Let's walk through this to show what I mean. Take Memphis. It has a population of , The total population of our four cities is , So the fraction of people who live in Memphis is Now let's take our fraction, 0. Now let's do the same thing for all the cities, and add up the answers: So our weight average population of the four cities is about , We can say from this figure that the average person lives in a city of about , That is more believable than saying that the average citizen lives in a city of , We do the same thing with polymers.
We calculate, with the same formula as we used for the weight average population of our four cities, the weight average molecular weight. See, for example, the following activities: Calculate the molecular weight of a polymer here. Or see an illustration of how molecular weight changes affect entanglement using string here.
The principle is a simple one: Bigger polymers molecules make a solution more viscous than small ones do. Of course, the molecular weight obtained by measuring the viscosity is a different from either the number average or the weight average molecular weight.
But it's closer to the weight average than the number average. To read more about how we measure the viscosity average molecular weight, go read the dilute solution viscometry page. Distribution With all these different molecular weights out there, things can get a little confusing.
No single one of them tells the whole story. So it's usually best to try to know the molecular weight distribution. The distribution is a plot, like the one in the picture. It plots molecular weight on the x -axis, and plots the amount of polymer at a given molecular weight on the y -axis. Just for fun, we've shown you just where on the distribution curve the number, viscosity, and weight averages generally show up. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry.
It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. The statement comes from my lecture slides on polymers. I hope someone can show me the maths proof for the inequality.
I will try come up with the proof, too. Mathematics has many examples of identities and concepts which are extremely powerful due to their simplicity, such as the pigeonhole principle and the triangle inequality.
One such identity will guide us through the problem. Now this last inequality has a very powerful interpretation. In words, the arithmetic mean of two positive real numbers will always be greater than or equal to their geometric mean. This is called the AM-GM inequality , and it often shows up in the most surprising of places. Let's get started. By doing so, the new numerator is smaller than or equal to the old numerator.
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.
Available here 2. Available here. With a mind rooted firmly to basic principals of chemistry and passion for ever evolving field of industrial chemistry, she is keenly interested to be a true companion for those who seek knowledge in the subject of chemistry. Your email address will not be published.
0コメント