The document discusses various concepts related to chromatography including migration rates of solutes. It defines key terms like distribution constant, dead time, retention time, retention factor, selectivity factor, theoretical plates, plate height, number of plates, and resolution. It explains how changing parameters like mobile phase composition, column temperature, and stationary phase composition can be used to optimize selectivity factor and resolution to improve separations. Temperature programming in gas chromatography is also discussed as a way to separate components that may not elute or have broad peaks under isothermal conditions.

1. PST351-POLYMER CHARACTERISATION
MIGRATION RATES OF SOLUTE

2. PST351-POLYMER CHARACTERISATION
BACKGROU
ND
• Chromatogram is useful for both qualitative and
quantitative analysis.
• The positions of peaks on the time axis - identify
the components of the sample;
• the areas under the peaks-quantitative measure
of the amount of each component.

3. PST351-POLYMER CHARACTERISATION
BACKGROU
ND
Graph showing detector response as a function of
elution time.

4. PST351-POLYMER CHARACTERISATION
• The effectiveness of a chromatographic column in
separating two solutes depends in part on 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.
BACKGROUND

5. PST351-POLYMER CHARACTERISATION
DISTRIBUTION
CONSTANT
The distribution equilibria involved in chromatography involve the
transfer of an analyte between the mobile and stationary phases.
The equilibrium constant (Kc ) for this reaction is called the
distribution constant, which is defined as;
Where;
cs is the molar concentration of the solute in the stationary phase
cm is its molar concentration in the mobile phase
K is constant over a wide range of solute concentrations.

6. PST351-POLYMER CHARACTERISATION
The Dead Time (tM), Stationary Time
(tS), & Retention Time (tR)
▪ The time between sample injection and the appearance of the
non-retained species peak is called as the dead or void time, (tM).
▪ It is the time it takes for an unretained species to
pass through chromatography column.
▪ All components spend the dead time in the mobile
phase
▪ Separation are based on the different times, ts that
components spend in stationary phase
▪ The dead time provides a measure of the average rate of
migration of a mobile phase and is an important parameter to
identifying analyte peaks.

7. PST351-POLYMER CHARACTERISATION
The time it takes after sample injection for the analyte peak to
reach the detector is called the retention time , (tR).
The analyte has been retained because it spends a time in the
stationary phase, (ts)
The retention time is then calculated by;
The Dead Time (tM), Stationary Time
(tS), & Retention Time (tR)

8. PST351-POLYMER CHARACTERISATION
The Dead Time (tM), Stationary Time
(tS), & Retention Time (tR)

9. PST351-POLYMER CHARACTERISATION
Retention Factor (k’)
The retention factor (capacity factor), k’ is an important parameter that is
widely used to describe the migration rates of solutes on columns
For a solute A, the retention factor k`A is defined as;
where;
k’A is the distribution constant for the species A.
tR and tM are readily obtained from a chromatogram

10. PST351-POLYMER CHARACTERISATION
Retention Factor (k’)
When the retention factor for a solute is much less than this range (1-
5), seperation occurs so rapidly that accurate determination of the
retention times is difficult.
When the retention factor is larger (20 to 30) , seperation times become
inordinately long.

11. PST351-POLYMER CHARACTERISATION
Selectivity Factor, 
The selectivity factor,  of a column for the two species A and B is defined as;
where;
KB is the distribution constant for species B
KA is the distribution constant for species A
A relationship between the selectivity factor and retention factors can be described
as:
Where;
k`B is the retention factor of species A.
k`A is the retention factor of species B.

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The theoretical Plate Model of Chromatography
• The plate model supposes that the chromatographic column is
contains a large number of separate layers, called theoretical
plates.
• Separate equilibrations of the sample between the stationary and
mobile phase occur in these "plates".
• The analyte moves down the column by transfer of equilibrated
mobile phase from one plate to the next.

