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Graph of Flow-Rate against Separation Ratio
î I p.s.i.
¦ 10 p.s.i
¦ 100 p.s.i.
<• 1000 p.s.i
1.00 1.02 104 1 C6 1.08 110 1.12 114
it is seen from figure 4 that the optimum flow rate is extremely small irrespective of the applied pressure. The maximum flow-rate for a column optimized to separate a critical pair having a separation ratio of 101, with an inlet pressure of I p.s.i, Is only about 0 5 microlitres per minute For a column optimized to separate a relatively simple mixture (a =1.07) with an inlet pressure of lOOOp.s.i., the optimum flow-rate would be only 0 00224 microlitres per minute and for simpler mixtures even smaller The small flow rates are a direct result of the very small optimum column rada that are necessary for open tubular columns if used in LC. Referring to eguatiori
(11) it is seen that the optimum radius is directly proportional to the square root of the diffusivity of the solute in the mobile phase It is because the diffusivity of a solute in a liquid is so small, in fact, four or five orders of magnitude less than in a gas, that causes in the optimum column radii, and consequently the optimum flow-rates, to also be so small For the same reasons, the optimum column radii and the optimum flow rates employed with open tubular columns in GC are several orders of magnitude greater than LC
Maximum Sample Volume and Maximum Extra Column Dispersion
In a packed column the HETP depends on the particle diameter ana is not related to the column radius As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extra column dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra column dispersion that the column can tolerate calculated Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation.
As already stated, the maximum extra column dispersion that can be tolerated, such that the resolution is not significantly reduced, will be equivalent to an increase of 10% of the column variance
Thus, oe2 = 0. loc2
where (np2'i is the variance of the extra column dispersion, and (ac2) is the variance of the peak eluted from the column
If the total extra column dispersion is shared equally Detween the sample volume and the detector,
os2 = 0 05oc2 od? = 0 05oc2
where (os2) is the extra column dispersion resulting from the sample volume
and (oo2) is the extra column variance resulting from dispersion in the detector
or os = 0.22oc f ?
and oo = 0 22oc (16-
Developing, the expression for the maximum permissible sample volume as in chapter (5),
Consider a volume (Vi), injected onto a column, forming a rectangular distribution at the front of the column. The variance of the final peak will be the sum of the variances of the sample volume, plus the normal variance of a peak for a small sample Now the variance of the rectangular distribution of sample volume at the beginning of the column is V,2/12 , and
where (vr) is the
the column variance (from the Plate Theory) is
retention volume of the solute. Assuming the peak variance is increased by 5% due to the sample volume, (Vi) will then be the maximum sample volume,
Substituting tne function for the retention volume for an open tube.
11 r opt1 oot
Substituting in equation (18) for (root) and ( lopt) from equations (I I) and (12) respectively and simplifying,
vr _16384(l+k2 )(l+kf 1+ 6k + 11k'2
k'4 (a - )4 3n [ P J V /
Substituting iri equation (17) for ( )L ) from equation (19.',
12616 (l + k2)(l + k')3 ^ ^a5
1 + 6k'+ 1 Ik2 E Î i
3n I p )
Furthermore, substituting for ( 4_ ) from equation (29) in equation (16)
3604 [Uk2j (Hkf l + 6k' »-llk'2 ftW yf
ê 4(o-'J4 Çë P
Maximum Sample Volume
The expression for the maximum permissible sample volume, given by equation (20), shows a strong dependence on the product of the solute diffusivity and the viscosity of the mobile phase It is also seen to vary as the inverse of the fourth power of (ot-i) so that for very difficult separations, where (a) is small, the sample volume will be a maximum
The curves in figure (5) snow the relationship between maximum sample volume and the separation ratio of the critical pair for a fully optimized column ana were obtained using equation (20) The curves give the first indication of the limitations of open tubular columns in LC and the reason why they have not achieved the popularity and success of the packed column
Graph of Log. Sample Volume against Separation Ratio
a 1 p.s i.
• 10 p s i
¦ 100 p.s.i.