Analyze polymer entanglement using flexible chemistry-focused tools. Visualize trends, test assumptions, and download reports easily. Built for students, researchers, and practical polymer formulation work.
The graph updates after each calculation. It shows how entanglement density changes with the chosen primary input.
Primary relation
νe = ρ / Me
Here, νe is molar entanglement density, ρ is polymer density, and Me is entanglement molecular weight.
Plateau modulus relation
Gₙ⁰ = νe × R × T
Rearranging gives νe = Gₙ⁰ / (R × T).
Extra outputs
chains per m³ = νe × NA
chains per nm³ = chains per m³ / 10²⁷
estimated spacing = (1 / chains per nm³)^(1/3)
This page reports a practical molar entanglement density and derived spacing estimate. The spacing value is a simple volume-based estimate, useful for screening and comparison.
| Sample | Density | Me | Temperature | νe | Plateau Modulus | Estimated Spacing |
|---|---|---|---|---|---|---|
| Sample A | 0.92 g/cm³ | 1250 g/mol | 200 °C | 736.0000 mol/m³ | 2.8954 MPa | 1.3116 nm |
| Sample B | 1.04 g/cm³ | 17500 g/mol | 190 °C | 59.4286 mol/m³ | 0.2289 MPa | 3.0345 nm |
| Sample C | 1.18 g/cm³ | 9200 g/mol | 180 °C | 128.2609 mol/m³ | 0.4832 MPa | 2.3481 nm |
It estimates how many effective entanglement constraints exist inside a unit volume of polymer. Higher values usually indicate tighter molecular packing and stronger elastic response.
Some users know density and entanglement molecular weight. Others only know plateau modulus from rheology. Both paths can estimate the same molar entanglement density.
Use either g/cm³ or kg/m³. The calculator converts both to internal SI units before running the formulas.
Me is the entanglement molecular weight. It represents the average molecular weight associated with one effective entanglement segment in the chosen convention.
Temperature enters the modulus relation through the gas constant term. A different temperature changes the inferred entanglement density from the same modulus value.
No. It is a screening estimate derived from calculated chain density. It is useful for comparison, not direct microscopic imaging.
Add density when you want the calculator to estimate Me along with entanglement density. Leave density blank if you only need νe from modulus and temperature.
They export the current result summary. CSV is ideal for spreadsheets, while PDF is useful for reports, lab notes, and quick sharing.
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.