ISSN:
0935-6304
Keywords:
Chromatography theory, GC and LC
;
Revised “stage” model of Said
;
Revised relaxation-time model of Giddings
;
Statistically independent partial differential contributions
;
Relation between HETP and true theoretical plate height ΔL
;
Chemistry
;
Analytical Chemistry and Spectroscopy
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
The mass balance changes of Said's so-called “stage” model, based on the movement of the mobile phase with mean velocity ū (=L/tm), are synchronized by introduction of the relaxation time of Giddings, tr=1/(km+ks) where km and ks are the general overall mass rate constants for sample transfer to and from the stationary phase, respectively. This makes the “stage” length equal to the true theoretical plate height, ΔL, related to the classical HETP contribution due to non-equilibrium, H(α), according to the “discontinuous-ΔL” relation \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm H}_{{\rm (\alpha)}} {\rm =}\frac{{{\rm L\sigma}^{\rm 2} _{{\rm (\alpha)}}}}{{\overline {\rm t} _{{\rm ms}}^{\rm 2}}}{\rm = \Delta L}\frac{{\overline {\rm k}}}{{{\rm 1 + k}}} $$\end{document} Here k= (tms - tm)/tm is the central moment-based capacity ratio, L the column length, and σ2(α) the second moment contribution from the non-equilibrium only. Correct application of the relaxation-time model to chromatography requires that the real sample concentration in the stationary phase at a given position and time, Cs,l,t, is in a continuous equilibrium with the real sample concentration in the mobile phase, Cm,l+ΔL/2,t at that time displaced down the column by a distance \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{{\rm \Delta L}}}{{\rm 2}}{\rm = t}_{\rm r} \overline {\rm u} {\rm =}\frac{{\rm L}}{{k_{\rm m} \overline {\rm t} _{\rm m}}}\frac{{\overline {\rm k}}}{{{\rm 1 +}\overline {\rm k}}} $$\end{document} This leads to the classical HETP contribution \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm H}_{{\rm (\alpha)}} {\rm =}\frac{{{\rm 2L}}}{{k_{\rm m} \overline {\rm t} _{\rm m}}}\frac{{\overline {\rm k}}}{{{\rm (1 +}\overline {\rm k})^2}} $$\end{document} obtained from various other continuous models, which implies that ΔL is a good estimation of the true theoretical plate height.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/jhrc.1240050307
Permalink
