lecture vak 02-6007 may 17, 2005 johannes...

Separation by ChromatographyLecture VAK 02-6007

May 17, 2005

Johannes Ranke

Separation by Chromatography – p.1/7

1D Separation methods

1

1

2

2

Electrophoresis

Separation by Chromatography – p.2/7

1D Separation methods

1

1

2

2

Electrophoresis

1

1

2

2

Chromatography

Separation by Chromatography – p.2/7

1D Separation methods

1

1

2

2

Electrophoresis

1

1

2

2

Chromatography

1

1

2

2

Membrane separation

Separation by Chromatography – p.2/7

1D Separation methods

1

1

2

2

Electrophoresis

1

1

2

2

Chromatography

1

1

2

2

Membrane separation

Separation according to

Kinetic properties

Equilibrium distribution

Combinations thereof

Separation by Chromatography – p.2/7

Elution techniques

A + B

Separation by Chromatography – p.3/7

Elution techniques

A

B

Separation by Chromatography – p.3/7

Elution techniques

A

B

Separation by Chromatography – p.3/7

Elution techniques

Time [min]

Det

ecto

r si

gnal

0 2 4 6 8 10

A

B

Separation by Chromatography – p.3/7

Equilibrium based separation

tM

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

k′ = nSnM

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

k′ = nSnM=

tStM

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

k′ = nSnM=

tStM=

tR−tMtM

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

k′ = nSnM=

tStM=

tR−tMtM

k′ = cS·VScM·VM

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

k′ = nSnM=

tStM=

tR−tMtM

k′ = cS·VScM·VM

= K · VSVM

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

k′ = nSnM=

tStM=

tR−tMtM

k′ = cS·VScM·VM

= K · VSVM

tM = F · VM

tR = F · VR

k′ = nSnM=

tStM=

tR−tMtM=

VR−VMVM

Separation by Chromatography – p.4/7

Equilibrium based separation

tMtR

k′ = nSnM=

tStM=

tR−tMtM

k′ = cS·VScM·VM

= K · VSVM

tM = F · VM

tR = F · VR

k′ = nSnM=

tStM=

tR−tMtM=

VR−VMVM

VR ≈ VM + K · VS

Separation by Chromatography – p.4/7

Equilibrium constant

Ki =cS

cM

Ki = exp(−∆G0i /RT) = exp(−

∆H0i − T∆S0

i

RT)

If ∆H0i ≈ 0, then

Ki ≈ exp(−∆S0i /R),

i.e. Ki is independent from temperature.

Separation by Chromatography – p.5/7

Equilibrium constant

Ki =cS

cM

Ki = exp(−∆G0i /RT) = exp(−

∆H0i − T∆S0

i

RT)

If ∆H0i ≈ 0, then

Ki ≈ exp(−∆S0i /R),

i.e. Ki is independent from temperature.

Separation by Chromatography – p.5/7

Peak shapes

Isotherm

Signal shape

Retention time

cS

cMA

ttR

Vi

Separation by Chromatography – p.6/7

Peak shapes

Isotherm

Signal shape

Retention time

cS

cMA

ttR

Vi

Separation by Chromatography – p.6/7

Peak shapes

Isotherm

Signal shape

Retention time

cS

cMA

ttR

Vi

Separation by Chromatography – p.6/7

Peak dispersion

Injection

Dispersion in connecting tubes/capillaries

Dispersion in columns

Dispersion caused by signal detection

Separation by Chromatography – p.7/7

Peak dispersion

Injection

Dispersion in connecting tubes/capillaries

Dispersion in columns

Dispersion caused by signal detection

Separation by Chromatography – p.7/7

Peak dispersion

Injection

Dispersion in connecting tubes/capillaries

Dispersion in columns

Dispersion caused by signal detection

Separation by Chromatography – p.7/7

Peak dispersion

Injection

Dispersion in connecting tubes/capillaries

Dispersion in columns

Dispersion caused by signal detection

Separation by Chromatography – p.7/7

Dispersion in columns

van-Deemter equation:

H = A + B/v + C v

Eddy diffusionA = 2λdR

Longitudonal diffusionB = 2ΨDM

Lateral diffusion, disequilibriumC = K1 · R · (1 − R) · d2

f/DS + K2/DM

Separation by Chromatography – p.8/7

Dispersion in columns

van-Deemter equation:

H = A + B/v + C v

Eddy diffusionA = 2λdR

Longitudonal diffusionB = 2ΨDM

Lateral diffusion, disequilibriumC = K1 · R · (1 − R) · d2

f/DS + K2/DM

Separation by Chromatography – p.8/7

Dispersion in columns

van-Deemter equation:

H = A + B/v + C v

Eddy diffusionA = 2λdR

Longitudonal diffusionB = 2ΨDM

Lateral diffusion, disequilibriumC = K1 · R · (1 − R) · d2

f/DS + K2/DM

Separation by Chromatography – p.8/7

Van Deemter plot

http://www.chromatography-online.org/Dispersion/Van-Deemter-Equation/rs49.html

Separation by Chromatography – p.9/7

Column performance

t

S

tR

� �

2σ� �

wb = 4σ

Separation by Chromatography – p.10/7

Column performance

t

S

tR

� �

2σ� �

wb = 4σ

N = ( tRσ )2

Separation by Chromatography – p.10/7

Column performance

t

S

tR

� �

2σ� �

wb = 4σ

N = ( tRσ )2

N = 16 · ( tRwb

)2

Separation by Chromatography – p.10/7

Column performance

t

S

tR

� �

2σ� �

wb = 4σ

N = ( tRσ )2

N = 16 · ( tRwb

)2

N = 8 · ln 2 · ( tRw0.5

)2

� �

w0.5

Separation by Chromatography – p.10/7

Column performance

N = 16 · ( tRwb

)2

Neff = 16 · ( tR−t0wb

)2

H = LN

H is the Height Equivalent of a Theoretical Plate (HETP).

Separation by Chromatography – p.11/7

Column performance

N = 16 · ( tRwb

)2

Neff = 16 · ( tR−t0wb

)2

H = LN

H is the Height Equivalent of a Theoretical Plate (HETP).

Separation by Chromatography – p.11/7

Column performance

N = 16 · ( tRwb

)2

Neff = 16 · ( tR−t0wb

)2

H = LN

H is the Height Equivalent of a Theoretical Plate (HETP).

Separation by Chromatography – p.11/7

Column performance

H N nsample

[mm] [s−1]

TLC 0.7 1 µg - mgHPTLC 0.02 50 20 ng - mgColumn 20 0.0005 mg - kgHPLC 0.01 400 ng - mgpacked GC 0.5 100 µg - gcapillary GC 0.25 400 pg - µg

Separation by Chromatography – p.12/7

Column performance

Resolution RS =tR,1−tR,2

0.5·(wb,1+wb,2)

Separation by Chromatography – p.13/7

Column performance

Resolution RS =tR,1−tR,2

0.5·(wb,1+wb,2)

Separation factor α =k′2k′1=

tR,2−t0tR,1−t0

=K2K1

Separation by Chromatography – p.13/7

Column performance

Resolution RS =tR,1−tR,2

0.5·(wb,1+wb,2)

Separation factor α =k′2k′1=

tR,2−t0tR,1−t0

=K2K1

RS =√

Neff4α−1α

Separation by Chromatography – p.13/7