Chromatography

1. Chromatography

5. Why do we get the overlap with R=1.0?

6. Fraction of time in mobile phase

7. Capacity factor k'= tr - tm/tm = KVs/Vm A large capacity factor favours good separation - but would give long tr�s we want a compromise want k' in range 2-10 GC- change Temperature HPLC- change solvent polarity

8. Selectivity Factor

9. Selectivity Factor ? = Kb/Ka K(distribution constant)= cs/cm numerator is the most strongly retained species therefore ? is always greater than 1 If ? is close to 1, there will be little separation. Change mobile phase, T, stat. phase (column), use special effects eg gradient

10. N=Plate Count orNumber of Theoretical Plates N is affected by any parameter that affects separation and/or retention time depends on the particular analyte , the column(stationary phase type and thickness, size of support phase particles), flow-rate, T, injection method and any other operating parameter you can think of.

11. To increase efficiency-increase N Doubling L will double N Gain in separation ? ?L because of band broadening Inc L is not always practical = new column! Changing other parameters is preferable

12. Increase N by Decreasing packing size Better packing For many parameters there is an optimum value, which changes with the flow N = L/H Factors that decrease H will increase N

13. Column Efficiency Plate height is variance per unit length H = ?2/L ? in cm Ideally, H should approach 0. If a peak is fitted with a triangle, it contains 96% of area of the peak Base of peak = base of triangle = 4 ? from ? 2 ? either side of middle (Gaussian)

14. Column Efficiency (cont.) When we are looking at the peaks, the base width W and therefore the s.d.�s are in secs. Call s.d in seconds ? W = 4 ? ? = W/4 sec. Distance = flowrate x time ?(cm) = L/tr x w/4 = LW/4tr H = ?2/L = L2W2/16tr2 x 1/L = LW2/16tr2

15. H = LW2/16tr2

16. Calculating N Some programs give the peak width at half-height = W1/2 Then we need to use a modified formula N = 5.54(tR/W1/2)2

17. Resolution

18. Theories Plate theory � explains the separation but not the band broadening The rate or kinetic theory has replaced plate theory. However, the efficiency can still be calculated in the same way and is still called H or N as appropriate.

19. Van Deemter Equation H = A + B/u + Csu +Cmu u is flow rate Cs and Cm are mass transfer coefficients They are nothing to do with concentrations - as represented by small c (cs, cm)

20. H = A + B/u + Csu +Cmu H is Plate Height Also called height equivalent to a theoretical plate (HETP) The smaller the value of H, the better the efficiency of the separation (H=L/N) We can choose a flow rate such that H is minimized

21. Reduce band broadening (&H)by: smaller particle diameters for packing minimum thickness of liquid stat phase smaller diameter columns lower T�s if gas is mobile phase evenly packed columns Difficult for liquid to flow through columns packed with small particles Need High P.

22. Rate or Kinetic Theory Plate theory does not account for band broadening Rate theory assumes eqm is never reached Widths of peaks depend on rate at which mass transfer occurs between phases. Still use N and H - but don�t give them a physical meaning

23. H = A + B/u + Csu +Cmu A is the multipath term many different paths for molecules to follow down a column -take different times leads to band broadening also called eddy diffusion

24. A = 2?dp The smaller the packing, the smaller the differences in paths dp is packing diameter The more even the packing, the smaller the differences in paths ? - constant that depends on packing quality A is small in most modern columns

26. Longitudinal Diffusion Term B/uB/u = 2 ?DM/u Molecules in a band undergo diffusion. DM is the diffusion coefficient of the analyte in the mobile phase Diffusion is hindered by column packing. ? is the obstruction factor ? is about 0.6 for a packed column is about 1 for an unpacked column

28. B/u The longer the time on the column, the broader the band Therefore we want fast flow B is less important in liquid chromatography where diffusion is small Diffusion in the gas phase (GC) is much greater

29. Mass Transfer Equilibrium is never reached The faster the flow-rate, the less equilibrium is approached. Therefore here we want slow flow. At equilibrium, K = cs/cm Note little c�s cs/cm ? K at leading edge cs/cm ?K at trailing edge Depends in a complicated way on k'

31. Stat. Phase Mass Transfer term Csu Molecules must travel from the interior of the stat. Phase to the interface. Stat.phase may be liquid or solid Liquid: Cs ? df2 df = film thickness Thinner films allow faster equilibration Tradeoff : decreased loading Inversely proportional to Ds (diffusion coefficient in stationary phase)

32. df = film thickness = thickness of stationary phase DS = Diffusion coefficient of analyte in stationary phase A low rate of mass transfer increases plate height - some get �left behind�

33. Mobile Phase Mass Transfer term Cmu Inversely depends on diffusion coefficient of analyte in mobile phase pools of mobile phase become trapped in pores of the stationary phase reduce by using smaller particles

34. DM = Diffusion coefficient of analyte in mobile phase Increases with temperature dp = Diameter of packing particle In an open tubular column, dp is replaced by d, the column diameter

36. Ultra Performance Liquid Chromatography (UPLC) With particles less than 2.5 �m, there is a significant gain in efficiency, which is not lost as the flow rate is increased. Thus can do good separations in very short times. Special particles were developed for this application.

38. Particles contain silica for mechanical strength, with organic bridges which increase the usable pH range

39. Upgraded Instrumentation To make use of these columns � need better instrument components. Everything has to be able to operate at higher pressures. Need 15,000 psi for a 15 cm column