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

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2X+

I 2W°5)

(l+6k'+1 Ik-2)

3(1 + k')2

Ôè

ôð

2\

\0.5

3Y(Uk)

(l+6k'+i ik'2) V' > i

+Y

05

(12)

Employing equation (12) the optimum column radius can be calculated that would be required to separate 25 g of solute for a range of separation ratios for the critical pair of 1.01 to 1.50. Curves were obtained relating optimum column radius to separation ratio for inlet pressures of 1,10,100,1000, and

10,000 p.s.i. respectively. The resulting curves are shown in figure A

Figure 4

Graph of Column Radius/Separation Ratio for a Load of 25 gram

1 p.s.i 10 p.s.i.

100 p.s.i. 1000 p.s.i. 1000 p.s.i. 10000 p.s.i. MAXIMUM

Separation Ratio

It is seen from figure A .that the optimum column radius ranges from a few millimeters to over 50 centimeters, it is also seen that, for a sample load of 25g, where the maximum the diameter of the column is restricted to about 30cm (c.a.l foot), the optimum radius can only be employed where the separation ratio of the critical pair Is 1.3 or less. Above 1.3, a longer column than optimum would have to be used in conjunction with the maximum column radius, and the excess resolution could then be discarded for an even larger sample load. There will of course also be an increase in separation time. It should also be pointed out that there will be another practical restriction to the column length and radius. The column radius should not be greater than the column length if the column is to be efficiently packed with the standard packing procedures available today. Employing normal packing procedures, short wide columns tend to leave a gap across between the top of the column packing and the flange cap. This results In poor sample distribution across the column, channelling in the top of the packing and a consequent loss of column efficiency and resolution.

The Optimum Flow-Rate

Having determined the optimum column radius, the optimum velocity being known then the optimum flow-rate volume is given by.

Gopt = ? ë r20pi Uopt ..............................................................................(13)

Substituting for (u0pt) from equation (9) in Chapter 12,

-,05

...................................... (14)

3Y(Uk')2

(i + 6k'+i Ik'2)

Substituting for (dp(0pt)) from equation (18) in Chapter 12 page 183 and for (ropt) from equation (12),

Qopt -

k(a-i)'

4(l+k)

91hyP

j]w (l+k'J

2\ +

/ I

y( 1 +6k' +1 ik'2) 3(1+k')2

05

2 ... (15)

It is seen that equation (15) is very similar to that for the optimum flow-rate for an analytical column except that (oe) is replaced by the expression (11 OM/to) as the extra column dispersion no longer controls the column radius.

Solvent Consumption

The solvent consumption (Vsoi)is equal to the product of the analysis time and the optimum flow rate,

Substituting for (Tmin) from equation (4) and for (Q0pt) from equation (15),

It is seen from equation (18) that the solvent consumption is directly proportional to the charge placed on the column and the capacity ratios of the first peak of the critical pair and the last eluted peak respectively. It is also seen that, as with the optimized analytical column, the diffusivity of the solute and the viscosity of the mobile phase play no part in controlling the solvent economy. It should be pointed out, however, that this is only true for a completely optimized column

Column Wall Thickness

Vsol = QoptTmin

(16)

VSol =

3(l + k')2

Simplifying,

Vso1 (ok'(a-l)

5824M(l + k'2)

(18)

It has become apparent that preparative columns will have significantly greater diameters than analytical columns in order to accommodate the greater sample loads. As a consequence, the wall thickness of the columns

249

will also be large in order to withstand the high pressures employed The relationship between wall thickness (th), column radius and inlet pressure for sate operation, is given by the following equation, which is an arbitrary relationship derived from experimental data (4),

tr, =-r^—ñ + c............................................... (13)

n 2(SE + PY)

Where (P) Is the inlet pressure in lb/sq.in,

(D0) is the exterior diameter of the tube in inches,

(C) is the sum of the allowances for corrosion and thread cutting and it is assumed that, for preparative columns, there is no corrosion and the connections are made to the pipe by flanges, as a consequence (C) is taken to be zero

(S) is the allowable stress and for Stainless Steel, TP 316 is taken to be 18750 lbs/sq.in. over the temperature range of 0-l00°C,(3) (E) is the longitudinal weld point factor and is taken for double welded butt joints as 0.85(3)

(Y) is the "metal coefficient" (4) which can be taken as 0 4

It should be noted that equation (13) is for a specific stainless steel and a particular type of tube. Before employing the equation to fabricate a column the original reference should be reviewed to ascertain the correct constants or function to employ Ãîã the type of steel and tube that Is intended for use.

Substituting the pertinent values for, (D0), (S), (E) and (Y) in equation (13) and simplifying, '

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