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Journal of Chromatographic Science, Vol. 39, October 2001
such materials could be either Teflon (or probably other polyflu-
orinated plastics), ceramic clay, epoxy, polyimide, or even
polyamide plastics, taking into account in the latter case that not
too high of a temperature must be applied in a short small-diam-
eter column. Depending on the mutual imbalance of the epoxy
resin and other ingredients in the starting liquid epoxy com-
pound, the final hardened epoxy plastic and consequently the
walls of channels must contain some quantity of unlinked sub-
stance that could serve as a liquid-phase coating. The plastics and
ceramics could probably be used for producing the “chromato-
graphic” gratings (Figure 4A) as either the base plates or thin
layers linked on glass or metallic plates (thus allowing for the
original “chromatographic” grooves to be ruled directly on the
plastic or ceramic surfaces).
It should also be noted that it would sometimes be expedient
to rule the grooves of different depths on the different sections of
one plate, perform there the different liquid-phase or adsorbing
coatings, or both. The separate outlet collectors and detectors
could be arranged on these plate sections, thus the multiposition
column would be realized. In regards to the inlet collectors, they
must be either separate collectors or a single common collector.
In the latter case, the sample will simultaneously be analyzed by
a few different columns and detectors. It would also be advanta-
geous to arrange these tiny elements (i.e., inlet, outlet, injector,
and detector) either on the backsides or in the bodies of the
matching or grating plates (or both).
where HETP is the height equivalent to a theoretical plate; dc is
the capillary diameter; df is the thickness of the liquid-phase
film; u is the average linear velocity of the carrier gas; Dg and Df
are the diffusivities of a sample substance in carrier gas and
liquid film, respectively; and k is the retention factor. For a con-
ventional capillary tube of approximately 200 µm and wider, the
third term on the right side of equation 1 is usually ignored
because its value is small when compared with the others, but for
the small-diameter capillaries this term must be taken into
account. Expressions (omitted here) for the optimal data on the
gas velocity (uo) at the column outlet (i.e., under the pressure of
p0 = 1 atm) and the optimal (HETPopt) were derived from equa-
tion 1 by the known algorithm (16–18). These data are presented
in Table I for different capillary diameters and lengths, and the
concrete values of diffusivities (Dg = 0.07 and Df = 0.00002
cm2/s), film thickness (df = 0.2 µm), and retention factor (k = 20)
were used in the calculations. The velocities obtained were used
to calculate the distributions of gas pressure P(x) and velocity
u(x) along the capillary:
64µ · p0 · uo · (L – x)
P(x) = po2 + —————————
Eq. 2
dc2
√
and
P0
u(x) = uo · ——
P(x)
Eq. 3
Estimations of resolution power and
operating pressure for a grating column
We used Golay’s equation for a round capillary even though
the grating columns contained channels of triangular, rectan-
gular, or trapezoid forms:
where x is the distance from the capillary inlet, L is the capillary
length, and µ is the dynamic viscosity of the carrier gas He. As
can be seen from Table I, the operating entry pressures were rel-
atively high, especially for the small-diameter channels. The
inequality of pressures along the capillary must have resulted in
an additional widening of chromatographic peaks owing to the
expandability of the carrier gas. In order to minimize the latter
effect, an increased pressure (e.g., approximately 10 atm) can be
maintained forcibly at the 5-cm × 5-µm capillary outlet, and in
this case the ratio between the new inlet (approximately 17 atm)
and outlet (10 atm) pressures would be much smaller than the
previous one (10.6:1, Table I). Therefore, the
2Dg
1 + 6k + 11k2
96·(1 + k)2
dc2
HETP = –––– + ––––––––––— · –––– · u
u
Dg
2
k
d2
ƒ
+ —— · ——–— · —— · u
Eq. 1
3
(1 + k)2
Dƒ
Table I. Optimal and Operating Characteristics of Grating Columns
influence of gas expandability would be slight.
Among other things, the small sizes of the
grating column and other parts of a hypothetical
Capillary diameter (µm) / length (cm)
miniaturized chromatograph could simplify
operating conditions at a higher gas pressure.
5/5
10/10
20/20
30/30
In regards to the HETPopt values calculated
either from equation 1 and the pressure and
velocity distributions (equations 2 and 3) or by
Optimal outlet gas velocity (m/s) and optimal height equivalent to a
theoretical plate for the capillary diameter (µm)
u
o / HETPopt
uo / HETPopt
2.56 1.1
uo / HETPopt
1.44 0.9
uo / HETPopt
0.99 0.9
equation 1 modified by Giddings (17), they were
approximately the same along the capillary
despite the inequality of gas velocities (Table I).
This was a result of the fact that the lower veloci-
ties near the capillary inlet were accompanied by
higher pressures and thus the lower diffusion
coefficients of a sample component in the carrier
gas. It is shown in Table I that the HETPopt was
approximately equal to the value of the capillary
diameter, thus the 5-cm × 5-µm capillary should
have approximately 7000 theoretical plates. As
3.77 1.5
Distributions of gas pressure (atm) and velocity (m/s) along the capillary
x (cm) P(x)
u(x)
0.36
0.42
0.56
1.08
3.77
x (cm) P(x)
u(x)
0.41
0.49
0.64
1.17
2.56
x (cm) P(x) u(x) x (cm) P(x) u(x)
0
1.5
3
4.5
5
10.6
8.9
6.7
3.5
1
0
3
6
6.2
5.2
4
0
3.4
2.9
2.3
1.4
1
0.42
0
2.4 0.41
2.1 0.48
1.7 0.58
1.2 0.81
6
0.5
9
12
18
20
0.63
1.00
1.44
18
27
30
9
10
2.2
1
1
0.99
448