Theoretical Investigations on the Light Scattering of Spheres. XIII. The ``Wavelength Exponent'' of Differential Turbidity Spectra

Abstract

The exact theory of the ``wavelength exponent'' of the turbidity is developed for Rayleigh scattering and ``Debye scattering'' and, particularly, for Mie scattering by nonabsorbing spheres. The basic exponent, n, defined by {α[∂ln(τ/c)0/∂α]+1} is computed from Mie turbidity data, reported previously, for α=0.40 (0.04) 0.68, 0.80 (0.2) 25.0 and m=1.05 (0.05) 1.20. For m=1.25 and 1.30, the smallest α values and the Δα intervals are the same, but the upper limiting α values are 14.0 and 11.6, respectively. In addition, α values<0.40 are considered for m=1.05. The actual exponent to be expected in a given dispersed system n0 is found to depend on three additional factors: (1) The rate of change of the turbidity with the relative refractive index of the spheres [this factor is evaluated for α=0.4, 1.0 (1.0) 7.0 and m=1.05 (0.05) 1.30 and approximating equations are given for purposes of interpolation]. (2) The dispersion of the relative refractive index of the spheres. (3) That of the refractive index of the medium. The advantages and limitations of an application of the wavelength exponent to particle size determinations are discussed and labor saving approximating n(α) relations, suitable for first approximation results on particle size, are given. The effect of heterodispersion upon the wave length exponent is briefly discussed.

Phase equilibrium, structure, and rheological properties of the carboxymethyl cellulose-water system

“…The radii of supramolecular particles, r w , in moder ately concentrated and concentrated solutions were determined through the method of the turbidity spec trum, proposed by W. Heller et al [16,17] and devel oped by V.I. Klenin et al [18].…”

Changes in the Protein Composition and Size Distribution of Bovine Casein Micelles Induced by Cooling

“…The particle size was obtained from the relationship between the size data 15 ) and the slope of log(turbidity) against log(wavelength) in the range of 400 to 700 nm. The turbidity was measured by a Hitachi 200 spectrophotometer with a cell holder maintained at the definite temperature.…”

Stabilization of Weakly Charged Microparticles Using Highly Charged Nanoparticles

“…To calculate the turbidity of the particle solutions, the absorbance spectrum from 500-700 nm (wavelength) was used. The data was fit to Equation 6 [36] to calculate the turbidity exponent, n. Equation 6 is derived from the relationship between the intensity of light scattered via Rayleigh scattering and wavelength , which depends on -4 . This relationship only applies to particles that are much smaller than the wavelength of the scattered light.…”