Model network structure with clear inputs and units. Switch methods for gels, rubbers, and resins. Export results to share, audit, and replicate experiments easily.
These are common approximations; fillers, entanglements, and non-ideal networks can shift apparent density.
| Sample | Method | Input | T (°C) | νe (mol/m³) | #/m³ |
|---|---|---|---|---|---|
| A | Shear modulus | 0.50 MPa | 25 | 201.697728 | 1.214652E+26 |
| B | Young's modulus | 1.50 MPa, ν=0.49 | 25 | 203.051404 | 1.222804E+26 |
| C | Swelling | v2s=0.25, χ=0.45, V1=106 cm³/mol | 25 | 178.550711 | 1.075258E+26 |
Values are illustrative and depend on material, test protocol, and model assumptions.
Network crosslink density describes how many effective elastically active chains occupy a unit volume. Higher density usually increases modulus, reduces creep, and improves solvent resistance, while lowering extensibility and tear initiation strain. In formulation work, small changes in cure time, catalyst level, or multifunctional monomer fraction can move the network from tacky to glassy. Track the same geometry and strain window to keep comparisons meaningful.
When you measure shear modulus in the rubbery plateau, the calculator estimates νe using νe = G/(R·T). Use temperatures well above Tg so the response is dominated by network elasticity rather than segmental relaxation or crystalline melting. Dynamic mechanical analysis can help locate a stable plateau before using a modulus value. If you only have Young’s modulus, convert to shear using Poisson’s ratio; for incompressible elastomers ν≈0.49 is a practical assumption.
For gels and lightly crosslinked polymers, equilibrium swelling provides an independent estimate. You enter polymer volume fraction in the swollen state v2s, solvent molar volume V1, and interaction parameter χ. Lower v2s indicates more swelling and typically a lower νe, but χ strongly affects the result, so use literature values near your temperature and solvent system. Measure mass uptake until it plateaus, and report how you calculated v2s from densities.
Report all moduli in Pascals and keep temperature in Kelvin internally. If your modulus is reported in MPa, multiply by one million before calculating. Swelling inputs need v2s between 0 and 1, and χ often ranges from 0.3–0.7. When results look unrealistic, recheck the assumed ν, confirm equilibrium swelling, and ensure V1 is in m³/mol or converted correctly from cm³/mol.
Compare νe across batches to monitor cure consistency, post‑cure effectiveness, or aging in practice. Translate νe to an estimated average mesh size trend: lower νe implies larger meshes and faster diffusivity for small molecules. Use the number density output to communicate scale in chains per cubic meter. Pair this output with hardness, extraction, and swelling kinetics to validate whether the network is chemically crosslinked or dominated by entanglements and physical associations.
What does νe represent in this calculator?
νe is the effective crosslink density: moles of elastically active network chains per cubic meter. It reflects the portion of the network that contributes to rubber-like elasticity, not every chemical bond formed during curing.
Which method should I choose: modulus or swelling?
Use modulus when you have rubbery-plateau mechanical data and temperature is well above Tg. Use swelling when you have equilibrium uptake in a known solvent and reliable χ and V1 values for that polymer–solvent pair.
Why do I need temperature?
Rubber elasticity links modulus to thermal energy through R·T. A higher temperature lowers the calculated νe for the same modulus. For consistency, use the temperature at which the modulus or swelling measurement was performed.
How sensitive is the swelling method to χ?
Very sensitive. χ enters the numerator and can change νe noticeably, especially at moderate v2s. If you lack a trustworthy χ value, report a range using plausible χ values to show uncertainty rather than a single point.
What is the number density output (#/m³)?
It converts νe from mol/m³ to chains per cubic meter using Avogadro’s constant. This helps compare network scale across materials and communicate results in absolute counts rather than moles.
Can this calculator replace lab characterization?
No. It summarizes standard models and unit conversions, but real networks may include entanglements, fillers, crystallinity, or gradients. Use it to organize calculations, then validate trends with repeat tests and complementary measurements.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.