Langmuir-type adsorption analysis

Sensitization of Ti02 nanosized particle films soaked in water was tried by dissolving a sensitizer and a sacrificial electron donor (EDTA) in the water phase (Fig. 19.7). Photocurrent was strongly dependent on the concentration of Ru(bpy)32+, reaching saturation at higher concentrations beyond 2 mM. By analysis of the photocurrent-vs.-concentration curve, a Langmuir-type adsorption of the dye was suggested. 

In order to facilitate the analysis of the shape and position of elution curves in inverse gas chromatography, such curves were generated in a computer for many well-defined situations. The effects of diffusion in the gas phase, of slow diffusion in the polymer phase (compared to an instantaneous equilibration of the probe), and of surface adsorption (Langmuir type) were simulated. 

So far in our discussion, the movement of solute was assumed to be entirely in one direction, i.e., from the flowing fluid to the stationary solid. This is the case in adsorption processes or in the uptake step of ion-exchange operations. When the direction of transfer is reversed, we speak of desorption, regeneration, or, in the case of environmental systems, of clearance. The theoretical treatment here becomes more complex, and requires a more profound approach based on PDEs. We do not address this problem here and instead present the final result that emerges from that analysis for the case of complete desorption from a Langmuir-type isotherm under eqiulibriiun conditions. The relevant equation is completely analogous in form to that for the adsorption step (Equation 7.27e), and reads... 

One of the assumptions made by Horvath and Kawazoe [35] in their original derivation was that the adsorbate behaved as a two-dimensional ideal gas. This implies that the isotherm obeys Henry s law and is therefore linear in nature. The equation of state shown in Eq. (30) was thus substituted in Eq. (29), which caused the term T/d) dli/dT) = RT to cancel out with the other RT term in the expression, resulting in Eq. (31). However, the isotherms for the typical sorbates used in HK analysis, such as N2 at 77 K and Ar at 87 K, clearly show a type 1 adsorption behavior. An example of such an isotherm is shown in Fig. 10. As is obvious from the figure, the assumption of linearity is only valid for the steeply rising portion of the isotherm, whereas the concave portion of the steep rise may also provide useful information. For this reason, Cheng and Yang [40] proposed the use of a Langmuir-type equation of state in place of Eq. (30) because it is known to represent type 1 isotherms in the best manner ... 

From the asymmetrical concentration profile with front tailing (see Figure 2.4b), it can correctly be deduced that (1) the adsorbent layer is already overloaded by the analyte (i.e., the analysis is being run in the nonlinear range of the adsorption isotherm) and (2) the lateral interactions (i.e., those of the self-associative type) among the analyte molecules take place. The easiest way to approximate this type of concentration profile is by using the anti-Langmuir isotherm (which has no physicochemical explanation yet models the cases with lateral interactions in a fairly accurate manner). 

Virtually all theoretical treatments of adsorption phenomena are based on or can be readily related to the analysis developed by Langmuir (5,6). The Langmuir isotherm corresponds to a highly idealized type 6f adsorption and the analysis is predicated on the following key assumptions. 

In the case of adsorbed species, a unique standard state—one that makes the bottom part of the logarithm equal to zero—is not defined because it will depend on the type of isotherm chosen to describe the process, i.e., it will depend on the function /(0) in Eq. (6.184) characteristic of each isotherm. Thus, it would be impossible to compare the adsorption energies (i.e., AG° s) of different adsorbates if they were represented by different adsorption isotherms. However, instead of a unique standard state, it is possible to define convenient standard states common to any isotherm. The way to choose this convenient standard state is explained in the following analysis of the Langmuir isotherm. 

The theoretical calculations described have recently been supported by an extraordinary kinetic analysis conducted by Vanrysellberghe and Froment of the HDS of dibenzothiophene (104). That work provides the enthalpies and entropies of adsorption and the equilibrium adsorption constants of H2, H2S, dibenzothiophene, biphenyl, and cyclohexylbenzene under typical HDS conditions for CoMo/A1203 catalysts. This work supports the assumption that there are two different types of catalytic sites, one for direct desulfurization (termed a ) and one for hydrogenation (termed t). Table XIV summarizes the values obtained experimentally for adsorption constants of the various reactants and products, using the Langmuir-Hinshelwood approach. As described in more detail in Section VI, this kinetic model assumes that the reactants compete for adsorption on the active site. This competitive adsorption influences the overall reaction rate in a negative way (inhibition). 

Calibration is necessary for in-situ spectrometry in TLC. Either the peak height or the peak area data are measured, and used for calculation. Although the nonlinear calibration curve with an external standard method is used, however, it shows only a small deviation from linearity at small concentrations [94.95 and fulfils the requirement of routine pharmaceutical analysis 96,97J. One problem may be the saturation function of the calibration curve. Several linearisation equations have been constructed, which serve to calculate the point of determination on the basis of the calibration line and these linearisation equations are used in the software of some scanners. A more general problem is the saturation function of the calibration curve. It is a characteristic of a wide variety of adsorption-type phenomena, such as the Langmuir and the Michaelis-Menten law for enzyme kinetics as detailed in the literature [98. Saturation is also evident for the hyperbolic shape of the Kubelka-Munk equation that has to be taken into consideration when a large load is applied and has to be determined. 

The isotherm data acquired from frontal analysis over a broad concentration range fitted well to the bi-Langmuir model, see Figure 18, demonstrating that the adsorption on Kromasil CHI-TBB is heterogeneous with two types of sites. The saturation capacity of site II obtained from the bi-Langmuir isotherm parameters were qs>n = 130 mM for (R)-(-)-2-phenylbutyric acid and qs,n= 123 mM for (S)-(+)-2-phenylbutyric. 

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... 

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