Determining Polymer Molar Mass: Which Average and Which Method
A polymer has no single molar mass, so the method you choose determines which average you get — and the two can differ substantially.
Why there is no single value
Polymerisation produces chains of many different lengths, so the sample contains a distribution rather than one species. Any reported molar mass is an average over that distribution, and different averaging methods weight the chains differently.
Polydispersity
The ratio measures the breadth of the distribution. A value of one means every chain has the same length, which occurs in certain natural polymers such as proteins, where the sequence is genetically specified. Synthetic polymers typically have values well above one, and the value depends on the polymerisation mechanism.
Chain-growth and step-growth polymerisations give characteristically different distributions, so the polydispersity itself carries information about how the polymer was made.
Which method gives which average
| Method | Average obtained | Why |
|---|---|---|
| Osmometry and other colligative methods | Number average | They count particles, regardless of size |
| Light scattering | Weight average | Scattering intensity increases with particle mass |
| Viscosity | Viscosity average | Empirical, lying between the two |
| Size exclusion chromatography | The whole distribution | Separates by size, so both averages follow |
Understanding why each method gives its particular average is what questions test. Colligative properties depend on particle number and nothing else, so a short chain counts as much as a long one. Light scattering depends on mass, so long chains dominate the signal.
The viscosity method
Dissolving a polymer raises the viscosity of the solvent, and the increase depends on molar mass. The intrinsic viscosity is obtained by extrapolating measurements to infinite dilution, and it relates to molar mass through the Mark–Houwink equation:
K and a are empirical constants for a given polymer, solvent and temperature. Because they must be determined by calibration against another method, viscometry is a relative technique rather than an absolute one — a limitation worth stating.
The exponent a carries information about chain shape: it is near 0.5 for a randomly coiled chain in a poor solvent, higher in a good solvent where the chain expands, and approaches 2 for a rigid rod.
Choosing a method in practice
- Osmometry where the number average is wanted and the polymer is soluble with a suitable membrane available.
- Light scattering where the weight average is wanted and the sample can be made dust-free, which is the main practical difficulty.
- Viscometry where speed and simplicity matter and calibration data exist.
- Size exclusion chromatography where the full distribution is needed, which is now the routine industrial method.
Frequently asked questions
Why is the weight average larger than the number average?
Because it weights each chain by its own mass, so longer chains contribute disproportionately. Only a perfectly uniform sample gives equal values.
Why do colligative methods give the number average?
Because colligative properties depend on the number of dissolved particles regardless of their size, so every chain contributes equally.
Why is viscometry not an absolute method?
Because the Mark–Houwink constants must be obtained by calibration against another technique for each polymer, solvent and temperature combination.
What does a polydispersity index of one mean?
That all chains have identical length. It occurs in proteins and other biologically specified polymers but essentially never in synthetic ones.
Preparing for a chemistry entrance exam?
ABC Chemistry runs focused IIT-JAM, CSIR-NET, GATE and CUET-PG Chemistry coaching at our centre and through live online classes for students across India.
Call / WhatsApp: +91 92121 42427