1. An Introduction to Chromatographic Separations
Lecture 36

2. Dividing both nominator and denominator by kB’:
R = (N1/2/4)(1 – kA’/kB’)/{(1+kB’)/kB’}
However, a = kB’/kA’
R = (N1/2/4)(1 – 1/a) (kB’)/(1+kB’)

3. Therefore, resolution can be viewed as a composite contribution of three terms:
a.       Efficiency term where R is proportional to N1/2
How to increase efficiency?
1. Increase column length as N = L/H

4. 2. Decrease H:
 a. In liquid chromatography
Resistance to mass transfer terms (K2 ds2 V/Ds and K3 dp2 V/DM) are most important in liquid chromatography and thus should be particularly minimized. This can be done by:
Decreasing particle size
Decreasing the thickness of stationary phase
Working at low flow rates
Increase DM by using mobile phases of low viscosities.

5.  a. In gas chromatography
Longitudinal diffusion term (k1DM/V) is the most important one in gas chromatography. Reducing this term involves:
Working at higher flow rates
Decreasing DM by using carrier gases of higher viscosities

6. b.      Retention term where R is proportional to k’/(1+k’) which suggests that the retention parameter should be optimized. A value for k’ in the range from 5-10 is preferred as smaller values (low retention) results in bad resolution while a very high k’ value means very long retention with exceedingly small improvements in resolution:

8. These data can be better viewed as a plot where as k’ was increased, almost a plateau was realized.

9. The overlap of two Gaussian peaks of equal area and amplitude, at various values of resolution (R) is presented below:
(1) R = 0.50                                   
Overlap of two peaks = 16%
(2) R = 1.00                         
Overlap of two peaks = 2.3% 
(3) R = 1.50
Overlap of two peaks = 0.1%
c.       Resolution is dependent on a selectivity term {(a – 1)/a)}. As the selectivity is increased, resolution increases as well. When a = 1, resolution is zero.

10. When a is close to unity, optimising k' and increasing N is not sufficient to give good separation in a reasonable time. In these cases, a is increased by one of the following procedures:
1.      Changing mobile phase composition
2.      Changing column temperature
3.      Changing composition of stationary phase
4.      Using special chemical effects (such as incorporating a species which complexes with one of the solutes into the stationary phase or use of surfactants)

11. Effect of Other Parameters on Resolution
a. The resolution of a column is proportional to the square root of its length since N = L/H.
 LA/LB = RA2/RB2
b. Retention time as related to resolution can be obtained by the following treatment:
N = L/H
tM = NH/u

12. tR,B = tM (1+kB’)
tR,B = (NH/u) (1+kB’)
N = 16R2{(1 + kB’)/kB’}2{a /(a - 1)}2
Substitution gives:
tR,B = (16R2H/u){(1 + kB’)3 /kB’2}{a /(a - 1)}2
Therefore, one can also write:
tR,A/tR,B = RA2/RB2

13. To obtain a high resolution, the three terms must be maximized
To obtain a high resolution, the three terms must be maximized. An increase in N, the number of theoretical plates can simply be done by lengthening the column. This leads to two opposing effects where resolution is increased but at the same time this causes an increase in retention time and thus increased band broadening. In addition, a longer column may not always be available. An alternative is to increase the number of plates, the height equivalent to a theoretical plate by adjusting elution variables (mobile phase composition), and other factors affecting selectivity.

14. Chromatographic Relationships

15. It is often found that by controlling the capacity factor, k', separations can be greatly improved. This can be achieved by changing the temperature (in Gas Chromatography) or the composition of the mobile phase (in Liquid Chromatography).

16. The General Elution Problem
Look at the chromatogram below in which six components are to be separated by an elution process:

18. Qualitative Analysis
Usually, the retention time of a solute is the qualitative indicator of a specific analyte. The retention time of an analyte is thus compared to that of a standard. If both have the same retention time, this may be a good indication that the identity of the analyte is most probably that of the standard. However, there can be important uncertainties since some different compounds have similar retention. In such cases, it is not wise to use the retention time as a guaranteed marker of the identity of compound, except in cases where the sample composition is known.