Gaussian peak shape

Most GPC columns are provided with vendor estimates of the plate count of the column and a chromatogram of a series of test peaks. These plate count estimates are usually obtained using small molecule analytes that elute at the total permeation volume (Vp) of the column. The Gaussian peak shape model... 

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

The main advantages of CE are its ease of use, speed and efficiency, while disadvantages are matrix effects causing shifts in retention time and variations in peak area response, non-gaussian peak shapes for certain molecules which are difficult to integrate, and limited detector sensitivity. 

Fig. 2.14. Influence of the reverse activation energy on KER and thus, on peak shapes in metastable ion decompositions, suitable experimental setup as prerequisite. From left no or small reverse barrier causes Gaussian peak shape, whereas medium or yields flat-topped peaks and large For causes dish-shaped peaks.

With the advent of linear quadrupole analyzers the full width at half maximum (FWHM) definition of resolution became widespread especially among instruments manufacturers. It is also commonly used for time-of-flight and quadrupole ion trap mass analyzers. With Gaussian peak shapes, the ratio of / fwhm to Rio% is 1.8. The practical consequences of resolution for a pair of peaks at different m/z are illustrated below (Fig. 3.17). 

A chromatogram without noise and drift is composed of a number of approximately bell-shaped peaks, resolved and unresolved. It is obvious that the most realistic model of a single peak shape or even the complete chromatogram could be obtained by the solution of mass transport models, based on conservation laws. However, the often used plug flow with constant flow velocity and axial diffusion, resulting in real Gaussian peak shape, is hardly realistic. Even a slightly more complicated transport equation... 

Fig. 11. High-resolution 29Si MAS NMR spectra of synthetic zeolites Na-X and Na-Y at 79.80 MHz (58). Experimental spectra are given in the left-hand columns Si(nAl) signals are identified by the n above the peaks. Computer-simulated spectra based on Gaussian peak shapes and corresponding with each experimental spectrum are given in the right-hand columns. Individual deconvoluted peaks are drawn in dotted lines.

In order to apply these equations to a femtosecond pump-probe experiment, an additional assumption has to be made regarding the shape of the time resolved signal. We wish to account for the finite relaxation time of the transient polarisation and so the signal must be described by a double convolution of an exponential decay function with the pump and probe intensity envelope functions. We will assume a Gaussian peak shape so that the convolution may be calculated analytically. As we will see, the experimental results require two such contributions, and hence, the following function will be used to fit the experimental data... 

All samples were characterized by x-ray diffraction (XRD) and by 29Si and 27A1 MAS NMR. The unit cell parameters, framework Si/Al ratios and the numbers of framework Si and A1 atoms per unit cell calculated from deconvolution using Gaussian peak shapes are given in Table n. All samples were fully hydrated over saturated NH4CI for 24 hours prior to NMR experiments. 

As columns are overloaded for preparative work, peak shape often deviates from the Gaussian shape typical of analytical work. In preparative work, the peaks can assume a triangular shape because the adsorption isotherm is nonlinear. A typical isotherm is shown in Figure 6-37, where CM is the concentration of sample in the mobile phase and Cs is the concentration of sample in the stationary phase. At low concentration of sample (CM) there is a linear adsorption isotherm which results in Gaussian peak shapes. At a point when either the sample adsorption in the stationary phase or the sample solubility in the mobile phase becomes limited, the isotherm becomes nonlinear, assuming either a convex or a concave shape. Convex isotherms are the most common and result in peak tailing. Conversely, concave isotherms cause fronting of the peaks. 

As shown in Fig. 2-4, these parameters can be obtained directly from the chromatogram. A resolution of R = 2.0 (corresponding to an 8quantitative analysis, if the peaks exhibit a Gaussian peak shape. The two peaks are thus completely baseline resolved, since the peak width at the base is given by... 

Eq. (23) follows from the assumption of the IA that the peak centre corresponds to scattering from an atom with zero momentum, with conservation of momentum and kinetic energy. The width in t due to the uncertainty in for example Ei, is calculated as At-MEi = (dtut/dEi) AEi with similar expressions for the other resolution components in Lo, L and 0. All resolution components other than the energy resolution are assumed to have a Gaussian peak shape in t and their widths are therefore added in quadrature... 

Figure 17 Crosses show oh/od obtained by fitting simulated data with non-Gaussian peak shapes for H and D, with the standard fitting programs, which assume that the peak shapes are Gaussian. The circles show values of oh /on obtained by fitting experimental data.

Methods involving chromatographic separations prior to detection require optimization of the chromatographic conditions for best performance. A Gaussian peak shape (no tailing or fronting), resolution (baseline separation from nearby peaks) and reproducible retention time are necessary for identification of the analytes of interest (Goldberger et al., 1997). 

The distributions of Si(nAl) in Si-MASNMR spectra of Y(4.8) were obtained by computer simulation of each spectrum, based on Gaussian peak shapes. Table 1 summarizes the peak intensities of Y(4.8) and (Si/Al) ratios from NMR and chemical analysis, that denote (Si/Al)nmr and (Si/AT)ca respectively. The (Si/Al)nmr ratios are calculated from the following equation(ref. 6) ... 

Under ideal conditions, chromatographic peaks should have Gaussian peak shapes with perfect symmetry. In reality, most peaks are not perfectly symmetrical and can be either fronting or tailing (Figure 2.8). The asymmetry factor (As) is used to measure the degree of peak symmetry and is defined at peak width of 10% of peak height (W0.i). Note that Tf is used here instead of T, as in the USP, because T often stands for temperature. 

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