Chapter 1 HPLC Theory

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Chapter 1HPLC Theory

Content

HistoryThe Chromatographic principleThe HPLC systemHPLC parameters & terms

V0, k, α, N & RThe Resolution equationStationary phase, physical propertiesUnderstanding the van Deemter curveColumn dimensions


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Definition of Chromatography

Analytical Science of Chemical SeparationsSeparate one compound from another at the molecular level in a liquid or gas stateCHROMATO = Color / GRAPHY = writing

First documented by the Russian Scientist Tswett, 1903-1906

Sample - Ground-up plant extract.Poured into a glass tube packed with calcium carbonate (column) - colored bands develop as the extract percolated down through the column.Compounds had separated.

Tswett´s Chromatographic System


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Principle of Chromatography

Mobile phase

Stationary phase

V

VV

VV

V

VV

V V

V

V

Elution

V

VV

V

V

V

XX

XX

XX

A

A

A

A

A

A

X

XX

X

X

X A

AA

A

A A

X

X

XX

XX

A

A

AA

A

A

Injection

Interaction

Type of Chromatography as a Function of Molecular Weight

Size Exclusion ChromatographyGel Permeation/Gel Filtration

Liquid ChromatographyIon Exchange

Liquid ChromatographyDistribution/Adsorption

Gas Chromatography

Molecular weight (MW)~50 ~500 ~10.000 ~2.000.000


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The Chromatographic System

Solvent

Pump

AutoSampler

HPLC Column

Detector

Waste

Data System

What is a Chromatogram?


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Terminology – Mobile Phase

The mobile phase is a liquid for HPLC.Total representative sample needs to be soluble in the liquid. Carrier of the sample, moving it through the stationary chromatographic packing material.

Terminology – Stationary Phase

The chromatographic packing material which is held in a fixed position within column hardware.Performs the chemical separation.

Also called the packing material, the chromatographic material, or the adsorbent.


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Stationary vs. Mobile Phases

The stationary phase and the mobile phase will have OPPOSITE properties to set up a competition for sample analytes.

Chromatographic Parameters

V = Retention volumeV0 = Void volumetr = Retention timek = Retention factor or capacity factorα = Selectivity or separation factorN = Plate countW = Peak widthR = Resolution


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Elution Volume and Peak Width

V0 = Elution volume of unretained compoundequals roughly one column volume

V1 = Elution volume of compound 1V2 = Elution volume of compound 2

W2= Peak width of compound 2 in terms of volume, measured where the tangent crosses the baseline

k = Retention FactorA Measure of Retention

TIME .5 1 2 5

V0

V1V2 V3

Describes how far the peak is from V0No dimension, independent of flow & column size

0.5k1 = 1-0.5 = 1

0.5k2 = 2-0.5 = 3

0.5k3 = 5-0.5 = 9

V0k1 =

V1-V0


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The Retention Factor, kk depends on the equilibrium of the analyte

between the stationary phase and the mobile phasek is an equilibrium constant

A(S)

A(M)

B(S)

B(M)

Mobile phase (M)

Stationary phase (S)

The Capacity Factor, k

The capacity factor depends on the polarity of themobile phase and column stationary phase.

The polarity of the mobile phase can be altered bychanging the percentage of organic in a mobile phase consisting of water and organic solvent.


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Changing k by Changing Mobile Phase Polarity

80 % MeOH

40 % MeOH

50 % MeOH

60 % MeOH 30 % MeOH

Column : Symmetry C18 4.6x50mmMobile phase : Methanol/phosphate bufferSample : Caffeine

AcetaminophenAspirinSalicylamide

α = SelectivityA Measure of Peak Separation

TIME .5 1 1.5 5

V0

V1V2 V3

Ratio between k-values for two adjacent peaksDefines the position of two peaks relative to each otherDepends on the “chemistry” of the system

1-0.5α1,2 = 1.5-0.5 = 2

1.5-0.5α2,3 = 5-0.5 = 4.5

α1,2 = V2-V0

k1α1,2 =

k2 or V1-V0


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α = SelectivityMobile Phase

40% Methanol60% Water

33% Acetonitrile67% Water

25% THF75% Water

Column : μBondapak C18

α depends on thechemistry of themobile phase,i.e.which organic solventis selected

R = ResolutionDegree of Magnitude of Separation


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R = ResolutionDegree of Magnitude of Separation

TIME .5 1 2 5

V0

V1V2 V3

R =V2 - V1

½(W1 + W2)

R1,2 =2 - 1

½(0.5 + 0.5)

R2,3 =5 - 2

½(0.5 + 1.0)

= 2

= 4

N = Theoretical PlatesA Measure of Efficiency


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Calculation of Column Efficiency5σ Method

7018.=RV

plates 8240

1.0318.7025N

2

5

=

⎥⎦⎤

⎢⎣⎡=

1.03W =

height4.4%

height4.4%

plates 3334

N5

=

⎥⎦⎤

⎢⎣⎡=σ

2

441631625

..

