Polymer Structure & Synthesis
Determination of Molecular Weight and
Molecular Weight Distribution
Cryoscopy
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Freezing point of a solvent is lowered when a nonvolatile solute is dissolved in it.
Freezing point of the solution will be depressed.
This phenomenon of depressing the freezing point
of a liquid by the addition of a solute is known as
Cryoscopy.
The extent of the freezing point depends on the
number of solute molecules dissolved per unit
volume of solution and its independent of the size
and nature of the solute molecule.
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Polymer Structure & Synthesis
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So, Number average molecular wt. is measured by this
technique.
If depression of the freezing point is denoted by  Tf
, Its related to the Number-average Molecular wt. and
concentration through following equation.
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 Tf /C = (RTf / Hf ) 1/M+BC
2
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Where, C is concentration of the solution, ρ the density of
the solvent, R the universal gas constant; Tf the freezing
point of the solvent, B is a constant and ΔHf is the heat of
fusion of the solvent.
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Graphical representation.
To find out the freezing point, solvent or solution is
carefully supercooled to a temperature that is about 5C
lower than the freezing point.
Once the freezing points of the solvent and solutions Tf
different concentrations are known, ΔTf can be calculated
for all these concentrations.
Drawback of this method is, measurement of temperatures.
Highly precised temperature sensors are required.
This method can measure molecular wt. upto 30,000.
Polymer & Process Engineering
Polymer Structure & Synthesis
Ebulliometry
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This technique is based on boiling point of
solutions.
Boiling point of solutions is higher than the pure
solvents. This phenomenon is used to determine
the molecular wt. of polymers.
 
 Tb /C=(RTb / Hv ) 1/M n +BC
2
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Where ΔHv and Tb are the heat of vaporization
and boiling of the solvent.
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Polymer Structure & Synthesis
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There are two types of ebulliometers.
In first type, the solution of the polymer whose
molecular wt. is to be determined is heated in a
boiler. The solution is then brought in contact with
a sensor. Another in pure solvent.
In second type, both of solution and pure solvent
are heated in identical containers and uniform
boiling is achieved.
It can also be used to determine the molecular wt.
upto 30,000.
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Polymer Structure & Synthesis
Membrane Osmometry
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It is most widely used technique to determine
number average molecular wt.
It is based on the phenomenon of osmosis.
What is Osmotic pressure?
 /RTC=1/M n +BC
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Π is the osmotic pressure.
Polymer & Process Engineering
Polymer Structure & Synthesis
Vapor Phase Osmometry
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This technique is based on the principle that at a
given temperature the vapor pressure of a solution
is less than that of the pure solvent.
The relationship between the vapor pressure
difference of solvent and solution,  P=(p -p )
and number average molecular wt. is given as
0
1
limc  0
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 P/C
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o
1
o
=-p 1 V1 /M
Experimental method.
Polymer & Process Engineering
Polymer Structure & Synthesis