An Introduction to Chromatographic Separations

1. An Introduction to Chromatographic Separations Lecture 35

2. W1/2

3. Rate Theory Band Broadening Apart from specific characteristics of solutes that cause differential migration, average migration rates for molecules of the same solute are not identical. Three main factors contribute to this behavior:

4. 1. Longitudinal Diffusion Molecules tend to diffuse in all directions because these are always present in a concentration zone as compared to the other parts of the column.  This contributes to H as follows: HL = K1DM/V Where, DM is the diffusion of solute in the mobile phase. This factor is not very important in liquid chromatography except at low flow rates.

5. This contributes to H as follows: HL = K1DM/V Where, DM is the diffusion of solute in the mobile phase. This factor is not very important in liquid chromatography except at low flow rates.

6. 2. Resistance to Mass Transfer Mass transfer through mobile and stationary phases contributes to this type of band broadening. a. Stationary Phase Mass Transfer This contribution can be simply attributed to the fact that not all molecules penetrate to the same extent into the stationary phase. Therefore, some molecules of the same solute tend to stay longer in the stationary phase than other molecules

7. Quantitatively, this behavior can be represented by the equation: Hs = K2 ds2V/Ds Where ds is the thickness of stationary phase and Ds is the diffusion coefficient of solute in the stationary phase.

8. b. Mobile Phase Mass Transfer Solute molecules which happen to pass through some stagnant mobile phase regions spend longer times before they can leave. Molecules which do not encounter such stagnant mobile phase regions move faster. Other solute molecules which are located close to column tubing surface will also move slower than others located at the center. Some solutes which encounter a channel through the packing material will move much faster than others.

9. HM = K3dp2V/DM Where dp is the particle size of the packing.

10. Green: Stagnant mobile phase • Red: Mobile phase filled pores

11. 3. Multiple Path Effects Multiple paths which can be followed by different molecules contribute to band broadening. Such effects can be represented by the equation: HE = K4 dp

12. The overall contributions to band broadening are then, Ht = HL + HS + HM + HE Where; Ht is the overall height equivalent to a theoretical plate resulting from the contributions of the different factors contributing to band broadening. Ht = k4dp + k1DM/V + K2 ds2V/Ds + K3 dp2V/DM Ht = A + B/V + CSV + CMV

13. H = A + B/V + CV It turned out that resistance to mass transfer terms (K2 ds2V/Ds and K3 dp2V/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.

14. On the other hand, the 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

15. Van - Deemter Equation From the abovementioned contributions to band broadening, the following equation was suggested to describe band broadening in liquid chromatography (LC) H = A + B/V + CV Where; A represents multiple path effects, B/V accounts for longitudinal diffusion, and CV accounts for resistance to mass transfer. The figure below shows a plot of H against the different factors in the equation

17. The optimum flow rate can be found by taking the first derivative of equation 23. H = A + B/V + CV dH /dV = O - B/V2 + C V is optimum when dH /dV = 0 , therefore, C = B/V2optimum Voptimum = {B/C}1/2 (24) This theoretically calculated velocity is always small and in practice almost twice as much as its value is used in order to save time.

18. Particle size and flow rate The relation of H and the flow rate of the mobile phase is highly dependent on particle size. H will become almost independent on flow rate at very small particle size. In this case, faster separations can be achieved, using higher flow rates, without affecting H, and thus band broadening. The figure below shows such an effect:

20. Resolution One of the basic and most important characteristic of a chromatographic separation is undoubtedly the resolution term. Resolution between two chromatographic peaks is a measure of how well these peaks are separated from each other, which is the essence of the separation process. Resolution of the two peaks in the figure below are different and one finds no trouble identifying that the lower chromatogram has the best resolution while the top one has the worst resolution:

21. Peak Resolution Poor resolution More separation Less band spread

22. Resolution can be defined from the following figure as:

23. R = DZ/(WA/2 + WB/2) = 2 DZ/(WA + WB) (18) R = 2(tR,B – tR,A)/(WA + WB) (19) For a separation where WA = WB = W, we can write: R = (tR,B – tR,A)/W However, we have the equation: N = 16 (tR/W)2, or for peak B we have: W = 4 tR,B /N1/2

24. R = (N1/2/4)(tR,B – tR,A)/tR,B We can now substitute for the retention time using the equation derived earlier: tR = tM (1+k’) Thus we have: R = (N1/2/4){(tM(1+kB’) - tM(1+kA’)) /tM(1+kB’)} Rearrangement gives: R = (N1/2/4)(kB’ – kA’)/(1+kB’)

25. 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’)