Adsorption symbols used

This chapter describes basic physico-chemical relations between the gas phase transport of atoms and molecules and their thermochemical properties, which are related to the adsorption-desorption equilibrium. These methods can either be used to predict the behavior of the adsorbates in the chromatographic processes, in order to design experiments, or to characterize the absorbate from its experimentally observed behavior in a process. While Part I of this chapter is devoted to basic principles of the process, the derivation of thermochemical data is discussed in Part n. Symbols used in the following sections of Part I are described in Section 5. For results, which were obtained applying the described evaluation methods in gas-adsorption chromatography, see Chapters 4 and 7 of this book. 

When we use the respective plot 7(1/Vt) a reasonable values of the equilibrium surface tension can be estimated. The same data of Fig. 28 are shown in this 1/Vt-plot are shown in Fig. 29. The linear extrapolation to t oo gives the isotherm shown in Fig. 30 by the symbols (O). When we however analyse the data given in Fig. 28 we can see that after the establishment of a temporary equilibrium the surface tension starts again to decrease. This phenomenon is typical for surfactant mixtures, and will be discussed in more detail at the end of this chapter. In order to find the properties of the main surfactant, in the present case of C10EO4, we have to analyse the data of Fig. 28 in a different way. The dotted line in this figure marks the time for each concentration, where the equilibrium surface tension should have been reached in case diffusion controls the adsorption process. Using these values, another surface tension isotherm is obtained, given in Fig. 30 by the symbols ( ). 

In this chapter we will present experimental information (Sect. 2.1), the theory of measurement (Sect 2.2), and uncertainties (Sect 2.3), and several examples (Sect. 2.4) of this method. Two modified versions of the measurement procedure which may be called densimetric-gravimetric and densimetric-volumetric / manometric methods (which especially seems to be suited for online industrial coadsorption measurements) are also outlined (Sect. 3). These methods also may be used to measure adsorption of gases and / or vapors on surfaces of arbitrary sohd materials as for example the inner walls of vessels, tubes, valves etc. of the experimental device(s) used (Sect.3.6). Advantages and disadvantages of the methods proposed are discussed in Sect. 4. A list of symbols used is given in Sect. 5, followed by references to journal articles and books cited. 

The material presented in this chapter is organized as follows In Sect. 2 the basic experiments necessary for dielectric permittivity measurements is given, followed by an outline of the theory of dielectric polarization, which considers the uncertainties of measurements and gives several examples related to gas adsorption equilibria on microporous solids. In Sect. 3 combined dielectric-manometric and dielectric-gravimetric measurements of adsorption equilibria are considered briefly. In Sect. 4 the pros and cons of dielectric measurements are discussed. A hst of Symbols used is given in Sect. 5 followed by the references cited. 

It is not uneommon to meet different opinions relating to the fundamentals of adsorption at above-eritieal temperatures, even the symbols used are sometimes confusing. Therefore, it seems useful to clarify some eoneepts and terminology used in the chapter before making any interpretation of isotherms. 

Figure 4.18 Adsorption isotherms of isobutane in Silicalite. Molecular simulations (open symbols) using the models of Vlugt et al. [36] (a = 3.60A, circles), Smit et al. [142] (cr = 3.64A, squares) and June et al. [141] (a = 3.364A, triangles), see table 4.1. Experimental data (closed symbols) from Zhu etal. [135] (circles) and Sun etal. [136] (diamonds).

We can think of a heterogeneous catalyst as a collection of active sites (denoted by ) located at a surface. The total number of sites is constant and equal to N (if there is any chance of confusion with N atoms, we will use the symbol N ). The adsorption of the reactant is formally a reaction with an empty site to give an intermediate I (or more conveniently R if we explicitly want to express that it is the reactant R sitting on an adsorption site). All sites are equivalent and each can be occupied by a single species only. We will use the symbol 6r to indicate the fraction of occupied sites occupied by species R, making N6r the number of occupied sites. Hence, the fraction of unoccupied sites available for reaction will be 1 - 0r The following equations represent the catalytic cycle of Fig. 2.7 ... 

Figure 2. Comparison of adsorption isotherms based on the present model (solid lines) with the statistical theory of Scheutjens and Fleer (symbols). The following values of the parameters were used...

Table 1 summarizes a few properties of the resulting fibers used in studies on their metal ion adsorption abilities. Hereafter, bifucntional fibers derived from PPPE-c and PPPE-f are denoted by symbols FPS-c and FPS-f, respectively, and respective symbols FP-c and FP-f denote monofunctional... 

In describing adsorption on an electrode, it is common to write 0 for the fraction of the surface covered. However, in purely thermodynamic analyses, the symbol r is used for the Gibbs surface excess. Describe the difference in meaning between these two quantities and the conditions under which they may tend to become nearly equal. (Bockris)... 

In subsequent chapters it will be the potential in the diffuse double layer that concerns us. It can be described relative to its value at the inner limit of the diffuse double layer, which may be either the actual surface or the Stern surface. We continue to use the symbol p0 for the potential at this inner limit. It should be remembered, however, that specific adsorption may make this quantity lower than the concentration of potential-determining ions in the solution would indicate. We see in Chapter 12 how the potential at some (unknown) location close to this inner limit can be measured. It is called the zeta potential. 

Although adsorption exists as a subject of scientific investigation independent of its role in heterogeneous catalysis, it requires particular attention here because of its central role in heterogeneous catalysis. Most or all catalytic reactions involve the adsorption of at least one of the reactants. Many terms related to adsorption have already been defined in Appendix II, Part I, 1.1. These include surface, interface, area of surface or interface, and specific surface area. Appendix II, Part I, recommends A or S and a or s as symbols for area and specific area, respectively. As and as may be used to avoid confusion with Helmholtz energy A or entropy S where necessary. 

