276 H. K. SCHACHMAN AND R. C. WILLIAMS 



may be measured is the ratio of i?g at 45 and 135°, the so-called "dissymmetry 

 ratio." For a given particle shape this ratio is a miique fmiction of the ratio 

 of the characteristic dimension of the particle to the wavelength of light, 

 L/X. [Characteristic dimensions are: diameter (sphere); length (rod); root- 

 mean-square end-to-end distance (random coil).] If a model shape for a 

 particle is presumed to be known (a sphere, a rod, or a random coil) a value 

 of LjX is directly obtained from the dissymmetry measurements, allowing 

 the correction factor P-^{6) to be evaluated. Hence, by the dissymmetry 

 method molecular weights can be determined for particles of size comparable 

 with a wavelength of light if a particle shape is assumed. Actually the shape 

 of the particles can be ascertained in various ways from the appropriate light- 

 scattering data. 



If many light-scattering measurements can be made at various 0's and 

 concentrations, it is possible to calculate molecular weights without making 

 any assumption as to particle shape (Zimm, 1948). In tliis method use is made 

 of the fact that at ^ = 0°, the value of P~^{6) is unity (no interference 

 effects), and at c = 0, there are no particle interactions. A "Zimm plot" is 

 made, which is a gridlike representation of KcJRq as a function of both d 

 and c. Extrapolations are made both to = and c = 0; the two extra- 

 polated lines should meet at the same point. This intercept is then simply 

 1 JM. The slope of the ^ = line near the origin gives the value of B, the 

 interaction term, while the mitial slope of the c = line yields a value for 

 the radius of gyration of the particle. The radius of gyration is defined as 

 that distance from the center of mass of a body such that its moment of 

 inertia remains the same if all the mass is concentrated at that radius. It 

 can be used to calculate the characteristic dimension of a particle, if the 

 shape is known. 



We have seen that under favorable conditions the methods of light 

 scattering will yield molecular weights of particles in the range of size of the 

 viruses. They will also provide a determination of a characteristic dimension, 

 although this is the Z-average dimension, and is heavily weighted toward the 

 larger particles in a polydisperse suspension. The beauty of the methods of 

 light scattering is that they can be made quickly, that they do not disturb 

 the particles mider measurement, and that they are essentially equilibrium 

 methods not involving any hydrodynamic effects. 



It should be emphasized that the value of M determined by light scatter- 

 ing is a weight-average molecular weight, while the calculated characteristic 

 dimension, L, is a Z-average value. This means that the determination of 

 both quantities is highly sensitive to the presence of small amomits of foreign 

 material of relatively large size. Contamination by dust particles is particu- 

 larly to be avoided. If the solute particles under investigation are poly- 

 disperse, such as partially aggregated solutions of tobacco mosaic virus, the 



