DP Number (Degree of Polymerization)
Definition and meaning of DP Number (Degree of Polymerization) in chemistry.
DP number (degree of polymerization) is the number of repeating monomer units linked together in a single polymer chain. It is the primary measure of how long a polymer molecule is and directly determines its molecular weight.
In more detail
Because most polymerization reactions produce chains of many different lengths, a bulk sample's DP is reported as an average, most commonly the number-average degree of polymerization, Xn. DP is linked to molecular weight through Mn = DP × M0, where M0 is the molar mass of the repeat unit. In step-growth polymerization, the Carothers equation, DP = 1/(1 − p), shows that DP rises sharply only as the fractional conversion p of functional groups approaches 1, explaining why high-molecular-weight polymers require near-complete conversion. Higher DP generally increases chain entanglement, raising viscosity, tensile strength, and melting or softening temperature.
Key facts
| Symbol | DP or Xn |
|---|---|
| Key relation | Mn = DP × M0 |
| Carothers equation | DP = 1/(1 − p) |
| Field | Organic Chemistry |
A polyethylene chain built from 10,000 repeating –CH2–CH2– units has DP = 10,000; since the repeat unit's molar mass is about 28 g/mol, its number-average molecular weight is Mn ≈ 10,000 × 28 g/mol = 280,000 g/mol.
Frequently asked questions
Is DP the same for every chain in a polymer sample?
No. Real polymerizations produce chains of varying length, so DP is usually reported as an average (commonly the number-average degree of polymerization, Xn) rather than a single fixed value.
How is DP related to molecular weight?
The number-average molecular weight equals DP times the molar mass of the repeating unit: Mn = DP × M0.