1. Lecture 8 Van Deemter Equation!

2. Resolution Describes how well 2 compounds are separated Rs = 1 4 N 1/2 (  -1) k’ 1+k’ ( ) efficiency selectivity retention k’ = t R -t M tMtM 1 < k’ < 10

3. Resolution Describes how well 2 compounds are separated Rs = 1 4 N 1/2 (  -1) k’ 1+k’ ( ) N = L H Maximize N L H

4. L - length of column Cannot increase indefinitely Limited by: Long runs times Back pressure (LC) Resolution H - height equivalent of a theoretical plate Measure of Efficiency Always want to minimize H Getting the best performance from system H depends on: column parameters mobile phase flow rate Described by Van Deemter

5. Van Deemter Equation H B  ∞A + + C   is flow rate

6. Van Deemter Equation H  (flow rate) H B  ∞ A + + C  A C B H min

7. Van Deemter Equation A term ‘Multipath Effect’

8. Van Deemter Equation A term ‘Multipath Effect’ A ∞ C e d p Ce = particle shape dp = diameter of particle A term Entirely dependent on column Only important in LC

9. H  (flow rate) H ∞ A A Van Deemter Equation A term ‘Multipath Effect’

10. Van Deemter Equation B term ‘Longitudinal diffusion’

11. Van Deemter Equation B term ‘Longitudinal diffusion’ B D MP  ∞ D MP = diffusivity of mobile phase B term Inversely proportional to flow rate (fast) Only important in GC (  D MP of a gas) Typical LC flow rate 0.2-0.5 mL/min Typical GC flow rate 1-2 mL/min

12. H  (flow rate) H B  ∞ B Van Deemter Equation B term ‘Longitudinal diffusion’

13. Van Deemter Equation C term ‘Mass transfer’ d t = diameter of tube D MP = diffusivity of MP GC C dt2dt2 D MP ∞  d p = diameter of particles D MP = diffusivity of MP  = tortuosity LC C dp2dp2 ∞  D MP

14. Van Deemter Equation C term ‘Mass transfer’ GC C dt2dt2 D MP ∞  LC C dp2dp2 ∞  D MP

15. Van Deemter Equation C term ‘Mass transfer’ GC C dt2dt2 D MP ∞  LC C dp2dp2 ∞  D MP

16. Van Deemter Equation C term ‘Mass transfer’ GC C dt2dt2 D MP ∞  LC C dp2dp2 ∞  D MP

17. H  (flow rate) H ∞ CC C Van Deemter Equation C term ‘Mass transfer’

18. Van Deemter Equation GC H  (flow rate) H B  ∞ A + + C  A C B H min X

19. Van Deemter Equation GC H  (flow rate) H B  ∞ + C  C B H min

20. dt2dt2 D MP  Van Deemter Equation GC H  (flow rate) H D MP  ∞ + C B H min   

21. Van Deemter Equation GC Ideal Column (open tubular): Small internal diameter (d t ) Use length to increase N (N=L/H) Ideal Mobile Phase: High diffusivity to  C term and allow higher flow rates

22. Van Deemter Equation LC H  (flow rate) H B  ∞ A + + C  A C B H min X

23. Van Deemter Equation LC H  (flow rate) H ∞ A + CC A C

24. Van Deemter Equation LC H  (flow rate) H ∞ +  A C dp2dp2 D MP C e d p    

25. Van Deemter Equation LC Ideal Column (packed): Small particles (d p ) Uniform particles (Ce and  ) Cannot use length to increase N Ideal Mobile Phase: High diffusivity (D MP ) to  C term and allow higher flow rates

26. Dong, M. Today’s Chemist at Work. 2000, 9(2), 46-48. Van Deemter Equation LC H ∞ +  dp2dp2 D MP C e d p

27. Van Deemter Equation LC H ∞ +  dp2dp2 D MP C e d p Ascentis Express, Supelco, technical information