Solvent-competition model

Two models have been proposed to describe the process of retention in liquid chromatography (Figure 3.3), the solvent-interaction model (Scott and Kucera, 1979) and the solvent-competition model (Snyder, 1968 and 1983). Both these models assume the existence of a monolayer or multiple layers of strong mobile-phase molecules adsorbed onto the surface of the stationary phase. In the solvent-partition model the analyte is partitioned between the mobile phase and the layer of solvent adsorbed onto the stationary-phase surface. In the solvent-competition model, the analyte competes with the strong mobile-phase molecules for active sites on the stationary phase. The two models are essentially equivalent because both assume that interactions between the analyte and the stationary phase remain constant and that retention is determined by the composition of the mobile phase. Furthermore, elutropic series, which rank solvents and mobile-phase modifiers according to their affinities for stationary phases (e.g. Table 3.1), have been developed on the basis of experimental observations, which cannot distinguish the two models of retention. 

Figure 3.3 Comparison of the (a) solvent-interaction and the (b) solvent-competition models of retention in liquid chromatography.

Both the solvent-interaction model (Scott and Kucera, 1979) and the solvent-competition model (Snyder, 1968, 1983) have been used to describe the effects of mobile-phase composition on retention in normal-phase liquid chromatography. The solvent interaction model on the one hand provides a convenient mathematical model for describing the relationship between retention and mobile phase composition. The solvent competition model on the other hand provides a more complete, quantitative description of the relative strengths of adsorbents and organic solvents used in normal-phase chromatography. 

Solvent competition model for normal-phase liquid chromatography. Like the solvent-interaction model, the solvent-competition model assumes that the stationary phase is covered with a monolayer of molecules of the strongest component of the mobile phase. This model also assumes that the concentration of analyte in the stationary phase is small compared with the concentration of solvent molecules and that solute-solvent interactions in the mobile phase are cancelled by identical interactions in the stationary phase. The competition between the analyte molecules, x, and the mobile phase molecules. A, for the active site or sites on the stationary phase is given by... 

The competition model and solvent interaction model were at one time heatedly debated but current thinking maintains that under defined r iitions the two theories are equivalent, however, it is impossible to distinguish between then on the basis of experimental retention data alone [231,249]. Based on the measurement of solute and solvent activity coefficients it was concluded that both models operate alternately. At higher solvent B concentrations, the competition effect diminishes, since under these conditions the solute molecule can enter the Interfacial layer without displacing solvent molecules. The competition model, in its expanded form, is more general, and can be used to derive the principal results of the solvent interaction model as a special case. In essence, it seems that the end result is the same, only the tenet that surface adsorption or solvent association are the dominant retention interactions remain at variance. 

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 solute competes with eluent molecules for the ac ve adsorption sites on the surface of the stationary phase. Interactions tetween solute and solvent molecules in the liquid phase are cancelled by milar interactions in the adsorbed phase. This model has been introdu d by Snyder (2) and by Soczewinski (77, 78) and is called the competition model."... 

Two models have been developed to describe the adsorption process. The first model, known as the competition model, assumes that the entire surface of the stationary phase is covered by mobile phase molecules and that adsorption occurs as a result of competition for the adsorption sites between the solute molecule and the mobile-phase molecules.1 The solvent interaction model, on the other hand, suggests that a bilayer of solvent molecules is formed around the stationary phase particles, which depends on the concentration of polar solvent in the mobile phase. In the latter model, retention results from interaction of the solute molecule with the secondary layer of adsorbed mobile phase molecules.2 Mechanisms of solute retention are illustrated in Figure 2.1.3... 

Figure 2.1 (a) Competition and (b) solvent interaction models of solute retention in normal-... 

Snyder [350] has given an early description and interpretation of the behaviour of LSC systems. He explained retention on the basis of the so-called competition model . In this model it is assumed that the solid surface is covered with mobile phase molecules and that solute molecules will have to compete with the molecules in this adsorbed layer to (temporarily) occupy an adsorption site. Solvents which show a strong adsorption to the surface are hard to displace and hence are strong solvents , which give rise to low retention times. On the other hand, solvents that show weak interactions with the stationary surface can easily be replaced and act as weak solvents . Clearly, it is the difference between the affinity of the mobile phase and that of the solute for the stationary phase that determines retention in LSC according to the competition model. 

