Description
Return a small-extension wormlike-chain stiffness and force.
Polymer elasticity and optical trapping relate small displacements or equilibrium fluctuations to an effective stiffness. A linear force law and a variance-based estimate depend on different assumptions; a supplied length or noise correction does not establish that a real system is harmonic or in equilibrium.
Return a small-extension wormlike-chain stiffness and force.
When to use this tool
Use Wormlike Chain Small Extension Slope when evaluating the stated polymer or harmonic-trap term under its supplied assumptions.
How to use the tool and how it works
- Enter thermalEnergy, persistenceLength, contourLength, extension. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read stiffness, force. Use the output convention below.
Return a small-extension wormlike-chain stiffness and force. Require nonnegative thermalEnergy, extension in [0,contourLength], positive persistence/contour lengths; stiffness = 3*thermalEnergy/(2*persistenceLength*contourLength), force = stiffness*extension.1
Polymer force-extension models have distinct limiting regimes. This helper uses the small-extension slope, which does not replace the nonlinear response near contour length.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| thermalEnergy | Supplied thermal energy kB*T in compatible energy units. | Required. Finite number; minimum 0. |
| persistenceLength | Positive polymer bending-persistence length, in the same length unit as contourLength and extension. | Required. Finite number; strictly above 0. |
| contourLength | Contour Length | Required. Finite number; strictly above 0. |
| extension | Extension | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| stiffness | Stiffness | Required. Finite number. |
| force | Force | Required. Finite number. |
{
"input": {
"thermalEnergy": 4,
"persistenceLength": 2,
"contourLength": 6,
"extension": 1
},
"output": {
"stiffness": 0.5,
"force": 0.5
}
}Limitations and assumptions
- The linear approximation requires small extension relative to contour length even though the accepted domain includes its endpoint; no nonlinear force law is solved.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the appropriate complete polymer/trap model, calibrated observations and a justified equilibrium/noise analysis for physical parameter inference.
References
Similar or alternative tools
- Trap Force Displacement Residual
Return restoring-force prediction and residual.
- Optical Trap Stiffness Variance Term
Return variance-corrected harmonic trap stiffness.