J. J. Van Deemter
Dr. J.J Van Deemter was one of the early pioneers of gas chromatography he studied at the University of Groningen wher he received his doctorate in 1945. In conjunction with A. Klinkenberg and F. J. Zuiderwg he described the first theory of dispersion in packed gas chromatography columns. He developed an equation that related the height of the theoretical plate (HETP or the variance per unit length of the column) to the linear mobile phase velocity and the various pertinent physical chemical properties of the solute and phase system. He showed that there was an optimum velocity that provide the minimum HETP and, thus, the maximum column efficiency. The validity of his equation was experimentally confirmed by A. I. M. Keulemans and A. Kwantes at the First International Symposium on Gas Chromatography held in London in 1956. His HETP equation has been found to be equally applicable to liquid chromatography packed columns and despite the introduction of a number of similar dispersion equations, the Van Deemter equation remains the most accurate form that described dispersion in both gas and liquid packed chromatography columns. The Van Deemter equation is used extensively in packed column design.
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Summary
system. However, for columns operated in the vicinity of the
optimum velocity (where the best performance is to be realized) the van Deemter
equation is simpler and give equally accurate and precise calculated data. In
GC columns, the compressibility of the mobile phase must be taken into account
and the exit mobile phase velocity (not the mean velocity) employed in the
dispersion function. In addition, the diffusivity of the solute must be taken
at atmospheric pressure. Only the Van Deemter equation, the Giddings equation
and the Knox equation fit experimental (H) versus (u) data accurately and only
the Van Deemter equation and the Giddings equation correctly account for other
physical properties of the chromatographic system. The Van Deemter equation
appears to be a special case of the Giddings equation, which simplifies to the
Van Deemter equation when the mobile phase velocity is close to, or around, the
optimum mobile phase velocity. The form of the Van Deemter equation
Dispersion Summary
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Alternative-Equations Huber
Van Deemter as the C term in the Van Deemter equation would now only
describe the resistance to mass transfer in the mobile phase contained in
the pores of the particles, and thus, would constitute an additional resistance to mass transfer in the stationary
(static mobile) phase. This concept has some indirect experimental
support in the development of the form of f1(k')
from experimental data which will be discussed later. The form of f1(k') is shown to be closer to the
original form given by Van Deemter for f2(k')
that is appropriate for the resistance to mass transfer in the stationary
phase. It is not known for certain, but it is possible and likely, that this
was the reason why Van Deemter et al. did not include a resistance to
mass transfer term for the mobile phase in their original form of the equation.
The Huber Equation
The next HETP
equation to be developed was that of Huber and Hulsman in 1967 (17). These
authors introduced a modified multipath term somewhat similar
Dispersion Alternative-Equations Huber
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Alternative-Equations Giddings
it was found that when
experimental data was fitted to the Van Deemter equation there was often very
poor agreement between theory and experiment (particularly for data measured at
high linear mobile phase velocities). In retrospect, this poor agreement
between theory and experiment appeared to be due largely to the presence of
experimental artifacts (such as those caused by extra column dispersion, large
detector sensor and detector electronic time constants etc.) than any
inadequacies of the Van Deemter equation. Nevertheless, it was the poor
agreement between theory and experiment at the time, that provoked a number of
workers in the field to develop alternative HETP equations. This work was
carried out in the hope that a more exact relationship between HETP and linear
mobile phase velocity could be obtained that would be compatible with
experimental data.
The Giddings Equation
In 1961,
Giddings (16) developed an HETP equation of which the Van Deemter equation was
shown to be
Dispersion Alternative-Equations Giddings
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Van-Deemter-Equation
The Van Deemter Equation
The Van Deemter
equation (9) was derived as long ago as 1956 and was the first rate equation to
be developed. There are, however, a number of alternative rate equations that
have been reported, but when subjected to experimental test, the Van Deemter
equation has been shown to be the most appropriate equation for the accurate
prediction of dispersion in chromatographic systems. The Van Deemter equation
is particularly pertinent at mobile phase velocities around the optimum
velocity (a concept that will shortly be explained). Consequently, as all
columns should be operated at, or close to, the optimum velocity for maximum
efficiency, the Van Deemter equation is particularly important in column
design.
Restating the
Van Deemter
Dispersion Van-Deemter-Equation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Experimental-Validation
Van Deemter equation extremely well.
J.Chromatogr.,270(1983)65.
Figure 25.
Graph of (C) Term against the Reciprocal of the Solute Diffusivity.
Katz et al.
(12) also examined the effect of particle diameter on the value of the overall
resistance to mass transfer constant (C). They employed columns packed with 3.2
m, 4.4 m,
7.8 m, and 17.5 m, and obtained HETP curves for the solute benzyl acetate in
4.3%w/w of ethyl acetate in n-heptane on each column. The data was curve
fitted to the Van Deemter equation and the values for the A, B and C terms for all
four columns calculated. According to the Van Deemter equation the (C) term
should be linearly related to the square of the particle diameter. A graph
relating the value of the (C) term with the square of the particle diameter is
shown in figure 26
Dispersion Experimental-Validation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Experimental-Validation
magnitude of the (A)
term and the effect of particle diameter on the mobile phase velocity at which
the Giddings equation simplifies to the Van Deemter equation. For very small
particles (e.g. 3 m) the Giddings
equation simplifies to the Van Deemter at a velocity of about 0.2 cm/sec but
for the larger particles (e.g., 10 m)
it occurs at about 1 cm/sec. However, at the optimum velocity, irrespective of
the particle diameter, the contribution from the coupling term is very small
and so the Van Deemter equation can be used with confidence in column design.
J.Chromatogr.,270(1983)62.
Figure
23. Graph of the (B) Term against Diffusivity
In summary,
the Data of Katz et al. shows some slight dependence of the (A) term on
Dm, (which can be explained on the basis of the calculations
given above). However, as a result of the curve fitting procedure to the
equation it is shown not to be dependent on
(u) and thus, supports the Van Deemter equation as opposed to
Dispersion Experimental-Validation