Isotherm peak-maximum method

Isotherm Measure by frontal analysis, perturbation Measure by peak-maximum method Measure with ECP... 

The nitrogen adsorption isotherms for the onion-like Fe-modified MLV-0.75 materials are of type IV, although their hysteresis loops are of complex types, HI, H2, and H3. The H2-type hysteresis loop indicates the presence of bottle-shaped pores. The pore sizes obtained with the BJH method can be assigned to entry windows of mesopores. For pure MLV-0.75 and Fe-modified MLV-0.75 (x = 1.25), the pore size distributions exhibit two peaks (Fig. Id). The first peak appears at 9.0 and ca. 6 nm for MLV-0.75 and Fe-MLV-0.75, respectively. The shift of the broad peak maximum of the distribution curve... 

In the MIP literature the most widespread method for establishing the selectivity of an MIP for its template against an interferent has been to determine by HPLC the corresponding a value. In the section on MIP HPLC we have shown, however, that the k values determined in MIP HPLC depend on the injected sample concentration. Therefore they do not provide a distribution ratio. Indeed, the distribution ratio is obviously concentration dependent when the isotherm is not linear. It is not self-evident but it has been shown [35] that the ratio of the apparent k values (as determined from the peak maximum positions) for two compounds with nonlinear isotherms is not a constant and such an a value is not suitable to quantitate the separation selectivity. 

Recentty Tremaine and Gray (97) used the peak maximum elution method to determine adsorption isotherms ctf cellulose surfaces. In this method (98), the adsorption isotherm is obtained from the variation of the peak maximum retention volume with the solute sample size injected. Approximately 25 peaks are recorded for one such determination. Surface areas, heats and entropies of adsorption were computed from the experimental adsorption isotherms and the results were discussed... 

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). 

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. 

T5rpical experimental conditions and procedure [21] are sample size 5-10 mg and flow rate of nitrogen 30 ml min For iso-thermosetting experiments on a resin, the DSC sample holder should be preheated to the desired isothermal temperature. The easiest method of determining the four appropriate isothermal temperatures is as follows (1) a sample of the thermoset is heated in the DSC at a rate of 5°C min", obtaining a heating DSC curve (2) the isothermal temperatures are selected in the range between 10 °C below the onset of the curve (e.g. 85 °C) and the midpoint of the peak maximum (e.g. 120 °C) and (3) the isothermal temperatures selected should be separated by 5-10 °C (in this case 85, 90, 100 and 110 °C, respectively). 

Kissinger relationship, the most extensively used method in kinetic studies since 1957 [13], was in use to determine the energy of activation and the order of reaction, from plots of the logarithms of the heating rate against the temperature inverse at the maximum reaction rate in isothermal conditions. This method is usually based on the Differential Scanning Calorimetry (DSC) analysis of formation or decomposition processes and in relation to these processes the endothermic and exothermic peak positions are related to the heating rate. 

Table 2. Characteristics of the silica templates and the corresponding carbon materials a unit cell parameter Sbet- specific surface area Vp total pore volume (at P/Po=0.95) Pore size determined according to the BJH method - Maximum value of the BJH pore size distribution peak calculated from the adsorption branch of the N2 isotherm.

Pore size determined according to the BJH method - Maximum value of the BJH pore size distribution peak calculatedfrom the adsorption branch of the N2 isotherm. 

These techniques do not differ only in terms of accuracy and experimental effort. Their application is also limited by the availability of the required equipment. Not all methods are suitable for columns with low efficiency, because peak deformations will affect the isotherm parameters. The actual setup and experimental conditions should be as close as possible to the operating conditions for later production purposes. However, to save time and solutes, the column dimensions are usually only of smaller (analytical) scale, or semipreparative at maximum. Preparative chromatography requires typically the application of adsorbents, with larger particle sizes compared to analytical applications. In isotherm measurements temperature control is crucial, since adsorption may show significant temperature dependence. Sometimes the costs of solutes prohibit the use of methods that need larger amounts of samples. 

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