What is the Difference Between Number Average and Weight Average Molecular Weight?
🆚 Go to Comparative Table 🆚The difference between number average and weight average molecular weight lies in the way they are calculated and the information they provide about a polymer sample. Here are the key differences:
- Number Average Molecular Weight (M_n): This is calculated from the mole fraction distribution of different sized molecules in a sample. It is determined by dividing the total weight of the polymer by the total number of molecules in the sample. Number average molecular weight gives an equal weight to each molecule in the sample, regardless of its size.
- Weight Average Molecular Weight (Mw): This is calculated from the weight fraction distribution of different sized molecules in a sample. It is determined by summing the weight fractions of each type of molecule in the sample. Weight average molecular weight gives a higher weight to larger molecules, making it skewed towards higher values. Since larger molecules in a sample weigh more than smaller molecules, Mw is always greater than M_n.
In summary, number average molecular weight gives an equal weight to each molecule in a sample, while weight average molecular weight gives a higher weight to larger molecules. Both parameters are used to describe the molecular weight of a polymer, but the choice of which value to use depends on the property being investigated and the technique used for determination.
Comparative Table: Number Average vs Weight Average Molecular Weight
The following table compares the difference between number average molecular weight and weight average molecular weight:
| Property | Number Average Molecular Weight (M_n) | Weight Average Molecular Weight (M_w) |
|---|---|---|
| Definition | The sum of the weights of all molecules in a polymer sample divided by the total number of molecules in the sample. | The sum of the weights of all molecules in a polymer sample times their respective mole fractions, divided by the total weight of the sample. |
| Mathematical Expression | M_n = (Σ NiMi) / Σ Ni | M_w = (Σ NiMi^2) / (Σ NiMi) |
| Ni is the number of molecules of a particular type | NiMi is the total weight of molecules of a particular type | |
| Calculation Method | The sum of the weights of all molecules in a polymer sample divided by the total number of molecules in the sample. Calculated using techniques like vapour pressure osmometry and end-group analysis. | The sum of the weights of all molecules in a polymer sample times their respective mole fractions, divided by the total weight of the sample. Determined using techniques like small angle neutron scattering, X-ray scattering, and sedimentation velocity. |
| Polydispersity | Ratio of weight-average and number-average molecular weights (Mw/Mn) is a measure of polydispersity, which indicates how widely distributed the range of molecular weights in the mixture is. A ratio around 1.0 indicates a narrow range of molecular weights. |
In summary, the number average molecular weight represents the total weight of the molecules present divided by the total number of molecules, while the weight average molecular weight takes into account the mass of individual chains and their respective mole fractions.
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