Journal of Chromatography A, 1033 (2004) 29–41 Two- and three-parameter equations for representation of retention data in reversed-phase liquid chromatography A. Pappa-Louisi, P. Nikitas ∗ , P. Balkatzopoulou, C. Malliakas Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece Received 14 October 2003; received in revised form 9 January 2004; accepted 20 January 2004 Abstract Two-parameter equations that describe the dependence of ln k upon ϕ, where k is the retention factor and ϕ the volume fraction of the organic modifier in the mobile phase, are examined in what concerns the underlying approximations and their performance to fit experimental data obtained from reversed-phase liquid chromatography. Using 293 experimental systems, it was found that the performance of these equations to describe ln k versus ϕ data is rather low, since the percentage of the systems that can be described satisfactorily ranges from 40 to 60% depending on the fitting equation. This percentage may be raised to 75%, if the discreteness effect is properly taken into account. A further improvement to 90% of the systems studied can be achieved only by the use of three-parameter equations, which may arise by refinements of the rough approximations of the two-parameter equations. Although the refinements do not lead always to better equations, we developed a new three-parameter expression of ln k that works more satisfactorily, since it combines simplicity, linearity of its adjustable parameters and the highest applicability. © 2004 Elsevier B.V. All rights reserved. Keywords: Liquid chromatography; Retention models; Mathematical modelling 1. Introduction The problem of the accurate representation of retention time, t R , versus ϕ data, where ϕ is the volume fraction of the organic modifier in the mobile phase, is of high im- portance in liquid chromatography and in particular in de- signing proper optimisation techniques. In the conventional approach, the original t R versus ϕ data is transformed into ln k versus ϕ data, where k is the retention factor, and these data are modelled using various empirical or strict theoret- ical equations. The tendency is to use as simple equations as possible in order to avoid numerical difficulties and re- duce the number of experiments needed for an optimisation technique. In this trend, the two-parameter equation pro- posed by Johnson et al. [1,2] and based on the E T scale for mobile phase polarity is extensively used for modelling retention data especially for practical optimisation and pre- diction techniques [1–14]. Here, we examine first whether two-parameter equations can actually be used for an accept- ∗ Corresponding author. Tel.: +30-2310-997773; fax: +30-2310-997709. E-mail address: nikitas@chem.auth.gr (P. Nikitas). able prediction of retention times in different ϕ values and second, if they can be modified to increase their predictive capabilities. 2. Theoretical part 2.1. Two-parameter equations Retention in reversed-phase liquid chromatographic columns is ruled by the solute multiple interactions with both the stationary and the mobile phase constituents. De- spite the complex nature of these interactions that may lead to different retention mechanisms, a common observation is that retention increases with the increase in mobile phase polarity. This observation has led Dorsey and co-workers to suggest the following linear relationship between ln k and the polarity of the mobile phase expressed through the E N T solvatochromic parameter [1,2]: ln k = m + nE N T (1) where m and n are adjustable parameters characteristic of the solute properties. Note that initially the polarity of the 0021-9673/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2004.01.021