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The polydispersity index of a polymer is given by the ratio of :

  • A.\(\bar{\mathrm{M}}\mathrm{v} / \bar{\mathrm{M}}\mathrm{w}\)
  • B.\(\bar{\mathrm{M}}\mathrm{w} / \bar{\mathrm{M}}\mathrm{z}\)
  • C.\(\bar{\mathrm{M}}\mathrm{w} / \bar{\mathrm{M}}\mathrm{n}\)
  • D.\(\bar{\mathrm{M}}\mathrm{n} / \bar{\mathrm{M}}\mathrm{w}\)

Answer: C

The polydispersity index is M̄w / M̄n, the weight-average over the number-average molecular weight.

The number average weights every chain equally, while the weight average gives heavier chains more weight. For any sample with a spread of chain lengths M̄w is larger than M̄n, so the ratio is at least 1, and the larger it is the broader the distribution. A perfectly uniform polymer has a ratio of exactly 1; a typical condensation polymer is near 2.

M̄n / M̄w is the inverse and would always be 1 or less. M̄w / M̄z and M̄v / M̄w use the z-average and the viscosity average, which are real averages but are not the ones that define the polydispersity index.

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