literature devoted to area determinations from gas adsorption data. Estimates of surfaces may also be obtained from electron micrographs, X-ray diffraction line broadening [279] and changes in the catalytic activity of the solid phase [ 280]. 

Adsorption isotherms obtained from the model have been shown to agree very closely with the predictions of recently published statistical theories (9,13). While there can be no doubt that the more sophisticated, statistical models provide more information on the nature of the adsorption process and the structure of the adsorbed film, because of its simple form, the macroscopic model can offer a powerful tool for the analysis, interpretation and utilization of adsorption data. 

A rigorous treatment of diffusion to or from a flat surface has been given by Lyklema (1991). Van Leeuwen (1991) has pointed out that in analyzing experimental adsorption data, that are always confined to a certain time window, it is tempting to fit the data to the sum of two or three exponential functions with different arguments. Although such fits are often apparently sucessful, the merit of the fit is purely mathematical a mechanistic interpretation in terms of a first order dependence is usually not justified. With porous materials, diffusion into the pores renders the adsorption process very slow often one gains the impression that the process is irreversible (e.g., Fig. 4.18). 

Mechanisms of Sorption Processes. Kinetic studies are valuable for hypothesizing mechanisms of reactions in homogeneous solution, but the interpretation of kinetic data for sorption processes is more difficult. Recently it has been shown that the mechanisms of very fast adsorption reactions may be interpreted from the results of chemical relaxation studies (25-27). Yasunaga and Ikeda (Chapter 12) summarize recent studies that have utilized relaxation techniques to examine the adsorption of cations and anions on hydrous oxide and aluminosilicate surfaces. Hayes and Leckie (Chapter 7) present new interpretations for the mechanism of lead ion adsorption by goethite. In both papers it is concluded that the kinetic and equilibrium adsorption data are consistent with the rate relationships derived from an interfacial model in which metal ions are located nearer to the surface than adsorbed counterions. 

In the following section, it is shown that mathematical methods which have been used to interpret adsorption data bias the interpretation towards chemical and electrostatic properties which lead to a significantly sub-Nernstian response this bias arises out of the need for mathematical simplifications, not from physical considerations. 

Example 7.5 illustrates how adsorption data can be interpreted if the data conform to the Langmuir model. 

With monolayer adsorption, we saw how the saturation limit could be related to the specific surface area of the adsorbent. The BET equation permits us to extract from multilayer adsorption data (by means of Equation (77)) the volume of adsorbed gas that would saturate the surface if the adsorption were limited to a monolayer. Therefore Vm may be interpreted in the same manner that the limiting value of the ordinate is handled in the case of monolayer adsorption. Since it is traditional to express both V and Vm in cubic centimeters at STP per gram, we write (see Equation (7.72))... 

Gas adsorption data may be analyzed for the distribution of pore sizes. What is generally done is to interpret one branch of the isotherm and use an appropriate equation to calculate the effective pore radius at a given pressure. The amount of material adsorbed or desorbed for each increment or decrement in pressure measures the volume of pores with that effective radius. 

S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area, and Porosity, 2nd ed., Academic Press, London, 1982, 303 pp. An indispensable text on the interpretation and significance of adsorption data. 

Precipitation of Hafnium Hydroxide. In order to interpret the adsorption data it was necessary to determine the conditions which lead to the precipitation of hafnium hydroxide. It is not usually advisable to depend on the solubility product because the information on this quantity is often unreliable for hydroxides of polyvalent metal ions. In addition, "radiocolloids may apparently form much below saturation conditions in radioactive isotope solutions. In the specific case of hafnium hydroxide only two measurements of the solubility seem to have been reported. According to Larson and Gammill (16) K8 = [Hf(OH)22+] [OH ]2 — 4 X 10"26 assuming the existence of only one hydrolyzed species Hf(OH)22+. The second reported value is Kso = [Hf4+] [OH-]4 = 3.7 X 10 55 (15). If one uses the solubility data by Larson and Gammill (Ref. 16, Tables I and III) and takes into consideration all monomeric hafnium species (23) a KBO value of 4 X 10 58 is calculated. 

The protein s intrinsic properties (size, molecular weight, 3-D structure, surface site density, conformational stability) are all very important and must be fully characterized and understood in order to interpret adsorption data. 

During the early years of the twentieth century, various quantitative investigations of gas adsorption were undertaken. The most important advances in the theoretical interpretation of gas adsorption data were made by Zsigmondy, Polanyi and Langmuir their ideas set the scene for much of the research undertaken over the past 80 years. 

Virial treatment provides a general method of analysing the low-coverage region of an adsorption isotherm and its application is not restricted to particular mechanisms or systems. If the structure of the adsorbent surface is well defined, virial treatment also provides a sound basis for the statistical mechanical interpretation of the adsorption data (Pierotti and Thomas, 1971 Steele, 1974). As indicated above, Kl in Equation (4.5) is directly related to kH and therefore, under favourable conditions, to the gas-solid interaction. 

In our view, an oversimplified application of fractal analysis may tend to obscure rather than clarify the interpretation of adsorption data. In practice, there are two complicating factors (1) the derived values of nm are not always reliable, and (2) the mechanisms of adsorption and pore filling are dependent on the adsorbent-adsorbate interactions and the ratio of pore width to molecular diameter and may not be the same for all the members of a series of adsorptives on a given adsorbent. 

We are drawn to the conclusion that log-log fractal plots are useful for the correlation of adsorption data - especially on well-defined porous or finely divided materials. A derived fractal dimension can also serve as a characteristic empirical parameter, provided that the system and operational conditions are clearly recorded. In some cases, the fractal self-similarity (or self-affine) interpretation appears to be straightforward, but this is not so with many adsorption systems which are probably too complex to be amenable to fractal analysis. 

In view of the commercial importance of active carbons, it is not surprising that a great deal of attention has been given to the presentation and interpretation of adsorption data Much of the discussion in the literature has been concerned with the derivation of the internal and external surface area and the micropore and mesopore size... 

The aims of this chapter are (a) to indicate the progress made in the development and characterization of some of the more important oxide adsorbents and (b) to illustrate the procedures described in earlier chapters for the interpretation of adsorption data. 

Some aspects of the interpretation of adsorption data were discussed by Bergaya et al. (1993), with the usefiil reminder that die packing of adsorbed molecules in narrow pores is strongly dependent on the pore width. It was suggested that the molecular confinement in interlamellar pores is a major source of underestimation of the gallery pore volume. These comments reinforce the IUPAC recommendation that no experimental method should be expected to provide an absolute assessment of the surface area or porosity of highly porous materials (Rouquerol et al., 1994). The following summary of other recent work will also illustrate the importance of this recommendation. 

It would be misleading, however, to interpret how well the molecular structure of the sorbed species is accommodated by the molecular structure of the monomer unit on the basis of the observed swelling power, C, because this parameter is proportional to the product of two variables, namely the number of adsorbed molecules per accessible phenyl group (a), and the molar volume of the sorbed liquid (V = M/d), where M and d are the molecular weight and density of the sorbed liquid). Since the density of the liquid reflects how well the molecules in that liquid are accommodated by one another, this effect would be superimposed on the adsorption data. This point of view is consistent with the observations of Fajans [166], who reported that the density of Z(CH2) H liquids exhibit odd-even alternation especially in the lowest three members of a given series. These results amplify the observation made earlier, i.e. that it is more meaningful to interpret on the basis of a how well the molecular structure of the adsorbed species is accommodated by the molecular structure of the monomer unit, rather than on the basis of C from which at is derived (Eq. 15). 

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