Difference equation model for isothermal gas chromatography expresses retention behavior of homologues of n-alkanes excluding the influence of holdup time

A difference equation (DE) model is developed using the methylene retention increment (Δtz) of n-alkanes to avoid the influence of gas holdup time (tM). The effects of the equation orders (1st–5th) on the accuracy of a curve fitting show that a linear equation (LE) is less satisfactory and it is not necessary to use a complicated cubic or higher order equation. The relationship between the logarithm of Δtz and the carbon number (z) of the n-alkanes under isothermal conditions closely follows the quadratic equation for C3–C30 n-alkanes at column temperatures of 24–260 °C. The first and second order forward differences of the expression (Δlog Δtz and Δ2log Δtz, respectively) are linear and constant, respectively, which validates the DE model. This DE model lays a necessary foundation for further developing a retention model to accurately describe the relationship between the adjusted retention time and z of n-alkanes.