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Su-Cheng Pai

Publications and source records attributed to Su-Cheng Pai.

6 recordsLinked to original sources
PubMed2006

Temporal shifting: a hidden key to the skewed peak puzzle.

The recorder-provided peak position for flow-type chemical instruments has been verified mathematically as being comprised of a "spatially-non-existent" shift, which is generated due to the relativity in accounting for the detection at a fixed point. This shift, denoted as Phi, can be approximated by Phi approximately 0.5micro(t)2, where micro(t) is the temporal expanding coefficient of the system given. For flow injection analysis, the shift is correlated to a longitudinal dispersion coefficient D and the flow speed u, i.e., Phi approximately D/u2. For linear chromatography, it is correlated to a dynamic partition ratio k'' and a scaling factor f of the column used, i.e., Phi approximately 0.5k''f. In combination, the temporal shift can be expressed as Phi approximately 0.5k''f+D(k''+1)2/u2. Although the shift may be small in scale, it provides a clue to decipher the basic parameters from a recorded peak. Under a linear isotherm, this parameter can be estimated readily from an experimental peak following a very simple procedure.

Algorithms↗
PubMed2006

Dispersion-convolution model for simulating peaks in a flow injection system.

A dispersion-convolution model is proposed for simulating peak shapes in a single-line flow injection system. It is based on the assumption that an injected sample plug is expanded due to a "bulk" dispersion mechanism along the length coordinate, and that after traveling over a distance or a period of time, the sample zone will develop into a Gaussian-like distribution. This spatial pattern is further transformed to a temporal coordinate by a convolution process, and finally a temporal peak image is generated. The feasibility of the proposed model has been examined by experiments with various coil lengths, sample sizes and pumping rates. An empirical dispersion coefficient (D*) can be estimated by using the observed peak position, height and area (tp*, h* and At*) from a recorder. An empirical temporal shift (Phi*) can be further approximated by Phi*=D*/u2, which becomes an important parameter in the restoration of experimental peaks. Also, the dispersion coefficient can be expressed as a second-order polynomial function of the pumping rate Q, for which D*(Q)=delta0+delta1Q+delta2Q2. The optimal dispersion occurs at a pumping rate of Qopt=sqrt[delta0/delta2]. This explains the interesting "Nike-swoosh" relationship between the peak height and pumping rate. The excellent coherence of theoretical and experimental peak shapes confirms that the temporal distortion effect is the dominating reason to explain the peak asymmetry in flow injection analysis.

Algorithms↗
PubMed2004

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.

Chromatography↗
PubMed2003

Parcel model for peak shapes in chromatography numerical verification of the temporal distortion effect to peak asymmetry.

The traditional plate concept has been reassessed and improved to a parcel matrix model, which can be used to imitate the chromatographic behavior of a hypothetic column on a computer worksheet. Under programmed conditions, various peak shapes (nearly Gaussian, and with prolonged or fronting tails) are generated. The peak tailing has been separated into two major fractions: spatial and temporal. The former fraction is caused by the retention nature of a column, whereas the latter is induced by the observer's relative position and the changing of the zone broadening rate. The temporal distortion effect can be identified qualitatively and quantitatively through a normalized peak-overlapping process. In general, a chromatographic peak may carry a prolonged (or normal type) tail under linear isotherms, while both prolonged and fronting tails will appear under non-linear conditions. The temporal distortion is proved to be significant, and may be regarded as the major cause of peak asymmetry in most cases. This is in contrast to the conclusions of many previous studies. The model is also eligible to simulate chromatographic peaks for various injection sizes.

Chromatography↗
PubMed2002

Evaluation of the temporal effect to the peak tailing in flow injection analysis.

The deformation of a flow injection analysis peak from a Gaussian shape has two components: spatial and temporal. The former is mainly attributed to the Poisseulie effect in the tubular flow, whereas the latter is related to the observing position (of a fixed detector) at which signal is measured. The combination of the two makes a skewed peak track on the recorder chart. Therefore, an observed peak may imply a substantial fraction of a "false" tail due to the effect of non-simultaneous detection. An expanding-Gaussian model is proposed to simulate the purely temporal effect, and the asymmetric factors were compared with that of the experimental peak shapes. In most cases the peak deformation occurring in flow injection analysis should be regarded as "temporal". The contribution of the spatial effects (Poisseulie profile and others) might not be as significant as it was thought previously.

Flow Injection Analysis↗