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Lecture 8. Van Deemter Equation!. (. ). k’. 1. 1+k’. 4. efficiency. selectivity. retention. Resolution. Describes how well 2 compounds are separated. Rs = . N 1/2 (  -1). t R -t M. 1 < k’ < 10. k’ = . t M. (. ). k’. 1. 1+k’. 4. Resolution.

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lecture 8

Lecture 8

Van Deemter Equation!

slide2

(

)

k’

1

1+k’

4

efficiency

selectivity

retention

Resolution

Describes how well 2 compounds are separated

Rs =

N1/2 (-1)

tR-tM

1 < k’ < 10

k’ =

tM

slide3

(

)

k’

1

1+k’

4

Resolution

Describes how well 2 compounds are separated

Rs =

N1/2 (-1)

L

Maximize N

N =

H

L

H

slide4

Resolution

  • L - length of column
  • Cannot increase indefinitely
  • Limited by:
    • Long runs times
    • Back pressure (LC)
  • H - height equivalent of a theoretical plate
  • Measure 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

slide5

B

Van Deemter Equation

A +

H

+ C

 is flow rate

slide6

Van Deemter Equation

B

A +

H

+ C

C

H

H min

A

B

(flow rate)

slide7

Van Deemter Equation

A term

‘Multipath Effect’

slide8

Van Deemter Equation

A term

‘Multipath Effect’

Ce = particle shape

dp = diameter of particle

A

Ce dp

  • A term
    • Entirely dependent on column
    • Only important in LC
slide9

Van Deemter Equation

A term

‘Multipath Effect’

A

H

H

A

(flow rate)

slide10

Van Deemter Equation

B term

‘Longitudinal diffusion’

slide11

Van Deemter Equation

B term

‘Longitudinal diffusion’

DMP

DMP = diffusivity of mobile phase

B

  • 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
slide12

Van Deemter Equation

B term

‘Longitudinal diffusion’

B

H

H

B

(flow rate)

slide13

Van Deemter Equation

C term

‘Mass transfer’

dt2

dt = diameter of tube

DMP = diffusivity of MP

GC

C

m

DMP

dp2

dp = diameter of particles

DMP = diffusivity of MP

 = tortuosity

LC

C

m

DMP

slide14

Van Deemter Equation

C term

‘Mass transfer’

dt2

GC

C

m

DMP

dp2

LC

C

m

DMP

slide15

Van Deemter Equation

C term

‘Mass transfer’

dt2

GC

C

m

DMP

dp2

LC

C

m

DMP

slide16

Van Deemter Equation

C term

‘Mass transfer’

dt2

GC

C

m

DMP

dp2

LC

C

m

DMP

slide17

Van Deemter Equation

C term

‘Mass transfer’

H

C

C

H

(flow rate)

slide18

Van Deemter Equation

GC

B

X

A +

H

+ C

C

H

H min

A

B

(flow rate)

slide19

Van Deemter Equation

GC

B

H

+ C

C

H

H min

B

(flow rate)

slide20

Van Deemter Equation

GC

DMP

dt2

+

H

m

DMP

C

H

H min

B

(flow rate)

slide21

Van Deemter Equation

GC

  • 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
slide22

Van Deemter Equation

LC

B

X

A +

H

+ C

C

H

H min

A

B

(flow rate)

slide23

Van Deemter Equation

LC

A +

H

C

C

H

A

(flow rate)

slide24

Van Deemter Equation

LC

dp2

+

Ce dp

H

DMP

C

H

A

(flow rate)

slide25

Van Deemter Equation

LC

  • 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
slide26

Van Deemter Equation

LC

dp2

+

Ce dp

H

DMP

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

slide27

Van Deemter Equation

LC

dp2

+

Ce dp

H

DMP

Ascentis Express, Supelco, technical information

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