Persistence length is not a material constant
The persistence length lp is the distance over which a chain keeps pointing the same way. Below it the chain is effectively a rigid rod; far above it, direction is forgotten and the chain is a random walk. It is the single number that decides whether a polymer behaves like a rod, a coil, or something awkward in between.
It belongs to a chain in a particular solvent at a particular temperature, and for a charged chain it moves with ionic strength as well. Single-stranded DNA is about 1 nm in high salt and roughly twice that when the salt is removed and the phosphates stop being screened. Xanthan is 120 nm as an ordered helix and far more flexible once heated through its order–disorder transition. Every value in this database is therefore quoted with the conditions it was measured under, and several materials carry more than one. Where they disagree, the disagreement is the data.
This is the worm-like chain, used in its exact form rather than the Gaussian approximation, so it stays correct through the rod-to-coil crossover instead of only in the coil limit. It collapses to ⟨R²⟩ = L² for a short chain and to 2 lpL for a long one, and the radius of gyration uses the matching Benoit–Doty expression.
DNA is the model system, and it is not a coincidence
Almost everything on this page is easiest to see in DNA, for three reasons that no synthetic polymer offers at once. Its persistence length is large enough to see: at about 50 nm it is a hundred times a synthetic coil’s, so a single molecule can be imaged and traced directly rather than inferred from a scattering average. Its stiffness is tunable without changing the chemistry: strip the second strand and it falls to about 1 nm, or remove the salt and electrostatic repulsion stiffens it again. And it comes in exact lengths, so contour length is known rather than averaged over a distribution.
The picture below is not an illustration. Each chain is a simulated two-dimensional worm-like chain generated at lp = 50 nm, with the direction of each step drawn from the same Gaussian the model specifies, so the shapes are real samples from the statistics this page computes. Two dimensions rather than three is also deliberate: it is what a DNA molecule adsorbed on mica looks like down an AFM, which is the subject of the next card. The red bar in each panel is one persistence length to the scale of that panel.
Same molecule, same persistence length, three lengths. At 100 bp the chain is shorter than its own persistence length and is a rod: it has no choice but to be straight. At 1 kb it bends but still remembers roughly where it started. At 10 kb the memory is gone within a small fraction of the chain and what is left is a random walk. Nothing about the molecule changed between panels except how much of it there is.
Calculator
Where this sits
Every measurement in the database on one logarithmic axis. The span from the most flexible synthetic chain to a cytoskeletal filament is close to five orders of magnitude, which is why no single mental model of “a polymer chain” covers all of it.
The database
Every measured value, with the conditions it was measured under. A polymer appears once per measurement.
| Polymer | lp (nm) | Solvent / state | T (°C) | Method | Confidence |
|---|
Predicting lp from the characteristic ratio, and where that fails
For a simple aliphatic backbone the persistence length follows from the characteristic ratio C∞ by geometry alone: b = C∞ l / cos(θ/2) with θ = 180° − the backbone bond angle, and lp = b/2. Since C∞ is tabulated far more widely than lp is, that route is often the only one available.
| Polymer | C∞ | Predicted lp | Measured lp | Ratio |
|---|
It fails for aromatic backbones, and not by a little. Bisphenol-A polycarbonate has C∞ = 2.4, which the formula turns into 0.22 nm — against a measured value near 1.0 nm. The ratio is defined per backbone bond, and a polycarbonate repeat is a rigid phenylene plus a long virtual bond, not the tetrahedral C–C the geometry assumes. Entries where the route does not apply are marked and no prediction is offered for them, rather than quietly printing a number that is wrong by a factor of four.
Related tools
A GPC molar mass is a hydrodynamic-volume measurement calibrated against polystyrene, so a stiff chain and a flexible one of the same true mass do not elute together — see GPC Calibration for the Mark–Houwink correction. The Polymer Search database covers structure and identity, and Thermal Analysis covers the DSC, TGA and DMA side.