Two- and three-parameter equations for representation of retention data in reversed-phase liquid chromatography

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.