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with the differences between the various average molecular weights increasing as the molecular-weight distribution broadens. A typical polymer sample will have the molecularweight distribution shown in Fig. 1-4. the approximate positions of the different average molecular weights are indicated on this distribution curve. For most practical purposes, one usually characterizes the molecular weight of a polymer sample by measuring M n and either M w or M v . M v is commonly used as a close approximation of M w , since the two are usually quite close (within 10 20%). Thus in most instances, one is concerned with the M n and M w of a polymer sample. The former is biased toward the lower-molecular-weight fractions, while the latter is biased toward the higher-molecularweight fractions. The ratio of the two average molecular weights M w =M n depends on the breadth of the distribution curve (Fig. 1-4) and is often useful as a measure of the polydispersity in a polymer. The value of M w =M n would be unity for a perfectly monodisperse polymer. The ratio is greater than unity for all actual polymers and increases with increasing polydispersity. The characterization of a polymer by M n alone, without regard to the polydispersity, can be extremely misleading, since most polymer properties such as strength and melt viscosity are determined primarily by the size of the molecules that make up the bulk of the sample by weight. Polymer properties are much more dependent on the larger-sized molecules in a
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MOLECULAR WEIGHT
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Fig. 1-4 Distribution of molecular weights in a typical polymer sample.
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sample than on the smaller ones. Thus, for example, consider a hypothetical mixture containing 95% by weight of molecules of molecular weight 10,000, and 5% of molecules of molecular weight 100. (The low-molecular-weight fraction might be monomer, a low-molecularweight polymer, or simply some impurity.) The M n and M w are calculated from Eqs. 1-15 and 1-17 as 1680 and 9505, respectively. The use of the M n value of 1680 gives an inaccurate indication of the properties of this polymer. The properties of the polymer are determined primarily by the 10,000-molecular-weight molecules that make up 95% of the weight of the mixture. The weight-average molecular weight is a much better indicator of the properties to be expected in a polymer. the utility of M n resides primarily in its use to obtain an indication of polydispersity in a sample by measuring the ratio M w =M n . In addition to the different average molecular weights of a polymer sample, it is frequently desirable and necessary to know the exact distribution of molecular weights. As indicated previously, there is usually a molecular weight range for which any given polymer property will be optimum for a particular application. The polymer sample containing the greatest percentage of polymer molecules of that size is the one that will have the optimum value of the desired property. Since samples with the same average molecular weight may possess different molecular weight distributions, information regarding the distribution allows the proper choice of a polymer for optimum performance. Various methods have been used in the past to determine the molecular weight distribution of a polymer sample, including fractional extraction and fractional precipitation. These methods are laborious and determinations of molecular weight distributions were not routinely performed. However, the development of size exclusion chromatography (SEC), also referred to as gel permeation chromatography (GPC) and the availability of automated commercial instruments have changed the situation. Molecular-weight distributions are now routinely performed in most laboratories using SEC. Size exclusion chromatography involves the permeation of a polymer solution through a column packed with microporous beads of crosslinked polystyrene [Potschka and Dublin, 1996; Yau et al., 1979]. The packing contains beads of different-sized pore diameters. Molecules pass through the column by a combination of transport into and through the beads and through the interstitial volume (the volume between beads). Molecules that penetrate the beads are slowed down more in moving through the column than molecules that do not penetrate the beads; in other words, transport through the interstitial volume is faster than through
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