Functionality of adsorbents

Figure 8 shows an example of the most common behavior of AEam/0 as a function of adsorbate coverage. Linear behavior, if ever observed, is seen at the air/solution interface.93 At metal/solution interfaces, if chemical interactions with the metal can be ruled out, electrostatic interactions cannot be avoided, and these are responsible for the downward curvature.91 Upward curvatures are often observed at air/solution interfaces as a consequence of lateral interactions.95... 

Figure 8. Typical adsorption potential shifts as a function of adsorbate surface concentration. (1) At the free surface of a solution (real behavior), (2) ideal behavior, and (3) at a metal (Hg)/solution interface. Experimental points for adsorption of 1,4-butanediol from Ref. 328.

Although MIL-47, and especially MIL-53(A1), had been found on many occasions to dynamically respond to adsorption of particular compounds, referred to as breathing [35] in the literature, in these liquid phase conditions, only minor changes of the lattice parameters have been observed. A study of xylene separations in vapor phase on MIL-5 3(A1) shows that breathing profoundly influences the shape of the obtained breakthrough profiles as a function of adsorbate concentration [97]. 

The fact of a transfer of an electron from an absorbed particle to adsorbent [25] is widely considered as a criterion to differentiate between various forms of adsorption. Yet, as it has been already mentioned in previous section, there is a neutral form of chemisorption, i.e. weak binding formed without changing the surface charge state which only affects the dipole component of the work function. On the other hand, in several cases the physical adsorption can result in electron transitions in solids. Indeed, apart from formation of a double layer, changing the work function of adsorbent [26] the formation of surface dipoles accompanying physical adsorption can bring free charge carriers to substan-... 

These results were extended by Tilton et a/.(n8) to adsorption of eosin-labeled BSA on polymer surfaces. They also found a component that surface diffuses, with coefficients ranging from 1.2 x 10 9 to 2.6 x 10 9cm2/s, depending on surface type. In this study, intersecting TIR laser beams rather than a focused stripe were used to define the spatial intensity variation. Surface diffusion was even noted for the most irreversibly adsorbed eosin-labeled BSA components this was evident on samples rinsed for long periods with unlabeled BSA after exposure to eosin-labeled BSA. The surface diffusion coefficient of the irreversibly bound BSA was found to be a strong function of adsorbed concentration.(n9)... 

Microcantilever deflection changes as a function of adsorbate coverage when adsorption is confined to a single side of a cantilever (or when there is differential adsorption on opposite sides of the cantilever). Since we do not know the absolute value of the initial surface stress, we can only measure its variation. A relation can be derived between cantilever bending and changes in surface stress from Stoney s formula and equations that describe cantilever bending [15]. Specifically, a relation can be derived between the radius of curvature of the cantilever beam and the differential surface stress ... 

Microcantilever deflection changes as a function of adsorbate coverage when adsorption is confined to a single side of a cantilever (or when there is differential adsorption... 

Figure 8. Magnetic susceptibility of palladium on silica gel as function of adsorbed hydrogen and NO at 0° C.

For a number of purposes it is expedient to consider the surface pressure (and other thermodynamic functions of adsorbates) per mole of adsorbate. One of the reasons is that we are often interested in the difference between adsorbates and corresponding liquids, for instance in considering thin adsorbed liquid films. 

Figure 5.25. The hydrodynamic layer thickness as a function of adsorbed amount F for (a) PEO/H2O/PSL and (b) PE0/H20/S102. In both cases a range of molecular weights was used. The data in diagram (a) were obtained by PCS ). those in diagram (b) by viscosity measurements on dispersions .

Fig. 5. Radial distribution function of adsorbed CO2 molecides in micropotous AC [10]...

The surface diffiisivity (Dp) is known to be a function of adsorbed phase concentration and is equal to the corrected diffiisivity (D p) multiplied by a thermodynamic correction factor (dlnP/dlnCp). Assuming that the driving force for surface diffusion is the gradient of the chemical potential and that the mobility constant is a function of adsorbed phase concentration. Do and Do [6] have introduced the following form for the corrected sur ce diffiisivity ... 

Figure 2. Ligand-promoted dissolution ofh-Al2Os (2.2 g/L). Part a Dissolution rates as a function of adsorbed ligand concentrations for a series of organic ligands. Part b Dissolution rate constants as a function of pH. Symbols (Q) oxalate, (A) malonate, (V) citrate, fD) salicylate, and (<>) benzoate. (Adapted with permission from reference 22. Copyright 1986 Pergamon Press.)...

The table shows the remarkable decrease in the micropore diffusivity of a gas when its molecular diameter approaches that of the zeolite pore. The temperature coefficients of and Dm are given by the Arrhenius relationship [ >s, Dm = D exp(— // 7)] because these diffusions are activated processes. E is the activation energy for the diffusion process and D° is a constant. These diffusivities can also be complex functions of adsorbate loadings and compositions. ... 