6316.=RV

1.44W =

Good Column Bad Column

Inje

ct

Inj e

ct

Efficiency Expressed as HETP

H = HETP (Height Equivalent to Theoretical Plate){Need H to be as Small as Possible so you can ‘fit” more “plates” into a column}

LNHETP =

N= # Plates

Plate

(From Distillation Theory) 5 Plates 10 Plates(Larger H) (Smaller H)

L columnlength


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Resolution Equation

Selectivity

Efficiency

Capacity

R = 1/4 α - 1α

k1+kN

What happens to R if N is increased 2x or 3x ?

Resolution EquationThe Efficiency Term

R = 1/4 α - 1α

k1+kN


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R = 1/4 α - 1α

k1+kN

What happens to R if k = 1, 2, 10 or 20 ?

Resolution EquationThe capacity term

Resolution Depends on k

k Value k Term k Resolution?0 0 01 1/2 0.502 2/3 0.673 3/4 0.75 10 10/11 0.9120 20/21 0.95

k

k Ideal Range ?

Res

olut

ion


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What happens to R if α = 1.1 or 1.4 ?

Resolution EquationThe selectivity term

R = 1/4 α - 1α

k1+kN

0.29

0.09

=−

=

=−

=

⎟⎠⎞

⎜⎝⎛ −

4.114.14.1

1.111.11.1

1

α

α

αα

Resolution Depends on α


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α, k, N Control Resolution

Initial

Increase N

Increase k

Increase α

Stationary Phase -Physical Properties

Column construction materialsParticle shape Particle size

The van Deemter plotParticle pore sizeColumn dimensions


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Column Construction - Materials

Stainless SteelGlassPlastic

HDPE (High Density PolyethylenePEEK (Polyetheretherketone)

Filters / Frits

Stationary Phase

EndFittings

Column Construction


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Frit

Spherical Particle Irregular Particle

Packed Bed (Stationary Phase)

Packing of the Column

Direction of flow to pack column

Types of Packing Materials

Silica (inorganic)Silicone Dioxide

Similar to beach sand

Alumina (inorganic)Aluminum Oxide

Zirconia (inorganic)Polymeric (organic)

PlasticHybrid (inorganic/organic)Carbon


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Particle Size of Packing Material

Particle size is measured in:

Microns = 10 –6 metersFor analytical columns: 2.5 – 5 μm (10 μm)

Highest Efficiency Columns are Packed with Smallest Particle Sizes!

Particle Size DistributionThe range of particle sizes presentExample: 5 μm (3 μm - 7 μm)

Narrower distribution gives higher performance, but are more costly to produce

3 5 7 4 5 6Microns


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Common Particle for HPLCChromatographic Silica is by far the most commonly used particle for HPLCMany different types of silica based packing materials are manufactured by many different Chromatographic performance is greatly determined by how the silica particle is made.

Surface Attribute of ParticlesHigh surface area particles

Key to high performance for all porous chromatographic sorbents

Particles are highly porous [similar to the pores in a sponge]

Pore size is measured in atomic size units, called Angstroms Å (10-10 meters)

Typical analytical packing material particles have pores ranging from 60-125 Å


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Comparison of Porosity and Surface Area

Many small pores60-125 Å

High surface area300-500 m2/g

Good for small molecules and pharmaceuticals

Few large pores250-4,000 Å

Lower surface area50-150 m2/g

Good for larger molecules and proteins

Plates vs. Flow Rate10000900080007000600050004000300020001000

1.0 2.0 3.0Flow Rate{mL/min}

N OptimumOnly one flow rate gives maximum efficiency

Every column will have its’ own specific curve – depending on dimensions and particle size

Typical Column Behavior For N (Plate Count)


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Why Does the Flow Rate Change the Plate Count?

van Deemter Equation

A= Interparticle channels - velocity independentB=Molecular diffusion axially -

inversely proportional to velocityC=Mass transfer kinetics - directly proportional to velocity

H = HETP (Height Equivalent to Theoretical Plate){Need H to be as Small as Possible so you can “fit”more “plates” into a column}

µ = Linear Velocity (speed) of Mobile Phase (mm/sec)

