Introduction toChromatography

Introduction

Chromatography permit the scientist to separate closely related components of complex mixtures.

In all chromatographic separations the sample is transported in a mobile phase, which may be a gas, a liquid, or a supercritical fluid. This mobile phase is then forced through an immiscible stationary phase, which is fixed in place in a column or on a solid surface. The two phases are chosen so that the components of the sample distribute themselves between the mobile and stationary phase to varying degrees.

Classification of Chromatographic Methods

Chromatographic methods can be categorized

in two ways. The first classification is based

upon the physical means by which the stationary

and mobile phases are brought into contact. In

column chromatography

planar chromatography

Classification of Chromatographic

Methods

Three general categories of chromatography:

(1) liquid chromatography,

(2) gas chromatography,

(3) supercritical-fluid chromatography.

Classification of Column Chromatographic MethodsGeneral Classification Specific Method Stationary Phase Type of Equilibrium

Liquid-liquid orpartition

Liquid adsorbed on solid Partition betweenimmiscible liquids

Liquid bondedphase

Organic liquids bonded on asolid surface

Partition between liquidand bonded phase

Liquid- solid oradsorption

Solid Adsorption

Ion exchange Ion exchange resin Ion exchange

Liquid chromatography(LC)(Mobile phase: liquid)

Size exclusion Liquid in interstices of apolymeric solid

Partition/sieving

Gas-liquid Liquid adsorbed on solid Partition between gas andsolid

Gas-bonded phase Organic species bonded to asolid surface

Partition between gas andbonded phase

Gas Chromatography(GC)Mobile phase: gas

Gas-solid Solid Adsorption

Elution Chromatography on Columns

Elution involves washing a species through a column by continuous addition of fresh solvent. The sample is introduced at the head of a column, whereupon the components of the sample distribute themselves between the two phases. Introduction of additional mobile phase (the eluent) forces the solvent containing a part of the sample down the column, where further partition between the mobile phase and fresh portions of the stationary phase occurs.

ChromatogramsIf a detector that responds to solute concentration is placed at the end of the column and its signal is plotted as function of time (or of volume of the added mobile phase), a series of peaks is obtained. Such a plot, called a chromatogram, is useful for both qualitative and quantitative analysis. The positions of peaks on the time axis may serve to identify the components of the sample; the areas under the peaks provide a quantitative measure of the amount of each component.

MIGRATION RATES OF SOLUTES

The effectiveness of a chromatographic column

in separating two solutes depends in part upon

the relative rates at which the two species are

eluted. These rates are determined by the

magnitude of the equilibrium constants for the

reactions by which the solutes distribute

themselves between the mobile and stationary

phases.

Increase in band separation

Decrease in band spread

Amobile Astationary

K=CS/CM

K Distribution coefficient

CS Molar concentration of solute in stationary phase

CM Molar concentration of solute in mobile phase

Distribution Coefficient

v = L/tR

v Linear rate of solute migrationL Length of column packingtR Solute retention time

Retention Time

u = L/tM

u Linear rate of movement of mobile phase moleculest M Dead time

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

Time

Det

ecto

r Si

gnal

tr

tM

Typical chromatogram for a two component mixture. The small peak on the left is represent a species that is not retained on the column and so reaches the detector immediately after elusion is started. Thus its retention time tm is approximately equal to the time required for a molecule of mobile phase to pass through the column.

The Relationship Between Retention Time and Distribution Coefficient

M

MRA

AMR

A

M

SAA

MS

MM

SSSSMM

MM

t

ttk

k1

1

t

L

t

L

k1

1uv

V

VKk

/VKV1

1uv

VcVc

1

1u

VcVc

Vcuv

solute of moles total

phase mobile the in solute of molesuv

phase mobile the in spends solute time of Fractionuv

Relative Migration Rates: The selectivity Factor

The selectivity factor of a column for the two species A and B is defined as

= KB/KA

where KB is the distribution constant for species B and KA is the distribution constant for species A. is always greater than unity. A relationship between the selectivity factor and retention factors:

= k`B/k`A

Where k`B and k`A are the retention factors. An expression for the determination of from an experimental chromatogram:

( )

( )

t t

t t

R B M

R A M

Distance migrated

Num

ber

of m

olec

ules Analyte profile at

end of columnL

L 1s L1s

Sample in To detector

Packing

H = s2/L

Definition of Plate Height

Time

Det

ecto

r S

igna

ltr

tMw

Determination of standard deviation from a chromatographic peak: w = 4

2

1/2

R

2R

R

2

R

R

)w

t5.54(N

)w

t16(N

16t

LwH

4t

Lw

4w

L/t

σ

τ

στ

Kinetic Process that contribute to Peak Broadening Process Term in vanDeemter

Equation Relationship to Column and Analyte Properties

Multiple flow paths

A A = 2k dP

Longitudinal diffusion

B/u u

2DuB M

Mass transfer to and from liquid stationary phase

CSu u

D

)dk(fuC

S

2

fSS

Mass transfer in mobile phase

CMu u

D

)dk(fuC

M

2

pM

M

H = A + B/u + ( CS + CM ) uPlate height

Multiple flow paths

Longitudinal diffusion

Mass transfer between phases

The Multipath Term(A)

Zone broadening arises in part from the multitude of pathways by which a molecule (or ion) can find its way through a packed column. The length of these pathways may differ significantly; thus, the residence time in the column for molecules of the same species is also variable. Solute molecules then reach the end of the column over a time interval, which leads to a broadened band. This effect which is called eddy diffusion, is directly proportional to the diameter of the particles making up the column packing.

