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Introduction and Theory of Chromatography

CU- Boulder CHEM 5181

Mass Spectrometry & Chromatography

Prof. Jose L. Jimenez

Reading: Braithwaite & Smith Chapters 1 & 2Last Updated: Nov. 2013

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Business Items

Next Tue: invited lecture from Lucas Smith, LECO HW due Tue (could extend some of it, but overlap with

1st LV HW) FCQs online + our own feedback form, response rate

counts towards class participation grade for everyone

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Chromatogram

Why is Chromatography So Successful?

Single-Step Thermogram

Much higher selectivity, by doing single step over and over

Ziemann et al.UC-Riverside(now CU-Boulder)

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Schematic of Column Chromatography

Sequence of events At t=0 we will open the gate and let the analyte into the column Analyte will be carried by mobile phase Analyte may partition to stationary phase Analyte will be detected by its absorption of light at the detector

Stationary Phase

Stationary Phase

MobilePhase

Detector

Data to Computer

Lase

r

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Schematic of Column Chromatography II

For simplicity, we will assume that the mobile phase moves in steps rather than continuously

If analyte had no affinity to the stationary phase, it would just follow the mobile phase Emerge at the detector after tM (mobile phase time)

Stationary Phase

Stationary Phase

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Schematic 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 tR

SP

MCCK s Distribution Ratio

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Mechanisms of Partitioning to the Stationary Phase

Stick to the surfaceDissolve into the bulk

Q: (A) Left is Absorption, Right is Adsorption(B) Left is Adsorption, Right is Absorption(C) I dont know

Fig. from McNair & Miller, Basic Gas Chromatography, Wiley, 1998

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Retention and Mobile Phase Time

Simplest chromatogram w/ 2 components Unretained peak (tM) Analyte peak (tR) Corrected retention time (tR)

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Chromatography Simulator

http://www.chem.uoa.gr/Applets/AppletChrom/Appl_Chrom2.html

Investigate- Effect of K- Effect of N- Effect of RR

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Using the Distribution Ratio: Single Step (Plate)

Mobile phase

Stationary Phase

Analyte A

Analyte B

Q: If each symbol represents a mol, given 10 cm2 of surface to which analytes adsorb, and 100 cm3of liquid in which analytes are dissolved, what are KA & KB? Large K has more affinity for stationary phase

Small K has more affinitiy for the mobile phase

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The first step in a separationX = 0 , t = 0

X = 1 , t = 1X = 0 , t = 1Pump

Q: does molecular-level kinetics matter?

Key concepts: Enriched in component which prefers mobile phase Not very good separation in 1-step (like thermogram). It is repetition that makes it great.

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Partitioning in Real Chromatography

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Factors Influencing Retention are those that influence distribution (equil.)

Stationary phase: type & properties Mobile phase: composition & properties Intermolecular forces between

Analyte & mobile phase Analyte & stationary phase

Temperature

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Intermolecular Forces I Based on electrostatic forces

Like-attracts like or oil and water (similar electrostatic properties)

Polar/polar & non-polar/non-polar Molecules with dissimilar properties are not

attracted Polar retention forces

Ionic interactions (IC) Hydrogen bonding (permanent dipoles) Dipole-Induced dipole

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Intermolecular Forces II (Dipole) Polar forces (cont.):

Energy of dipole-dipole interaction

Factor of 10 variation on permanent dipole moment Factor of 104 variation on interaction energies

As r6 => mainly at the surfaces

kTrSA

D 6

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A dipole moment, A: analyte, S: stationary phase

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Intermolecular Forces III (London) Londons Dispersion Forces

Most universal interaction between molecules Only one for non-polar species

Due to induced dipoles Relatively weak

Energy of interaction:

is the polarizability, I: ionization potential, A: analyte, S: stationary phase

)(23

6SA

SAPAL IIr

II

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Clicker QuestionA. The chemical nature of the mobile phase

affects distribution in gas-chromatography (GC) & liquid chromatography (LC)

B. The mobile phase affects distribution in GC but not LC

C. The mobile phase affects distribution in LC but not GC

D. The mobile phase affects doesnt affect distribution in either GC or LC

E. I dont know

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Separating Efficiency Peak WidthAssume Gaussian Peaks FWHM = wh = 2.36HWHM = 1.18

Base Width of Peak (wb) Width at intersection of

tangents at inflexion points (+/- ) and the baseline

wb = 4 95.5% of molecules are

within wb Assuming that the

Gaussian model holds!

Figure 2.3, Braithwaite & Smith

When in doubt, use NORMDIST in Excel or GAUSS in Igor

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Resolution in Chromatography Objective: accurate measurement

of individual peak areas (spectra) FWHMtRs *2

What is the resolution if this is a mass spectrum? If it is a chromatogram?

0

0.5

1

1.5

2

2.5

46 51 56

m/z OR t'R

Sign

al In

tens

ity (A

rbitr

ary

Uni

ts)

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Clicker Question

Analysis B is more desirable than AA. In MS & Chrom.B. In MS but not Chrom.C. In Chrom but not MSD. In neither MS nor ChromE. I need a coffee

0

0.05

0.1

0.15

0.2

0.25

100 110 120 130 140 150 160 170 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

100 110 120 130 140 150 160 170 180

A B

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Resolution vs Peak Integration

http://www.vias.org/simulations/simusoft_peakoverlap.html

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Can One Have Too Much Resolution?

