Peak separation function

Figure 4.30 Definition of the peak separation function P - f/g. (Reproduced with permission fron ref. 479. Copyright Elsevier Scientific Publishing Co.)...

For manual optimization methods the peak separation function, P, is easy to determine and can be calculated as shown in Figure 4.30 (479). The chromatographic response function for the chromatogram is then simply the sum of the In P values for the n adjacent peak pairs. 

Another criterion suitable for evaluating the quality of separation of two peaks is the so-called peak separation function, P, introduced by Kaiser 111 (see Fig. 1.2). This... 

Once a suitable HPLC separation mode has been selected, the experimental conditions should be adjusted to suit the objective of the separation. To proceed in this way, either empirical or systematic (statistical or predictive) HPLC method development strategies can be used. Any method development necessitates a convenient measure of the quality of separation. The separation of two sample compounds is most often measured either by resolution or by peak separation function (see Section 1.1.2). The resolution is an especially useful criterion of separation as its definition Eq. (1.3) can be transformed to another expression relating directly to the experimental conditions of separation v/A k... 

The P criterion is quite robust but difficult to calculate automatically and its performance begins to decline for P < 0.75, aeOcing it less satisfactory for difficult separations. A major disadvantage of the P criterion is that separations can give rise to equal values for the separation function as peak order changes or as resolution between different peedc pairs change. In addition there is no consideration given to the importance of the separation time. 

Rather than the separation function, resolution between individual peak pairs is used in most automated optimization procedures because it is easier to calculate, although non-Gaussian pe2dcs and overlapping peaks can present problems due to the difficulty of estimating peak widths. A simple objective function would be to consider only the separation between the worst separated peak pair, ignoring all others. If a set of... 

It means that, for reversible one-electron processes, the peak-to-peak separation assumes different values as a function of the temperature namely ... 

In it the peak-to-peak separation, AEP, is plotted as a function of the above discussed parameter . Thus, if one knows the number of electrons, n, exchanged per molecule of Ox, measuring the peak-to-peak separation (preferably at different scan rates) the corresponding value of is obtained. Then, from the previous relationship ... 

The fact that either the peak-to-peak separation, AEp, somewhat departs from the value of 59 mV or the current function ipJvl/2 is not rigorously constant seems to contrast with the diagnostic criteria (illustrated in Chapter 2, Section 1.1.1) for an electrochemically reversible one-electron process. This can be largely attributed to the non-compensated resistance given by the dichloromethane solution, which is a low conducting solvent. 

The spatial uniformity of temperature in the cell is difficult to determine, and we are not aware of a careful study of this problem. In most experiments, it is the temperature of the electrode-solution interface or that of the diffusion layer that is relevant. A possible internal thermometer could be created by measuring a temperature-sensitive voltammetric function, for example, the peak separation in the cyclic voltammogram of a reversible reaction, which is 2.22RT/ F. The resolution is not likely to be outstanding, but such a technique would probably allow detection of serious differences between the thermocouple reading and the actual temperature of the electrode-solution interface. 

Figure 23.5 Plots of current function, ip/v1/2 ( ) and AEp (O), against v,/2 for oxidation of 0.5 mM Cp2Fe in CH2Cl2/0.1 M Bu4NPF6 at Pt disc of area 0.086 cm2, showing the effect of uncompensated resistance on the peak current and peak separation.

Example Determination of ks from AEp Measurements The ks value of a quasireversible system is conveniently determined by monitoring the peak separation of the CV wave as a function of sweep rate, using the results of calculations by Nicholson [12] that relate AEp to the dimensionless parameter vj/, through Equation 23.12 ... 

