Formula used
- From persistence length: b = 2lp
- From end-to-end RMS: b = Rrms2 / L
- From radius of gyration: b = 6Rg2 / L
- From characteristic ratio: b = C∞ · l
These relations map real chains to an equivalent freely-jointed chain. Provide contour length when you need NK = L/b.
How to use this calculator
- Select an estimation method that matches your measurement type.
- Choose the unit used by your length inputs.
- Enter the required values; add contour length when requested.
- Enable uncertainties if you want ± propagation on b.
- Press Calculate to display results above the form.
- Use CSV or PDF buttons to export the computed summary.
Example data table
| Method | Inputs | Example values | Estimated b |
|---|---|---|---|
| Persistence length | lp | lp = 50 nm | b = 100 nm |
| End-to-end RMS | Rrms, L | Rrms = 120 nm, L = 1000 nm | b = 14.4 nm |
| Radius of gyration | Rg, L | Rg = 40 nm, L = 1000 nm | b = 9.6 nm |
| Characteristic ratio | C∞, l | C∞ = 9.5, l = 0.154 nm | b = 1.463 nm |
Values are illustrative and depend on solvent, temperature, and chain chemistry.
Professional guide to Kuhn length estimation
Kuhn length is a practical stiffness metric that turns diverse measurements into one comparable segment length. It supports quick model comparisons across datasets. Use the same input units for all lengths, then export results to document assumptions, conditions, and uncertainty ranges.
1) Meaning of Kuhn length in polymer physics
The Kuhn length b maps a real chain onto a freely-jointed chain with the same mean-squared size. Larger b implies stronger local alignment and fewer independent steps for a given contour length L.
2) Persistence length link for semiflexible chains
For a wormlike chain, a standard mapping is b = 2lp. As a benchmark, double-stranded DNA often has lp ≈ 50 nm (so b ≈ 100 nm), while F-actin can reach lp ≈ 10–20 µm.
3) Using end-to-end RMS distance data
When you know the RMS end-to-end distance Rrms and contour length L, the estimator uses b = Rrms2/L. This route is common in simulations and single-molecule work where Rrms is measured directly.
4) Inferring b from radius of gyration
Scattering experiments often report Rg. For Gaussian coils, ⟨R2⟩ = 6Rg2, giving b = 6Rg2/L. Use this when the measured length scales behave close to ideal.
5) Characteristic ratio route for chemical detail
If you have structural data, b = C∞·l connects chemistry to stiffness via the characteristic ratio C∞ and an effective backbone bond length l. Polystyrene is frequently cited with C∞ around 9–10, depending on definition and conditions.
6) Interpreting NK and chain size checks
The calculator reports NK = L/b. Large NK usually supports Gaussian statistics, while small NK signals semiflexibility. The shown √NK·b is a quick check against measured RMS dimensions.
7) Sensitivity to environment and sample details
Kuhn length can shift with solvent quality and temperature because torsional populations and effective interactions change. For polyelectrolytes, ionic strength can strongly alter apparent lp. Report conditions and avoid mixing datasets from different environments.
8) Practical workflow and uncertainty reporting
Choose the method matching your experiment, then keep all lengths in consistent units. If you have error bars, enable uncertainties for first-order propagation. Export CSV/PDF to capture inputs, computed b, and notes for lab notebooks and reports.
FAQs
1) What is a typical Kuhn length for flexible polymers?
Many flexible synthetic polymers have Kuhn lengths on the order of 0.5–2 nm, but it depends on chemistry, solvent, and temperature. Use literature values measured under matching conditions for the best comparison.
2) When should I prefer the persistence-length method?
Use b = 2lp when your system is well-described as a wormlike chain, such as DNA, actin, or semiflexible biopolymers. It is also appropriate when lp is directly measured from tangent correlations.
3) Do I need contour length for every method?
No. The persistence-length and characteristic-ratio methods can estimate b without L. Contour length is required for the Rrms and Rg routes, and it enables reporting NK for all methods.
4) Why does b change between experiments?
Different techniques probe different length scales and assumptions. Solvent quality, ionic strength, temperature, and chain polydispersity can shift the effective stiffness. Always compare values only when conditions and definitions are consistent.
5) What does NK tell me in practice?
NK estimates how many statistically independent segments the chain contains. Large NK generally indicates coil-like behavior and better applicability of Gaussian statistics, while small NK suggests semiflexible behavior.
6) How are uncertainties handled in the calculator?
The calculator uses standard first-order error propagation for products, ratios, and squares. It is a practical estimate for small relative uncertainties. For strongly non-linear regimes or large errors, consider a Monte Carlo approach.
7) Can I use this for branched or crosslinked polymers?
You can estimate an effective Kuhn length, but interpretation becomes model-dependent. Branching changes how Rg and Rrms relate to contour length. For networks, segment-based elasticity models may be more appropriate.