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Chapter 23

Analytical Separations

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What is Chromatography

• We have looked briefly at distillation and more fully at extraction. How does this apply to chromatography?

• Both separations were based on multiple equilibria.

• For Distillation this was a evaporation / condensation step. (in a vertical column)

• For extraction this was a solvent extraction step (in a piece of glassware).

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Chromatography

• Each step has enhanced purity of one of the compounds.

• To improve this equilibrium step in distillation we force interaction between the vapor and liquid. This is done a variety of ways but one common way is to place plates in the column to collect the liquid.

• This has become a key term in separations.• It now means a separation step.

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Chromatography

• Gas Chromatography based on volatility.

• Liquid Chromatography based on partitioning.

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History

• Pliny the Elder• Purification of water in antiquity.• Tswett Plant Physiologist - Russian 1906• Martin & Synge Nobel Prize• Craig • Van Deemter• Giddings

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History

• 1848 Way and Thompson: Recognized the phenomenon of ion exchange in solids.

• 1850-1900 Runge, Schoenbein, and Goeppelsroeder: Studied capillary analysis on paper.

• 1876 Lemberg: Illustrated the reversibility and stoichiometry of ion exchange in aluminum silicate minerals.

• 1892 Reed: First recorded column separation: tubes of kaolin used for separation of FeCI3 from CuSO4.

• 1903-1906 Tswett: Invented chromatography with use of pure solvent to develop the chromatogram; devised nomenclature; used mild adsorbents to resolve chloroplast pigments.

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History

• 1930-1932 Karrer, Kuhn, and Strain: Used activated lime, alumina and magnesia absorbents.

• 1935 Holmes and Adams: Synthesized synthetic organic ion exchange resins.

• 1938 Reichstein: Introduced the liquid or flowing chromatogram, thus extending application of chromatography to colorless substances.

• 1938 Izmailov and Schraiber: Discussed the use of a thin layer of unbound alumina spread on a glass plate.

• 1939 Brown: First use of circular paper chromatography.

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History

• 1940-1943 Tiselius: Devised frontal analysis and method of displacement development.

• 1941 Martin and Synge: Introduced column partition chromatography.

• 1944 Consden, Gordon, and Martin: First described paper partition chromatography.

• 1947-1950 Boyd, Tompkins, et al: Ion-exchange chromatography applied to various analytical problems.

• 1948 M. Lederer and Linstead: Applied paper chromatography to inorganic compounds.

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History

• 1951 Kirchner: Introduced thin-layer chromatography as it is practiced today.

• 1952 James and Martin: Developed gas chromatography.

• 1956 Sober and Peterson: Prepared first ion-exchange celluloses.

• 1956 Lathe and Ruthvan: Used natural and modified starch molecular sieves for molecular weight estimation.

• 1959 Porath and Flodin: Introduced cross-linked dextran for molecular sieving.

• 1964 J. C. Moore: Gel permeation chromatography developed as a practical method.

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Resources

• Journals– Journal of Chromatography– Journal of Chromatographic Science– Analytical Chemistry– Trade Journals

• LC-GC• American Laboratory• Today’s Chemist at Work• Other Free-bees

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What happens

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Terms

• Stationary Phase - The part of the system that does not move.

• Mobile phase – The part of system that moves• Elution – Eluent (in), eluate (out)• Packed column• Open tube column.

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Mechanisms

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The Chromatogram

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Terms of Chromatography

• Chromatogram - The instrumental output. A signal as a function of time (or volume)

• Retention Time - How long a compound stays in the column. (tr) or could be expressed in terms of

volume (Vr)

• Dead volume Vm or could be expressed as a time (tm)

– Volume to get through the system even without any interaction. A constant for a given column.

• Adjusted retention time tr’

– tr’ = tr - tm

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Terms

alpha Relative Retention or Relative volatility, I will also refer to this as a separations factor.

• = (tr2’ / tr1’)

• Capacity factor – measure of the amount of extra time a compound stays in the system beyond the tm. Will correlate with the equilibrium constant.– k’ = (tr – tm)/tm

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Retention time and partition coefficient

• Capacity factor can be restated as the ratio of the time a compound is in the stationary phase over the time the compound is in the mobile phase.

• This can be converted to moles. Thus the capacity factor is molesstat / molesmobile

• This allows us to write k’ the following way

• k’ = CsVs / CmVm

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Relationships

• Recall that K = Cs/Cm

• So k’ = K (Vs/Vm) = (tr – tm) / tm = tm’ / tm

• Relative Retention can also be expressed as = (tr2’/tr1’) = k2’/k1’ = K2/K1

• To convert between volume and time one just needs the flow rate as a conversion factor.

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Terms

• Flow rate uv (ml/min)

• Vr = tr * uv

• Some types of chromatography will use volume and others time. However time is preferred.

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Scale Up

• Chromatography is known mostly as an analytical procedure. Separation of micrograms of material. The object of the game is to separate and quantify.

• The system can be scaled up to separate at the gram scale.

• Develop an analytical scale separation and then scale it up.

