Calculator Inputs
Use direct molecular mass data, step-growth conversion, or ideal chain-growth inputs. The layout becomes three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
These sample rows show how degree of polymerization relates repeat unit mass, molecular weight, and dispersity in practical polymer systems.
| Polymer | Repeat Unit Mass (g/mol) | Mn (g/mol) | Mw (g/mol) | Approx. DPn | Approx. Đ |
|---|---|---|---|---|---|
| Polyethylene | 28.05 | 12,000 | 18,000 | 427.81 | 1.50 |
| Polystyrene | 104.15 | 35,000 | 52,000 | 335.66 | 1.49 |
| PMMA | 100.12 | 22,000 | 30,800 | 219.74 | 1.40 |
| PLA | 72.06 | 14,500 | 20,300 | 201.22 | 1.40 |
| Nylon 6,6 | 226.32 | 18,000 | 28,800 | 79.53 | 1.60 |
Formula Used
Direct molecular-mass route
DPn = (Mn - Mend) / M0
DPw = (Mw - Mend) / M0
Use this when number-average or weight-average molecular weight is already measured.
Dispersity
Đ = Mw / Mn
This shows how broad the molecular weight distribution is. Values closer to 1 indicate a narrower distribution.
Step-growth route
DPn = (1 + r) / (1 + r - 2rp)
Carothers equation with stoichiometric imbalance. Here, p is conversion and r is the smaller-to-larger functional group ratio.
Ideal chain-growth route
DPn ≈ (Monomer moles × p) / (Initiator moles × f)
This simplified estimate is useful for quick scoping, but real systems may deviate because of transfer, termination, and side reactions.
How to Use This Calculator
- Enter the repeat unit molar mass for your polymer system.
- Add end-group mass if you want chain-end correction.
- Fill Mn and Mw for direct DPn, DPw, and dispersity results.
- Enter conversion and stoichiometric ratio for step-growth predictions.
- Use monomer moles, initiator moles, and initiation efficiency for the ideal chain-growth estimate.
- Press the calculate button to display the result summary above the form.
- Use the CSV or PDF buttons to export the calculated table.
Frequently Asked Questions
1) What does degree of polymerization mean?
It is the average number of repeat units in a polymer chain. Higher values usually indicate longer chains and often change strength, viscosity, melting behavior, and processing response.
2) Why are DPn and DPw different?
DPn weights chains by count, while DPw weights chains by mass. Because larger chains contribute more strongly to mass, DPw is usually greater than DPn.
3) When should I use Carothers equation?
Use it for step-growth polymerization when you know functional group conversion and stoichiometric balance. It is especially useful for condensation systems and equilibrium-limited reactions.
4) What does the stoichiometric ratio r represent?
It is the smaller amount of reactive functional groups divided by the larger amount. Perfect balance gives r = 1, which usually maximizes achievable DPn at a given conversion.
5) Why include end-group mass?
End groups add mass that is not part of repeat units. Including them improves DP estimates, especially for low-molecular-weight oligomers where chain ends contribute more noticeably.
6) Is the chain-growth equation exact?
No. It is a simplified estimate. Real chain-growth systems are influenced by initiation efficiency, termination, transfer reactions, branching, solvent effects, and reactor conditions.
7) What does dispersity tell me?
Dispersity describes the breadth of the molecular weight distribution. A lower value means chains are more uniform, while a higher value indicates broader size variation.
8) Can I use percent conversion directly?
Yes. This calculator accepts conversion as a percent. It internally converts that value into the fractional form required by the equations.