Other Molecular Weight Averages

Other characterizations of average moiecular weight also exist, giving increasing importance to the larger molecules. For example, M, which is strongly related to melt elasticity, is defined as  

However, for most purposes, and Q adequately characterize the MWD of unblended polymers, and are commonly used in the plastics industry. 

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The product M(t) W (t) is the integrand in this case and a plot of M(t) W (t) versus t is the moment analysis plot for Mw. Similar plots can be made for the other molecular weight averages. Figure 6 shows moment analysis plots for Mn, Mw and Mz. 

Combinations of other molecular weight averages are also possible to give analogous Q and U values. For a monodisperse material Q = 1 and U = 0. 

It is apparent that numerous other special systems or effects could be considered to either broaden the range or improve the applicability of the derivation presented. Our interest, however, is in illustrating concepts rather than exhaustively exploring all possible cases, so we shall not pursue the matter of gelation further. Instead, we conclude this section with a brief examination of the molecular weight averages in the system generated from AA, BB, and Af. For simplicity, we restrict our attention to the case of r . = u... 

Ziegler-Natta type catalysts can generate a very high cis-1,4 stmcture (>90%), which is the choice polymer for tires. It is made to specifications similar to SBR, ie, molecular weight average of 100,000—200,000, Mooney viscosity 50, and od-extended. Lithium catalysts on the other hand yield variable chain stmctures, depending on the solvent used, ie, mixed stmctures of cis-1,4 and trans-1,4 and 1,2. These polymers are generally ia the lower... 

While this example shows an extreme difference in the two molecular weight averages, the other extreme is where all of the molecules have the same size, i.e. they are said to be monodisperse. In tbis case the two averages will have the same value. 

These two types of molecular weight averages are representative of the type called absolute methods, in that well-established thermodynamic equations can be used to convert the experimental data directly into a value of the molecular weight. However, some other methods require calibration. The most important of these indirect methods involves a measurement of the intrinsic viscosity. This quantity is a measure of the extent to which a polymer molecule increases the viscosity of the solvent in which it is dissolved. The viscosity method can be calibrated to yield a viscosity-average molecular weight, defined by... 

Amyloses of different origins and molecular weights have been extensively studied.151 Results indicate that cereal amyloses are smaller than other amyloses. Amyloses isolated from high-amylose maize starches display substantially smaller molecular weights (average DP 690-740 and chain lengths 215-255).161 There is about an equal... 

Molecular weight averages VPO, Light scattering and other Ageing of resin-... 

Once the pgPs for units in the root and higher generations have been formulated, it is not difficult to calculate other structural parameters like the molecular weight averages, sol fraction or concentration of EANC s. 

Various molecular weight averages are current in polymer science. We show here that these are simply arithmetic means of molecular weight distributions. It Tiiay be mentioned in passing that the concepts of small particle statistics that are discussed here apply also to other systems, such as soils, emulsions, and carbon black, in which any sample contains a distribution of elements with different sizes. 

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