The wavelength dependence of the turbidity of solutions of macromolecules

The experimental parameter describing the wavelength dependence of the turbidity of solutions of macromolecules is usually the negative slope of the graph of the logarithm of optical density vs the logarithm of the in vacuo wavelength, λ₀. Such slopes are the apparent exponents of 1/λ₀ in the turbidity equation. Their values depend upon the way the destructive interference of the scattered light, the refractive index increment, and the solvent refractive index change with wavelength. In this study, expressions for the wavelength exponents for isotropic rods, spheres, and random coils have been obtained and evaluated by representing the intraparticle interference functions, Q(λ₀), with series in even powers of 1/λ₀ and the refractive properties with Cauchy relations. Comparisons of calculated and observed exponents at wavelengths in the visible spectral region for aqueous solutions of four viruses have been made: for R17, T7, and PM2 bacteriophage, the exponents are greater than four; whereas for tobacco mosaic virus, they are less than four. The application of the turbidity relations to determine the size and molecular weight of biological macromolecules is discussed.