Nonlinear adsorption isotherms

There are a number of causes of peak asymmetry in both gas and liquid chromatography, including heat of adsorption, high activity sites on the support or absorbent, and nonlinear adsorption isotherms. Assuming that good quality supports and adsorbents are used, and the column is well thermostatted, the major factor causing peak asymmetry appears to result from nonlinear adsorption isotherms. 

Volume overload results from too large a volume of sample being placed on the column, and this effect will be discussed later. It will be seen that volume overload does not, in itself, produce asymmetric peaks unless accompanied by mass overload, but it does broaden the peak. Mass overload, however, frequently results in a nonlinear adsorption isotherm. However, the isotherm is quite different from the Langmuir isotherm and is caused by an entirely different phenomenon. 

Calculation of the SMB flowrates The criterion C + K - Cg<0. (Equation 10) equaling now approximately 0.22, the system is operating under nonlinear adsorption isotherm conditions. 

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. 

For the case of nonlinear adsorption isotherms, no analytical solutions exist the mass balance equations must be integrated numerically to obtain the band profiles. Approximate analytical solutions are only possible for the cases where the solute concentration is low and accordingly, the deviation from linear isotherm is only minor. All the approximate analytical solutions utilize a parabolic adsorption isotherm q = aC( -bC). This constraint prevents us from drawing general conclusions regarding most of the important consequences of nonlinearity. 

Abstract Most analytical applications of molecularly imprinted polymers are based on their selective adsorption properties towards the template or its analogs. In chromatography, solid phase extraction and electrochromatography this adsorption is a dynamic process. The dynamic process combined with the nonlinear adsorption isotherm of the polymers and other factors results in complications which have limited the success of imprinted polymers. This chapter explains these problems and shows many examples of successful applications overcoming or avoiding the problems. 

Fig. 1 Nonlinear effects in elution chromatography (a) nonlinear adsorption isotherm (b) the corresponding chromatographic peak shapes at N = 10,000 for different injected concentrations (c) the corresponding chromatographic peak shapes at N = 500 for different injected concentrations. Isotherm Langmuir type. Concentrations 2.5, 5.0, 7.5, and 10.0 units. Length of column 10 cm...

Toth B et al (2006) Nonlinear adsorption isotherm as a tool for understanding and characterizing molecularly imprinted polymers. J Chromatogr A 1119(1—2) 29—33... 

The solution of such an equation is complicated because the equilibrium is generally described by a nonlinear adsorption isotherm. Moreover, the mass transfer kinetics are extremely complex and include the film mass transfer resistance, the diffusion of the protein into the pores of the support, and the interaction with the immobilized species. 

Peak tailing is the most commonly observed effect of sample overloading. In essence, in most cases this effect is associated with nonlinear adsorption isotherms. In Chapter 2 the relationship of the retention volume and the derivative of the excess adsorption isotherm of the analyte on given stationary phase surface was derived. If the isotherm is linear within the injected concentration region, all components of the chromatographic zone are moving... 

Determination of Nonlinear Adsorption Isotherms from Column Experiments an Alternative to Batch Studies... 

Measurements of isotherms are commonly obtained in the laboratoiy by performing batch experiments. As has been pointed out recently by Biirgisser et al. (1993), another alternative to the classical batch experiment that allows simple and rapid measurements of an entire possibly nonlinear adsorption isotherm relies on column experiments and the use of techniques borrowed from nonlinear chromatography (Burgisser et al., 1993 Schweich et al., 1983). Experimentally, the column experiment (column is packed with the material in question) is carried out near the relevant solid/solution ratio, and the percolating solution may easily be adjusted to the composition of interest (e.g., composition of groundwater). 

Biirgisser, C., Cemik, M., Borkovec, M., and Sticher, H. (1993) Determination of Nonlinear Adsorption Isotherms from Column Experiments, an Alternative to Batch Studies, Environ. Sci. Technol. 27, 943-948. 

For preparative chromatography, where we almost always have to deal with high feed concentrations and nonlinear adsorption isotherms, the following approach to the appropriate choice of feed concentration during model-based optimization is recommended ... 

The present study reports the measurements of intracrystalline diffusion and adsorption equilibrium for ethanol, propanols and butanols from aqueous solution in silicalite using a modified HPLC technique. The unique feature of the present work is the use of a mathematical model with a nonlinear adsorption isotherm equation to obtain the intracrystalline diffusivity and adsorption isotherm parameters. The adsorption equilibrium data for alcohols from aqueous solution in silicalite measured by the conventional batch method are also reported and compared with the results measured by the HPLC technique. 