5.12.1 sR

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What to do if you have too much resolution?

If you have too much resolution, you can Shorten the column Increase temperature (GC), flow rate=> Shorten the analysis

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Separating Efficiency Peak Asymmetry

Q: what can cause peak asymmetry?

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Separating 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 chromatography

h 10%at s abA

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, 1983

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Separating Efficiency Peak Width II Described by variance 2 (units: s2)

determined from Gaussian fit to peak Classical chromatography theory

Separation in N discrete steps (plates)

or

Also broadening increases as tR increases:

and in practice:

N12

N1

NtR

1 2

RtN

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Height Equivalent of a Plate

Height Equivalent to One Theoretical Plate (HETP)N

LH

Application: Calculate H and N for peak 18, assuming a 60 m column

A. H ~ 5 mB. H ~ 50 mC. H ~ 500 mD. H ~ 5 mmE. I dont know

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Concept of Peak Capacity ()

Fig. 4. Mobilitymass 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 mobilitymass trends for each class of molecule.

of IMS-MS for peptides ~ 2600 for LC-FTICR ~ 6 x 107

PeakIndividualan ofAreaor TimeSeparationfor Available Areaor Time

Peak 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)00566-4

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Diffusion: Ficks 1st Law

dydCDj AAA

When there is a gradient in concentration of a species that can diffuse in medium

jA: molecular flux of A (moles cm-2 s-1) CA: concentration of A (moles cm-3) DAB: diffusivity of A in B (cm2 s-1)

~ 0.1-0.01 cm2 s-1 in gases~10-5 cm2 s-1 in liquids

Concentration (y)

Y (position in SP)

SP

Concentration (y)

Y (position in SP)

SP

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Clicker Question When an analyte is diffusing in the

stationary phase, equilibrium will be reached faster

A. When DA is smallB. When DA is largeC. When SP thickness is largeD. A and CE. I dont know

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Mass Transfer Kinetics: Ficks Law

Stat. Phase

From Bird, Stewart & Lightfoot, Transport Phenomena, 2nd Ed. 2002

YD

SW A

ABAy 00

dydDj AABAy

Initially no substance A Pulse at the surface Transient concentration Steady state profile at long

times

WAy: mass flux of A A: mass fraction of A DAB: diffusivity of A in B S: surface area; : density

jAy: molecular mass flux of A

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Situation in Column Chromatography

Stat. Phase

t = 1

t = 2

Mass transfer takes time => separation + limit on resolution

t = 3

t = 4

t = 5

t = 6

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Diffusion: Ficks 2nd Law

Conservation of mass for diffusing species in control volume Per unit area

perpendicular to diffusion

Concentration (y)

y (position in SP)

SP

outinA jj

ttyC

),( 1

jin

joutC(y1,t)

ytyyCD

ytyCDy

ttyC AAA

),(),(),( 111

y1y1+y

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Diffusion: Ficks 2nd Law II

When things are changing in time:

Once CA is the same everywhere, we have reached equilibrium in the SP

Concentration (y)

y (position in SP)

SP

2

),(),(y

tyCDt

tyC AA

A

Q: can we estimate order-of-magnitude of time needed?

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Time Scale of Mass Transfer For transfer across SP

thickness Y Start with:

Order-of-magnitude analysis

Simplifying:

2

),(),(y

tyCDt

tyC AA

A

2YCDC AA

D

A

AD D

Y 2

Concentration (y)

y (position in SP)

SP

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Numerical Example of Mass Transfer Assume

Column diameter = 100 m Film thickness: Y = 1 m Diffusivity of analyte in stationary phase

DAB= 10-6 cm2 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?

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Band 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 model

Stationary Phase

Stationary Phase

Mobile Phase

Detector

Lase

r

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Schematic 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 tR

SP

MCCK s

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GC 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 dont know

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Effect 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, 4th Ed

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Van 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. Dont know

)(uf

Clicker 2. B term isA. more imp in GCB. More imp in HPLCC. Similar importanceD. I dont know

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Van 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 m, HPLC: 5-10 m

PdA ClickerA. A term as u B. A term as u C. A term D. Dont know

)(uf

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Van Deemter Model: C Terms I Accounts for finite time for mass transfer (equil. btwanalyte in stationary and mobile phase not instantaneous) Most important effect in GC & HPLC CS accounts for stationary phase mass transfer

df: stationary phase film thickness DS: diffusion coeff. of analyte in SP Thinner films reduce mass transfer time& broadening

But also reduce capacity of the column

s

fs D

dC

2

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Van Deemter Model: C Terms II CM accounts for mass transfer on themobile phase interface with the SP In packed columns:

dp is particle diameter In open columns

dc is column diameter

M

PM D

dC2

M

CM D

dC2

Clicker 1A. C term as u B. C term as u C. C term D. Dont know

)(uf

Clicker 2. CM term isA. More important in GCB. More important in HPLCC. Similar importanceD. I dont know

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Van Deemter Model of Band Broadening

Tries to explain previous experiment H: plate height u: average linear velocity

H: as small as possible (calculate Hmin?) Some terms decrease, other increase with u

There should be optimum u There are alternative models (see reading)

uCuCuBAH MS

MtLu

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Optimum Mobile Phase Velocity We want N highest, H lowest Do we want something else?

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Optimum Mobile Phase Velocity: GC & HPLC

Q: differences in A, B, C between Supercritical Fluid Chrom. & HPLC?