Journal of Chromatography A, 1139 (2007) 109–120 Dispersion-convolution model for simulating peaks in a flow injection system Su-Cheng Pai a,∗ , Yee-Hwong Lai a,b , Ling-Yun Chiao c , Tiing Yu d a Division of Marine Chemistry, Institute of Oceanography, National Taiwan University, Taipei, Taiwan b Chemical Laboratory, National Center of Ocean Research, Taipei, Taiwan c Division of Marine Geology and Geophysics, Institute of Oceanography, National Taiwan University, Taipei, Taiwan d Department of Applied Chemistry, National Chiao Tung University, Hsinchu, Taiwan Received 12 April 2006; received in revised form 28 October 2006; accepted 3 November 2006 Available online 20 November 2006 Abstract 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 (t ∗ p , h* and A ∗ t ) from a recorder. An empirical temporal shift (Φ*) can be further approximated by Φ*= D*/u 2 , 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)= δ 0 + δ 1 Q + δ 2 Q 2 . The optimal dispersion occurs at a pumping rate of Q opt = √ δ 0 /δ 2 . 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. © 2006 Elsevier B.V. All rights reserved. Keywords: Dispersion-convolution model; Flow injection analysis; Peak simulation 1. Introduction Flow injection analysis (FIA) was first introduced by Ruz- ick and Hansen in 1975 [1], and has been widely adopted as an efficient analytical tool in many scientific fields. Although the principle seems to be well understood, Kolev [2] has sug- gested that the theoretical foundation for generating a flow injection peak is still far from complete due to the complexity of mechanisms involved (dispersion, convection and other kinetic reasons). He concluded that, in general, the Uniform Dispersion Model (UDM) [3,4] and Random Walk Model (RWM) [5–7] are theoretically preferred. But, they require difficult mathematics and computations, and thus have limited utilization in a practi- ∗ Corresponding author at: Division of Marine Chemistry, Institute of Oceanography, National Taiwan University, P.O. Box 23-13, Taipei, Taiwan. Tel.: +886 2 23627358; fax: +886 2 23632912. E-mail address: scpai@ntu.edu.tw (S.-C. Pai). cal system. On the other hand, the Tanks-in-Series Model (TSM) [8,9] and Axially Dispersed Plug Flow Model (ADPFM) [10] have gained more popularity not only because of the lesser math- ematics involved, but also due to the fact that it is not necessary to know the exact flow pattern in a tubular system. Apart from those models, several mathematical approaches have also been proposed to construct a peak curve including the Exponentially-Modified Gaussian functions (EMG) [11,12] and the Polynomial-Modified Gaussian functions (PMG) [13–17]. Recently, a Temporally-Convoluted Gaussian equation (TCG) [18] has been developed which is not only the simplest, but also indicates that a very basic and long-ignored principle can be an important key to solve the ambiguous skewed peak problems. This equation involves only two basic principles: (1) that the expansion of the sample zone is proportional to the square root of distance or time travelled; and (2) that the concentration pro- file is gradually turned into a Gaussian-like distribution along the tubular channel. The difference between this approach and 0021-9673/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2006.11.011