H = A + B + µCµ

Linear Velocity of the Mobile Phase - u

Flow RateArea

cm3/min.cm2 cm3 = mL

T e r m in o lo g yL in e a r V e lo c ity (c m /s e c ) - - S p e e d a t w h ic h th e m o b ile p h a s e is f lo w in g th r o u g h th e c o lu m n - - fu n c t io n o f th e F lo w R a te a n d C o lu m n In te r n a l D ia m e te r

L in e a r V e lo c ity (c m /s e c )

0 .1 0 .3 0 .5 0 .8 1 .0

4 .6 m m ID

m L /m in0 .8 2 .4 4 .0 6 .2 7 .8

4 .0 m m ID

m L /m in0 .6 1 .8 3 .0 4 .8 6 .0

2 .0 m m ID

m L /m in0 .1 5 0 .4 5 0 .7 5 1 .2 1 .5

Linear Velocity u = =

= cmmin.

or cmsec.

or mmsec.

Cross-sectionalArea of ID

{ }

Column


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Smaller particles, spherical, well packed => less interstitial volume => tight band, sharp peak ==> less A

A

A

Larger particles, +/or irregular shape => larger interstitial channels/more interstitial volume (between particles) => broader band, broader peak, less efficiency ==> more A

No impact of linear velocity

Particle Size A

H EfficiencyH = A + B + uCu

Sample/Analyte “BANDS” and van Deemter A Term (Interstitial Volume or Channels)

B

B

Slower linear velocity u, (or, flow rate), more axialdiffusion of band => broader peak ==> more “B” Term

Higher linear velocity u, less time for axial diffusion of band => sharper peak ==> less “B” Term

u B H Efficiency u

H = A + B + uCu

Sample/Analyte “BANDS” and Van Deemter B Term (Diffusion of Band)


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Sample/Analyte “BANDS” and Van Deemter C Term (mass transfer)

X

XX

X

Stationary phasemass transfer

Mobile phasemass transfer

Bandspreading

X X

X

XBandspreadingBandspreading

X X X X

Influence of particle size

X

XXX

Sample molecules Sample

molecules

Solvent

Packingmaterial

Packingmaterial

Solvent

C

High linear velocity, u, causes “spreading” of analyte molecules (band) due to effect on mass transfer (into and out of the stationary phase– not enough time to adsorb/partition)=> broad bands => broad peaks == > more “C” Term

C

Lower linear velocity, u, causes reduced “spreading” of analyte molecules => narrower bands => sharper peaks == > less “C” Term

u Cu H EfficiencyH = A + B + uCu

Sample/Analyte “BANDS” and Van Deemter C Term (Mass Transfer)


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Hei

ght E

quiv

alen

t to

Theo

retic

al P

late

Linear Velocity

HET

P

u

Lowest HETP => Optimum Plate Count

Note: Once past optimum,as flow rate increases so doeslinear velocity - HETP Increases - plate count DECREASES

Note: Minimum HETP point is related to viscosity. As viscosity increases,the minimum HETP point occursat slower linear velocity

{cm/sec}

HETP PLATESH

H = A + B + uCu

The Van Deemter Curve

Comparison of the Van Deemter Plots for 5 µm and 2.5 µm Particles

2

4

68

10

12

14

16

18

20

22

24

26

28

30

0 0.5 1 1.5 2 2.5 3 3.5 4

Linear Velocity (mm/sec)

H (µ

m)

5 µm XTerra® Particle

2.5 µm XTerra® Particle

(50/50, acetonitrile / water mobile phase) Alden

Speed with maximum efficiency (resolution) should be achievable with smaller particles

Benefit of Smaller Particle* Reduction in HETP* Higher Linear Velocity Range


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Effect of Temperature on Column Efficiency -- Van Deemter

0 1 2 3 4 5 6 7 8 910

15

20

25

30

35

HET

P, H

[µm

]

5°C 25°C

60°C

As temperature is increased, lower HETP, higher N, higher linear velocity, reduced viscosity, improved masstransfer

u Linear velocity, u [mm/s]

Column Dimensions

Length: Millimeters or Centimeters

Internal Diameter: Millimeters

Internal diameter Analytical : 1mm - 4.6mmPreparative : 7.8mm - 50mm

Length2cm - 30cm20mm – 300mm


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Summary of Column Geometry

DiameterSmaller diameter INCREASES sensitivity.Larger diameter INCREASES column Capacity.

LengthLonger column has a HIGHER resolving power and capacity.Shorter Column has FASTER speed of separation and LOWER capacity.

Summary of Theory

DefinedV0, k, α, N & R

Learned the effect of k, α, and N on resolutionLearned the importance of particle size and flow on column efficiency (van Deemter plot)Looked at the effect of column dimensions

Chapter 1 HPLC Theory

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Transcript of Chapter 1 HPLC Theory