Rate theory, Plate Theory and System suitability Parameters

2. Plate Theory of Chromatography
The plate theory of chromatography is an older concept and does not
give a realistic view of column efficiency and what is happening in the
column. The theory was integrated into the chromatography technique
in 1941 by Martin and Synge.
According to the model, the chromatographic column consists of
separate layers known as the theoretical plates. These plates are
hypothetical zones or stages that help in establishing an
equilibrium between two phases.
Unlike the rate theory of chromatography, it gives a hypothetical
picture of the separation of the analytes in a chromatographic
column.
These plates provide separation equilibrium of the sample between
the mobile and stationary phase.

4. As the mobile phase passes through the stationary phase in a column,
the analytes in the mobile phase are distributed between the two
phases establishing an equilibrium.
Once the equilibrium is obtained, the solute from the mobile phase
is carried from one plate to another and continues till it is eluted
out of the column. The nature and solute type determine the retention
time and peak width.
As the theoretical plate number increases in the column, it narrows the
solute peak and provides better resolution between different
components in the sample.
The number of the theoretical plate in a column is represented by N.
The efficiency of the column is represented by HETP (Height
Equivalent to a Theoretical Plate). A measure of the efficiency of a
chromatography column is the height equivalent to a theoretical plate
or plate height.

5. As the number of theoretical plates is increased in a column, the
solute peak becomes narrower and this results in a much better
resolution between different sample components in a run.
The number of theoretical plates is denoted by N.
A large N value indicates greater resolving or separation power of
the column. This is what is referred to as the Efficiency of the
column.
Another term which describes the efficiency of the column is HETP
(Height Equivalent to a Theoretical Plate) which can be calculated as
H = L/N,
where, L is the column length in mm
And
N s the number of theoretical plates.

6. Hence a large value for N or a very low value for HETP indicates
high efficiency of the chromatographic column.
The chromatographic resolution is related to the number of theoretical
plates of the column, the selectivity factor and the retention factors of
two solutes by the following equation:
R=1/4(√N ) (α-1/α) (k’/k’+1)
If all the variables in the resolution equation are kept constant, except
the number of theoretical plates, then the resolution is proportional
to the square root of N.
Therefore, increasing the number of theoretical plate by 4 will
increase the resolution by a factor of 2.

7. Rate Theory of Chromatography
The theories help understand how the analytes move in the
stationary phase as the mobile phase flows through it.
The rate theory of chromatography defines the activity in a
chromatography column. It shows that when solute elutes out of the
column, it impacts the band shape and is affected by the elution
rate.
The rate theory provides information about the shape and breadth of
the elution bands as the mobile phase migrates and flows through a
column. It helps understand the process of peak dispersion and factors
impacting band broadening.
It gives a realistic explanation of the process occurring in a
chromatographic column. It considers and measures the time taken by
the solute to equilibrate between the stationary and mobile phase.
It considers the rate of elution on the resulting band shape or the
chromatographic peak.
The rate theory of chromatography is expressed mathematically by the
van Deemter equation. The equation helps calculate the variance per
unit length of a column in terms of mobile phase velocity and analyte
properties.

8. The relationship between a column’s efficiency and the mechanism
behind band broadening is described by the Van Deemter equation.
It is represented by
HETP = A + B/u (Cs + Cm). u
Where
A = Eddy diffusion parameter
B = diffusion co-efficient of eluting particles in the longitudinal direction
C = Resistance to mass transfer coefficient of the analyte between the
stationary and mobile phase
u = speed
Cm = dispersive convection in the mobile phase
Cs = sorption, and desorption of the solute from the stationary phase
HETP is the measure of zone broadening.

9. Eddy Diffusion:
In a packed column, the solute molecules take different paths at
random while passing through the column.
This leads to broadening of the peak because different paths in a
packed column are of different lengths.
To minimize A term, reduce the particle size of the packing
material and also pack the column more uniformly.
Note that A term is not applicable to Open Tubular (capillary) columns.
https://youtu.be/p2KvzK81s2g

10. Longitudinal Diffusion:
As the analyte is passing through the column, it diffuses out towards
the edges of the column.
Hence the concentration of the analyte is always more at the
centre as compared to the edges.
This leads to band broadening.
If the velocity of the mobile phase is high, then the analyte will
spend less amount of time in the column which will reduce the effect of
longitudinal diffusion.
https://youtu.be/wG5nDzKuGDU

11. Resistance to Mass Transfer : The analyte takes a certain amount of
time to equilibrate between the stationary and mobile phases. If the
velocity of the mobile phase is high and the analyte has a strong
affinity towards the stationary phase, then the portion of analyte in the
mobile phase will move ahead of the portion of analyte in the stationary
phase. This will lead to band broadening. The higher the velocity of
mobile phase, more will be the band broadening. The effect of C term
can be reduced by decreasing the stationary phase content (film
thickness in case of capillary column), reducing the column radius
and increasing the temperature.
https://youtu.be/u7EPAPQDLlY

12. The ultimate goal of the chromatographer is to achieve the highest
possible resolution in the shortest possible time by optimizing
various parameters.

