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Lecture 4 Band broadening

Lecture 4 Band broadening. Lecture 4 Band broadening. Factors leading to band broadening work against the chromatographic efficiency because they increase peaks widths. Detector signal. Why different peak widths?. Factors that lead to peak broadening in a chromatographic column:. 0. 1. 2.

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Lecture 4 Band broadening

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  1. Lecture 4 Band broadening

  2. Lecture 4 Band broadening Factors leading to band broadening work against the chromatographic efficiency because they increase peaks widths

  3. Detector signal Why different peak widths? Factors that lead to peak broadening in a chromatographic column: 0 1 2 3 4 5 6 7 8 9 10 min

  4. Detector signal Why different peak widths? Factors that lead to peak broadening in a chromatographic column: A) Column packing / system dead volumes 0 1 2 3 4 5 6 7 8 9 10 min

  5. Detector signal Why different peak widths? Factors that lead to peak broadening in a chromatographic column: A) Column packing / system dead volumes B) Longitudinal diffusion 0 1 2 3 4 5 6 7 8 9 10 min

  6. Detector signal Why different peak widths? Factors that lead to peak broadening in a chromatographic column: A) Column packing / system dead volumes B) Longitudinal diffusion C) Resistance to mass transfer 0 1 2 3 4 5 6 7 8 9 10 min

  7. Detector signal Why different peak widths? Factors that lead to peak broadening in a chromatographic column: A) Column packing / system dead volumes B) Longitudinal diffusion C) Resistance to mass transfer Which of the three that is most important depends on many things, but the the velocity of the mobile phase is among the the critical factors 0 1 2 3 4 5 6 7 8 9 10 min

  8. A) Column packing (multiple paths)

  9. A) Column packing (multiple paths) Liquid chromatography system Column packing consists of (spherical) particles

  10. A) Column packing (multiple paths) Molecule passing through the column Liquid chromatography system

  11. A) Column packing (multiple paths) Molecule passing through the column Liquid chromatography system Molecules follow different paths

  12. Molecules follow different paths A) Column packing (multiple paths) Different paths have different lengths

  13. Molecules follow different paths A) Column packing (multiple paths) Different paths have different lengths The “different paths effect” will affect all compounds equally, irrespective of their retention

  14. Molecules follow different paths A) Column packing (multiple paths) Different paths have different lengths The “different paths effect” will affect all compounds equally, irrespective of their retention The effect is also independent of the mobile phase velocity

  15. Molecules follow different paths A) Column packing (multiple paths) spread Constant mobile phase velocity

  16. B) Diffusion

  17. B) Diffusion If we have a band of molecules (e.g. a chromatographic peak) in solvent or gas phase it will gradually spead out because of diffusion

  18. B) Diffusion If we have a band of molecules (e.g. a chromatographic peak) in solvent or gas phase it will gradually spead out because of diffusion

  19. B) Diffusion If we have a band of molecules (e.g. a chromatographic peak) in solvent or gas phase it will gradually spead out because of diffusion

  20. B) Diffusion Diffusion takes time  The faster we can get the analyte through the column, the less will the peak be broadened by the diffusion

  21. B) Diffusion spread inverse relationship to mobile phase velocity mobile phase velocity

  22. C) Resistance to mass transfer

  23. Mobile phase C) Resistance to mass transfer

  24. Mobile phase C) Resistance to mass transfer Net transfer

  25. Mobile phase C) Resistance to mass transfer distribution in the mobile phase Mobile phase distribution in the stationary phase Stationary phase

  26. Mobile phase C) Resistance to mass transfer Increased mobile phase velocity increases contribution to spread by resistance to mass transfer distribution in the mobile phase Mobile phase distribution in the stationary phase Stationary phase

  27. Mobile phase C) Resistance to mass transfer Simplified: Once the molecules have entered one of the phases it is “difficult” to get out again Increased mobile phase velocity increases contribution to spread by resistance to mass transfer distribution in the mobile phase Mobile phase distribution in the stationary phase Stationary phase

  28. C) Resistance to mass transfer spread mobile phase velocity Increased mobile phase velocity increases contribution to spread by resistance to mass transfer distribution in the mobile phase Mobile phase distribution in the stationary phase Stationary phase

  29. The sum of effects There are three different effects with different dependence of the mobile phase velocity spread mobile phase velocity

  30. The sum of effects There are three different effects with different dependence of the mobile phase velocity spread The multiple paths effect (effect of column packing) is independent of the mobile phase velocity packing ++ mobile phase velocity

  31. The sum of effects There are three different effects with different dependence of the mobile phase velocity spread The diffusion effect is inversely proportional to the mobile phase velocity packing ++ diffusion mobile phase velocity

  32. The sum of effects spread The mass transfer effect is proportional to the mobile phase velocity resistance to mass transfer packing ++ diffusion mobile phase velocity

  33. The sum of effects Sum of effects spread Sum resistance to mass transfer packing ++ diffusion mobile phase velocity

  34. The sum of effects There exists an optimal mobile phase velocity where the spread of the peaks are minimized spread Optimal velocity Sum resistance to mass transfer packing ++ diffusion mobile phase velocity