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Scaling Rules (1)

• Keep column length the same.• Cross-sectional area of column proportional to mass on

column.

2

1

2

1

2

radius

radius

mass

mass

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Scaling Rules (2)

• Maintain constant linear flow rate. (This will mean that the volume flow rate will change.)

1

2

1

2

mass

mass

flowvolume

flowvolume

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The Peak

• Ideal chromatographic peaks are Gaussian in peak shape.

• This comes directly from the Craig Model.• We know certain facts about Gaussian peaks.

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Efficiency of Separation

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Resolution

• The more peaks we can resolve the better the separation.

• How do we quantify Resolution.

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Good Resolution

Chromatogram

0

0.5

1

1.5

2

2.5

0 200 400 600 800 1000 1200 1400

Time (seconds)

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Poor Resolution

Chromatogram

0

0.5

1

1.5

2

2.5

0 200 400 600 800 1000 1200 1400

Time (seconds)

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Factors for Resolution

• Two– The separation of the

peaks– The widths of the peaks

• Both separations are the same but the widths are wider for the bottom example.

Chromatogram

0

0.5

1

1.5

2

2.5

0 200 400 600 800 1000 1200 1400

Time (seconds)

Chromatogram

0

0.5

1

1.5

2

2.5

0 200 400 600 800 1000 1200 1400

Time (seconds)

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Resolution

• Resolution = tr / wave = 0.589tr/w1/2 ave

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Diffusion

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Diffusion

• A fundamental process. Leads to broadening of peaks in separation methods.

• Flux (mol/m2s) = J = -D(dc/dx)

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Diffusion

• Broadening of band by diffusion.

• c concentration (mol/m3)• t is time• x distance along column

• Standard deviation of the band will be

)4/(2

4Dtxe

Dt

mc

Dt2

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Plate Height

• Terms– Linear flow rate ux

– Distance peak has traveled along the column x

– Time on column then would be t = x / ux

• 2 = 2Dt = 2D(x/ ux) = (2D/ ux)*x = Hx

• 2D/ux is the plate height giving us

• H = 2 / x

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Plate Height is a Measure of Column Efficiency

• The longer a compound is in the column the wider the peak.

• Narrow peaks will allow us to resolve peaks coming out at nearly the same time.

• Different compounds passing through a column at different times might have different plate heights since they will generally have different diffusion coefficients.

• Plate theory calls for constant plate height since diffusion is ignored in this model.

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Typical Plate Heights

• GC ~0.1 to 1 mm• HPLC ~ 0.01 mm • CZE ~ 0.001 mm

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Plates

• N = L/H = Lx/2 = L2/2 = 16L2/w2

2

2

2

216

rr t

w

tN

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What if is difficult to measure the width of a baseline?

• We could potentially measure the width at half height and knowing it is a Gaussian peak derive the following.

22/1

2

55.5w

tN r

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Asymmetric Peaks

25.1/

)/(7.41 21.0

BA

wtN r

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Factors Affecting Resolution

• Resolution can also be expressed with the following equation.

'

'2

1

1

4 avek

kNR

LNR

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Band Spreading

• We have gone to a great deal of effort to separate our peaks. We can see that diffusion is working against us.

• We measure this spreading as the standard deviation squared (Variance). 2

• Variance comes from many sources but we can express it as a sum.

224

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22

21

2iobs

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Outside the Column

• Injector, detector, tubing and tubing junctions.

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22det

2 tectorinjection

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Van Deemter Equation• Tells us the contribution to H of three sources.

• Recall that we want a minimum number for H!

• A Multiple paths B Longitudinal diffusion C Equilibration time

• ux is the linear flow rate

xx

CB

AH

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Optimum Flow Rate

• You can see from the previous plot that that best flow rate for your system.

• Where the H value is minimum• How do we find this point.

• Run about 20 or more experiments at different flow rates, find H and then plot the resulting curve. Pick Hopt from this plot.

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Optimum Flow Rate

• Or ………• Make three injections, find the values of A, B

and C.• Find the minimum point.

• How?

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Optimum Flow Rate

• Take the derivative of the van Deempter equation.

• At the minimum point the derivative will be zero so:

Cu

B

d

dH

xux

C

Buopt

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A Term – multiple paths(eddy diffusion)

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Longitudinal Diffusion

x

mm u

DtD2

22

xx

mD u

B

u

D

LH

22

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Equilibrium Time(Mass Transport)

xMsxtransportmass uCCCuH

ss D

d

k

kC

2

2'

'

13

2

Mm D

r

k

kkC

2

2'

2''

124

1161

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Mass Transport Band Spreading

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Heat as a separations tool.

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Comparison of open tubular and packed columns.

• Open tube columns– Higher resolution– Shorter Analysis time– Increased sensitivity– Lower sample capacity

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Open Tubular Columns

• At a constant pressure• Flow rate is proportional to cross sectional area• Flow rate is inversely proportional to the column length

length

areaflow

For open tubular column this means that we can get

Increased linear flow rate and/or a longer columnDecreased Plate height, which means improved better resolution

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Comparison

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Asymmetric Bands