13. Various Chromatographic
Parameters in HPLC
A chromatogram is a graphical
representation of separated
eluents, which can be used to
identify compounds and to
determine their relative
concentrations.
It is a visual output of the
chromatograph (instrument).
It can also be defined as a visible
record (such as a graph) showing
the result of separating the
components of a mixture.

14. The various parameters in a chromatogram are as follows:
System suitability.
Retention time.
Retention volume.
Tailing factor.
Asymmetry.
Theoretical plates.
HETP.
Resolution.
System suitability.

15. System Suitability
It is defined by ICH as "the checking of a system, before
or during the analysis of unknowns, to ensure system
performance.
This may include such factors as plate count, tailing,
retention, and/or resolution.
It is a test to determine the suitability and effectiveness of
the chromatographic system before use.
The performance of any chromatographic system may
continuously change during their regular use, which can
affect the reliability of the analytical results.

16. Retention Time
Retention time (RT/tr)
is a measure of the
time taken by a solute
to pass through the
column.
It is calculated as the
time from injection
for detection.
Retention Volume (VR)
Retention volume for a solute is
the volume of the mobile phase
required to carry the solute
through the column to elution.

17. Theoretical Plates
A theoretical plate is a hypothetical zone in which two
phases, such as the liquid and vapor phases of a
substance, establishes an equilibrium with each other.
Such equilibrium stages may also be referred to as an ideal
stage, or a theoretical tray.
It gives information regarding column
efficiency/performance.
n=16(RtWb)2
Where,
n = No of theoretical plates.
Rt= Retention time.
Wb= Width of the peak.

18. HETP (Height Equivalent to the Theoretical Plate)
It is the number of theoretical plates in a chromatography column.
It is used to relate the column height with the number of theoretical
plates.
It is numerically equal to the column length divided by the Platter of
theoretical plates in the column.
HETP (H)=L (Lenght of the column)N (No of theoretical plates)
HETP is given by Van Deemter equation as:
HETP (H)=A + BC + Cs.u. Cm.u
A = Eddy diffusion term or multiple path diffusion, which arises due to
the packing of the column.
B = Molecular diffusion that depends on the flow rate.
C = Effect of mass transfer that depends on the flow rate.
U = Flow rate.

19. Resolution
The resolution of elution is a
quantitative measure of how well two
elution peaks can be differentiated in
chromatographic separation.
Resolution is generally defined as the
difference in retention time between
the two peaks, divided by the
combined widths of the elution peaks.
Asymmetry
The asymmetry is a measure of peak
tailing, and it is defined as the distance
from the centerline of the peak to the
back slope divided by the distance from
the centerline of the peak to the front
slope (with all measurements made at
10% of the maximum peak height).

20. Peak Tailing and Fronting
Peak tailing is the most common
chromatographic peak shape
distortion.
It occurs when the peak asymmetry
factor (As) is greater than 1.2 —
although peaks with As greater than
1.5 are acceptable for many assays.
Tailing occurs when some sites on the
stationary phase retain the solute
more strongly than other sites.
Peak fronting is the result of
overloading the column with a
sample.
Injection of too much sample and
overloading effect results from the poor
sample solubility in the stationary
phase as too much sample is
injected.

21. Retardation Factor (RF)
In chromatography, the retardation
factor is the fraction of an analyte in
the mobile phase of a chromatographic
system, and in planar
chromatography, the retardation factor
(RF) is defined as the ratio of the
distance traveled by the center of a
spot to the distance traveled by the
solvent front.
Retention/Capacity Factor
(K)
A retention or capacity factor
means measuring the retention
of the analyte on the
chromatographic column.
It is defined as the ratio of an
analyte in the retention of
the stationary phase to the
time it is retained in the
mobile phase.
This is inversely proportional
to the retardation factor.