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CHROMATOGRAPHIC
METHODS OF SEPARATION

1

BASIC PRINCIPLES
•
•
•
•

•

All chromatographic separations rely on the
differences in interaction between analytes
and the two characteristic phases
Mobile phase: carries/transports the
analytes
Stationary phase: interacts with the
analytes as they are moving through it
...

Analytes separate into bands

•

Analytes are detected at the exit of the
column and their signals recorded

•

Plot: chromatogram

2

• Classification based on the types of mobile and
stationary phases and the kinds of equilibria involved in
the transfer of solutes between phases
• Name based on type of Mobile

3

Elution
• Elution: washing a
species through a
column by continuous
addition of fresh mobile
phase
• Mobile phase: eluent
• Partition between
mobile and stationary
phase

4

General Classification of Chromatographic
Methods
• Classification based on the types of mobile and stationary
phases and the kinds of equilibria involved in the transfer
of solutes between phases
...

Linear chromatography:

Amobile ⇔ Astationary
(a )
Kc = A S
(a A )M
c
n /V
Kc = S = s s
cM nM / VM

– Kc is constant, does not change with
solute concentration
– Gaussian-type peak
– Retention times independent of amount
of analyte injected

8

Retention Time
• Retention time depends on
KC
• tM: time for the unretained
species, dead or void time
• tS: time spent in the stationary
phase
tR = tM + tS
L
tR
v ≡ average − linear − velocity − of − solute − migration
L
u=
tM
u ≡ average − linear − velocity − of − mobile − phase
v=

v = u×

1
1 + K C V S VM

9

tR = tM + tS
v=
u=

L
= average − linear − rate − of − solute − migration
tR
L
tM

= average − linear − velocity − of − mobile − phase

v = u × ( fraction − of − time − solute − spends − in − mobile − phase)
v=u

moles − of − solute − in − mobile − phase
total − moles − of − solute

v = u×

c M VM
1
= u×
1 + c S VS c M VM
c M V M + c S VS

v = u×

1
1 + K CVS VM

10

Retention/Capacity Factor
• Used to compare
migration rates of solutes
in columns
• Does not depend on
column geometry or
volumetric flow rates
• Can be calculated from
measured retention times
• For example, for a solute
A, the capacity factor kA
is given by:

kA =

K AVS
VM

v = u×

1
1
= u×
1 + K AVS VM
1 +k A

L
L
1
=
×
tR tM 1 + k A
kA =

tR − tM
tM

tR-tM: adjusted retention time

11

Relative Migration Rates: Selectivity Factor
• The selectivity factor
(α) compares
migration rates
• For two solutes A
and B, B being the
more strongly
retained species, α
is given by:

α=

KB
KA

α=

kB
kA

(t R )B − t M
α=
(t R )A − t M

12

Band Broadening and Column Efficiency
•
•

Band broadening affects the efficiency of the chromatographic
column
Why do bands become broader as they move down the column?

•

Rate theory of Chromatography:
– random-walk mechanism
• Although the general direction of migration is towards the bottom of the
column, random walk is superimposed on the general movement forward

– Random motion during migration explains the shape and the breath of
chromatographic peaks –
• Gaussian Distribution around mean retention time
...
Some particles lag behind because they
are incorporated in the stationary phase for a time longer than the
average
...


13

Tailing and Fronting
• Tailing: occurs when
the distribution
constant varies with
concentration
• Fronting: occurs when
the amount or sample
introduced is too large

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Quantitative Description of Column Efficiency
•

•
•

•
•

Column efficiency is expressed in terms of plate
height (H) and plate count/ the number of theoretical
plates (N)
...

– Migration from center to either side (opposed
to the direction of flow)
– Important in GC, less significant in LC

22

• The Stationary-Phase Mass-Transfer Term Csu
– For immobilized liquid stationary phase
– The mass transfer coefficient is directly proportional
to the square of the thickness of the film on the
support particle (df) and inversely proportional to the
diffusion coefficient Ds of the solute in the film
...


23

• Mobile-Phase Mass-Transfer Term CMu
...

– for packed column is proportional to the
square of the particle diameter of the packing
material (dp)

24

25

λ and γ: constants depending on quality of packing

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Optimization of Column Performance
• Reduce band broadening
• Alter relative migration rates of solutes
• Reduce separation time
___________________________________
• Zone broadening is increased by kinetic
variables that increase plate height
• Migration rates are varied by changing
variables that affect retention and selectivity
factors

27

Resolution
• How far apart two
bands are relative
to their widths
• Quantitative
measure of the
ability of the
column to separate
two analytes

RS =

2[(t R )B − (t R ) A ]
2∆Z
∆Z
=
=
W A WB W A + WB
W A + WB
+
2
2

RS =

N
(α − 1)⎛ k ⎞
⎜
⎟
4
⎝1+ k ⎠

k : average − of − k A − and − k B

α →1

28

Variables that Affect Column Performance
• Kinetic factors (1st term)
– Related to N

• Thermodynamic factors (2nd and 3rd terms)
– 2nd term: depends solely on properties of the
solutes for a given mobile-phase and
stationary-phase combination
– Third term: depends on properties of both the
solute and the column

• α, k, N or H

29

General Elution Problem
• Optimization (k ~1 to 5) for solutes with shorter
retention times, generally leads to very long
retention time for the other solutes and
excessive broadening
• Solution: decrease k during the separation
– Gradient elution (as opposed to Isocratic
elution)
• In GC: temperature gradient is applied

30

Application of LC for Bio-analysis

31



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