Adsorption isotherms mobile molecules

When the amount of the sample is comparable to the adsorption capacity of the zone of the column the migrating molecules occupy, the analyte molecules compete for adsorption on the surface of the stationary phase. The molecules disturb the adsorption of other molecules, and that phenomenon is normally taken into account by nonlinear adsorption isotherms. The nonlinear adsorption isotherm arises from the fact that the equilibrium concentrations of the solute molecules in the stationary and the mobile phases are not directly proportional. The stationary phase has a finite adsorption capacity lateral interactions may arise between molecules in the adsorbed layer, and those lead to nonlinear isotherms. If we work in the concentration range where the isotherms are nonlinear, we arrive to the field of nonlinear chromatography where thermodynamics controls the peak shapes. The retention time, selectivity, plate number, peak width, and peak shape are no longer constant but depend on the sample size and several other factors. 

Adsorption isotherms for mobile adsorbates were proposed by de Boer4,88) who though assuming lateral interactions between adsorbed molecules stays at the model of energetically uniform adsorbent surface. Starting from the analogy of the van der Waals equation for a three-dimensional system, de Boer developed an equation for a non-ideal behaviour of adsorbate in a two-dimensional adsorbed film ... 

In addition to the factors listed in Table VIII, the nature of the surfactant-modified stationary phase affects P (partition coefficient for distribution of solute between bulk solvent and modified stationary phases) and thus will influence the retention observed. It should be realized that most of the normal and reversed-phase packing materials will adsorb/absorb surfactant molecules from the mobile phase solution and become coated to different degrees when surfactant mobile phases are passed through them. Numerous adsorption isotherms have been reported for various surfactant - stationary phase combinations illustrating this point (82,85,106,115-128,206). The presence of additives can mediate the amount of surfactant surface coverage obtained (110-129,175,206). It has been postulated that the architecture which adsorbed surfactant molecules can assume on conventional stationary phases can range from micellar, hemi-micellar, or admicellar to mono-,bi-, or multilayered, and/or other liquid crystalline-type structures (93,106,124,128,129,... 

Determinations of the adsorption isotherms for a number of organic solvent-water systems in contact with hydrocarbonaceous stationary phases have shown that a layer of solvent molecules forms on the bonded-phase surface and that the extent of the layer increases with the concentration of the solvent in the mobile phase. For example, methanol shows a Langmuir-type isotherm when distributed between water and Partisil ODS (56). This effect can be exploited to enhance the resolution and the recoveries of hydrophobic peptides by the use of low concentrations, i.e., <5% v/v, of medium-chain alkyl alcohols such as tm-butanol or tert-pentanol or other polar, but nonionic solvents added to aquo-methanol or acetonitrile eluents. It also highlights the cautionary requirement that adequate equilibration of a reversed-phase system is mandatory if reproducible chromatography is to be obtained with surface-active components in the mobile phase. 

The method of elution on a plateau was first suggested by Helfferich in Science more than forty years ago [126], In the PP method, the chromatographic column is equilibrated with a constant stream of molecules in the mobile phase and a concentration plateau is established. A perturbation is then accomplished by injecting a sample containing an excess or a deficiency of the molecules as compared to the concentration at the plateau. [118-120, 127], The response at the column outlet will be small peaks, known as perturbation peaks, and their retention times are used to determine the adsorption isotherm parameters. The retention time of the perturbation peak is related to the isotherm through the equation ... 

The classical theory of the Gibbs adsorption isotherm is based on the use of an equation of state for the adsorbed phase hence it assumes that this adsorbed phase is a mobile fluid layer covering the adsorbent surface. By contrast, in the statistical thermod)mamic theory of adsorption, developed mainly by Hill [15] and by Fowler and Guggenheim [12], the adsorbed molecules are supposed to be localized and are represented in terms of simplified physical models for which the appropriate partition function may be derived. The classical thermodynamic fimctions are then derived from these partition fimctions, using the usual relationships of statistical thermodynamics. 

As we have explained in the previous sections, the Langmuir model has been established on firm theoretical groimd for gas-solid adsorption, a case where there is no competition between the adsorbate and the mobile gas phase. On the contrary, in liquid-solid adsorption, there is competition for adsorption between the molecules of any component and those of the solvent. Although we can choose a convention canceling the apparent effect of this competition on the isotherm [30,36], the conditions of validity of Eq. 3.47 are not met. These conditions are (i) the solution is ideal (ii) the solute gives monolayer coverage (iii) the adsorption layer is ideal (iv) there are no solute-solute interactions in the monolayer (v) there are no solvent-solute interactions. These conditions cannot be valid in liquid-solid adsorption, especially at high concentrations. 

