Peak profile

Since the term (1 -i- k i)/k approaches unity for large /c -value, the number of plates is equal to one half the number of transfer units for a strongly retained component. For these conditions, when Np = N/2, Eq. (16-174) and Eq. (16-161) produce the same peak retention time, peak spreading, ana predict essentially the same peak profile. 

Solute Transferring From the Stationary Phase to the Mobile Phase at the Back of the Peak Profile... 

The sum expressed by equation (21) lends itself to a digital calculation and can be employed in an appropriate computer program to calculate actual peak profiles. In doing so, however, as (v) is measured in plate volumes and sample volumes are usually given in milliliters, they must be converted to plate volumes to be used with equation (21). To demonstrate the effect of a finite charge and the use of equation (21), the peak profiles resulting from a sample dispersed over the twenty-one consecutive plates of a column are shown in Figure 16. 

The sum expressed by equation (25) also lends itself to a digital solution and can be employed in an appropriate computer program to calculate actual peak profiles for different volumes of pure mobile phase that have been injected onto an equilibrated column. The values of (Xg) were calculated for a column having 500 theoretical plates and for sample volumes of 20, 50, 100 and 200 plate volumes, respectively. The curves relating solute concentration (Xe) to plate volumes of mobile phase passed through the column are shown in Figure 17. 

Figure 13. Peak Profiles from Detector Having Different Cell Volumes...

The area of a peak is the integration of the peak height (concentration) with respect to time (volume flow of mobile phase) and thus is proportional to the total mass of solute eluted. Measurement of peak area accommodates peak asymmetry and even peak tailing without compromising the simple relationship between peak area and mass. Consequently, peak area measurements give more accurate results under conditions where the chromatography is not perfect and the peak profiles not truly Gaussian or Poisson. 

The peak profile analysis techniques allow separating the intrinsic and extrinsic causes producing peak broadening and shift. Accurate peak profile analysis requires the instrumental broadening well characterized and, in general, significantly smaller than the one due to sample defects (size and strain). New high quality X-ray sources and... 

It is a known property of Fourier transforms that given a convolution product in the reciprocal space, it becomes a simple product of the Fourier transforms of each term in the real space. Then, as the peak broadening is due to the convolution of size and strains (and instrumental) effects, the Fourier transform A 1) of the peak profile I s) is [36] ... 

In this short summary of peak profile analysis, we only considered the broadening due to the dimension and the strain, and we have considered only the Fourier-cosines transform (i.e. the symmetric part of the peak) that is the most frequent case. 

So far no hypotheses are required concerning the true shape of the peak profile. Flowever, in order to avoid or reduce the difficulties related to the overlapping of the peaks, the experimental noise, the resolution of the data and the separation peak-background, the approach most frequently used fits by means of a least squared method the diffraction peaks using some suitable functions that allow the analytical Fourier transform, as, for example, Voigt or pseudo-Voigt functions (4) which are the more often used. 

This approach also allows an easy correction of the diffraction peaks from the instrumental broadening that can be obtained by fitting the peak profile of a standard... 

In this chapter, we are going to show that using the one- and the two-component multilayer adsorption isotherm models or the models taking into the account lateral interactions among the molecules in the monolayer (discussed in Section 2.1), the overload peak profiles presented in Section 2.4 can be qualitatively modeled. 

The exemplary peak profiles, simulated with use of Equation 2.20 for the linear, Langmuir, and the anti-Langmuir isotherms of adsorption are presented in Figure 2.21. 

It is clearly visible that longitudinal cross sections of the spots are very similar to the peak profiles shown in Figure 2.1, Figure 2.2, and Figure 2.3 and calculated with the equihbrium-dispersive model (Equation 2.21) ... 

The most spectacular peak profiles, which suggest self-associative interactions, were obtained for 5-phenyl-1-pentanol on the Whatman No. 1 and No. 3 chromatographic papers (see Figure 2.15 and Figure 2.16). Very similar band profiles can be obtained using the mass-transfer model (Eqnation 2.21), coupled with the Fowler-Guggenheim isotherm of adsorption (Equation 2.4), or with the multilayer isotherm (Equation 2.7). 

In Figure 2.22, the exemplary peak profiles calculated using the Fowler-Guggenheim isotherm are presented. These calculations were performed for the parameter values given in Table 2.1. 

As it can be seen from the subsequent plots, for the coefficient characterizing interaction energy X = 3, the theoretical peak profile is very similar to the experimental one. Additional calculations for X = 3 and the concentrations equal to 2, 1.5, 1, and 0.5 mol 1 resulted in the plots given in Figure 2.23. The obtained plots confirm our... 

Terms of the Models Used to Simulate Densitometric Peak Profiles... 

The experiments showing the influence of lateral interaction on coelution of the two species were discussed in Subsection 2.4.2. Figure 2.18 and Figure 2.19 give a comparison of single profiles of acid and ketone or of alcohol and ketone with those attained for the binary mixture. Very similar peak profiles can be obtained upon solving Equation 2.21 separately for the alcohol, acid, and ketone with isotherms (Equation 2.4 and Equation 2.7a), and for the binary mixture with the isotherms (Equation 2.9 and Equation 2.10). 

Nnmerical values of the model parameters assumed in Table 2.2, were chosen so as to obtain the best qualitative agreement between the shapes of the experimental and the theoretical peak profiles. 

As it is apparent from the results obtained, a relatively good qualitative agreement was obtained between the experimental peak profiles and the theoretieal profiles simulated for the aeid-ketone and for the aleohol-ketone eoelution experiments, thus eonfiiming the possibility of the lateral interaction between these species. 

Figure l.S Representative peak profiles for different interactions in coluaui chronatography. 

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