Figure 9. Radial distribution functions of adsorbed H2O (d> = 1) and bulk liquid H2O (solid and dotted lines, respectively).

The selectivity of adsorption (S = niyj/njyi) of water vapour (component 1, mole fraction yi) on aluminas over component j (mole fraction yj) of a gas mixture can be complex functions of adsorbate loadings (ni,nj), system temperature and pressure. There is a scarcity of published data on water adsorption from multicomponent gas mixtures on alumina. Typically, it is assumed that water is exclusively adsorbed on aluminas (S — oo,nj —> 0) from non- polar gases such as air or natural gas. The assumption may not be valid when the gas mixture contains polar components. The mixed gas Langmuir or Toth models may be used to describe multicomponent Type I equilibria on aluminas [6,7]. No isotherm model is available to describe adsorption of water from gas mixtures when there is partial condensation of water in the mesopores of the alumina. 

Thackeray J. W., Natan M. J., Ng P. and Wrighton M. S. (1986), Interaction of diethyldithiocarbamate with n-type cadmium sulfide and cadmium selenide efficient photoelectrochemical oxidation to the disulfide and flat-band potential of the semiconductor as a function of adsorbate concentration , J. Am. Chem. Soc. 108, 3570-3577. 

The chromatographic separation of polymer and surfactant caused by the polymer s inaccessible pore volume cause the polymer to flow ahead of the surfactant thus, polymer is sacrificed for adsorption. Because some adsorption sites are covered by polymer molecules, fewer of the sites are available for surfactant adsorption this is called competitive adsorption. To consider competitive adsorption, we treat surfactant adsorption as a function of adsorbed polymer concentration. 

Scholtz, E.C. et al., Point of zero charge of amorphous aluminum hydroxide as a function of adsorbed carbonate, J. Pharm. Sci., 74, 478, 1985. 

The different values of m in equation (10.21) are attributed to the different pore structures of the adsorbents. The adsorption enthalpies, calculated using the DA isotherm, remain below 5 kJ/mol as a function of adsorbed density (within the range of validity of the Dubinin model), consistent with physisorption. 

Fig. 4.9. Integrated electric field as a function of adsorbate layer thickness. The points labeled A, B, and C refer to specific locations on the surface of the particle as indicated in Fig. 4.8, while D is the average over the particle surface.

Thus, the catalytic activity as a function of adsorbability passes through a maximum, and, therefore, strong adsorption does not favor catalysis. 

An expression for the Helmholtz free energy relates it with the canonical partition function and the partition function of adsorbed molecules and the transition state ... 

Apart from our interest in optimizing adsorbent selectivity, there are other reasons for being interested in sample A values as a function of the adsorbent. First, it is often desired to duplicate a previous adsorbent for the purpose of controlled separation i.e., sample A" values on the second adsorbent must be the same as those on the original adsorbent. It is rarely possible to prepare adsorbents which are precisely equivalent in this respect by merely repeating a previous scheme for the preparation or treatment of an adsorbent. Residual differences in adsorbent activity can be adjusted for or eliminated, however, if we know how these differences are related to adsorbent proce.ssing and sample /f" values. Second, we often want to use experimental A"" values (i.e., Ay, or A values) for the purpose of identifying unknown components in a separated sample. This requires comparison of A values for the unknown sample component with values determined for known compounds. In many cases these latter values have been measured previously on another adsorbent of the same type (e.g., in another laboratory), and it is then necessary to relate A values on one adsorbent to those on another. This generally requires the correlation of sample A values with adsorbent activity. Finally, comparisons of experimental A values as a function of adsorbent activity can serve occasionally to clarify the mechanism of adsorption [e.g., Refs. 1,2)]. 

The chemical and physical structure of the adsorbent surface controls the energy of adsorption of an individual compound and hence determines its A value i.e., adsorbent selectivity is determined by adsorbent surface structure. Unfortunately, the structure of an adsorbent surface can seldom be determined by direct methods. In most cases we are forced to infer the nature of the surface from the gross physical properties and composition of the adsorbent and from its performance in chromatographic separation. Section 6-1 summarizes and discusses those adsorbent properties which we of major interest in this connection. Section 6-2 provides a general treatment of sample A values as a function of adsorbent surface area, surface activity, and extent of water deactivation. Section 6-3 discusses the standardization of the adsorbent with respect to sample A values. 

For an adsorbent of particular type, e.g., alumina, fine pore silica, or coarse pore silica, sample K - values for a given sample and solvent can vary widely as a function of adsorbent surface area and surface activity. Differences in surface area and surface activity can exist in the starting adsorbent, can arise during thermal activation of the adsorbent, or can be created by the addition of varying amounts of water or other deactivator to the adsorbent. We will now proceed to develop a simple theory which relates sample /f values to the surface area and surface activity of a given adsorbent type. We will conclude the present section by examining several cases where our simple theory breaks down or requires correction. 

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