Chromatography separates components of a mixture through differential partitioning between a stationary and mobile phase. Martin and Synge developed the concept of theoretical plates to describe chromatography. The column is considered divided into theoretical plates where analytes completely equilibrate between phases. Greater separation occurs with more theoretical plates and lower plate height. The Van Deemter model describes how plate height is affected by eddy diffusion, longitudinal diffusion, and resistance to mass transfer between phases, which influence peak dispersion at different flow rates.

1. CHROMATOGRAPHY

2.  Martin and synge in 1941 developed the concept of the ‘theoretical plate’ in
order to establish a satisfactory theory for partition chromatography.
 The column is considered as being made up of large number of parallel
layers of ‘ theoretical plates’.
 When the mobile phase passes down the column distribute themselves
between the stationary and mobile phases in accordance with their partition
coefficients.
Plate theory

3. View column as divided into a number (N)
of adjacent imaginary segments called
theoretical plates
 Within each theoretical plate analyte(s)
completely equilibrate between stationary phase
and mobile phase
Column
Theoretical plate

4. Chromatographic principle
The molecules of the
mixture interact with the
molecules of the Mobile
and Stationary Phase
Retardation of rate
of movement of
molecules
Each molecule
interacts differently
with MP and SP
Different distribution
coefficients and different
net rates of migration
Stationary phase
Mobile phase
Sample
mixture Equilibrium
establishes at each
point (ideally)

5.  Greater separation occurs with:
–greater number of theoretical plates (N)
–as plate height (H or HETP) becomes smaller
L = N H or H = L / N
where L is length of column
N is number of plates
H is height of plates or height equivalent
to theoretical plate (HETP)
The smaller HETP, the narrower the eluted peak

6. •N = 5.55 (tR / w1/2) = 16 (tR /w)
2 2
where:
tR is retentiontime
w1/2 is width at h0.5
w is width measured at baseline
N is a ratio of tR and σ of Wb which is 4σ

7. Where:
N = Number of theoretical plates
Ve = elution volume or retention time (mL, sec,
or cm)
h = peak height
w1/2 = width of the peak at half peak height
(mL, sec, or cm)

8. • Nmax = 0.4 * L/dp where:
Nmax - maximum column efficiency
L - column length
dp - particle size
• So, the smaller the particle size the higher the
efficiency!
Band spreading - the width of bands increases as
their retention time (tR) or retention volume (VR)
increases

9. Van Deemter model
u = L/ tM
H = A + B/u + u [CM +CS]
A: random movement through stationary phase
B: diffusion in mobile phase
C: interaction with stationary phase
H: plate height
u: average linear velocity
It predicts a minimum plate height at an optimum
velocity and, thus, a maximum efficiency. All such
equations give a type of hyperbolic function

10. the height of the theoretical plate, HETP
H = σ2/L
σ = Standard deviation of the band
H = plate height, which is equal to H/dP
dP = particle diameter

11. Van Deemter plot
A plot of plate height vs average linear velocity of mobile
phase
Such plot is of considerable use in determining the optimum
mobile phase flow rate
The Rate Theory of Chromatography

12. Term A
-molecules may travel
unequal distances
- independent of u
-depends on size of
stationary particles or
coating (TLC)
H = A + B/u + u [CM +CS]
Van Deemter model
time
Eddy diffusion
MP moves through the column
which is packed with stationary
phase. Solute molecules will take
different paths through the
stationary phase at random. This
will cause broadening of the
solute band, because different
paths are of different lengths.

13. Van Deemter model
H = A + B/u + u [CM +CS]
Term B
Longitudinal diffusion
B = 2γ DM
γ: Impedance factor due to
packing
DM: molecular diffusion
coefficient
B term dominates at low u, and
is more important in GC than LC
since DM(gas) > 104 DM(liquid)
One of the main causes of
band spreading is
DIFFUSION
The diffusion
coefficient measures
the ratio at which a
substance moves
randomly from a region
of higher concentration
to a region of lower
concentration

14. Van Deemter model
H = A + B/u + u [CM +CS]
Term B
Longitudinal diffusion
B = 2γ DM
γ: Impedance factor due to
packing
DM: molecular diffusion
coefficient
more important in GC than LC
since DM(gas) > 104 DM(liquid)
B - Longitudinal diffusion
The concentration of analyte is less
at the edges of the band than at
the centre. Analyte diffuses out
from the centre to the edges. This
causes band broadening. If the
velocity of the mobile phase is high
B term dominates at low u and is then the analyte spends less time
in the column, which decreases the
effects of longitudinal diffusion.

15. C : stationary phase-mass transfer
s
Cs = [(df)2]/Ds
f
d : stationary phase film thickness
s
D : diffusion coefficient of analyte in SP
CM: mobile phase–mass transfer
CM = [(dP)2]/DM
CM = [(dC)2]/DM
packed columns
open columns
Van Deemter model
H = A + B/u + u [CM +CS]
Term C
dP: particle diameter
dC: column diameter
Bandwidth
Stationary
phase
Mobile
phase
Elution
Broadened bandwidth
Slow
equilibration

16. H = A + B/u + u [CM +CS]
Van Deemter model
Term C (Resistance to mass transfer) Bandwidth
Stationary
phase
Mobile
phase
Elution
Slow
equilibration
Broadened bandwidth
The analyte takes a certain amount of time to equilibrate between the
stationary and mobile phase. If the velocity of the mobile phase is high,
and the analyte has a strong affinity for the stationary phase, then the
analyte in the mobile phase will move ahead of the analyte in the
stationary phase. The band of analyte is broadened. The higher the
velocity of mobile phase, the worse the broadening becomes.

17. Eddy diffusion, the A term, is caused by a turbulence in
the solute flow path and is mainly unaffected by flow
rate.
Longitudinal diffusion, the B term, is the movement of an
analyte molecule outward from the center to the edges
of its band. Higher column velocities will limit this
outward distribution, keeping the band tighter.
Mass transfer, the C term, is the movement of analyte,
or transfer of its mass, between the mobile and
stationary phases. Increased flow has been observed to
widen analyte bands, or lower peak efficiencies.

18. H = A + B/u + u [CM +CS]
Van Deemter model Figure 1

19. Decreasing particle size has been observed to limit the
effect of flow rate on peak efficiency—smaller particles
have shorter diffusion path lengths, allowing a solute to
travel in and out of the particle faster. Therefore the
analyte spends less time inside the particle where peak
diffusion can occur.
Van Deemter plots for various particle sizes. It is clear
that as the particle size decreases, the curve becomes
flatter, or less affected by higher column flow rates.
Smaller particle sizes yield better overall efficiencies,
or less peak dispersion, across a much wider range of
usable flow rates.

20. Smaller particle sizes yield higher overall peak
efficiencies and a much wider range of usable
flow rates