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Lecture 3: Efficiency, Selectivity, and Resolution in Chromatography

This lecture covers the anatomy of a peak in chromatography, including measures of resolution and chromatographic efficiency. It discusses different ways to estimate peak width and explains the equations involved in calculating resolution. The lecture also explores factors that affect resolution between peaks and provides strategies to improve resolution.

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Lecture 3: Efficiency, Selectivity, and Resolution in Chromatography

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  1. Lecture 3 Efficiency, selectivity and resolution

  2. The anatomy of a peak In chromatographic theory the peaks are usually assumed to have (perfect) gaussian shapes. Measures of resolution and chromatographic efficiency usually involve estimates of the chromatographic peak width Peak widths can be estimated in several ways

  3. μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ The anatomy of a peak A closer look at the normal distribution curve

  4. μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ The anatomy of a peak A closer look at the normal distribution curve If we draw a triangle where the sides are tangents of the inflection points they will cross the baseline at 4σ. Tangent of inflection point

  5. μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ The anatomy of a peak A closer look at the normal distribution curve If we draw a triangle where the sides are tangents of the inflection points they will cross the baseline at 4σ. Therefore, a peak width at baseline (wb) is usually defined as 4σ Tangent of inflection point Baseline width, wb = 4

  6. μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ The anatomy of a peak A closer look at the normal distribution curve However, it is difficult to measure peaks widths at baseline. The widths are therefore often measures at half the peak height (wh) where the width is 2.355σ, or at the inflection points (wi) where the width is 2σ. 2σ 2.355σ Tangent of inflection point Baseline width, wb = 4

  7. 1.000 0.882 0.607 0.500 0.324 0.134 0.044 μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ The anatomy of a peak σ 2σ Width at inflection point, wi = 2 2.355σ Fraction of peak height Width at half height, wh = 2.355 3σ 4σ Width at “baseline”, wb = 4 5σ Tangent of inflection point Baseline width, wb = 4

  8. 1.000 0.882 0.607 0.500 0.324 0.134 0.044 μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ The anatomy of a peak Equations involving peak width come in many variants, depending on where the width is measured. Always pay attention to whether the peak with is given as wb, wh, or wi (or something else). Where to measure may also be given as fractions or percents of the peak height (wh = w50% = w0.5) Use the following relationships to convert between equations: wi = wb• 0.5 wh = wb • 0.589 σ 2σ Width at inflection point, wi = 2 2.355σ Fraction of peak height Width at half height, wh = 2.355 3σ 4σ Width at “baseline”, wb = 4 5σ Tangent of inflection point Baseline width, wb = 4

  9. Chromatographic resolution

  10. Chromatographic resolution A chromatogram with two analytes, A and B B A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  11. Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds B A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  12. B A Poor resolution Detector signal 0 1 2 3 4 5 6 7 8 9 10 min Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds

  13. Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds B A Good resolution Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  14. Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds B Two factors affect resolution between peaks: 1) The distance between the peak maxima 2) The average peak width A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  15. (Eq 5) Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds B The resolution between two peaks, Rs is defined as: A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  16. tR(B) – tR(A) Rs = (wb(A) + wb(B)) 1 2 Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds B A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min wb wb is width at baseline and is defined as four times the standard deviation of the peaks

  17. 1 2 Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds B wh = 2.355σ (tR(B) – tR(A)) •0.589 Rs = A Detector signal (wh(A) + wh(B)) wh(B) wh(A) 0 1 2 3 4 5 6 7 8 9 10 min There are variants of the equations when the the peak widths are measured at half height

  18. Chromatographic resolution Resolution (separation) between A and B is of course neccessary for quantification of the compounds B wh = 2.355σ (tR(B) – tR(A)) •1.178 Rs = A Detector signal (wh(A) + wh(B)) wh(B) wh(A) Removed 1/2 0 1 2 3 4 5 6 7 8 9 10 min There are variants of the equations when the the peak widths are measured at half height

  19. B A Poor resolution Detector signal 0 1 2 3 4 5 6 7 8 9 10 min Chromatographic resolution If the resolution (Rs) is too poor there are two ways to improve it:

  20. 1 2 Chromatographic resolution If the resolution (Rs) is too poor there are two ways to improve it: Increase the distance between the peaks - Change in chromatographic selectivity B tR(B) – tR(A) Rs = A (wb(A) + wb(B)) Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  21. 1 2 Chromatographic resolution If the resolution (Rs) is too poor there are two ways to improve it: Reduce the peak widths - Increased chromatographic efficiency B tR(B) – tR(A) Rs = A (wb(A) + wb(B)) Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  22. Chromatographic selectivity

  23. Chromatographic selectivity Chromatographic selectivity or relative retention between two peaks can be described by the separation factor, α: α = kB / kA B A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  24. Chromatographic selectivity Chromatographic selectivity or relative retention between two peaks can be described by the separation factor, α: α = kB / kA Since k is directly proportional to t′R (adjusted retention time) α = t′R(B) / t′R(A) B A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  25. Chromatographic selectivity Chromatographic selectivity or relative retention between two peaks can be described by the separation factor, α: α = kB / kA Since k is directly proportional to t′R (adjusted retention time) α = t′R(B) / t′R(A) B Eq (6) A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  26. Chromatographic selectivity The unadjusted relative retention is calculated from the unadjusted retention times: γ = tR(B) / tR(A) Since γwill depend also on tM it is not a pure estimate of selectivity. γmay also be denoted αG. B Eq (7) A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  27. Chromatographic efficiency

