Degree of polymerization

The degree of polymerization, or DP, is usually defined as the number of monomeric units in a macromolecule or polymer or oligomer molecule.

For a homopolymer, there is only one type of monomeric unit and the number-average degree of polymerization is given by ${\displaystyle DP_{n}\equiv X_{n}={\frac {M_{n}}{M_{0}}}}$, where M_n is the number-average molecular weight and M₀ is the molecular weight of the monomer unit. For most industrial purposes, degrees of polymerization in the thousands or tens of thousands are desired. This number does not reflect the variation in molecule size of the polymer that typically occurs, it only represents the mean number of monomeric units.

The number of monomeric units in a macromolecule,
an oligomer molecule, a block, or a chain.

Some authors, however, define DP as the number of repeat units, where for copolymers the repeat unit may not be identical to the monomeric unit. For example, in nylon-6,6, the repeat unit contains the two monomeric units —NH(CH₂)₆NH— and —OC(CH₂)₄CO—, so that a chain of 1000 monomeric units corresponds to 500 repeat units. The degree of polymerization or chain length is then 1000 by the first (IUPAC) definition, but 500 by the second.

In step-growth polymerization, in order to achieve a high degree of polymerization (and hence molecular weight), X_n, a high fractional monomer conversion, p, is required, according to Carothers' equation${\displaystyle {\bar {X}}_{n}={\frac {1}{1-p}}}$ For example, a monomer conversion of p = 99% would be required to achieve X_n = 100.

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