Number average relative molecular

Osmotic pressure, which is a colligative property, depends simply on the number of solute molecules present and so yields a number-average relative molecular mass ... 

Figure 3.20. The time-of-flight SIMS spectrum of a polystyrene oligomer whose number average relative molecular mass is 4964, deposited as a thin film on a silver substrate. After Bletsos et al. (1987).

Figure 6.23. The eifect of polydispersity on the interfacial tension. The interfacial tension between polybutadiene (M = 4100 and Mv,/M = 1.40) and polystyrene samples made by blending three fractions of narrow relative molecular mass to achieve a constant number average relative molecular mass (M — 5500) and various polydispersity indices was measured at 150 °C. After Nam and Jo (1995).

Hence equation (8.1.3) could be used to analyse surface pressure data to obtain number average relative molecular masses from the intercept at = 0 of a plot of yr/Fs as a function of Fg. The interpretation of the virial coefficients in molecular terms depends on which theory is used Huggins (1965) has collected together the correspondences between the virial coefficients for each of the theories. For the case of the original Singer derivation... 

For polydispersed systems an average relative molecular mass intermediate between number-average (a = 0) and mass-average (a = 1) usually results. 

Calculate the number average and weight average relative molecular mass for a sample of polystyrene made by blending eight separate fractions, each of which has a very narrow molecular mass distribution, as follows ... 

Molecular formula of Isomer groups Trivial name Basic relative molecular weight Average relative molecular weight Chlorine content (% w/w) Number of isomers... 

This result shows that the square root of the amount by which the ratio M /M exceeds unity equals the standard deviation of the distribution relative to the number average molecular weight. Thus if a distribution is characterized by M = 10,000 and a = 3000, then M /M = 1.09. Alternatively, if M / n then the standard deviation is 71% of the value of M. This shows that reporting the mean and standard deviation of a distribution or the values of and Mw/Mn gives equivalent information about the distribution. We shall see in a moment that the second alternative is more easily accomplished for samples of polymers. First, however, consider the following example in which we apply some of the equations of this section to some numerical data. 

Fig. 13. The relationship between viscosity and relative number-average molecular weight for a certain resole. Different resoles will have different relationships. Note the non-linearity.

PET powder was prepared from commercial PET bottles and had a number-average molecular weight of 30,000. PET powder (0.2 g) was placed in 30 mL of relatively dilute sulfuric acid (10 M) in a sealed Pyrex tube and heated to 150°C for 1-6 h in an oven. After the reaction mixture was allowed to cool, the precipitate of TPA and PET residue deposited was filtered through a 1G-5 glass filter. TPA was separated as the ammonium salt by dissolving it in 12 mL of 5 M NH3. The TPA was reprecipitated by sulfuric acid solution. The yield of TPA was 100% in 10 M sulfuric acid solution. 

The polymerization of 1,3,3-trimethyl-2,7-dioxabicyclo[2.2.1 Jheptane 35 was carried out in methylene chloride, toluene, and 1-nitropropane at temperatures between —78 and 0 °C32l Boron trifluoride etherate, triethyloxonium tetrafluoro-borate, antimony pentachloride, and iodine were used as initiators. Irrespective of the solvents and initiators employed, the products obtained at 0 °C were white powders with melting points of 50—55 °C, while those obtained at tower temperatures were sirups. The number average molecular weight of the unfractionated products ranged from 400 to 600. The molecular weight distribution of the oligomers prepared at 0 °C was broad, in contrast to the relatively narrow distribution of those obtained at -40 °C. 

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