  28. Eq (8) Chromatographic efficiency Chromatographic efficiency is traditionally given as the plate number, N, which is a measure of how narrow a peak is compared to its retention time B Note that increasing the retention time or decreasing peak width (keeping the other constant) will increase N Note that the unadjusted retention time is applied A Detector signal tR(A) 0 1 2 3 4 5 6 7 8 9 10 min wb

  29. Chromatographic efficiency Chromatographic efficiency is traditionally given as the plate number, N, which is a measure of how narrow a peak is compared to its retention time Note:N is only meaningful if chromatographic conditions are kept constant during the run (constant mobile phase composition and temperature) Eq (8) B Note that increasing the retention time or decreasing peak width (keeping the other constant) will increase N Note that the unadjusted retention time is applied A Detector signal tR(A) 0 1 2 3 4 5 6 7 8 9 10 min wb

  30. L L Eq (9) H = H = N N Chromatographic efficiency The plate height, H, is a measure of the chromatographic efficiency per meter column. H should be minimized to achieve optimal contitions. Eq (8) B A Detector signal tR(A) 0 1 2 3 4 5 6 7 8 9 10 min wb

  31. Chromatographic efficiency The effective plate number applies t′R instead of tR. Similarly, there is an effective plate height Heff = L / Neff Eq (10) B N and Neff are related by: k + 1 k N = Neff A Detector signal t′R(A) 0 1 2 3 4 5 6 7 8 9 10 min wb

  32. The Purnell equation

  33. The Purnell equation The three factors leading to chromatographic separation, efficiency, selectivity, and retention, are summarized in the Purnell equation Eq (11)

  34. The Purnell equation The three factors leading to chromatographic separation, efficiency, selectivity, and retention, are summarized in the Purnell equation Eq (11) Retention Selectivity Efficiency

  35. The Purnell equation The three factors leading to chromatographic separation, efficiency, selectivity, and retention, are summarized in the Purnell equation Eq (11) Retention Selectivity Efficiency If either of the terms is zero, resolution is zero

  36. The Purnell equation The three factors leading to chromatographic separation, efficiency, selectivity, and retention, are summarized in the Purnell equation Eq (11) Retention Selectivity Efficiency If either of the terms is zero, resolution is zero The equation may tell us where to put the effort if we need improved resolution. Example: If k is 2, you will get a 20% increase in resolution by doubling k, because the retention term increase from 0.667 to 0.800. If k is 10 you will only get a 5% increase in resolution by doubling k because the retention term increases from 0.91 to 0.95.

  37. The Purnell equation The three factors leading to chromatographic separation, efficiency, selectivity, and retention, are summarized in the Purnell equation Eq (11) Retention Selectivity Efficiency The resolution increases proportionally with N, and N increases proportionally with L. To double the resolution by increasing the column length (keeping all other factors constant) requires a column that is four times as long.

  38. The Purnell equation The three factors leading to chromatographic separation, efficiency, selectivity, and retention, are summarized in the Purnell equation Eq (11) Retention Selectivity Efficiency If you can solve a poor resolution by changing the selectivity it will usually be the best choice

  39. The Purnell equation The three factors leading to chromatographic separation, efficiency, selectivity, and retention, are summarized in the Purnell equation Eq (11) Retention Selectivity Efficiency You may see variants of the equation above, referred to as the Purnell equation or under other names

  40. The Purnell equation Resolution can also be expressed as function of the unadjusted relative retention, γ Eq (12) Selectivity & retention Efficiency γis a function of both retention and selectivity

  41. How to resolve peak overlaps • Rules of thumb: • If the compounds differ in type or number of functional groups: try to change selectivity • If the compounds are isomers or highly similar in properties: increase the efficiency • In complex chromatograms: increase the efficiency

  42. How to resolve peak overlaps • Rules of thumb: • If the compounds differ in type or number of functional groups: try to change selectivity • If the compounds are isomers or highly similar in properties: increase the efficiency • In complex chromatograms: increase the efficiency Difference in retention between different compounds

  43. How to resolve peak overlaps • Rules of thumb: • If the compounds differ in type or number of functional groups: try to change selectivity • If the compounds are isomers or highly similar in properties: increase the efficiency • In complex chromatograms: increase the efficiency The maximum number of peaks that (in theory) can be separated by a method

  44. How to resolve peak overlaps Increase efficiency (same functional groups) p-xylene m-xylene Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  45. How to resolve peak overlaps Increase efficiency (same functional groups) p-xylene m-xylene Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  46. How to resolve peak overlaps Change selectivity (different functional groups) p-cresole m-xylene Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  47. How to resolve peak overlaps Change selectivity (different functional groups) p-cresole m-xylene Detector signal 0 1 2 3 4 5 6 7 8 9 10 min

  48. Signal strength Retention time How to resolve peak overlaps Complex chromatograms: Changing selectivity will probably lead to new overlaps

  49. B A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min Selectivity How to change selectivity in LC Change mobile phase composition Change type of stationary phase

  50. B A Detector signal 0 1 2 3 4 5 6 7 8 9 10 min Selectivity How to change selectivity in GC Change mobile phase composition Change type of stationary phase A gas has no selectivity

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