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liquid chromatography column - Scott R.P.W.

Scott R.P.W. liquid chromatography column - John Wiley & Sons, 2001. - 144 p.
Download (direct link): liquidchromatographycolumntheory2001.djvu
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On the basis of the irrational fits of the data to the Huber and Horvath equations, these equations will not be considered to satisfactorily describe the relationship between (H) and (u). According to Katz et a/ the same irrational behavior of the Huber and Horvath equation was observed if the data for hexamethyl benzene was also fitted to them.
It is seen that, although a good fit is obtained to the Giddings equation, the value of (E) is numerically equal to zero. Thus, the van Deemter equation can be considered to be a special case of the Giddings equation, where at the linear velocities employed (i.e those normally employed in practical LC) the constant (E) was zero. It might well be, however, that at mobile phase velocities outside the range studied, the Giddings equation might be more appropriate. To date, sufficiently precise data has not become available to test this possibility. In any event, the Van Deemter equation and the Knox equation are the two that must be further considered as they do describe the experimental data accurately.
To proceed further and determine which of the two equations are the most appropriate the explicit equations must be used.
The Van Deemter equation In explicit form is,
2yD,tw fl(k)do
H = 2*dp + -^(1+00 + + ~TT^U .................. (1)
and that of Knox,
u Dm Ds
/OV
V4/
where, (g) and (g ) are constants
and the other symbols the meanings previously ascribed to them.
Comparing equations (I) and (2) it is seen that there is a significant difference between them, in that, only the Van Deemter equations should provide an (A) term that is independent of both the linear mobile Dhase velocity and the solute diffusivity. The fit of the Van Deernter equation to the experimental data confirms the former condition and the plot of the (A) term against the solute diffusivity, data taken from tables (l) and (2) and shown in figure 2 confirms the latter.
Figure 2 Graph of (A) Term against Solute Diffusivity for Benzyl Acetate
2.500e-3
2.000e-3 < w
E
{5 I .S00e-3 h-
C 1.000e-3 a *>
5.000e-4 O.OOOe+O
Oe+O le-5 2e-5 3e-5 4e-5
Diffusivity
It is seen from figure 2 that the magnitude of the (A) term appears, within experimental error, independent of the diffusivity of the solute in the mobile phase. On close examination, however, there could be a slight residual dependance of the (A) ierm on diffusivity indicating , perhaps, that the velocity range over which the data was taken was not quite sufficiently high enough to ensure that the first term of the Giddings equation was reduced to a constant value resulting in the simple Van Deemter equation.
This can be examined further by considering the detailed expression for the first term of the Giddings equation.
The expanded expression for the first term in the Giddings equation (7) is as
it is seen that when the value of (u) is sufficiently large the right hand function in the denominator becomes negligible and the term simplifies to 2XdPi the same as the first term in the Van Deemter equation. However, if
(u) takes values, where the right hand side of the denominator was not quite zero, then the value of the (A) term would show a slight decrease with increasing values of Dm. This effect may well be substantiated by the slight slope of the straight line in figure 2.
Figure 3, which is the same plot of the value of the (A) term against solute diffusivity for hexamethylbenzene gives even stronger confirmation of this possibility.
Graph of (A) Term against Solute Diffusivity for Hexamethylbenzene
follows.
Figure 3
O.O015
=0.0012 - 9 607x R = 0.95
L.
0
H
E
0.0010-
<
0 0005-
0.0000
le -5 2e-5 3e-5
Diffusivity
143
Thus, although the Data of Katz et a! shows some slight dependence of the (A) term on Dm, by definition, and as a result of the curve fitting procedure
D
to the equation H = A + - +Cu it is shown not to be dependent on (u) and u
thus, supports the Van Deemter equation as opposed to the Knox equation. It does, however, also support the idea that the Van Deemter equation is a special case of the Giddings equation.
Further examination of equations (1) and (2) indicates that both the Knox equation and the Van Deemter equation predict a linear relationship between the value of the (B) term (the longitudinal diffusion term) and solute diffusivity. A plot of the (B) term against diffusivity for benzyl acetate and hexamethyl benzene is shown in figure 4.
Figure A
Graph of (B) Term against Diffusivity
Diffusivity
It is seen that the predicted linear relationship is indeed realized. However, it can be shown that the values for the (B) term from the Knox equation curve fit also give a linear relationship with solute diffusivity so the linear curves shown in figure 4 do not exclusively support the Van Deemter equation.
144
The stationary phase, for a silica gel column would consist almost entirely of that portion of the 'mobile phase' that is 'static' and trapped in the pores of the silica gel. As a consequence, in equation (1) it would appear reasonable to assume that,
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