Van Deemter Equation

1. Van Deemter Equation

2. Column EfficiencyKinetic variables

3. Kinetic variables affecting column efficiency (H) • Mobile phase velocity - Higher mobile phase velocity, less time on column, less zone broadening - However, plate height H also changes with flow rate Fig. Effect of mobile-phase flow on plate height for GC.

4. Zone BroadeningFlow Rate of Mobile Phase Liquid chromatography Gas chromatography Note the differences in flowrate and plates height scales Why GC normalluy has high H, but also high overall efficiency?

5. Zone BroadeningKinetic Processes Van - Deemter Equation λ and γ are constants that depend on quality of the packing. B is coefficient of longitudinal diffusion. Cs and Cm are coefficients of mass transfer in stationary and mobile phase, respectively.

6. Zone BroadeningKinetic Processes Van - Deemter Equation

7. van Deemter Equation A: multipath term • Molecules move through different paths • Larger difference in path length for larger particles • At low flow rates, diffusion allows particles to switch between paths quickly and reduces variation in transit time Fig. Typical pathways of two molecules during elution

8. Zone BroadeningMultiple Pathways • Eddy Diffusion: band broadening process results from different path lengths passed by solutes. • Directly proportional to the diameters of packing • 2. Offset by ordinary diffusion • 3. Lower mobile-phase velocity, smaller eddy diffusion Stagnant pools of mobile phase retained in stationary phase.

9. Van Deemter Equation A term ‘Multipath Effect’

10. Van Deemter Equation A term ‘Multipath Effect’ Ce = particle shape dp = diameter of particle A Ce dp ∞ • A term • Entirely dependent on column • Only important in LC

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

12. Van Deemter Equation B term ‘Longitudinal diffusion’

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

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

15. Van Deemter Equation C term ‘Mass transfer’ dt2 dt = diameter of tube DMP = diffusivity of MP ∞ GC C m DMP dp2 dp = diameter of particles DMP = diffusivity of MP  = tortuosity ∞ LC C m DMP

16. Van Deemter Equation C term ‘Mass transfer’ dt2 ∞ GC C m DMP dp2 ∞ LC C m DMP

17. Van Deemter Equation C term ‘Mass transfer’ dt2 ∞ GC C m DMP dp2 ∞ LC C m DMP

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

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

20. B/: Longitudinal diffusion term • Diffusion from central zone to front and tail • Proportional to analyte diffusion coefficient • Inversely proportional to flow rate • high flow, less time for diffusion C: Mass transfer coefficients (CS and CM) • CS is rate for adsorption onto stationary phase • CM is rate for analyte to desorb from stationary phase • Effect proportional to flow rate – at high flow rates less time to approach equilibrium Fig. van Deemter plot

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

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

23. Van Deemter Equation GC   DMP dt2 ∞ + H m DMP   C H H min B (flow rate)

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

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

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

27. Van Deemter Equation LC    dp2  + Ce dp ∞ H  DMP  C H A (flow rate)

28. Van Deemter Equation LC • Ideal Column (packed): • Small particles (dp) • Uniform particles (Ce and ) • Cannot use length to increase N • Ideal Mobile Phase: • High diffusivity (DMP) to C term and allow higher flow rates

29. Van Deemter Equation LC dp2 + Ce dp ∞ H  DMP Dong, M. Today’s Chemist at Work. 2000, 9(2), 46-48.

30. Van Deemter Equation LC dp2 + Ce dp ∞ H  DMP Ascentis Express, Supelco, technical information

31. Optimization of Column Performance Column resolution:- • - u (linear flow rate): low flow rate favors increased resolution (van Deemter plot) • H (plate height) (or N number of plates): use smaller particles, lengthen column, reduce viscosity of mobile phase (diffusion) • -  (selectivity factor): vary temperature, composition of column/mobile phase • - kA (retention factor): vary temperature, composition of column/mobile phase Fig. Separation at three resolution values

32. ( ) k’ 1 1+k’ 4 efficiency selectivity retention Resolution Describes how well 2 compounds are separated Rs = N1/2 (-1) tR-tM 1 < k’ < 10 k’ = tM

33. ( ) k’ 1 1+k’ 4 Resolution Describes how well 2 compounds are separated Rs = N1/2 (-1) L Maximize N N = H L H

34. Resolution • L - length of column • Cannot increase indefinitely • Limited by: • Long runs times • Back pressure (LC) • 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

35. Chromatographic Definitions

36. Chromatographic Relationships

37. General elution problem: for multiple components, conditions rarely optimum for all components. Fig. The general elution problem in chromatography Change liquid mobile phase composition – gradient elution or solvent programming 2. Change temperature for gas chromatography – temperature programming