An HPLC experimental technique has been developed to determine the intracrystalline diffusivity and nonlinear adsorption isotherm for the adsorption of liquids in molecular sieve crystals. The application of the experimental technique was demonstrated by the determination of the adsorption isotherms and diffusivities of the five alcohols (ethanol, i-propanol, n-propanol, i-butanol and n-butanol) from aqueous solutions in silicalite crystals. 

From the experimental adsorption isotherms both heats of adsorption and surface areas can be derived. For nonlinear adsorption isotherms the heat of adsorption varies with surface coverage and results are expressed as an isosteric heat of adsorption, at a specified coverage, a,... 

Even if it is not possible to attain the desired ideal conditions of operation, and less desirable conditions (nonlinear adsorption isotherm, fluctuating numbers of adsorbing centers, induction time, or delay not related to adsorption) occur, the time At is in every case characteristic of the particular catalyst and is sensitive to the smallest alteration in its condition. Thus, one may learn much about differences in particle size, porosity, and bulk factor, as well as about the surface area of a catalyst. The method also is... 

Another modification of the classical SMB process is the so-called ModiCon approach by Schramm et al. (2003). In contrast to the partial-feed process, where the feed flow rate is varied during one switching interval, in ModiCon the feed concentration is altered instead of the feed flow rate. Figure 5.22 illustrates this variation of the feed concentration during the switching interval tshia- In the example shown, which is suitable for systems with favorable isotherms, at the beginning only pure solvent is fed to the plant while in the second part feed at a rather high concentration is used. The modulation of the feed concentration allows for improved process performance for systems with nonlinear adsorption isotherms. 

Gao, W. and Engell, S. (2005h) Estimation of general nonlinear adsorption isotherms from chromatograms. 

Ktipper, A. and Engell, S. (2006) Parameter and State Estimation in Chromatographic SMB Processes with Individual Columns and Nonlinear Adsorption Isotherms. Proceedings of the lEAC Symposium ADCHEM, Gramado, pp. 611-616. 

Another variant of IR spectroscopic technique is known as Fourier Transform IR Attenuated Total Reflection Spectroscopy (ATR FT-IR) has been described by Poston et al. [123] to study adsorbates at the silica-solution interface. The authors reported the preparation of ZnSe internal-reflection elements coated with a porous silica layer of ca. 700 nm thick. They studied the adsorption of ethylacetate from n-heptane solutions. This technique allows the determination of IR spectra in-situ and its dependence on the solution concentration. They found a nonlinear adsorption isotherm of ethylacetate on... 

However, among the drawbacks, it is necessary to take into the account that the intrinsically polyclonal nature of the noncovalently imprinted polymers causes the presence of a small number of highly enantioselective binding sites and a large number of less selective binding sites, and it is associated to nonlinear adsorption isotherms. As a consequence, enantioseparations are frequently affected by asymmetric peaks and slow association-dissociation kinetics that result in low peak resolution and a marked sensitivity to the amount of sample introduced in the column. 

If one of the phases is a solid, the distribution is more appropriately described in terms of adsorption. Such adsorption can be a combination of unspecific adsorption of the environmental chemical to the solid smface, electrostatic interactions between the charged chemical and oppositely charged sitrface sites, and the covalent reaction of the chemical with reactive sites at the surface. Quantitative expressions rely again on concentration ratios, but equihbrium adsorption coefficients are less likely to be constant over wide concentration ranges. These relationships thus need to be characterized by nonlinear adsorption isotherms, such as those formulated by Langmuir and Freimdhch. 

Real danger of asymmetric chromatographic zone as a result of nonlinear adsorption isotherm for a number of analyzed compounds... 

Onyegbado, C.O., and Susu, A.A., Theoretical study of nonlinear adsorption isotherm by chromatography Application to methyl linoleate and methyl oleate adsorption on supported copper catalyst. Chem. Eng. Commun., 91. 79-90 (1990). 

Hassan, M.M. Rahman, A.K.M.S., and Loughlin, K.F., Numerical simulation of unsteady continuous countercurrent adsorption system with nonlinear adsorption isotherm, Sep. Technol., 4(1), 15-26 (1994). 

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