Asymmetric peak models

There is peak overlap. In this case, it is necessary to decompose the peak by modelling using software. A least squares error minimisation procedure can be employed to adjust the positions, intensities and full width half maxima of the components and provides an indication of the quality of the model in relation to the actual shape of the peak. Various peak shapes are available for modelling purposes in particular the use of experimentally obtained shapes becomes extremely useful in the case of asymmetric peaks of transition metals (Fig. 5.7). 

Notably, concerning the overall peak shape, as with the equilibrium dispersive model (Section 6.2.4.1), the analytical solution of the transport dispersive model is always an asymmetric peak, and the asymmetry is enhanced by increasing Dax as well as decreasing keff (Lapidus and Amundson 1952). 

The retention time tRjin and the second moment for the Gaussian profile (Eq. 6.61) have been replaced by variables indexed with g . These parameters tg and og must be optimized by curve fitting. Equation 6.143 is only suitable for symmetric peaks. Analytical solutions of, for example, the transport dispersive model (which describes asymmetric band broadening only for a very low number of stages) are not suited to describing the asymmetry often encountered in practical chromatograms. Thus, many different, mostly empirical functions have been developed for peak modeling. A recent extensive review by Marco and Bombi (2001) lists over 90 of them. 

The agreement between the theoretical result and a Gaussian curve is fairly poor for Np = 25, especially for p-values close to 1 (where the plate model predicts quite asymmetrical peaks), but it is already quite good for Np = 1000. For columns with many thousands of theoretical plates, it is clearly justified to treat the resulting peaks as Gaussians, with the values of tr and [Pg.246]

In general, the a-process is well defined in the frequency domain and shows a relatively broad and asymmetric peak. Several functions such as the Cole-Cole and Cole-Davison in the frequency domain are able to describe broad symmetric and asymmetric peaks. The most general one is the model function of Havriliak and Negami (HN function) [41]. 

The diffusion coefficient of n-tetradecane on polystyrene in a fluid-viscous state calculated from free volume shows a sudden increase near Tg this behaviour was marked by its temperature dependence [219]. The introduction of diffusion coefficients into kinetic theory (which governs the shape of peaks [218]) yields very broad and asymmetric peaks above T,. This simplified model ignores adsorption and therefore fails to explain the behaviour of the retention volume at and below Tg. 

The S region consists of a rather broad and slightly asymmetric peak centered around 164 eV. It can be modeled by two components (each a doublet with an intensity ratio of 2 1). The S 2p3/2 and S 2pi/2 peaks at... 

The air stream velocity profile downstream of a bifurcation is asymmetrical. The peak velocity occurS near the inner wall of the daughter branches in the plane of the bifurcation (Olson, et al., 1973). We observed this skewed distribution and unsteady flow when the velocity was measured near the open end of recently bifurcated airways for this model cast (Sussman, et al., 1985). 

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