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The characterization of nanoparticle size and structure by means of classical light scattering measurements from monodisperse suspensions is examined from both the Rayleigh-Gans (R-G) approximation as well as (for various spherical structures) the exact Lorenz-Mie theory. A means by which the traditional limits of the R-G theory may be extended and simplified is shown by a detailed discussion of the characteristic mean-square radius. This becomes particularly important for irregular particle shapes, where scattering depends on the orientation of such particles with respect to the direction of the incident illumination. A variety of particle structures are addressed, including rods, tubes, ellipsoids, rings, and superellipsoids.

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Measurements of scattered light intensity as a function of angle (often called differential [l] or total intensity light scattering) from an eluting sample separated into its particulate/molecular constituents by various chromatographic means permit the improvement of subsequent analyses {in the Rayleigh-Gans-Debye (RGD) approximation [2]} in three distinct ways. First, the ability to make repeated simultaneous measurements at several angles improves the precision of the derived weight averaged mass values. Secondly, for particles/molecules which are sufficiently large, the z-average square radius ('radius of gyration' squared) may be derived [3], as well. Finally, if a distribution of particles/molecules is present in the sample and they have been sufficiently separated so that both mass and radius may be derived at each elution fraction, then by plotting the root z-average square radius against the weight averaged mass on a log-log scale, the molecular/particulate configuration (rod, sphere, coil, etc.) may be deduced [4]. For particles that do not satisfy the RGD criteria, a series of other deductions from the recorded data are possible, including size, refractive index, and structural non-homogeneity.For macromolecules, and other particles of mean radius u satisfying the RGD approximation criteria:Im-ll*l and the inversion of the scattering data to yield mass and structural information is straightforward [ 51.Here, the incident wavelength in vacuum is A,, and the medium refractive index no. The relative refractive index of the particles, n/no = m. The inversion is far more difficult when the RGD criteria are not satisfied. The broad range of particles separable by various field flow fractionation and gradient phase techniques further confirms the power of differential light-scattering measurements. For molecules such as heparin and pectin, the light-scattering measurements indicate the presence of features that cannot be noticed by conventional gel permeation chromatography techniques.