Adsorption isotherms retention time method

Direct determination of the column saturation capacity requires measurement of the adsorption isotherm. Use of methods such as frontal analysis, elution by characteristic point are classical techniques. Frontal analysis and elution by characteri.stic point require mg or gram quantities of pure product component. It is also possible to estimate the column saturation capacity from single-component overloaded elution profiles using the retention time method or using an iterative numerical method from a binary mixture [66J. 

A possibility to reduce the influence of column efficiency on the results obtained by the ECP method is to detect the position of the peak maximum only, which is called the peak-maximum or retention-time method. Graphs like Fig. 6.23 are then achieved by a series of pulse injections with different sample concentrations. The concentration and position of the maximum is strongly influenced by the adsorption equilibrium due to the compressive nature of either the front or the rear of the peak (Chapter 2.2.3). Thus, the obtained values are less sensitive to kinetic effects than in the case of the ECP method. The isotherm parameters can be evaluated in the same way as described in Section 6.5.7.6, but the same limitations have to be kept in mind. For some isotherm equations, analytical solutions of the ideal model can be used to replace the concentration at the maximum (Golshan-Shirazi and Guiochon, 1989 and Guiochon et al., 1994b). Thus, only retention times must be considered and detector calibration can be omitted in these cases. 

The primary use of isotherm data measurements carried out on single-component elution profiles or breakthrough curves is the determination of the single-component adsorption isotherms. This could also be done directly, by conventional static methods. However, these methods are slow and less accurate than chromatographic methods, which, for these reasons, have become very popular. Five direct chromatographic methods are available for this purpose frontal analysis (FA) [132,133], frontal analysis by characteristic point (FACP) [134], elution by characteristic point (ECP) [134,135], pulse methods e.g., elution on a plateau or step and pulse method) [136], and the retention time method (RTM) [137]. 

For the access of the adsorption isotherm, the volumes injected are in very small quantities less than 0.1 /jL of gaseous probes for the infinite dilution, and in the range of 0.1 fjL to about 10 fiL of liquid probes for the finite dilution up to the saturation of the adsorbate (or, up to the increase of net retention time when the quantity adsorbed increased) in the chromatography, on account of the sensitivity of detector. In the chromatographic approach, the peak maxima method [115] is generally used to determine the net retention volumes, which are corrected by the compressibility, temperature as well as flow rate, as shown in Fig. 13. 

Chromatographic methods are widely used for the study of both physisorption and chemisorption. In its simplest form the technique consists of passing a pulse of the adsorbate through a column of the adsorbent and measuring the retention time and registering the elution curve. Measurement of the variation in the retention time as a function of temperature permits the evaluation of the enthalpy of adsorption, and analysis of the shape of the elution curve provides information about the adsorption isotherm. 

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 ... 

After the adsorption isotherm experiments have been completed, an isotherm equation must be chosen. This equation should fit the experimental data. Often are the experimental data (the experimental adsorption data acquired by the FA method or the perturbation retention times acquired by the PP method) only compared with the ones calculated using the adsorption isotherm parameters acquired from some adsorption isotherm models [131], This is sometimes the only validation done in this field [131], However, the adsorption isotherm parameters should preferably be validated in two step (1) the different isotherm models should be compared using statistical calculations, e.g., an F-test, and (2) by using the parameters to computer simulate elution profiles and then compare them with experimental ones. 

The retention time is determined from the peak maximum in the case of symmetrical peak shapes. For well-packed columns symmetrical peaks should be achieved as long as the amount injected into the column is in the linear concentration range of the adsorption isotherm. If increased amounts of substances in the nonlinear concentration range of the adsorption isotherm are injected the peak is often heavily distorted and asymmetric. In that case the retention time has to be calculated from the centroid following the momentum method (Eq. 2.27). 

The method consists of monitoring and analyzing the response of an adsorption column to a pulse input or a step change in concentration of an adsorbate. The carrier gas is a mixture of an inert gas and the adsorbate of known composition. The retention time of the pulse is related to slope of the equilibrium curve at the carrier gas composition. The slopes of the equilibrium curve at different points on the curve can be determined by carrying out experiments with different carrier gas compositions. The equilibrium curve can, then, be easily obtained by integration of the slopes of the isotherm curve. For binary sorption equilibria, the experiments are similar except the carrier gas is a mixture of the two adsorbates. 

Inverse gas chromatography provides accurate thermodynamic data for solid surfaces [20]. It can be used to determine the DN and AN values of oxides and to establish adsorption isotherms [20, 21]. In this method, the solid is placed in a gas chromatographic column as the stationary phase, and probe gases are introduced into an inert carrier gas. The measured quantity is the retention time, which is related to the adsorption interaction energy and the equilibrium between adsorbed and non-adsorbed gas molecules. 

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