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.

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.