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

Abstract

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.

Accuracy verification of surface energy components measured by inverse gas chromatography

“…(22), which is the same as that of Conder-Young [14], averages out ln K a CH 2 from the n-alkane line (lnt n vs. n). Ideally, if t rC6 , t rC7 , t rC8 , t rC9 and t rC10 are measured accurately, the standard deviation of the slope of Eq.…”

“…This is because the linear relationship between ln(t r − t 0 ) and n under isothermal conditions (Conder-Young concept) has been widely used (since the 1950s) to calculate t 0 [14]. t 0 was then used to calculate t n s, and ln K a CH 2 using Eqs.…”

A new accurate quadratic equation model for isothermal gas chromatography and its comparison with the linear model

“…The t MCH 4 and t MNe values were determined experimentally. The other data and statistical analysis were previously described [1]. …”

“…The difference equation (DE) model that expresses the relationship between methylene retention increment with z carbon number (Δ t z ) and the carbon number ( z ) of n -alkanes has been proposed by Wu et al [1]. $$\text{log}\Delta t_z=A{z}^2+Bz+C$$…”

“…It has been shown that the accuracy of curve fittings of LE was worse than that of the DE model that excludes t M [1]. In the present work, we compare the QE model [Eq.…”