Typical pathways of several molecules during elution.

The Longitudinal Diffusion Term (B/u)

Longitudinal diffusion in column chromatography is a band broadening process in which solutes diffuse from the concentrated center of a zone to the more dilute regions ahead of and behind the zone center. The longitudinal diffusion term is directly proportional to the mobile-phase diffusion

coefficient DM. The contribution of

longitudinal diffusion is seen to be inversely proportional to the mobile phase velocity.

Mass-transfer Coefficients (Cs and CM)

The need for the two mass-transfer coefficients Cs and

CM arises because the equilibrium between the mobile

and the stationary phase is established so slowly that a chromatographic column always operates under nonequilibrium conditions.

Effect of Mobile-Phase Velocity

Fig. 26-10 provides the quality of the fit of the van Deemter equation. The upper curve was obtained from a numerical fit of the van Deemter equation to the data. The lower plots in the figure also show the contribution of the longitudinal diffusion, and the masstransfer effects.

0.2 0.6 0.80

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.4Linear flow rate cm/s

H m

m

A van Deemter plot for a packed liquid chromatographic column. The points on the upper curve are experimental. The contribution of various rate terms are shown by the lower curves. A: multipath effect; B/u, longitudinal diffusion; Cu, mass transfer for both phases.

H = A + B/u + ( CS + CM ) u

Methods for Reducing Zone Broadening

Two important controllable variables that affect column efficiency are the diameter of the particles making up the packing and the diameter of the column. To take advantage of the effect of column diameter, narrower and narrower columns have been used in recent years. With gaseous mobile phases, the rate of longitudinal diffusion can be reduced appreciable by lowering the temperature and thus the diffusion coefficient DM. The consequence is significantly smaller

plate heights at low temperatures.

Variables That Affect Column Efficiency Variable Symbol Units Linear velocity of mobile phase u cm/s Diffusion coefficient in mobile phase

DM cm2s-1

Diffusion coefficient in stationary phase

DS cm2s-1

Retention factor k’ Unitless Diameter of packing particles dp cm Thickness of liquid coating df Cm

0.1

0.2

5 10 20

Linear flow rate cm/s

H m

m

15

0.1-0.15 mm

0.25-0.3 mm

0.3-0.4 mm

0.4-0.6 mm0.6-0.8 mm

Effect of particle size on plate height. The numbers to the right are particle diameters.

Methods for Reducing Zone Broadening

Two important controllable variables that affect column efficiency are the diameter of the particles making up the packing and the diameter of the column. To take advantage of the effect of column diameter, narrower and narrower columns have been used in recent years. With gaseous mobile phases, the rate of longitudinal diffusion can be reduced appreciable by lowering the temperature and thus the diffusion coefficient DM. The consequence is significantly smaller

plate heights at low temperatures.

Column ResolutionThe resolution Rs of a column provides a quantitative measure of its ability to separate two analytes. Column resolution is defines as

It is evident from Fig.26-12 that a resolution of 1.5 gives an essentially complete separation of the two components, whereas a resolution of 0.75 does not. At a resolution of 1.0, zone A contains about 4% B and zone B contains a similar amount of A. At a resolution for 1.5, the overlap is about 0.3% . The resolution for a given stationary phase can be improved by lengthening the column, thus increasing the number of plates.

RZ

W W

Z

W W

t t

W Ws

A B A B

R B R A

A B

/ /

[( ) ( ) ]

2 2

2 2

0

0

RS = 0.75

RS = 1.0

wA/2

A B

wB/20

RS = 1.5

(tR)A

(tR)B

Z

tM

Separation at three resolutions. Here RS = 2Z/(wA + wB)

2B

B2SBR

BR

BR

)k(

)k(1)

1α

α(

u

H16R)(t

u

)kNH(1)(t

)(t

Lv B

5.0 15.00 10.0Retention factor kB’

RS/Q

or

(tR) B

/Q’

Effect of retention factor kB’ on resolution RS and elution time (tR)B. It is assumed that Q and Q’ remain constant with variation in kB

’

(a)70% Methanol

30% water

(b)60% Methanol

40% water

(c)50% Methanol

50% water

(d)40% Methanol

60% water

Inje

ct

Inje

ct

Inje

ct

Inje

ct

1

2

3

4

5

1

2

3

4

5

12

3

4

5

Effect of solvent variation on chromatograms. Analytes: (1) 9,10-anthraquinone; (2) 2-methyl 9,10-anthraquinone; (3) 2-ethyl-9,10-anthraquinone; (4) 1,4-dimthyl 9,10-anthraquinone; (5) 2-t-butyl-9.10-anthraquinone.

1 23 4

5 6

12

3 4 5 6

1 2

3 45 6

Time

Sig

nal

Illustration of general elution problem in chromatography

4

N

Bk1

Ak

Bk

SR

4

N

B)

R(t

B)

R(t

A)

R(t

SR

wB

)R

(tA

)R

(t

SR

wBwAwB

wA

w

)B

)R

(tA

)R

2((t

BwAwZ2

B/2wAwZ

SR

2)k

k1(2)

1α

1(S16RN

)k1

k1)((α

4

NSR

2)

Bk

Bk1

(2)1α

α(S16RN

)

Bk1B

k)(

α

1α(

4

NSR