It is worth noting that these plots are sometimes shown with molecular weight decreasing along the x -axis. In many cases, it is important to know not only the average molecular weight, but also the distribution of molecular weights. This is illustrated in the example below, in which no molecules would actually have a weight equal to the number average molecular weight, since this would lie between the two peaks. Number average molecular weight, M N The number average molecular weight is defined as the total weight of polymer divided by the total number of molecules.
Weight average molecular weight, M w The weight average molecular weight depends not only on the number of molecules present, but also on the weight of each molecule. The weight average molecular weight is therefore weighted according to weight fractions. It gives the average of the molecular masses of the individual macromolecules in the polymer sample. We can find this parameter using the following equation:.
Where M w is the weight average molecular weight, N i is the number of molecules of molecular mass M i. We can determine this parameter using static light scattering, small angle neutron scattering, X-ray scattering, and sedimentation velocity.
More importantly, the weight average molecular weight is always greater than the weight average molecular weight since larger molecules in a sample weigh more than smaller molecules. Since polymer samples contain molecules of different sizes, we cannot give the exact molecular weight of the polymer. Therefore, we use averages of different parameters to indicate the molecular weight of the polymer. The number average and weight average molecular weight are such two forms. Another difference between number average and weight average molecular weight is that we can determine the number average molecular weight using gel permeation chromatography , viscometry and colligative methods such as vapour pressure osmometry while we can determine the weight average molecular weight using static light scattering, small angle neutron scattering, X-ray scattering, and sedimentation velocity.
The below infographic presents the difference between number average and weight average molecular weight in tabular form. The number average and weight average molecular weight are two parameters that we use to express the molecular weight of a polymer sample. Let us now explain: Consistency Let's think about a small molecule, say, hexane. Hexane has a molecular weight of Every hexane molecule has a molecular weight of Now if we add another carbon to our chain, and the appropriate amount of hydrogen atoms, we've increased our molecular weight to That's fine, but the molecule is no longer hexane.
It's heptane! If we have a mixture of some molecules of hexane and some of heptane, the mixture won't act like pure heptane, nor will it act like pure hexane. The properties of the mixture, say, its boiling point, vapor pressure, etc. But polymers are different. Imagine polyethylene. If we have a sample of polyethylene, and some of the chains have fifty thousand carbon atoms in them, and others have fifty thousand and two carbon atoms in them, this little difference isn't going to amount to anything.
If you really want to know the truth, one almost never finds a sample of a synthetic polymer in which all the chains have the same molecular weight. Instead, we usually have a bell curve, a distribution of molecular weights. Some of the polymer chains will be much larger than all the others, at the high end of the curve. Some will be much smaller, and at the low end of the curve.
The largest number will usually be clumped around a central point, the highest point on the curve. So we have to talk about average molecular weights when we talk about polymers. And we're not going to stop there. The average can be calculated in different ways, and each way has its own value. So let's talk about some of these averages, why don't we? It is just the total weight of all the polymer molecules in a sample, divided by the total number of polymer molecules in a sample.
It's based on the fact that a bigger molecule contains more of the total mass of the polymer sample than the smaller molecules do. Demographics A good way to understand the difference between the number average molecular weight and the weight average molecular weight is to compare some American cities.
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