  35. The van Deemter equation Eq (13) H Optimal velocity A + B/u + C∙u Plate height C∙u A B/u mobile phase velocity,u

  36. The van Deemter equation Eq (13) Knowing A, B and C may help you decide where to put the effort if you need higher efficiency H Optimal velocity A + B/u + C∙u Plate height C∙u A B/u mobile phase velocity,u

  37. The van Deemter equation Eq (13) The optimal mobile phase velocity is found where A + B/u + C∙u has a local minimum, meaning that the derivative is 0.  uopt = √B/C H Optimal velocity A + B/u + C∙u Plate height C∙u A B/u mobile phase velocity,u

  38. The van Deemter equation Eq (13) A: - “Multiple paths term” B/u: - “Longitudinal diffusion term” C•u: - “Mass transfer term” / - “Finite equilibration time” - Mass transfer kinetics of the analyte between mobile and stationary phase - C is often split in one factor for the stationary phase and one for the mobile phase: C = CS + CM

  39. The van Deemter equation Eq (13) A: - “Multiple paths term” B/u: - “Longitudinal diffusion term” C•u: - “Mass transfer term” / - “Finite equilibration time” - Mass transfer kinetics of the analyte between mobile and stationary phase - C is often split in one factor for the stationary phase and one for the mobile phase: C = CS + CM

  40. The van Deemter equation Eq (13) • C = CS + CM • CM is inversely proportional to the diffusion coefficient of the analyte in the mobile phase. • For packed columns CM is proportional to the square of the particle diameter of the coumn packing. • For open tubular columns CM is proportional to the square of the column diameter.

  41. The van Deemter equation Eq (13) • C = CS + CM • CM is inversely proportional to the diffusion coefficient of the analyte in the mobile phase. • For packed columns CM is proportional to the square of the particle diameter of the coumn packing. • For open tubular columns CM is proportional to the square of the column diameter. • CS is proportional to the square of the film thickness. • CS is inversely proportional to the diffusion coefficient. • In adsorption chromatography CS is proportional to the time required for a compound to be adsorbed or desorbed (first order rate constant).

  42. The van Deemter equation Eq (13) Solving the equation Knowing A, B and C may help you decide where to put the effort if you need higher efficiency Since the equation has three unknowns you will need at least three experiments to solve it, but in most cases you will need much more experiments to compensate for experimental error (peak width measurements are rarely very accurate).

  43. The van Deemter equation Eq (13) Solving the equation Knowing A, B and C may help you decide where to put the effort if you need higher efficiency Since the equation has three unknowns you will need at least three experiments to solve it, but in most cases you will need much more experiments to compensate for experimental error (peak width measurements are rarely very accurate). Moody, Journal of chemical Education 59 (1982) 290-291

  44. The van Deemter equation Eq (13) • Alternatives • The van Deemter equation is the simplest and most general equation that explains band broadening in chromatography. There exist expanded and alternative forms of the van Deemter eqation, as well as other equations explaining the same or similar relationships: • The Giddings equation • The Huber equation • The Knox equation • The Horvath equation Remember that all these are models of reality (they are not laws of Nature). Even though they may not fit reality 100% they are accurate enough to be of practical value and to explain the phenomena that occurs in chromatographic columns.

  45. H Optimal velocity A + B/u + C∙u Plate height C∙u A B/u mobile phase velocity,u Factors affecting H in packed columns (LC)

  46. Factors affecting H in packed columns (LC) A = 2λdp A  dp λ is a constant dependent on particle quality dp = particle diameter u = mobile phase velocity Smaller particles will give more similar paths, limiting peak broadening by the multiple path effect (The A-term)  Small particles are good

  47. Factors affecting H in packed columns (LC) Good Bad Smaller particles will give more similar paths, limiting peak broadening by the multiple path effect (The A-term)  Small particles are good Particles should also be uniform in size and shape

  48. f′(k) dp2 DM CM = u CM dp2 Factors affecting H in packed columns (LC) Smaller particles leads to more exchange between the phases and therefore reduce the CM-term: f′(k) is a function of k DM = Diffusion coefficient in mobile phase u = mobile phase velocity dp = particle diameter  Small particles are good

  49. f′(k) dp2 DM CM = u CM dp2 Factors affecting H in packed columns (LC) Smaller particles leads to more exchange between the phases and therefore reduce the CM-term: f′(k) is a function of k DM = Diffusion coefficient in mobile phase u = mobile phase velocity dp = particle diameter Why is the properties of the stationary phase affecting transfer in the mobile phase, CM ?

  50. f′(k) dp2 DM CM = u CM dp2 Factors affecting H in packed columns (LC) Smaller particles leads to faster equilibrium between the phases and therefore reduce the CM-term: f′(k) is a function of k DM = Diffusion coefficient in mobile phase u = mobile phase velocity dp = particle diameter Why is the properties of the stationary phase affecting transfer in the mobile phase, CM ? The void volumes of mobile phase between the particles are smaller with smaller particle diameter

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