The strong dependence of the isotherm parameters on the composition of the mobile phase conJfirms that adsorption of small molecules on chemically bonded Cis silica is more complex than is usually beUeved. Most prior work has been based on data acquired under linear conditions, that is, at infinite dilution. Chro-matographers have long ignored the way in which consideration of the whole equilibrium isotherm and its modeling may inform on the detail of the retention mechanisms involved [131]. 

In contrast to localized adsorption, mobile adsorption models assume that molecules can diffuse freely on the surface. One of the most popular equations used to describe mobile adsorption is that proposed by Hill and de Boer [105] as an analogue of the FG isotherm. This equation can be obtained by combining the two-dimensional form of van der Waals equation with the Gibbs adsorption isotherm. Note that the pre-exponential factors for localized and mobile adsorption are different. In the case of localized adsorption, the pre-exponential factor Kq takes into account the vibrations of adsorbing molecules in X, y and z direction, whereas the factor for the mobile adsorption contains only the partition functions for vibration in the z-direction and the transnational partition function describing mobility of adsorbing molecules in the (x,y)-plane. 

Tompkins (1978) concentrates on the fundamental and experimental aspects of the chemisorption of gases on metals. The book covers techniques for the preparation and maintenance of clean metal surfaces, the basic principles of the adsorption process, thermal accommodation and molecular beam scattering, desorption phenomena, adsorption isotherms, heats of chemisorption, thermodynamics of chemisorption, statistical thermodynamics of adsorption, electronic theory of metals, electronic theory of metal surfaces, perturbation of surface electronic properties by chemisorption, low energy electron diffraction (LEED), infra-red spectroscopy of chemisorbed molecules, field emmission microscopy, field ion microscopy, mobility of species, electron impact auger spectroscopy. X-ray and ultra-violet photoelectron spectroscopy, ion neutralization spectroscopy, electron energy loss spectroscopy, appearance potential spectroscopy, electronic properties of adsorbed layers. 

A problem with active carbon is that the usual /-plot is not obtained for adsorption isotherms measured on carbon. At 77 K adsorption is often limited because migration of adsorbed molecules over the surface is required to enter narrow pores. At 77 K the mobility of adsorbed species is often not sufficient. Carbon dioxide adsorption is therefore employed to assess the surface area of activated carbon supports. 

The steps additionally necessary to reach the solid surface may involve transport down pores within the solid into the interior the reactant molecule may dissociate (if it can) as it approaches the solid surface dissociated or undissociated, the molecules or atoms may adsorb immediately or may move over the surface before final capture (mobile adsorption) and when adsorbing, the ease of adsorption may or may not depend on the coverage (thus affecting the extent of adsorption and the adsorption isotherm to be obeyed). 

In contrast to small molecules, proteins are amphiphilic and interact with the stationary phase only via a small part of the molecule, whereas the hydrophilic parts of the protein are in contact with the mobile phase. The mobile phase at the start of the gradient is typically an aqueous solution. During development of the gradient, a protein will almost completely desorb from the stationary phase at a specific organic solvent concentration. Before this concentration, the protein has an almost infinite retention on the stationary phase and will therefore not migrate through the column. This principle, often referred to as on/off retention mechanism, is also indicated by the steep adsorption isotherms of proteins. As a result, closely related proteins can be separated by small adjustments in the mobile phase composition. Hence, isocratic elution of proteins is not an attractive technique. 

The last section deals with the multi-site adsorption model of Nitta and his coworkers. In such model each adsorbate molecule is adsorbed onto n active sites and the adsorption is localised. For surfaces where mobile adsorption is possible, the approach using the scaled particle theory can be used in the statistical thermodynamics to obtain the required adsorption isotherm equation. This has been addressed by Nitta and co-workers and what to follow is the brief account of then-theory (Nitta et al., 1991). 

When the adsorbed molecules on a surface are mobile and the free area is governed by the scaled particle theory, Nitta and his co-workers have derived the following adsorption isotherm equations (see Section 2.5)... 

In the final part of considerations about early adsorption science it should be stated that only the most important conceptions and equations of adsorption isotherms have been discussed. However, the isotherms including the lateral interactions between molecules in the surface monolayer as well as the equations concerning mobile and mobile-localized adsorption have been omitted. These equations can be derived in a simple way by assuming that molecules in the surface phase produce the surface film whose behaviour is described by the so-called surface equation of state. This equation is a two-dimensional analogue of the three-dimensional equation of state and relates the surface pressure (spreading pressure) of the film to the adsorption. This adsorption can be expressed by the Gibbs adsorption isotherm [26]. Consequently, it is possible to... 

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