Prediction peak shape

The models used to predict peak shape, based on Gaussian distributions, have the advantage of using very intuitive parameters, related to properties which can directly be measured on the chromatograms (position and height of the maxima, and width of the peaks). The equation describing a pure Gaussian peak is ... 

It has been found that the equations describe correctly the peak shape determined experimentally, and can be applied for the prediction of peak distortion [118]. 

The ICLS model contains pure spectra of caustic, salt, water, and temperature. The conclusion of the model validation is that the ICLS model adequately describes the water peak shape changes due to caustic, salt, and temperature. Furthermore, it meets the required performance criterion for the prediction of caustic. The measures of performance are as follows (see Table 5.1 for a description of these figures of merit) ... 

The success of this modeling can be ascertained by the ability to replicate the observed peak shapes using Gaussian peaks centered at peak positions suggested by the modeling (Fig. 3). For the case where n = 3/2, five peaks were needed 1 for the monomeric A1 and 2 peaks each for each of the two dinuclear A1 species. These peaks were combined to successfully replicate the observed NMR peaks recorded for this sample. When n = 2, the data were reproduced using only 4 peaks, two each for each of the two dinuclear A1 species. Our earlier predictions (11) showed that HCl could combine with either of the dinuclear Al-species in three different positions, which showed different acid strengths. 

Further, in atomic spectrometry we must face the serious problem that the behaviour (atomisation/excitation characteristics) of the analyte in the calibration samples should be the same as in the future unknown samples where the analyte of interest has to be quantified, otherwise peak displacement and changes of the peak shape may cause serious bias in the predictions. Fortunately, many atomic techniques analyse aqueous extracts or acid solutions of the (pretreated) samples and current working procedures match the amount of acids in the calibration and treated samples, so the matrices become rather similar. Current practices in method development involve studying potential interferents. The analyte is fixed at some average concentration (sometimes studies are made at different concentrations) and the effects of a wide number of potential interferents are tested. They include major cations, anions and... 

In the early years of GC, more consideration was given to partition (GLC) than to adsorption (GSC) systems. For GLC, the mechanism of retention was well understood, all of the mathematics were derived, and the chromatographic peak shapes were symmetrical. At that time, GSC had been utilized only for the separation of permanent gases. In recent years much has been accomplished in the determination of thermodynamic parameters in GSC separations. Part of the reason for the upsurge of interest was due to the desire to predict sample separations at any temperature, since most GSC data was reported at only one temperature. 

The observed cross sections for the 18s (0,0) collisional resonance with v E and v 1 E are shown in Fig. 14.12. The approximately Lorentzian shape for v 1 E and the double peaked shape for v E are quite evident. Given the existence of two experimental effects, field inhomogeneties and collision velocities not parallel to the field, both of which obscure the predicted zero in the v E cross section, the observation of a clear dip in the center of the observed v E cross section supports the theoretical description of intracollisional interference given earlier. It is also interesting to note that the observed v E cross section of Fig. 14.12(a) is clearly asymmetric, in agreement with the transition probability calculated with the permanent electric dipole moments taken into account, as shown by Fig. 14.6. 

The main argument for making MIP CEC is to combine the selectivity of the MIPs with the high separation efficiency of CEC. This argument appears to fail, however, if the adsorption isotherm of the MIP is nonlinear, which seems to be the rule. In the case of nonlinear isotherms, the peak shapes depend mainly on the isotherm, particularly so if the separation system is otherwise very efficient (has low theoretical plate height, see Fig. 1). In the case of ionized analytes the situation is more complex. If an ionized analyte is not adsorbed at all on the MIP, then it is separated only due to electrophoresis, and its peak will not be widened due to the nonlinear effect. In this case, however, the MIP is merely behaving like an inert porous material. In intermediate cases an ionized analyte may participate in both separation mechanisms and for this case we do not have exact predictions of the peak shape. 

A similar argument holds for the influence of the peak shape on the separation criterion. In the non-linear part of the distribution isotherm, the shape of the peak will be a function of the injected quantity. Hence, once again, the location of the optimum may be affected by the composition of the sample. Also, the effect of column dimensions on the peak shape may be hard to predict, and the peak shape may to a large extent be determined by the characteristics of the instrument, rather than of the column. Therefore, if the composition (or the concentration) of the sample can be expected to vary considerably, and if it is desirable that the result of an optimization process can be extrapolated to different columns (of the same type) and to different instruments, then it is advisable to use criteria that are not affected by the relative peak areas, nor by the shape of the peaks. 

Enantioseparation can be achieved on a conventional achiral stationary phase by the inclusion of an appropriate chiral additive into the mobile phase. It is theoretically predicted that the enantioselectivity in CEC with a chiral additive may be higher than that using a chiral column with the same chiral selector [10]. Lelievre et al. compared an HP-/3-CyD column and HP-/3-CyD as an additive in the mobile phase with an achiral phase (ODS) to resolve chlortalidone by CEC [22]. It was demonstrated that resolution on ODS with the chiral additive was superior on the CSP however, efficiency was low. With an increasing amount of acetonitrile, the peak shape was improved and the migration time was decreased. We achieved the separation of salsolinol by the use of CEC with /3-CyD as a chiral... 

Clearly, it would be desirable if the area under the peak was a measure of the enthalpy associated with the transition. However, in the case of DTA, the heat path to the sample thermocouple includes the sample itself. The thermal properties of each sample will be different and uncontrolled. In order for the DTA signal to be a measure of heat flow, the thermal resistances between the furnace and both thermocouples must be carefully controlled and predictable so that it can be calibrated and then can remain the same in subsequent experiments. This is impossible in the case of DTA, so it cannot be a quantitative calorimetric technique. Note that the return to baseline of the peak takes a certain amount of time, and during this time the temperature increases thus the peak appears to have a certain width. In reality this width is a function of the calorimeter and not of the sample (the melting of a pure material occurs at a single temperature, not over a temperature interval). This distortion of peak shape is usually not a problem when interpreting DTA and DSC curves but should be borne in mind when studying sharp transitions. 

Cyclic ac voltammograms for completely nernstian systems are easy to predict on the basis of results from the previous section. The mean surface concentrations, Co(0, Om Cr(0, Om adhere to (10.5.3) and (10.5.4) unconditionally hence at any potential they are the same for both the forward and reverse scans. The cyclic ac voltammogram should therefore show superimposed forward and reverse traces of ac current amplitude dc-We expect a peak-shaped voltammogram that adheres in every way to the conclusions reached in Section 10.5.1 about the general ac voltammetric response to a reversible system at a planar electrode. 

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