# liquid chromatography column - Scott R.P.W.

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Thus,

î i°5 1

8(1+k') 21 3y (1 + Ê‘Ã + Y

k'(a -1) ôÐ (l + 6k' + Hk'2)

where (>}) is the viscosity of the mobile phase,

(Dm) is the diffusivity of the solute in the mobile phase, (ô) is D'Arcy’s constant,

(P) is the column inlet pressure and (A. andy) are packing constants as previously defined.

As in the previous chapters on column design, the characteristics of many of the equations discussed in this chapter will be examined employing realistic chromatographic conditions and the typical conditions chosen for a preparative column are given in table 1.

The conversion factor used to change pounds per square inch to dynes per square centimeter was again taken as 68948 (3). it is seen that there are some changes from the data used for analytical packed columns. Due to the difficulty in packing preparative columns the packing factors will be larger and values of 0.65 and 0.80 are taken for (X) and (y) respectively as typical for preparative columns. The separation ratio values are also larger as in preparative chromatography there is more freedom to adjust the phase system to achieve a larger (a) value for the critical pair. Furthermore,

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columns of targe diameter must have very thick walls to withstand high pressures and often the limited mechanical strength of the column wall wili restrict the maximum inlet pressure that can be applied to the column. For this reason the applied pressure is considered to be about 500 p.s i.

Table 1

Typical Chromatographic Operating Conditions for a Preparative

Column

Separation Ratio (a, range 1.10-1.50) (Critical Pair) 1.20

Capacity Ratio (first eluted peak of the Critical Pair) 2.5

Capacity Ratio of the last eluted peak (k'2) 5.0

Viscosity of the mobile phase (h) 0.023 Poises

Diffusivity of Solute (Dm) 3.5X10-5 cm2/sec

Inlet Pressure (P), (range 1~6000p.s.i.) 500 p.s.i.

Multipath Packing Factor (X) 0.65

Longitidinal Diffusion Packing Factor (ó) 0 8

Fraction of Column Cross-Section Containing Mobile Phase (c) 0.65

Concentration of Solute in Sample Solution,"(ó) 5.0 %w/v

Sample Load 25g

Employing Equation (2) and the data given in table I, the optimum particle diameter was calculated for the preparative separation of a solute where the separation ratio of the critical pair ranged from 1.01 to 1.50 at inlet pressures of 1,10,100,1,000 and 10,000 p.s.i. The results obtained are shown in figure I

it is seen from figure 1 that the optimum particle diameter covers a large range including many, that in practice, would be extremely difficult to pack efficiently. In general, it is difficult to pack preparative columns with particles having diameters less than 5 micron and closely graded particles greater than 100 micron are not, at present, readily available As a consequence, there is a relatively narrow window of particle size, between

5 and 100 micron, that can be used in preparative LC. It is also seen that if the separation of the critical pair is greater than about 1.15 (which may often occur in practice) very low inlet pressures may have to be used in conjunction with particles having relatively large dimeters.

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Such limitations that are imposed on the preparative column design is inevitable. There will be practical limits to the column length, the analysis time and the column diameter. There will also be more subtle limitations,

Figure 1

Graph of Log. Optimum Particle Diameter against Separation Ratio

e

î

L

U

L.

to

Î

E

e

u

e

0.

d)

e

1.0

1.2 1.3 1.4 Separation Ratio

1.5

1.6

1 p.s.i.

10 p.s.i.

100 p.s.i. 1000 p.s.i. 10,000 p.s.i. MINIMUM MAXIMUM

such as the column aspect ratio i.e. the ratio of the column length to the column radius. It is obvious that a very large diameter column, a few centimeters in length, would also be difficult to pack.

The Column Length and Analysis Time

By using exactly the same procedures as those used in the design of packed columns the same equations can be derived for the column length and the analysis time. Namely,

'opt -2

4(1+k')

k'(a-D

2A.+

( I, ...........

^i+ui4 + i ii4 j

Y

3(1 + k')

,\2

^0.5'j

?X

ôÐ

i

0.5

(1 +6k +1 Ik'21

V' ÷

0.5

(3)

242

×Ï1Ï

= (uk2)

8(1 +Þ'

Kto-0

<pP

2Ë +

y( i+ 6K +11k*2)'

3(1+ k')

.\2

0.5

(4)

Where (k‘2) is the last eluted peak of the mixture and the other various symbols have the meanings previously ascribed to them.

Employing Equation (3) and the data given in table 1, the optimum column length was calculated for the preparative separation of a solute where the separation ratio of the critical pair ranged from 1.01 to 1.50, again at inlet pressures of 1,10,100,1,000 and 10,000 p.s.1. The results obtained are shown in figure 2

Figure 2

Graph of Optimum Column Length against Separation Ratio

1 p.s.i.

10 p.s.i.

100 p.s.i. 1000 p.s.i. Þ,000 p.s.i. MINIMUM MAXIMUM

Separation Ratio

It is seen from figure 2 that the optimum column length ranges from over 500 meters to a fraction of a millimeter. It is also obvious that there must be further limitations placed on the design of the column to ensure its practical use. A preparative column less than 5 cm in length would be very difficult to pack as would a preparative column that had a length greater

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