Weight-Average Molecular Weights How To Pick a Football Team Frank L. Pilar University of New Hampshire, Durham, NH 03824
Students of polymer chemistry are exposed to a number of different tvDes of averaee molecular weiehts: - . the two most commo& enmuntercd are the number-average molecular weight defmed by
have the same number-average weight but one group has a higher weight-average weight; he is to assume that all other factors are unknown and thus must be considered equal between the two groups. Group I has the individual weights: 200 lb, 150 lb, and 100 lb. Group I1 has the individual weights: 210 lb, 190 lb, and 50 lb. Note that the number-average weight in each group is the same: 150 lb. The weight-average weight m Group I is given by
and the weight-average molecular weight defined by and the weight-average weight in Group I1 is
In the above equations, M,is the molecular weight of fraction z, n,is the number of moles of fraction i, and w, is the mass of fraction i. The number-average molecular weight causes no problems in understanding since it represents the type of average most of us have used all our lives, and-in fact-is the only kind of average most people are familiar with. Consequently, the weight-average definition strikes most students as strange and even illogical. To keep numerical manipulations to a minimum, we shall consider computing the average weight of three objects. Furthermore, let the objects be potential members of a football team. A wach is asked to choose which of the following three-man groups he wishes to add to his team. The only information he is given is that the two groups
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Clearly, Group I1 has the higher weight-average weight (and thus the higher polydispersity).Is this of any possible physical significance? Assuming the coach is interested in building up the strength of his line, he might be better off in choosing Group I1 since he would be more apt to get a larger number of players with weights over some lower acceptable limit, say 180 lb. (He could use the 50-lb weakling as a water-boy!).This is analogous, of course, to how a polymer sample scatters incident light; the larger the mass of a polymer 'molecule", the better it is at scattering light. Thus if you want the best polymer for scattering light, i.e., the heavier line, choose the "sample" with the highest weight-average weight.
