Band shape, asymmetric Gaussian

A band of solute broadens as it moves through a chromatography column. Ideally, an infinitely narrow band applied to the inlet of the column emerges with a Gaussian shape at the outlet (Figure 23-11). In less ideal circumstances, the band becomes asymmetric. 

The Franck-Condon factors of polarizable chromophores in Eq. [153] can be used to generate the complete vibrational/solvent optical envelopes according to Eqs. [132] and [134]. The solvent-induced line shapes as given by Eq. [153] are close to Gaussian functions in the vicinity of the band maximum and switch to a Lorentzian form on their wings. A finite parameter ai leads to asymmetric bands with differing absorption and emission widths. The functions in Eq. [153] can thus be used either for a band shape analysis of polarizable optical chromophores or as probe functions for a general band shape analysis of asymmetric optical lines. 

Fig. 6. Computer simulated excitation bands (n = — 2 to 2) by a Gaussian shaped PIP (Table 2), where the centre band (w = 0) is shifted to 10 kHz and the spectral width of each band is 4 kHz. The amplitudes of the profiles are asymmetric in response to the asymmetric effective RF fields.

The asymmetric shape of the absorption band of the hydrated electron at temperatures below the critical region is well fitted by Gaussian and Lorentzian functions on the low- and high-energy sides, respectively. ... 

If the peak of a test sample is not close to Gaussian shape, errors in the calculation may result. A column that gives an asymmetrical band sometimes has a high value of N in spite of peak tailing. To account for unrealistically high plate numbers for the asymmetrical band, the next equation has been proposed [ref. 10]... 

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