Adsorption chromatography competition model

The retention behavior of solutes in adsorption" chromatography can be described either by the "competition" model or by the "solute-solvent interaction" model depending on the eluent composition. It appears that both mechanisms are operative but their importance depends on the composition of the eluent mixture 84). 

The subscripts n and a in the above equation represent a molecule in a nonsorbed and adsorbed phase, respectively. In other words, retention in adsorption chromatography involves a competition between sample and solvent molecules for sites on the adsorbent surface. A variety of interaction energies are involved, and the various energy terms have been described in the literature [7,8], One fundamental equation that has been derived from the displacement model is... 

The retention mechanism in the normal phase is often referred to as adsorption chromatography. It is described as the competition between analyte molecules and mobile-phase molecules on the surface of the stationary phase. It is assumed that the adsorbing analyte displaces an approximate equivalent amount of the adsorbed solvent molecules from the monolayer on the surface of the packing throughout the retention process [18]. The solvent molecules that cover the surface of the adsorbent may or may not interact with the adsorption sites, depending on the properties of the solvent. This retention model, proposed by Snyder, was originally used to describe retention with silica and alumnina adsorbents, but several other studies have shown that this model may also be used for polar bonded phases, such as diol, cyano, and amino bonded silica [10,19]. 

The semiempirical model of adsorption chromatography, analogous to that of Martin and Synge, was established only in the late 1960s by Snyder [3] and Soczewinski [4] independently, and it is often referred to as the displacement model of solute retention. The crucial assumption of this model is that the mechanism of retention consists in competition among the solute and solvent molecules for the active sites of the adsorbent and, hence, in a virtually... 

Figures 4.26A and 4.26B compare the results of the experimental determination of isotherms using the traditional mass balance method (MMB) and those obtained with MMC. The adsorption isotherm predicted by MMC deviates significantly from the isotherm data obtained by MMB. This may be due to the limited applicability of the Langmuir competitive model for the modeling of the adsorption behavior even of such simple systems as p-cresol and phenol in reversed-phase chromatography. Figures 4.26C and 4.26D compare the results obtained by MMB and HMMB for the same system. Over most of the concentration range, the agreement between the experimental data and the results of these two methods is...

Retention mechanisms of adsorption chromatography have been extensively studied. There are two popular models for this process. The displacement model, originally proposed by Snyder, treats the distribution of solute between a surface phase, usually assumed to be a monolayer, and a mobile phase as a result of a competitive solute and solvent adsorption. A treatment of this model, including the significance of predictions of solvent strength and selectivity in terms of mobile-phase optimization strategies, has been published by Snyder (81). 

The retention model in adsorption chromatography developed by Snyder and Soczewinski is based on the assumption that there is flat adsorption in a monomolecular layer on a homogeneous adsorption surface. The adsorption is understood as a competition phenomenon between the molecules of the solute and the solvent on the adsorbent surface, so that the retention of a sample molecule requires the displacement of one or more previously adsorbed polar solvent molecules. Later, the model was corrected for adsorption on a heterogeneous surface of adsorbent. To first approximation, the solute-solvent interactions in the mobile and stationary phases are assumed to compensate each other and possible liquid-liquid partition effects are neglected. In this case, the retention in a mixed binary mobile phase comprising a nonpolar solvent, A (usually an aliphatic hydrocarbon), and a polar solvent, B, can be described by eqn [1] ... 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

The steps when designing a SMB which would allow one to process a given amount of feed per unit time have been described in detail [46, 57]. The procedure described was based on modeling of nonlinear chromatography. The procedure is rigorous, versatile and mainly requires the determination of competitive adsorption isotherms. If the adequate tools and methods are used, the procedure is not tedious and requires less work than is sometimes claimed. The procedure is briefly described below. 

Separations in hydrophobic interaction chromatography have been modeled as a function of the ionic strength of the buffer and of the hydrophobicity of the column, and tested using the elution of lysozyme and ovalbumin from octyl-, butyl- and phenyl-Sepharose phases.2 The theoretical framework used preferential interaction analysis, a theory competitive to solvophobic theory. Solvophobic theory views protein-surface interaction as a two-step process. In this model, the protein appears in a cavity in the water formed above the adsorption site and then adsorbs to the phase, with the free energy change... 

Preparative chromatography is widely used for the purification of different compounds, but this procedure needs to be optimized to achieve the minimum production costs. This can be done by computer-assisted modeling. However, this approach requires a priori determination of accurate competitive adsorption isotherm parameters. The methods to determine this competitive information are poorly developed and hence often a time limiting step or even the reason why the computer-assisted optimization is still seldom used. In this thesis in papers IV-VI, a new injection method was developed that makes it possible to determine these competitive adsorption isotherm parameters more easily and faster than before. The use of this new... 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

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]. 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

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