Advanced Calculation Form
Formula Used
Bending rigidity: Lp = κ / (kB × T). Here κ is bending rigidity, kB is Boltzmann constant, and T is Kelvin temperature.
Tangent correlation: Lp = -s / ln(〈t(0) · t(s)〉). This uses tangent direction decay along contour separation s.
Force extension: F = (kB × T / Lp)[1 / 4(1 - x/Lc)² - 1/4 + x/Lc]. The calculator rearranges it for Lp.
End-to-end estimate: 〈R²〉 = 2LpLc[1 - (Lp/Lc)(1 - exp(-Lc/Lp))]. The calculator solves this equation numerically.
How to Use This Calculator
- Select the method that matches your available data.
- Enter the required measurements and choose correct units.
- Add Kelvin temperature when the method uses thermal energy.
- Choose the output unit for the final persistence length.
- Press the calculate button and review the result above the form.
- Use the CSV or PDF button to save the current result.
Example Data Table
| Sample |
Method |
Input |
Expected Scale |
| Flexible polymer |
Tangent correlation |
s = 100 nm, correlation = 0.1353 |
About 50 nm |
| Stiff filament |
Bending rigidity |
κ = 205.7 pN·nm², T = 298.15 K |
About 50 nm |
| Stretching test |
Force extension |
F = 0.1 pN, x = 900 nm, Lc = 1000 nm |
High stiffness estimate |
| Coil image |
End-to-end estimate |
Rrms = 300 nm, Lc = 1000 nm |
Model fitted value |
Persistence Length in Physics
Persistence length describes how far a chain keeps its direction before thermal motion bends it. It is a central quantity in polymer physics, biophysics, and soft matter studies. A large value means a stiff chain. A small value means a flexible chain.
Supported Methods
The calculator supports several common routes. The bending rigidity method uses thermal energy and stiffness. It is useful when the material constant is known. The tangent correlation method uses the average cosine between two local tangent vectors. It is common in simulations and image analysis. The force extension method follows the worm like chain relation. It is useful for stretching experiments. The end to end method estimates the value from contour length and root mean square span.
Unit and Temperature Care
Good input units matter. Convert all lengths carefully before comparing samples. Temperature also matters because thermal energy changes with Kelvin value. At higher temperature, the same stiffness gives a shorter persistence length. That is why the temperature field is included for stiffness and force calculations.
Reading the Result
The result should be read as a model based estimate. Real polymers may have sequence effects, salt effects, surface sticking, or measurement noise. For example, DNA stiffness changes with ionic conditions. Protein filaments can also show bundling, defects, or local curvature. These effects may shift the apparent value.
Uncertainty Use
Use the uncertainty box to add a simple percentage range. This does not replace a full error analysis. It gives a quick working interval for reports. For detailed work, repeat measurements and fit all raw data together.
Why It Matters
Persistence length helps compare materials. It links microscopic stiffness with visible shape. It also helps choose models for simulations. When the contour length is much larger than the persistence length, the chain behaves flexibly. When the contour length is shorter, it behaves like a rod. This simple idea makes the value useful in many experiments.
Method Choice
Always choose the method that matches your data. Use bending rigidity for known stiffness. Use tangent correlation for angle data. Use force extension for pulling data. Use end to end fitting for coil shape data. Check the formula section after calculation. It shows the equation used and the converted result.
Record assumptions beside every value, so later readers can repeat the calculation without guessing hidden settings.
FAQs
What is persistence length?
Persistence length is the distance over which a polymer keeps its tangent direction. A larger value means the chain resists bending more strongly.
Which method should I choose?
Choose bending rigidity for known stiffness, tangent correlation for angle data, force extension for pulling data, and end-to-end for coil shape data.
Why does temperature affect the result?
Thermal energy equals kB times temperature. Higher thermal energy bends chains more easily, so the same rigidity gives a shorter persistence length.
Can correlation be equal to one?
No. A value of one gives an infinite length in the exponential model. Enter a value greater than zero and less than one.
What is contour length?
Contour length is the full length measured along the chain backbone. It is not the straight distance between the ends.
Why must extension be less than contour length?
The worm-like-chain force equation approaches a limit as extension nears contour length. Equal or larger extension is not physically valid here.
Does the uncertainty range replace error analysis?
No. It gives a simple percentage range for quick review. Use repeated measurements and fitting for formal uncertainty analysis.
Can I export the calculation?
Yes. After calculating, use the CSV or PDF button. The file includes the method, formula, result, and converted values.