1 hplc theory

7/29/2019 1 HPLC Theory

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Basic HPLCBasic HPLC

Dr. Hans Ulrich Kuffner January 2001


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The chromatographic ProcessThe chromatographic ProcessSubstance 1

Substance 2

to = time spent in mobile phase

tR = time spent in stationary phase

tR1

= t0

+ t1

t0

tR1 = t0 unretained substance

t1

=oo irrevesible adsorption

Start

t1

t1

t1

to

tr1


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Equilibrium step

Transportation step

Cm

Cs

= 1


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V Sk = Skeleton Volume (volume of the stationary phase)

Vp = Pore Volume

V0 =Interstistial Volume

V0 + Vp = Vm (volume of the mobile phase)


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Packing structuresPacking structures

Fully porous

75 - 105

Fully porous

10

Porous layer

47 -75

Porasil Corasil -Porasil


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Tswetts Chromatographic SystemTswetts Chromatographic System


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SOLVENT A

COLUMN

Pump A

INJECTOR

DETECTOR

DATA SYSTEM


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SOLVENT A

COLUMN

Pump A

INJECTOR

DETECTOR

SOLVENT B

Pump B

MIX

Data System

GRADIENT

Data System


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Gradient FormationGradient FormationLow and High Pressure SystemsLow and High Pressure Systems


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Pumps in Gradient SystemPumps in Gradient System

Gradient proportioning valve

2 pump gradient system

Mixing on high pressure side

1 pump gradient system

Mixing on low pressure side


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Gradient SystemsGradient Systems

High-pressure mixing

z

Advantages Usually lower system

volume

Degassing not as critical

z Disadvantages

One pump per solvent

Only practical with up to 3

solvents (usually only 2)

Low-pressure mixing

z

Advantages Only one pump

Usually more solvents

(normally 4)

z Disadvantages

Usually higher system

volume

Degassing more critical


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RV

Pump B

Pump A

B Pulse Dampener

A Pulse Dampener

Solvent A

Solvent B

To Waste

To column

To injector

Optional Mixer

Waters Breeze System HardwareWaters Breeze System HardwareFluid path of Breeze Gradient SystemFluid path of Breeze Gradient System


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Retention TimeRetention Time --Retention VolumeRetention Volume

30

tr2

tr1

t0

min

ml

1 2 43

2

5

4 6 8 10

ms

mm

Adsorption Isotherm


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Capacity factor kCapacity factor k

mobile

phasestat

Amount

Amount

V

V

Kkm

s.

==

K =

Cs

Cm

substitute

=

Ms Vm

Mm Vs

k=vr-v0

v0=

tr-t0

t0


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k= Retention time measured in [k= Retention time measured in [tt00]]

kk= Retention volume measured in [= Retention volume measured in [vvoo]]

30

k2= (3.4 - 0.8) / 0.8 = 3.25

k1

V0= 0.8

k

ml

0 2 43

1

5

2 34

1

k=

vr-v0v0


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SelectivitySelectivity

to

t2 - to

t1 - tot1

t2

=t2 - to

t1

- to

=

k1

k2

= 1No separation


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Resolution R

R = 1 2% Overlap 4

R = 1.5 baseline separation 6


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MathematicalMathematicalEffect of IncreasingEffect of Increasing

ResolutionResolution

1.0 1.25

99.4

98

95

0.8

8883

Rs=0.40.5 0.6

0.7

92


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EfficiencyEfficiency

Peak broadening during separationPeak broadening during separation

minutes0 126

W = 0,55 min

10,2 min

N = 16 (tr/w)2 = 16 *(10,2 / 0,55)2 = 5500


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Calculation of Column EfficiencyCalculation of Column Efficiency

55 MethodMethod

7018.R

V

plates8240

1.03

18.7025N

2

5

==

1.03W =height4.4%

height4.4%

plates3334

N5

==2

441

631625

..

6316.RV

1.44W =Good Column Bad Column

Inje

ct

Inje

ct


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N = Theoretical PlatesN = Theoretical PlatesA Measure of EfficiencyA Measure of Efficiency


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Definition of HETPDefinition of HETP

HETP = Column Length

No. of Plates

(HETP=height equivalent to atheoretical plate)


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How to Control Plate CountHow to Control Plate Count

z System Bandwidth

z The VanDemter Equation


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The VanThe Van DeemterDeemterEquationEquation

velocitylinear

CB

AH

=


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A = Eddy diffusion

LINEAR VELOCITY()

HETP

VanVan DeemterDeemterPlotPlot

0

12

3

6

9

B = Longitudinal diffusion

C = Mass transfer

Optimum flowrate


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Plates vs.Plates vs. FlowrateFlowrate

FLOWRATE (cm/min)

PLATES

x310

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

5

10

15


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Comparison of the vanComparison of the van DeemterDeemterPlots forPlots for

5 m and 2.5 m5 m and 2.5 mXTerraXTerra MS CMS C1818 ParticlesParticles

2

4

6

8

10

12

14

16

18

20

22

24

2628

30

0 0.5 1 1.5 2 2.5 3 3.5 4

Linear Velocity (mm/sec)

H(m)

5 m XTerra Particle

2.5 m XTerra Particle

(50/50, acetonitrile/water mobile phase)


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0 1 2 3 4 5 6 7 8 9Linear velocity, u [cm/s]

10

15

20

25

30

35

40

Pla

teheight,H[

m]

5C

25C

60C

Effect of Temperature on ColumnEffect of Temperature on ColumnEfficiencyEfficiency


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300 C

500 C

8.00 9.00

600 C

400 C

N= 1680

N=2250

1920 psi

1160 psi

5.00Minutes

0.00 1.00 2.00 3.00 4.00 7.00

Effect of TemperatureEffect of Temperature


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Expanded Plate FormulaExpanded Plate Formula

( )N V VW W

col nc

col nc

= ++162

2 2


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Asymmetry FactorAsymmetry Factor

A

BAs =

4.4%A B


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Resolution EquationResolution Equation


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

( )

=

1

N1

4

1R

Resolution EquationResolution EquationThe Capacity TermThe Capacity Term


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k Value k Term k Resolution?

0 0 0

1 1/2 .50

2 2/3 .67

3 3/4 .75

10 10/11 .91

20 20/21 .95

k

k Ideal Range ?

Resolution

Resolution Depends on kResolution Depends on k


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

=

1

1

4

1R N

Resolution EquationResolution EquationThe Efficiency TermThe Efficiency Term


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( ) ResultsCountPlate Change%NN

73%54.730003000N41%44.720002000N

31.610001000N

=

73%122.415,00015,000N

41%10010,00010,000N

70.75,0005,000N

=

Resolution Depends onResolution Depends on NN


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What happens to R if = 1.1 or 1.4 ?

( )

=

1

N

4

1R1

Resolution EquationResolution EquationThe Selectivity TermThe Selectivity Term


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0.29

0.09

=

=

=

=

4.1

14.14.1

1.1

11.11.1

1

Resolution Depends onResolution Depends on


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Resolution EquationResolution Equation

Physical Cemistry

Polarity

Solvent strength

Physics

Mechanics of packing

Particle size

Cemistry

pH

Nature of Solvent

Modifier


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Selectivity

Sample Chemistry

Solvent Chemistry Column Chemistry


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,, kk, N, N Control ResolutionControl Resolution


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Column ExamplesColumn Examples

1 hplc theory

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