Surface complexation constants. For reactions involving adsorption on surfaces the symbol =SOH is often used to designate a surface complexation site. So, for example, the reaction between lead and a surface can be written as... 

In the above equations the symbols A, B, C, D designate phenol, hydrogen, cyclohexanone and cyclohexanol. Table 5.7 presents the model parameters at 423 K and 1 atm. The model takes into account the effect of the products on the reaction rate in the region of higher conversion. This feature is particularly useful for describing the product distribution in consecutive catalytic-type reactions. Note that the adsorption coefficients are different in the two reactions. Following the authors, this assumption, physically unlikely, was considered only to increase the accuracy of modeling. 

This scheme mimics, e.g., CO or H2 oxidation on the noble metal catalysts Pt, Pd, or Rh, where symbol A stands for CO or H, and B2 for 02. The reaction was simulated on a 2D lattice of adsorption sites. To compare the rates of diffusion and reaction, it is useful to employ the Arrhenius form to represent the rate constants of diffusion jumps of A and B particles to nearest-neighbor vacant sites and for the reaction between two nearest-neighbor reactants, respectively. The diffusion of A is usually rapid when compared to the LH step, while the rate constant for the LH step might be higher, close to, or lower than that for the diffusion of B2. The MC algorithm used to simulate the A + B2 reaction is as follows ... 

Fig. 5. Hydrogen adsorption isotherms at 293 K with platinum-gold/Aerosil catalysts V, Pt 98, Au 2 mol %, 1.0 wt % metal 0.516 g catalyst A, Pt 90, Au 10 mol %, 0.9 wt % metal, 0.510gcatalyst , Pt 67, Au 33 mol %,0.9wt % metal, 0.500g catalyst O.Pt 15, Au 85 mol %, 1.0 wt % metal, 0.450 g catalyst standard pretreatment (cf. text). Filled symbols, amount of adsorbed hydrogen remaining after pumping at 293 K for 30 min, after equilibration at indicated pressure. Catalyst samples identified from corresponding symbols above. Within the limits of experimental accuracy, no adsorption could be detected on a Pt 0, Au 100 mol %, 1.0 wt % catalyst, using a 0.500 g sample (20).

Permeability of a membrane is determined partly by gas diffu-sivity, but adsorption phenomena can also exist at higher pressures, which affects the outcome. Separation factors of two substances are approximately in the ratios of their permeabihties, which can be defined by ocab = Poa/Pob, or more simply olab = Pa/Pb, where the symbol P represents the permeability at a stated reference condition. Some data of permeabilites and separation factors are listed in Table 19.7, together with a list of membranes that have been used commercially for particular separations. Similar but not entirely consistent data are tabulated in the Chemical Engineers Handbook (Li and Ho, 1984, pp. 17.16, 17.18). The different units used for permeability will undergo further inspection in a subsequent section. 

The following notes and symbols will be used in the other tables as well T, adsorption temperature Si/Al, silicon to aluminum ratio q, differential heat of adsorption n, surface coverage < inai < location of the maximum distribution of sites in the site energy distribution plot, with letters indicating the relative number of sites under the peak L, large I, intermediate S, small. 

It may be good to note here that various molecular cross-sections have now been considered. In the treatment of adsorption on solid surfaces was introduced. Interpreting this area in terms of lattice models is not a property of the adsorptive molecule but of the adsorbent. It is possible to imagine a situation where greatly exceeds the real molecular cross-section. On the other hand, for mobile monolayers on homogeneous surfaces is the real molecular cross-section or, for that matter, it is the excluded area per molecule. To avoid an undue abundance of symbols we have used the same symbol for both situations, for instance in table 3.3 in sec. 3.4e. It is to be expected that a and a, obtained by compression of monolayers, are more similar to the a s for adsorbed mobile monolayers on homogeneous substrates than to those for localized monolayers. 

The pure component adsorption equilibrium of ethane and propane are measured on Norit AC at three temperatures (30, 60 and 90 °C). All experimental data of two species at three temperatures are employed simultaneously to fit the isotherm equation to extract the isothermal parameters. Since an extended Langmuir equation is used to describe the local multicomponent isotherm, the maximum adsorbed capacity is forced to be the same for ethane and propane in order to satisfy the thermodynamic consistency. The saturation capacity was assumed to be temperature dependent while the other parameters, bo and u], are temperature independent but species dependent. The derived isotherm parameters for ethane and propane are tabulated in Table 1. The experimental data (symbols) and the model fittings (solid lines)... 

Figure 21. Experimental and simulated elution profiles for different sample compositions. The symbols are experimental data, the lines are simulated elution profiles using the competitive bi-Langmuir adsorption parameters determined by the PP method. Sample 20 pL 5.0 mM L-enantiomer and 5.0 mM D-enantiomer.

Figure 6.28 compares measured and simulated profiles for the batch separation of EMD53986. Very good agreement between theory (solid lines) and experiment (symbols) is achieved using the multi-component modified-Langmuir isotherm (Fig. 6.21). Also shown are the simulation results neglecting component interaction by using only the single-component isotherms (dashed line), which deviate strongly from the observed mixture behavior. Typical for competitive adsorption is the displacement of the weaker retained R-enantiomer and the peak expansion of the stronger adsorbed S-enantiomer.

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