Macro-Ions. I. Light Scattering Theory and Experiments with Bovine Serum Albumin

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Abstract
The theory of light scattering is extended to include solutions of macro‐ion salts such as charged proteins and polymeric electrolytes. Equations for the angular intensity distribution are obtained for three types of interaction potential: (1) that of rigid, non‐interacting spheres, (2) an electrostatic potential consistent with the Verwey‐Overbeek theory, and (3) a simple Gaussian‐type repulsion. Because the repulsive forces between the macro‐ions are generally strong and long range, the concentration and angular distribution of the scattering may be very pronounced. Two unique and important extremes exist. If the concentration of the macro‐ion salt is altered without introducing additional electrolytes, the effective diameter of the macro‐ion is inversely proportional to the cube root of the concentration. In this situation the essential features of the scattering are quite novel. First, the reciprocal reduced intensity rises steeply from the intercept at zero concentration, bends over and becomes nearly horizontal at moderate concentrations, and second, the dissymmetry falls sharply from the limiting value at zero concentration, passes through a minimum and rises slowly at higher concentrations. With small particles the dissymmetry is always less than unity. In experiments with bovine serum albumin carrying charges up to 50 protons, all of these features have been found and can be accounted for at least semiquantitatively. The second unique case is that occurring when the concentration is altered by isoionic dilution which keeps the effective diameter of the macro‐ion constant. Since it is shown that in the scattering problems the difference between the hard sphere and electrostatic potential is relatively minor, the virial coefficients of Boltzmann can be used to describe the concentration dependence of the absolute intensity of scattering. This procedure permits, in contrast to the previous case, a precise evaluation of the effective ionic diameter. The values so obtained are compared with estimates from the Debye‐Huckel theory. As a consequence of these investigations, it appears that both the thermodynamic behavior and diffraction behavior of macro‐ion solutions are consistent with a relatively simple electrostatic picture.

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