The partition and displacement model considers retention to result from a two step process. The first involves formation of a mixed stationary phase by intercalation of solvent molecules from the mobile phase. The composition of the solvents in the stationary phase is established according to thermodynamic equilibrium and is usually different to the bulk mobile phase composition. Competitive sorption of solvents is modeled as a displacement process and is complete before the solute is introduced into the two-phase system. Solute retention is then modeled as a partition process between the solvent modified stationary phase and the mobile phase by taking into account all solute-solvent interactions in both phases. The phenomenological model of solvent effects attempts to model retention as a combination of solute-solvent interactions (the solvation effect) and solvent-solvent interactions (the general medium... 

The retention of polar solutes is also affected by site-competition delocalization. A moderately polar non-localizing solvent molecule can interact laterally with sites upon which a solute molecule is localized. This added competition for the site by both the solute and solvent molecules weakens the net interaction of the solute with the surface. For solvents of increasing polarity a greater decrease in the retention factor with increasing polarity of the non-localizing solvent occurs than is predicted by the simple competition model. This effect can be quantitatively accounted for by assuming a larger value of As than is calculated from the molecular dimensions of the solute. 

The calculation of solvent (elution) strength parameters by the competition model is rather involved and a more empirical approach can be justified for routine purposes or for the separation of simple mixtures. For method development an estimate of solvent... 

Many CG models have been developed and used in the past two decades, and not surprisingly, applications have been focusing primarily on the phenomenon of self-assembly and the equilibrium between phases. To some extent, all models that simplify the chemical structure of a macromolecule to focus on its physical properties can be considered as CG models of varied complexity. However, a marked distinction between these models is whether the solvent is modeled implicitly as a continuous medium interacting only with the solute, or explicitly as an ensemble of particles that also interact with each other. For brevity, we discuss only the latter kind of models because the competition between intermolecular forces is crucial to simulate self-assembly. For the purpose of modeling the mechanical properties of membranes and other known stmctures, implicit solvent models are relatively accurate [28, 29] and are typically lower in computational cost than explicit solvent models. 

Various functional forms for / have been proposed either as a result of empirical observation or in terms of specific models. A particularly important example of the latter is that known as the Langmuir adsorption equation [2]. By analogy with the derivation for gas adsorption (see Section XVII-3), the Langmuir model assumes the surface to consist of adsorption sites, each having an area a. All adsorbed species interact only with a site and not with each other, and adsorption is thus limited to a monolayer. Related lattice models reduce to the Langmuir model under these assumptions [3,4]. In the case of adsorption from solution, however, it seems more plausible to consider an alternative phrasing of the model. Adsorption is still limited to a monolayer, but this layer is now regarded as an ideal two-dimensional solution of equal-size solute and solvent molecules of area a. Thus lateral interactions, absent in the site picture, cancel out in the ideal solution however, in the first version is a properly of the solid lattice, while in the second it is a properly of the adsorbed species. Both models attribute differences in adsorption behavior entirely to differences in adsorbate-solid interactions. Both present adsorption as a competition between solute and solvent. 

The stereoselectivity of an addition reaction is considerably lower when the reactions are conducted in polar solvents, complexing additives such as /V./V,A. A, -tetramethylethylenedi-arnine arc used, or when the stereogenic center carries a methoxy group instead of a hydroxy group. This behavior is explained as competition between the cyclic model and a dipolar model, proposed for carbonyl compounds bearing a polar substituent such as chlorine with a highly... 

Solvent selectivity is seen as the factor that distinguishes individual solvents that have solvent strengths suitable for separation. In reality, separations result from the competition between the mobile and stationary phases for solutes based on the differences of all intermolecular interactions with the solute in both phases. Solvents can be organized on selectivity scales that are useful for initial solvent selection, but in a chromatographic separation the properties of the stationary phase must be taken into consideration. Methods that attempt to model chromatographic separation need to consider simultaneously mobile and stationary phase properties [38]. 

One can further elaborate a model to have a concrete form of /(ft), depending on which aspect of the adsorption one wants to describe more precisely, e.g., a more rigorous treatment of intermolecular interactions between adsorbed species, the activity instead of the concentration of adsorbates, the competitive adsorption of multiple species, or the difference in the size of the molecule between the solvent and the adsorbate. An extension that may be particularly pertinent to liquid interfaces has been made by Markin and Volkov, who allowed for the replacement of solvent molecules and adsorbate molecules based on the surface solution model [33,34]. Their isotherm, the amphiphilic isotherm takes the form... 

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