Tri-Langmuir model

The bi-Langmuir model (Equation (2)) or tri-Langmuir model, the sum of two or three Langmuir isotherms, correspond to models that assume the adsorbent surface... 

The bi-Langmuir model (equation (4)) or tri-Langmuir model, the sum of two or three Langmuir isotherms, correspond to models that assume the adsorbent surface to be heterogeneous and composed of two or three different site classes. Finally the Freundlich isotherm model (equation (5)) assumes no saturation capacity, but instead, a continuous distribution of sites of different binding energies. 

The fact that the isotherm data for L-PA were better fitted to the Freundlich isotherm at lower concentrations agrees with previous studies on other template systems, where the isotherm data were often best fitted to tri-Langmuir models [25]. Competitive assays using radiolabelled substrates allowed the identification of a class of sites with a very low surface coverage ca. 1 nmol/g) and high binding constants (up to 1 x 10 /M) (Table 5.3). 

Initially they tried to calculate the value of n from the Bohr model of the atom and then from the Lewis-Langmuir model. However the inapplicability of these models was soon realized and the value of n was determined empirically from the compressibility. 

This equation has rarely been reported as accoimting well for a set of experimental data. The adsorption of aniline on Kromasil Cig is a case in point [11,32], see Figure 3.11. Chromatographers seem to prefer the Langmuir model and rarely try to use this alternative. Accurate data acquired in a wide range of concentrations are needed to show that one of the two models is significantly better than the other... 

This isotherm model has been used successfully to accoimt for the adsorption behavior of numerous compounds, particularly (but not only) pairs of enantiomers on different chiral stationary phases. For example, Zhou et ah [28] foimd that the competitive isotherms of two homologous peptides, kallidin and bradyki-nine are well described by the bi-Langmuir model (see Figure 4.3). However, most examples of applications of the bi-Langmuir isotherm are found with enantiomers. lire N-benzoyl derivatives of several amino acids were separated on bovine serum albumin immobilized on silica [26]. Figure 4.25c compares the competitive isotherms measured by frontal analysis with the racemic (1 1) mixture of N-benzoyl-D and L-alanine, and with the single-component isotherms of these compounds determined by ECP [29]. Charton et al. foimd that the competitive adsorption isotherms of the enantiomers of ketoprofen on cellulose tris-(4-methyl benzoate) are well accounted for by a bi-Langmuir isotherm [30]. Fornstedt et al. obtained the same results for several jS-blockers (amino-alcohols) on immobilized Cel-7A, a protein [31,32]. 

The Langmuir model is based on the assumption of ideal localized adsorption without interaction on a set of identical sites as outlined in Section 2.4. The special case of sorption of CH4 or Ar in sodalite was noted in Section 3.5 as an example of a system for which the basic assumptions of the Langmuir model are in fact fulfilled and for which the isotherms conform, as expected, to the Langmuir equation (Eq. (2.28)]. Sorption of normal tri- or tetradecane in 5A zeolite is another example of a zeolitic system in which each cage can accommodate only one sorbate molecule. Approximate conformity... 

Figure 4.7. Single component isotherms of (top) proteins and (bottom) synthetic tri-block copolymers measured at room temperature for Octyl-sepharose stationary phase. The affinity constants calculated from an isotherm fit according to the Langmuir model seemed to indicate that the proteins bind more strongly than the copolymers and hence could not be displaced by them [reproduced with permission from reference 14].

Why do we want to model molecules and chemical reactions Chemists are interested in the distribution of electrons around the nuclei, and how these electrons rearrange in a chemical reaction this is what chemistry is all about. Thomson tried to develop an electronic theory of valence in 1897. He was quickly followed by Lewis, Langmuir and Kossel, but their models all suffered from the same defect in that they tried to treat the electrons as classical point electric charges at rest. 

Studies of the order within surfactant monolayers have been reported for many decades. Multilayer assemblies have been studied by electron as well as infrared absorption. Motivated by an older model proposed for the orientation of molecules (Langmuir, 1933 Epstein, 1950), and by recent theoretical calculations, these two potential models for tilt disorder in the monolayer have been examined. Both models arise because the monolayer structure tries to compensate for the difference between the equilibrium head-head and chain-chain distances that each piece of the molecule would want to attain if it were independent. In one model, the magnitude of the tilt is fixed, but the tilt direction wanders slowly through the lattice. In the second... 

Different charge-compensating cations in zeolite L have been tested for their promotional effect in n-hexane aromatization. Apparently, high basicity of the alkaline and alkaline earth promoter favors n-hexane aromatization. Basicity and selectivity both increase from Li and Cs 331) and from Mg to Ba (22,25). Bezouhanova et al. studied the FTIR bands of linearly adsorbed CO in the range of 2060-2075 cm . One band at 2075 cm", which is also found on unsupported Pt, is attributed to extrazeolite Pt particles, a second band shifts from 2060 cm" for Li to lower wavenumbers with K and Rb 331). Another criterion, used by Larsen and Haller, is the measured rate of competitive hydrogenation of benzene and toluene, which has been found to correlate with the zeolite basicity (25). As described in a previous section, this method had previously been used by Tri el al. to probe for the electron deficiency of Pt particles in acidic zeolites 332). The rate data are analyzed in terms of a Langmuir-Hinshelwood model and the ratio of the adsorption coefficients of toluene and benzene, A, /b, is determined. It was found to decrease from 8.6 for Pt/Si02, and 5.4 for Pt/MgL, to 4.4 for Pt/BaL. As direct electron transfer from the cations to neutral Pt particles is unlikely, an interaction of Pt with the zeolite framework or with... 

This model was used by Gritti and Guiochon to account for the behavior of propranolol on several Cig-bonded silica adsorbents, from methanol/water solutions. Similar results were obtained for Kromasil-Cig [101,102], XTerra-Cjs [84], Symmetry-Ci8 [103]. When the mobile phase contains a high concentration of a monovalent salt, the adsorption follows bi-Langmuir isotherm behavior [101]. In the absence of salt, at low concentrations of a monovalent salt or with di- (e.g., phthalate, succinate, naphthalene sulfonate) or tri-valent salts (e.g., citrate), the isotherm data are best modeled by a bi-Moreau isotherm [91,104]. 

From the above discussion, it is apparent that two-site binding models are too simple to accurately characterize most heterogeneous MIPs. Higher order Langmuir binding models have also been applied to MIPs such as tri- and tetra-Langmuir isotherms [9]. However, all of these models assume that MIPs contain a specific number of different types of sites, which is unlikely given the sources of the structural diversity of... 

Langmuir, Irving (1881-1957) American chemist. In 1919 Langmuir extended the model of electrons in atoms proposed by Gilbert lewis to try to account for the chemical valence of all atoms. In the 1920s he investigated the chemistry of surfaces very extensively. He won the 1932 Nobel Prize for chemistry for his work on chemical reactions at surfaces. 

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