Some days ago, I tried for the first time a chromatography machine. The data I collected are the following:

$$ \begin{array}{lrrr} \hline \text{Compound} & t_\mathrm{R}/\pu{min} & w/\pu{min} & N \\ \hline \text{Benzene} & 2.325 & 0.047 & 39153 \\ \text{Toluene} & 2.712 & 0.067 & 26214 \\ \text{Chlorobenzene} & 3.690 & 0.099 & 22228 \\ \textit{p}\text{-Chlorotoluene} & 4.332 & 0.106 & 26723 \\ \hline \end{array} $$

I know the relationship between retention time $t_\mathrm{R},$ peak width $w$ and theoretical plates $N.$

Known the different properties, boiling points, polarities, or shapes of the molecules involved, is there a way to predict which molecule will yield an higher number of theoretical plates?

Which characteristics of the molecules affect the different number of plates for each molecule?


The number of theoretical plates can be calculated as:

$\mathrm{N_t = \frac {H}{HETP}}$

$\mathrm{N_t =}$ number of theoretical plates
$\mathrm{H =}$ total height (or usually length) of the column [$\mathrm{m}$]
$\mathrm{HETP =}$ Height Equivalent to a Theoretical Plate [$\mathrm{m}$]

Where $\mathrm{HETP =}$ can be calculated from the Van Deemter equation:

$\mathrm{HETP = A + \frac {B}{u} + (C_s + C_m) * u}$

$\mathrm{A =}$ Eddy-diffusion parameter, related to channeling through a non-ideal packing [$\mathrm{m}$]
$\mathrm{B =}$ diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [$\mathrm{m^2 s^{−1}}$]
$\mathrm{C =}$ Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [$\mathrm{s}$]
$\mathrm{u =}$ Linear Velocity [$\mathrm{m s^{−1}}$]

So, the characteristics specific to the analyte molecule that determine the number of theoretical plates are B and, unfortunately from the standpoint of developing an ab initio model, C.

Various models have been developed, however. Below is a list of references to some articles of interest in this field.

[ 1 (abstract)]"The problem of plate modeling: Theoretical and computational results", Computer Methods in Applied Mechanics and Engineering, Volume 100, Issue 2, October 1992, Pages 249–273

[ 2 ]"Plate Models in Chromatography: Analysis and Implication for Scale Up", Chromatograpy,Springer-Verlag

[ 3 (abstract)]"Neural Network Modeling of Structured Packing Height Equivalent to a Theoretical Plate", Ind. Eng. Chem. Res., 2000, 39 (5), pp 1520–1525

  • $\begingroup$ I think it may be worth noting explicitly in this answer that the column chemistry is a primary determinant of it HETP and of N. GC usually uses nonpolar stationary phases such that vapor pressure is a primary determinant of these parameters. Would the same be true if an e.g. an aqueous stationary phase was used to analyze ammonia gas? $\endgroup$
    – Curt F.
    Dec 28 '20 at 17:10

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