Relative molar mass number average

If it is possible to analyse end groups of a particular specimen of polymer, it may be possible to use the data to determine number average relative molar mass. If the molecules are branched the degree of branching can be measured from a combination of end group analysis and relative molar mass determination (determined by an alternative method). 

The average degree of polymerization, denoted X, were k represent the type of average (i.e., arithmetic, geometric), represents the dimensionless number of monomer units or residues R constitutive of a macromolecular chain. It can be defined as the ratio of the relative molar mass of the macromolecule to the relative molar mass of the monomer unit ... 

The first quantity is a colHgative property called the number-average relative molar mass or simply the number-average molar mass denoted M and defined as the weighed average of the number fraction of each macromolecule by the following equation. 

A sample of polyisoprene (density 1300 kgm, monomer of relative molar mass 68) has a shear modulus of 4 X 10 Pa at room temperature. Calculate the average number of monomers between cross-links. 

M number-average relative molar mass of the copolymer... 

Gelation occurs at relatively low conversions of monomer to polymer hence the number-average molar mass at the gel point is low. By contrast, however, the weight-average molar mass becomes infinite at the gel point. 

Furthermore, polymeric samples are usually a mixture of macromolecular chains terminated by different end-groups and thus, an interesting quantity to be determined (in order to characterize the mixture) is the relative abundance of end-groups [1—3]. Other two important quantities are Mn and Mw, the number-average and the weight-average molar masses [1—3]. 

The molar masses of elements are determined by using mass spectrometry to measure the masses of the individual isotopes and their abundances. The mass per mole of atoms is the mass of an individual atom multiplied by the Avogadro constant (the number of atoms per mole). However, there is a complication. Most elements occur in nature as a mixture of isotopes we saw in Section B, for instance, that neon occurs as three isotopes, each with a different mass. In chemistry, we almost always deal with natural samples of elements, which have the natural abundance of isotopes. So, we need the average molar mass, the molar mass calculated by taking into account the masses of the isotopes and their relative abundances in typical samples. All molar masses quoted in this text refer to these average values. Their values are given in Appendix 2D. They are also included in the periodic table inside the front cover and in the alphabetical list of elements inside the back cover. 

The experimental measurement of these averages has largely been performed on polymers in solution (Hunt and James, 1999). Since M depends on the measurement of the number of polymer chains present in a given mass, colligative properties such as vapour-pressure depression AP (measured by vapour-phase osmometry) and osmotic pressure (measured by membrane osmometry) relative to the pure solvent, can in principle provide the molar mass through an equation of the form... 

Fig. 4 a Relative amount of indicator products, i.e. dicarboxjdic acids and lactones formed dming thermo-oxidation of PE and EVA at 190 and 230 °C. b Number average molar mass after thermo-oxidation. Reprinted with permission from [52]... 

During photo-oxidation, dicarboxylic acids were the class of products that clearly increased in the most severely degraded samples. As during thermooxidation, the most abundant of the dicarboxylic acids was butanedioic acid. Comparison between the number average molar mass and the relative amount of butanedioic acid, Fig. 6, showed a connection between the formation of butanedioic acid and the degree of degradation in the polyethylene matrix. However, the relative sum of all the carboxylic acids correlated even better with the number of chain scissions than the amoimt of only butanedioic acid. Fig. 7. 

---