13. PST351-POLYMER CHARACTERISATION
Column Efficiency
To obtain optimal separations, sharp, symmetrical
chromatographic peaks must be obtained. This means that band
broadening must be limited. It is also beneficial to measure the
efficiency of the column.
Two related terms are widely used as quantitative measures of
chromatographic column efficiency
Plate Height, H Number of Plate, N
The two are related by the equation;
where L is the length (usually in centimeters) of the column packing.
The efficiency of chromatographic columns can be increases by
• Increase the number of plates, N
• Reduce the plate height
N= L/H

14. PST351-POLYMER CHARACTERISATION
Column
Efficiency • No of plate, N = the
more plates the
better
• Plate height, H = the
smaller the better

15. PST351-POLYMER CHARACTERISATION
The number of theoretical plates that a real column possesses can
be found by examining a chromatographic peak after elution;
Column Efficiency
As can be seen from this equation, columns behave as if they
have different numbers of plates for different solutes in a mixture.
where w1/2 is the peak width
at half-height.

16. PST351-POLYMER CHARACTERISATION
Column
Resolution (Rs)
The resolution Rs of a column provides a quantitative measure of
its ability to separate two analytes.
The resolution of two species, A and B, is defined as
Baseline resolution is achieved when R = 1.5

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It is useful to relate the resolution to the number of plates in the
column, the selectivity factor and the retention factors of the two
solutes;
Column
Resolution (Rs)
From this equation, it is known that to obtain high resolution, the
three terms must be maximised.
• An increase in N, the number of theoretical plates,
• Reduce the column height by
- reducing the size of the stationary phase particles.

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Column
Resolution
(Rs)
Apart from improving column resolution to improve
separation, it is often found that by controlling the capacity
factor, k', separations can be greatly improved.
This can be achieved by:
• Changing the temperature (in Gas Chromatography) or
• Changing the composition of the mobile phase (in Liquid
Chromatography).

19. PST351-POLYMER CHARACTERISATION
The selectivity factor,  can also be manipulated to improve separations.
In these cases, k' is optimised first, and then a is increased by one of the
following procedures:
1. Changing mobile phase composition
2. Changing column temperature
3. Changing composition of stationary phase
4. Using special chemical effects (such as incorporating a
species which complexes with one of the solutes into the
stationary phase)
Column
Resolution (Rs)

20. PST351-POLYMER CHARACTERISATION
Column
Temperature
• The retention time of a compound depends not only on the
type of stationary phase but also the column temperature.
• In general you can analyze your sample under isothermal
conditions in which the temp of the column remains constant
throughout the analysis.
• As the temperature increases, compounds move through the
column faster and consequently, the retention time decreases.
• Thus, we can potentially reduce the analysis time by
increasing column temperature; however, we need to allow
sufficient time for the compounds to interact with the
stationary to provide the required separation of sample
components.

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Column
Temperature
In the simplest GC analysis, the column is maintained at a constant
temperature and is termed “isothermal” analysis.
The chromatogram in this figure shows the separation of a mixture of
normal alkanes (straight-chained hydrocarbons) ranging from C6 to C21
using isothermal conditions at 150 C.
The low molecular weight alkanes <C10 elute very quickly and are not
resolved.
The higher molecular weight components >C16 do not elute from the
column at this temperature and C14 and C15 are broad, asymmetrical
peaks.

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Column
Temperature
The chromatogram shows the same alkane mixture analyzed
using “temperature programmed” conditions.
In this case, the column temperature is increased from 50 to 250
C at 8 C/ min during the analysis.
All of the alkane components are completely separated into
narrow, symmetrical peaks.

23. PST351-POLYMER CHARACTERISATION
Column
Temperature Comparing that separation of the same
mixture with the lower chromatogram
which is temperature programmed from
50 degrees to 250 degrees at 8 degrees
per minute , it can be seen that;
- The separation efficiency is much
greater here (graph b).
- Higher molecular weigh components
longer chain hydrocarbons that being
eluted
In a conclusion, it can be said that;
- The longer the compound is in the
column the broader the peaks become.
- These peaks become quite broad and
present some integration difficulties as
they become broader (graph a).