Number-average molecular weight discussion

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

T is the glass-transition temperature at infinite molecular weight and is the number average molecular weight. The value of k for poly(methyl methacrylate) is about 2 x 10 the value for acrylate polymers is approximately the same (9). A detailed discussion on the effect of molecular weight on the properties of a polymer may be found in Reference 17. 

The details of the measurements made on these samples are discussed elsewhere (4, 5). The certified values from the certificates for all the samples are shown in the Appendix. For SRM 705 the number-average molecular weight by osmometry, 170,900, and the weight-average... 

Epoxy networks may be expected to differ from typical elastomer networks as a consequence of their much higher crosslink density. However, the same microstructural features which influence the properties of elastomers also exist in epoxy networks. These include the number average molecular weight and distribution of network chains, the extent of chain branching, the concentration of trapped entanglements, and the soluble fraction (i.e., molecular species not attached to the network). These parameters are typically difficult to isolate and control in epoxy systems. Recently, however, the development of accurate network formation theories, and the use of unique systems, have resulted in the synthesis of epoxies with specifically controlled microstructures Structure-property studies on these materials are just starting to provide meaningful quantitative information, and some of these will be discussed in this chapter. 

Before we leave molecular weight discussion mention should be made of the heterogeneity index (HI), or polydispersity index. This is defined as the weight average molecular weight divided by the number average molecular weight ... 

The uniaxial PF2/6 alignment can be quantified in terms of the mean-field theory discussed previously. The degree of alignment in equilibrium (f2) is a function of the number-averaged molecular weight (M ) as described by Eq. 6. This prediction has been studied by photoabsorption in [55] and there it has been shown that the solid angle T2 is expressed in terms of the dichroic ratio in absorption (R) as... 

The mass of the linear polymer chain is thus related directly to the number of monomer units incorporated into the chain (DP) and will be Mq x DP, where Mq (g/mol) is the molar mass of the monomeric repeat unit. Thus, if all chains grew to exactly the same DP, then Mq X DP, would be the molar mass of the polymer. If the end groups on the chain can be readily and uniquely analysed, then an average molar mass, M , or number-average molecular weight (as discussed in the next section) can be immediately determined since, if there are amol/g of end group A and hmol/g of end group B then... 

Tg increases asymptotically towards Tgoo with increasing number-average molecular weight (Mn). The dependence of Tg on Mn will be discussed in detail, and a new correlation will be developed for this dependence, in Section 6.C. 

Number-average molecular weight, which will be discussed further in Section 6.C. 

One final area for discussion is the use of NMR for the determination of polymer number average molecular weights. End group resonances were clearly visible in the 13c NMR spectrum of the ethylene-l-hexene copolymer in Figure 3. An opportunity to determine polymer degrees of polymerization or number average molecular weights should not be overlooked. 

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