Column Chromatography

To a reasonable approximation, the three contributions to resolution (efficiency, selectivity and time) can be treated independently and optimized separately. Resolution increases only as the square root of N, so although the influence of efficiency is the most predictable parameter in the resolution equation, it is also the most limited. In practice all separations have to be made in the range N = 103-106 (Table 1). For GC this full range is available, so that increasing the column length or, better, reducing the column internal diameter of an open-tubular column at a constant length (separation time is proportional to column length), is often an effective strategy. For LC only a modest number of theoretical plates can be obtained in a reasonable time. In this case the general approach is to use the maximum available value for N and optimize resolution by changing the other variables. SFC is an intermediate case in which the general strategy depends on whether the fluid is more gas-like or liquid-like.

Figure 15 Influence of the separation factor (a) and the retention factor (k) on the resolution of two closely eluting peaks in column chromatography. (Reproduced with permission from Poole CF and Poole SK (1991) Chromatography Today, p. 31, copyright © Elsevier Science B.V.)

Figure 15 Influence of the separation factor (a) and the retention factor (k) on the resolution of two closely eluting peaks in column chromatography. (Reproduced with permission from Poole CF and Poole SK (1991) Chromatography Today, p. 31, copyright © Elsevier Science B.V.)

The separation factor determines the ability of the chromatographic system to differentiate between the two components based on the difference in their thermodynamic interactions with the mobile and stationary phases. When a = 1 a separation is impossible but, as can be seen from Figure 15, only a small increase in a above unity is required to improve resolution considerably. At comparatively large values of a, resolution is little influenced by further changes; indeed, separations in which a > 2 are easy to achieve. Selectivity optimization is the general approach to improve resolution in LC, where a wide range of mobile and stationary phases are available to choose from and a wide range of different retention mechanisms can be employed. Empirical or statistically based experimental approaches to selectivity optimization are often used because of a lack of formal knowledge of exact retention mechanisms for computer-aided calculations. Although powerful, selectivity optimization in LC can be a time-consuming process. The ease of achieving a separation by selectivity optimization can be

Table 3 Factors affecting resolution in column chromatography

Value ofN needed for Value of N needed for RS= 1 at

RS= 1atk = 3for different differentk values fora = 1.05and values of a 1.10

Value ofN needed for Value of N needed for RS= 1 at

RS= 1atk = 3for different differentk values fora = 1.05and values of a 1.10

a

N

k

a " 1.05

a " 1.10

1.005

1 150 000

0.1

853 780

234 260

1.01

290 000

0.2

254 020

69 700

1.02

74 000

0.5

63 500

17 420

1.05

12 500

1.0

28 220

7 740

1.10

3 400

2.0

15 880

4 360

1.20

1 020

5.0

10160

2 790

1.50

260

10.0

8 540

2 340

2.00

110

20.0

7 780

2 130

illustrated by the data in Table 3, which indicate the number of theoretical plates required for a separation. These data can be compared to the data in Table 1, which indicates the number of theoretical plates available for different chromatographic systems. This is a clear indication of the need for selectivity optimization in LC and SFC, and the more relaxed constraints for GC.

Resolution will initially increase rapidly with retention, starting at k = 0, as shown in Figure 15. By the time k reaches a value around 5, further increases in retention result in only small changes in resolution. The optimum resolution range for most separations occurs for k between 2 and 10. Higher values of k result in long separation times with little concomitant improvement in resolution, but they may be necessary to provide sufficient separation space to contain all the peaks in the chromatogram.

The separation time is given by:

tR = (H/u) x 16R2 x [«/(a - 1)2] x (k2 # 1)3/k2) [5]

If the separation time (tR) is to be minimized, then the acceptable resolution should not be set too high (RS =1); the separation factor should be maximized for the most difficult pair to separate; the retention factor should be minimized (k = 1-5) for the most difficult pair to separate; and the column should be operated at the minimum value for the plate height corresponding to the optimum mobilephase velocity.

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