a chain-folded lamella
Here is a puzzle. A single polyethylene chain, laid out straight, might be a thousand nanometres long — but the tiny crystals it forms are only about ten nanometres thick. How does a chain a hundred times too long fit into a crystal a hundred times too thin? The answer, discovered in the 1950s, is that the chain folds back on itself again and again, like a fire hose flaked down on a deck or a ribbon folded into a neat concertina. The thin plate-like crystal this builds is a chain-folded lamella, and it is the fundamental building block of every crystalline polymer.
In detail, the chain runs across the short thickness of the plate, reaches the top surface, hairpins back down, crosses again, folds at the bottom, and repeats, so that many parallel strands of the same molecule stand side by side inside the lamella, all roughly perpendicular to the two flat faces. The lamella is thin (typically 10-20 nm) but can spread microns wide. How far the chain travels before each fold — the fold length, which fixes the lamellar thickness — is set by the crystallization temperature: crystallize hotter and the folds are longer and the lamellae thicker. In an idealized single crystal grown slowly from dilute solution the chain re-enters right next to where it left (adjacent re-entry, the neat concertina); in a real melt the folding is messier, with loose loops and chains wandering off to neighbouring crystals (the switchboard model).
The chain-folded lamella explains the whole shape of polymer crystallinity. It is why polymer crystals are thin flakes rather than chunky blocks, why a polymer never fully crystallizes (the fold surfaces and the loops hanging off them are inherently disordered), and why lamellar thickness controls the melting point: by the Gibbs-Thomson relation a thinner lamella has proportionally more high-energy fold surface and so melts at a lower temperature, which is why annealing a polymer thickens its lamellae and raises its melting point. Stack these lamellae with amorphous material between them and radiate them outward from a centre, and you have built the next level up — the spherulite.
Crystallize polyethylene slowly from a dilute solution and it grows flat diamond-shaped single crystals about 10 nm thick. Electron diffraction shows the chains stand perpendicular to those flat faces — impossible unless a chain far longer than 10 nm folds back and forth across the thickness. A 1250 nm chain in a 10 nm lamella must fold on the order of a hundred times.
A lamella is a ~10 nm-thick crystal in which a long chain folds back and forth; thickness sets the melting point.
The surprise for beginners: inside the crystal the chain is folded, not stretched fully straight. Extended-chain crystals do exist (under pressure, or in rigid polymers), but the everyday crystalline unit is the thin chain-folded lamella.