29Lecture C1 – Part 2:Introduction and Theory of ChromatographyCU- Boulder CHEM 5181Mass Spectrometry & ChromatographyProf. Jose L. JimenezFall 2007Reading: Braithwaite & Smith Chapters 1 & 230Review Clicker Question• In chromatographic separations…A. Equilibrium is always reached at every position along the columnB. The solubility of the analyte in the stationary phase is the most important parameterC. The kinetics of mass transfer play an important roleD. A and CE. I don’t know31Concept of Peak Capacity (φ)Fig. 4. Mobility–mass plot of a complex mixture containing multiple classes of ions. In this case peptide, DNA, and carbon cluster ions are observed. Lines are superimposed onto the plot to indicate the mobility–mass trends for each class of molecule. •φof IMS-MS for peptides ~ 2600•φfor LC-FTICR ~ 6 x 107PeakIndividualan ofAreaor TimeSeparationfor Available Areaor Time=φPeak capacity of ion mobility mass spectrometry: Separation of peptides in helium buffer gas. Brandon T. Ruotolo, Kent J. Gillig, Earle G. Stone and David H. Russell. Journal of Chromatography B 782, 1-2, 25, 2002, Pages 385-392. http://dx.doi.org/10.1016/S1570-0232(02)00566-432Separating Efficiency – Peak Width II• Described by variance σ2(units: s2)–σdetermined from Gaussian fit to peak (last lecture)• Classical chromatography theory– Separation in N discrete steps (“plates”)– or – Also broadening increases as tRincreases:– and in practice:N12ασN1 ασNtR1 ασ2 ⎟⎠⎞⎜⎝⎛=σRtN33Height Equivalent of a “Plate”• Height Equivalent to One Theoretical Plate (HETP)NLH =Application: Calculate H and N for peak 18, assuming a 60 m columnA. H ~ 5 μmB. H ~ 50 μmC. H ~ 500 μmD. H ~ 5 mmE. I don’t know34Separating Efficiency – Peak AsymmetryQ: what can cause peak asymmetry?35Separating Efficiency – Peak Asymmetry• Tailing: some part of the stationary phase binds analyte molecules more strongly• Fronting: some molecules move ahead (inject too much sample => saturate Stat. Phase)• Peak Asymmetry• 0.9 < As< 1.2 for acceptable chromatographyh 10%at sabA =Equations for Calculation of Chromatographic Figures of Merit for Ideal and Skewed Peaks, J.P. Foley and J.G. Dorsey, Anal. Chem., 55: 730-737, 198336Diffusion: Fick’s 1stLawdydCDjAAA−=• When there is a gradient in concentration of a species that can diffuse in medium• jA: molecular flux of A (moles cm-2s-1)• CA: concentration of A (moles cm-3)• DAB: diffusivity of A in B (cm2s-1)~ 0.1-0.01 cm2s-1in gases~10-5cm2s-1in liquidsConcentration (y)Y (position in SP)SPConcentration (y)Y (position in SP)SP37Mass Transfer Kinetics: Fick’s LawStat. Phase From Bird, Stewart & Lightfoot, Transport Phenomena, 2ndEd. 2002YDSWAABAy00−=ωρdydDjAABAyωρ−=• Initially no substance A• Pulse at the surface• Transient concentration• Steady state profile at long times– WAy: mass flux of A–ωA: mass fraction of A– DAB: diffusivity of A in B– S: surface area; ρ : density– jAy: molecular mass flux of A38Situation in Column ChromatographyStat. Phase t = 1t = 2Mass transfer takes time => separation + limit on resolutiont = 3t = 4t = 5t = 639Clicker Question• When an analyte is diffusing in the stationary phase, equilibrium will be reached faster A. When DAis smallB. When DAis largeC. When SP thickness is largeD. A and BE. A and C40Diffusion: Fick’s 2ndLaw• Conservation of mass for diffusing species in control volume– Per unit area perpendicular to diffusionConcentration (y)y (position in SP)SPoutinAjjttyC−=∂∂ ),(1jinjoutC(y1,t)ytyyCDytyCDyttyCAAA∂Δ+∂+∂∂−=Δ∂∂ ),(),(),(111y1y1+Δy41Diffusion: Fick’s 2ndLaw II• When things are changing in time:•Once CAis the same everywhere, we have reached equilibrium in the SPConcentration (y)y (position in SP)SP2),(),(ytyCDttyCAAA∂∂=∂∂Q: can we estimate order-of-magnitude of time needed?42Time Scale of Mass Transfer• For transfer across SP thickness Y• Start with:• “Order-of-magnitude analysis”• Simplifying:2),(),(ytyCDttyCAAA∂∂=∂∂2YCDCAADAΔ=ΔτADDY2=τConcentration (y)y (position in SP)SP43Numerical Example of Mass Transfer• Assume– Column diameter = 100 μm– Film thickness: Y = 1 μm– Diffusivity of analyte in stationary phaseDAB= 10-6cm2 s-1– Solubility of A in B is 1% of volume–MWA= 100 g mol-1• Questions– What is the time scale of mass transfer?– What should be the time scale of flow along 1 mm of the column?– What is the max. amount of analyte that can be in the stationary phase per 1 mm of column length?44Band Broadening Processes• Non-column broadening– Dispersion of analyte in• Dead volume of injector• Connection between injector & column• Connection between column & detector– Emphasis on minimizing dead volume (injectors, fittings…)• Column broadening: Van Demteer modelStationary PhaseStationary PhaseMobile PhaseDetectorLaser45Schematic of Column Chromatography III• If analyte has some affinity to the stationary phase, it will be retarded– Equilibrium– Kinetics• Molecular mass transfer: diffusion– Emerge at the detector after “retention time” tRSPMCCKs=46GC vs. HPLC ColumnsGC HPLC• Most GC columns do NOT have particles• Most HPLC columns do have particles• Why?A. Particles are needed to prevent liquid flow for being too fastB. Particles are needed in HPLC to shorten diffusion distance in MPC. Particles are not needed in GC because diffusion is very fastD. B & CE. I don’t know47Effect of Mobile Phase velocity on H• Experiment– Repeat the same separation, same column and mobile phase– Determine H vs. flow rate– Observe an optimum, H increases to both sides– Goethe: “there is nothing more practical than a good theory”Skoog & Leary, 4thEd48Van Deemter Model: “A Term” Broadening• ‘Eddy diffusion’ &unequal pathways• Molecules may travel unequal distances• Particles (if present) cause eddies & turbulence• A depends on size of stationary particles (want small) and their packing (want uniform) (or coating in TLC plate)– GC: 150 μm, HPLC: 5-10 μmPdAλ=ClickerA. A term ↑ as u ↑B. A term ↓ as u ↑C. A term D. Don’t know)(uf≠49Van Deemter Model: “B” Term• Longitudinal Diffusion• Basically molecular diff., as ifmobile phase was not moving Clicker 1A. B term ↑ as u ↑B. B term ↓ as u ↑C. B term D. Don’t know)(uf≠Clicker 2. B term isA. more imp in