Theory of Light Scattering from a Flexible Chain Molecule

The standard Rayleigh—Gans theory is applied to evaluate the scattered intensity of light due to a perfectly flexible chain molecule in solutions. Depending on statistically different averaging processes, two different expressions for the intensity may be derived from the theory, one asymptotically reducing to the well-known Debye formula, and the other to the formula given previously by the present author. It is found that the scattered intensity is not only dependent on the variable x = (8π2Nb2 sin2½θ)/3λ2 but also on the molecular weight of the polymer molecule. Here, N is the number of repeated units in the polymer which are considered to be scattering centers, b the bond length, θ the scattering angle, and λ is the wavelength. The applicability of these asymptotic formulas is determined by the scattering angle and the molecular weight. Use of the asymptotic formulas for low-molecular-weight polymers at large scattering angles is not advisable. Instead, it is reommended to use the new formulas derived in this paper for arbitrary N and θ.