the degree of polymerization

If a polymer chain is a necklace of identical beads, the degree of polymerization is simply how many beads are on the string. It is the chain length counted in repeat units — the number n in that (mer)n formula. A short chain with a low degree of polymerization is a stubby little necklace; a long chain with a high one stretches on and on. This single number is one of the most important handles you have on how a plastic will behave.

You compute it by dividing the molecular weight of the whole chain by the molecular weight of one mer. Take polyethylene with an average molecular weight of 280,000 g/mol; one mer (-CH2-CH2-) weighs 28 g/mol, so the degree of polymerization is 280,000 / 28 = 10,000 repeat units. There is a catch that makes this an average rather than a fixed number: in any real batch the chains are not all the same length, so we quote an average degree of polymerization built from an average molecular weight. There are two common averages — number-average (counting each chain equally) and weight-average (giving heavier chains more say) — and the weight-average is always the larger of the two.

It matters because chain length quietly controls strength, stiffness, viscosity, and melting behaviour. Longer chains tangle and grip their neighbours more, so as the degree of polymerization rises the material gets stronger and tougher and its melt gets thicker and harder to pour. Below a threshold length a polymer is just a weak, waxy solid — the same chemistry, but too short to entangle. One honest note: because chains come in a spread of lengths, a single degree-of-polymerization number hides a whole distribution, and the width of that distribution (the polydispersity, Mw/Mn) is itself a property engineers care about.