HETP Curve
The HETP curve is a graph relating the variance per unit length of a column to the linear velocity of the mobile phase. The variance per unit length of a column, for a specific solute, can be calculated as the ratio of the column length to the column efficiency. For an LC column the mobile phase velocity can be taken as the ratio of the column length to the retention time of an unretained solute of sufficient size so that it can not enter any pores of the support or stationary phase (e.g. a dispersion of silica smoke). The linear velocity in a GC column can be determined by dividing the column exit flow rate by the column cross-sectional area. However, in GC, the linear velocity calculated in this way must also be corrected for the compressibility of the gas. The relationship between the variance per unit length of the column and the linear mobile phase velocity is given by the HETP equation which takes the form of a hyperbolic function. This hyperbolic function may contain three or four individual expressions depending on whether it is for a packed column or for a capillary column. The HETP curve shows a minimum at a particular velocity, which is called the optimum velocity. It follows, that at the optimum mobile phase velocity, the column will provide a maximum number of theoretical plates.
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Van-Deemter-Equation
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The HETP curve
is the result of a curve fitting procedure to the experimental points shown.
The column was 25 cm long, 9 mm in diameter and packed with 8.5 micron (nominal
10 micron) Partisil silica gel. The mobile phase was a solution of 4.8%w/v
ethyl acetate in n-decane. The hyperbolic form of the curve is
confirmed, the minimum is clearly indicated and the fit of the points to the
curve is good. From the curve fitting procedure the values of the Van Deemter
constants could be determined and the separate contributions to the curve from
the multipath dispersion, longitudinal dispersion and the resistance to mass
transfer calculated and included in the figure.
It is seen
that the major contribution to dispersion at the optimum velocity (where the
value of (H) is a minimum) is the multipath effect. Only at much lower
velocities, does the longitudinal diffusion effect become significant.
Dispersion Van-Deemter-Equation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Van-Deemter-Equation
where, A=2ldp,
B=2gDm
and
Equation (33)
is a hyperbolic function which has a minimum value of (H) for a particular
value of (u). Thus, a maximum efficiency will obtained at a particular linear
mobile phase velocity.
An example of
an HETP curve obtained in practice showing this hyperbolic relationship is
given in figure 11.
Figure 11.
HETP Curve for Hexamethylbenzene
Dispersion Van-Deemter-Equation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Golay-Equation
;
(54)
Where, and
The form of
the HETP curve for a capillary column is the same as that for a packed column
and exhibits a minimum value for (H) at an optimum velocity.
Differentiating
equation (54) with respect to (u),
Thus,
when H = Hmin,
then,
and
thus, &
Dispersion Golay-Equation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Alternative-Equations Huber
The form of
the HETP curve that is produced by the Huber equation is shown in figure 15.
Figure
15.H versus U Curves for the Huber Equation
It is seen
that the composite curve obtained from the Huber equation is indeed similar to
that obtained from that of Van Deemter but the individual contributions to the
overall variance are different. The contributions from the resistance to mass
transfer in the mobile phase and longitudinal diffusion are common to both
equations. However, the (A
Dispersion Alternative-Equations Huber
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Compressibility-Effects-GC
Figure 9.
HETP Curves for the Same Column and Solute Using the Average Mobile Phase
Velocity and the Exit Velocity
The two curves
are clearly quite different and, if the results are to be fitted to the HETP
equation, only the data obtained using the exit velocity will give
meaningful values for the exclusive dispersion processes. This problem is
further emphasized in the graphs shown in figure 10. In figure 10, the
individual contributions from the different dispersion processes are obtained
by deconvoluting the HETP curve obtained using the average velocity
data
Dispersion Compressibility-Effects-GC
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Alternative-Equations Huber
takes place between
the particles. Huber's equation implies (but, in fact, was not explicitly
stated by the authors) that the mixing effect between the particles (that
reduces the magnitude of the resistance to mass transfer in the mobile phase)
does not commence until the mobile phase velocity approaches the optimum
velocity (as defined by the Van Deemter equation). Furthermore, it is not
complete until the mobile phase velocity is well above the optimum velocity.
Thus, the shape of the HETP/u curve will be a little different from that
predicted by the Van Deemter equation
Dispersion Alternative-Equations Huber