Weight-Average Molecular Weights and Radii of Gyration

6 WEIGHT-AVERAGE MOLECULAR WEIGHTS AND RADII OF GYRATION 

If the atoms, molecules, or particles are not organized into a regular array, scattering will be observed at all angles. In general, the angular variation of the scattering intensity provides a measure of the size of the structures. 

DILUTE SOLUTION THERMODYNAMICS, MOLECULAR WEIGHTS, AND SIZES 

The phenomenon of light-scattering is caused by fluctuations in the refractive index of the medium on the molecular or supermolecular scale. For example, the blue-of-the-sky scattering mentioned previously is caused by the random presence of gas molecules in what is otherwise a vacuum. The blue of large bodies of water is caused by sUght fluctuations in the spacing of the water molecules. In both cases the scattered intensity varies as the wavelength to the inverse fourth power, which causes the characteristic blue color. 

The basic theory of Hght-scattering applied to polymer solutions dates from the works of Debye (31), who formulated the absolute molecular weight determination in terms of an optical constant H, as shown in equation (3.42). The corresponding theory for X rays was developed by Guinier and Foumet (34). The theory for small-angle neutron scattering was derived by Kirste, Ballard, and Ibel (35). Several reviews have been written (36-39). 

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Table 1 Weight-Average Molecular Weights and Radii of Gyration for...

Similar equations could be derived for weight- and Z-average molecular weights respectively. According to equation 11, molecules with have a radii of gyration equal to R. This result cannot be generalized to macromolecules which are not rod-like (18). 

Table V shows a calculation of the corresponding weight-average radii of gyration calculated from the z-average radii of gyration. More Importantly, Table V also shows that the molecular weights obtained vary as equations (11) and (13) with respect to their radii of gyration.

Figure 4-16. Weight-average radii of gyration of poly(methyl methacrylates) in acetone (O), butylchloride ( ), and in the solid state (A), as a function of the weight-average molecular weights. Measurements at 20and 35.4°C (butylchloride). (After R. G. Kirste and W. Wunderlich.)...

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