Light Scattering, Classical: Size and Size Distribution Characterization

Abstract

The use of classical, or time‐averaged, light scattering methods to characterize the size and size distribution of macromolecules in dilute solutions or particles in dilute dispersions is discussed. The necessary scattering relations are presented systematically, starting with three cases at infinite dilution: the scattering extrapolated to zero angle, the scattering at small angle, and the scattering for arbitrary angle, including the inversion of the scattering data to estimate the size distribution. The relationships needed to effect an extrapolation to infinite dilution from data on dilute solutions are also discussed. These are followed by remarks on light scattering methods, and the concluding sections give examples for several applications. The Rayleigh–Gans–Debye (RGD) approximation is usually appropriate in the scattering from dilute polymer solutions and is also adequate for the scattering from dilute dispersions of small particles. The approximation is assumed when appropriate, but more complete theories are introduced where necessary, as in the use of the Mie–Lorentz theory for large spherical particles.

Structure of Poly(vinylidene difluoride) Solutions in Acetone

“…Multiple scattering is an additional issue, which should be discussed in this paper. Normally, it contributes to the V V scattering and affects the accuracy of measured sizes of scattering elements: 24,25 the larger the polymer concentration, the more the influence of multiple scattering. Nevertheless, it is hardly to expect that multiple scattering sways the H V scattering.…”

Light Scattering, Classical: Size and Size Distribution Characterization

“…The berry 1/6/99 2 reader should be forewarned that owing to its history and variety of applications, the nomenclature in light scattering varies among authors (e.g., see reference 21a). In the interests of consistency, the nomenclature used herein will follow that used previously by the author, (1,4,10,18) and where appropriate, these sources will be cited for further detail, in addition to, or in lieu of citations to the original literature referenced therein.…”

“…(21,22) The notation R Si (ϑ,c) will be used in the following to designate the polarization states of the scattered and incident light rays, where subscripts S and i will designate the polarization of the electric vectors of the scattered and incident light, respectively, relative to the scattering plane. Thus, for vertically polarized incident light, and horizontally or vertically polarized scattered light, respectively, the observed scattering may be expressed as, (4,10) R Hv (ϑ,c) = R aniso (ϑ,c)…”

“…(30) For many cases discussed below, ψ solute is equal to the refractive index increment (∂n/∂c) Π at osmotic equilibrium of solvent components. (10,16,18) For a solute in a single component solvent, (∂n/∂c) Π ≈ n medium (ñ -1)/ρ solute , with ρ solute the density of the solute, and ñ = n solute /n medium , where n solute and n medium are the refractive indices of the solute and medium, respectively. (31) This form is also used for a suspension of particles in a gas or vacuum for small ñ -1; a revised expression for large ñ -1 is discussed below.…”

“…with (A 2 ) LS the light scattering averaged second virial coefficient, etc. The virial expansion may fail for charged scatterers in a solvent with very low ionic strength, so that electrostatic interactions are not shielded (see Examples), (10,16,18,32) and other forms for Γ iso (c) may be required for moderately concentrated (or semidilute) solutions. (3,4,33) The general interpretation of the functions P iso (ϑ,c), H iso (ϑ,c) and the parameters M LS , (A 2 ) LS , and (R 2 G ) LS may be complex for scatterers that are optically anisotropic or exhibit intramolecular and/or intermolecular heterogeneity.…”