Temporally convoluted Gaussian equations for chromatographic peaks

Both spatial and temporal peaks that are produced by the discrete parcel model can be mathematically approximated by Gaussian functions, but the transformation from a spatial pattern to a temporal image requires a convolution treatment. A first-order convolution is given for temporal peaks under a linear isotherm, whereas a second-order convolution is proposed for those under non-linear isotherms. Numerical tests show that the peak shapes generated by the proposed temporally convoluted Gaussian equations (TCG) match perfectly with those obtained by the discrete parcel model. Although the full TCG equation may be quite complicated, it can be made easier by a recursion calculation technique, and a group of peak curves can be plotted simultaneously on computer worksheet. The results also suggest that the temporal distortion effect should be predominately considered, in addition to those known-to-exist spatial effects, for explaining the peak asymmetry.