E1 Chain Structure: Molecular Weight and Distribution

Topic

In this polymer—unlike a material where the relevant structural unit is the individual atom—the relevant unit is the entire molecular chain; furthermore, this chain does not have a single fixed length. Instead, the various molecular chains within the polymer span a distribution of lengths, with some chains being longer and others shorter. To characterize the polymer, this length distribution is summarized by two distinct molecular weight averages: the number-average molecular weight, which weights each chain equally regardless of length, and the weight-average molecular weight, which weights each chain according to its mass—meaning the longer chains in the distribution carry more weight in the latter average than in the former.

The ratio of the weight-average molecular weight to the number-average molecular weight defines the polymer's polydispersity index. The broader the length distribution, the further this ratio deviates from unity, because the longer chains in a broad distribution raise the weight-average molecular weight far more than they raise the number-average molecular weight. Conversely, if the length distribution is narrower—meaning the chains are more similar in length—the polydispersity index moves closer to unity.

Thus, within this model—defined by the length distribution and the two molecular weight averages mentioned earlier—the number-average molecular weight also determines the polymer's degree of polymerization (the average number of repeating units making up each chain in the distribution): the higher the number-average molecular weight, the more repeating units each chain contains on average, and consequently, the higher the degree of polymerization. This same average molecular weight and polydispersity index are what the experimental method—described by another model in this set—measures directly based on the hydrodynamic size of these molecular chains; conversely, they are also the values ​​reduced by the random chain scission described by a different application model in this set, as it cleaves each of these molecular chains into shorter ones within that same distribution.

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