Lecture 8

Van Deemter Equation!

ResolutionDescribes how well 2 compounds are separated

Rs = 14

N1/2 (-1)k’

1+k’( )efficiency selectivity

retention

k’ = tR-tM

tM

1 < k’ < 10

ResolutionDescribes how well 2 compounds are separated

Rs = 14

N1/2 (-1)k’

1+k’( )N =

L H

Maximize N

LH

L - length of columnCannot increase indefinitely

Limited by:• Long runs times• Back pressure (LC)

Resolution

H - height equivalent of a theoretical plateMeasure of Efficiency

Always want to minimize H• Getting the best performance from system

H depends on:• column parameters• mobile phase• flow rate

Described by Van Deemter

Van Deemter Equation

H B

∞ A + + C

is flow rate

Van Deemter Equation

H

(flow rate)

H B

∞ A + + C

A

C

B

H min

Van Deemter EquationA term

‘Multipath Effect’

Van Deemter EquationA term

‘Multipath Effect’

A ∞ Ce dpCe = particle shapedp = diameter of particle

A term• Entirely dependent on column• Only important in LC

H

(flow rate)

H ∞ A

A

Van Deemter EquationA term

‘Multipath Effect’

Van Deemter EquationB term

‘Longitudinal diffusion’

Van Deemter EquationB term

‘Longitudinal diffusion’

B DMP

∞ DMP = diffusivity of mobile phase

B term• Inversely proportional to flow rate (fast)• Only important in GC (DMP of a gas)

• Typical LC flow rate 0.2-0.5 mL/min• Typical GC flow rate 1-2 mL/min

H

(flow rate)

H B

∞

B

Van Deemter EquationB term

‘Longitudinal diffusion’

Van Deemter EquationC term

‘Mass transfer’

dt = diameter of tubeDMP = diffusivity of MPGC C

dt2

DMP

∞

dp = diameter of particlesDMP = diffusivity of MP = tortuosity

LC C dp

2∞ DMP

Van Deemter EquationC term

‘Mass transfer’

GC C dt

2

DMP

∞

LC C dp

2∞ DMP

Van Deemter EquationC term

‘Mass transfer’

GC C dt

2

DMP

∞

LC C dp

2∞ DMP

Van Deemter EquationC term

‘Mass transfer’

GC C dt

2

DMP

∞

LC C dp

2∞ DMP

H

(flow rate)

H ∞ C

C

Van Deemter EquationC term

‘Mass transfer’

Van Deemter EquationGC

H

(flow rate)

H B

∞ A + + C

A

C

B

H min

X

Van Deemter EquationGC

H

(flow rate)

H B

∞ + C

C

B

H min

dt2

DMP

Van Deemter EquationGC

H

(flow rate)

H DMP

∞ +

C

B

H min

Van Deemter EquationGC

Ideal Column (open tubular):• Small internal diameter (dt)• Use length to increase N (N=L/H)

Ideal Mobile Phase:• High diffusivity to C term and

allow higher flow rates

Van Deemter EquationLC

H

(flow rate)

H B

∞ A + + C

A

C

B

H min

X

Van Deemter EquationLC

H

(flow rate)

H ∞ A + C

A

C

Van Deemter EquationLC

H

(flow rate)

H ∞ +

A

C

dp2

DMP

Ce dp

Van Deemter EquationLC

Ideal Column (packed):• Small particles (dp)• Uniform particles (Ce and )• Cannot use length to increase N

Ideal Mobile Phase:• High diffusivity (DMP) to C term and allow higher flow rates

Dong, M. Today’s Chemist at Work. 2000, 9(2), 46-48.

Van Deemter EquationLC

H ∞ + dp

2DMP

Ce dp

Van Deemter EquationLC

H ∞ + dp

2DMP

Ce dp

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