Mossbauer spectrometry is a powerful means for the elucidation of the state of iron in materials [44,138-142,145]. Figure 4.63 [44] shows the 57Fe Mossbauer spectra of the natural zeolite rocks, such as MP, C2, Cl, and C4 (see Table 4.1). In Table 4.12, the Mossbauer parameters calculated with the help of the numerical resolution of the spectra presented in Figure 4.63 are reported. That is, with the help of the recorded spectra, the accurate peak positions, integrated intensities, as well as the FWHM of each peak were calculated. This calculation was carried out by fitting the spectra with three quadrupole doublets one for site 1, another for site 2, and a last one for site 3 [44], The peaks were simulated with Gaussian functions and the fitting process for the numerical resolution of the spectra was carried was carried out with a peak separation and analysis software, developed for this purpose [44,145] based on a least square procedure [48],... 

For a quasi-reversible process, both charge transfer and mass transfer affect the current. The shape of the cyclic voltammogram is a function of k° It mi D (where a = nFv/RT). The peak separation between the anodic and cathodic peaks can give information about k°. 

A review appeared on the practice and theory of enantioselective CGC with optically active selectors, e.g. 3-(perfluorobutyryl)-(17 )-camphorate residues forming complexes on a functionalized polysiloxane stationary phase (e.g. Chirasil, 65) SEC operates at temperatures lower than those of CGC, thus allowing better resolution, especially of thermally unstable enantiomers (e.g. those based on restricted free rotation, as is the case of dimethyl l,l -binaphthyl-2,2 -dicarboxylate, 66 ). Various analytical problems were addressed, such as determination of enantiomeric excess, assignment of absolute configuration, the elusive separation of protio- and deuterio-substituted enantiomers and the semipreparative separation of enantiomers. The following chromatographic parameters are related to the chemical and thermodynamic properties enclosed in parentheses of the enantiomeric system (i) peak retention (chemoselectivity, —AG), (ii) peak separation... 

Figure 2.38. The appearance of the powder diffraction pattern a) - only Bragg peak positions (e.g. see Eq. 2.28) are represented by the vertical bars of equal length b) - in addition to peak positions, their intensities are indicated by using the bars with variable lengths (the higher the intensity, the longer the bar) c) - peak shapes have been introduced by convoluting individual intensities with appropriate peak shape functions, and a constant background has been indicated by the dash-double dotted line d) - the resultant powder diffraction pattern is the sum of all components shown separately in (c), i.e. discrete but partially overlapped peaks and continuous background.

In Eq. 2.61 a is a free variable, i.e. the asymmetry parameter, which is refined during profile fitting and z,- is the distance fi om the maximum of the symmetric peak to the corresponding point of the peak profile, i.e. z,-= 20yfc - 20 . This modification is applied separately to every individual Bragg peak, including Kaj and Ka2 components. Since Eq. 2.61 is a simple intensity multiplier, it may be easily incorporated into any of the peak shape functions considered above. Additionally, in the case of the Pearson-VII function, asymmetry may be treated differently. It works nearly identical to Eq. 2.61 and all variables have the same meaning as in this equation but the expression itself is different ... 

Yogeswaran et al., designed a new bimetallic nanoparticles (Au and Pt) modified electrodes for simultaneous determination of AA, EP and UA [169], First, a composite film comprising of functionalized multiwall carbon nanotubes and nafion was formed on the GC electrode. Then Au and Pt NPs were electrochemically deposited on to the composite film modified GC electrode. The voltammetric peaks of AA, EP and UA are well resolved with the peak separations of 222 mV and 131 mV respectively. Lu et al., demonstrated the determination of UA on GC electrode electrodeposited with AuNPs and DNA [170], Clean GC electrode was immersed into a AuNPs colloidal solution and a potential of +1.5 V is applied for 60 min for the deposition of AuNPs. Then the electrode was dipped into a DNA solution (0.1 mg/ml) and a potential of +1.5 V is applied for 30 min to electrodeposit DNA. Finally, DNA/AuNPs modified electrode excellently separates the voltammetric signals of UA, NEP and AA. Li et al., electrodeposited AuNPs on the GC electrode modified with the ultrathin overoxidized polypyrrole film [171], The modified determines the UA in the presence of EP and AA with a lowest detection limit of 1.2 x 10"8 M. 

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