Langmuir behavior

The most strongly pronoimced anti-Langmuir behavior (when comparing the three classes of carboxylic acids) was observed for phenyl-substituted monocarboxylic acids (Figure 2.9). 

Herrero and Abruna [25] have also studied the kinetics and mechanism of Hg UPD on Au(lll) electrodes in the presence and absence of bisulfate, chloride, and acetate ions. In the absence of the interacting anions (in perchloric acid), the Hg UPD was significantly controlled by gold-mercury surface interactions. In sulfuric acid solutions, the kinetics of the initial and final stages of mercury deposi-tion/dissolution was altered. The presence of two well-ordered structures at potentials below and above mercury deposition led to the formation of two pairs of sharp spikes in cyclic voltammograms. In the chloride medium, the voltammetric profile exhibited two sharp peaks and thus it was very similar to that obtained in sulfuric acid solution. Neither nucleation, nor growth kinetics mechanism was found to be linked to the process of formation/disruption of the mercury chloride adlayer. The transients obviously deviated from the ideal Langmuir behavior. 

Adsorption isotherms of cyanine dyes on silver halide crystals are consistent with Langmuir behavior, and indicate a close-packed monolayer of dye on the surface of the silver halide crystal [163]. This is supported by the observation of large shifts in the absorption spectra of the adsorbed dyes compared with the absorption spectra of the dyes in dilute organic solution. An example is shown in Figure 46. 

The Langmuir equation has been used to describe adsorption of p carotene from solution onto activated bleaching clays (8) and free fatty acid from isooctane solution by acid-washed rice hull ash (9). Likewise, isotherm analysis of the commercial bleaching of rubber and melon seed oil by Fullers earth, activated carbon, and Fullers earth/activated carbon mixture (10) followed Langmuir behavior at 55°C and 80°C, suggesting the possibility of monolayer adsorption with little competition. This behavior was not observed at 30°C where the isotherm no longer applies, because of desorption. The amount of adsorbent was kept constant while varying... 

Other examples are isotherms for the isomers fructose and glucose. Figure 6.22 shows that the resulting isotherms exhibit an upward curvature and the slope of the isotherm is increased in the case of mixtures. This anti-Langmuir behavior is explained from the specific interaction between the hydrated solute molecules and the eluent (water) (Saska et al. 1991 and 1992). These isotherms are expressed by the following empirical correlations ... 

The resulting isotherms are illustrated as lines in Fig. 6.25b. The stronger adsorbing S-enantiomer isotherm exhibits an inflection point and is assumed to be independent of the R-enantiomer concentration. The R-enantiomer isotherm shows typical Langmuir behavior and minor interaction with the S-enantiomers. The rather uncommon case of higher loadings of the R-enantiomer in mixtures can be explained with multi-layer adsorption processes (Mihlbachler et al., 2001). 

For an adsorption shock front, the time for the front s breakthrough under Langmuir behavior can be calculated according Eq. 7.72, where the isotherm s secant at feed concentration is relevant. The smaller the ratio the higher the velocity of the shock front. 

A quadratic isotherm has been used by Guiochon et al. [77] to calculate the band profiles obtained in the case of an S-shaped equilibrium isotherm. The same isotherm has been used by Svoboda [78]. An example of an isotherm with one inflection point, accormted for by the quadratic model is shown in Figure 3.25 [79]. It corresponds to the adsorption of the (+) isomer of Troger s base on microcrystalline cellulose triacetate, while the (-) isomer follows a Langmuir behavior in... 

Jandera et al. [35] measured by frontal analysis the competitive isotherms of the enantiomers of mandeHc acid, phenyl-glycine and tryptophan on the glyco-peptide Teicoplanin, in water/methanol or ethanol solutions. The less retained L enantiomers of the two amino acids follow Langmuir isotherm behavior while the D isomers foUow bi-Langmuir behavior. The enantiomeric separation factors increase with increasing alcohol concentration while the solubilities of these com-poimds decrease. Similar results were reported by Loukih et al. [36] for the separation of the enantiomers of tryptophan on a teicoplanin- based CSR The authors insisted on the importance of the nature of the ions in a supporting salt. Optimization of the experimental conditions for maximum production rate must take this effect into account. 

The FA method gives isotherm data. To be useful in preparative chromatography, these data must be fitted to an isotherm model. There are presently no numerical procedures available to smooth the data from multidimensional plots, similar to the 2-D splines or French curves and obtain purely empirical isotherms. Therefore, the major difficulty is the selection of adequate models. The Langmuir isotherm is too simplistic in most cases, and the LeVan-Vermeulen isotherm is complicated and difficult to use as a fitting fimction. Several methods have been described to extract the "best" set of Langmuir parameters which could accormt for a set of competitive adsorption data [108]. These methods have been compared. The most suitable method seems to depend on the aim of the determination and on the deviation of the system from true Langmuir behavior [108]. 

As expected, the two methods give basically the same results [16]. Both theories are valid only in the case of competitive Langmuir isotherms. This restriction should be kept in mind, because deviations from Langmuir behavior are the most probable explanation for the not so inconsequential disagreements observed sometimes between theoretical predictions and experimental observations reported in the literature [14,34]. 

Both Equations [18.1] and [18.5] describe ideal cases. In many experimental situations, sorption isotherms are non-linear, showing a negative behavior compared to Henry s law. Some cases can be described using a dual sorption theory (Paul and Koros, 1976) in which the global sorption capacity is the result of two different contributions, one that follows Henry s law and a second that follows Langmuir behavior ... 

In this formulation the concentration dependence of the activity coefficient is described by a one-parameter expression (Eq. (3.64)). To extend the analysis to allow for more pronounced deviations from ideal Langmuir behavior it is only necessary to use a two-parameter expression for the activity coefficient. Danner and Suwanayuen used the Wilson expression ... 

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