Isothermal diffusion and quasielastic light-scattering of macromolecular solutes at finite concentration

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Abstract
The Brownian motion of a group of hydrodynamically interacting particles suspended in a low‐Reynolds‐number fluid is described by a generalization of the Einstein diffusion relation. The time integral of each velocity self‐ or cross‐correlation function is found to be equal to one of the mobility tensors governing steady movement of the particles through the fluid. Using the approach of nonequilibrium thermodynamics and linear response theory, this result allows formulation of an expression for the concentration dependence of the Fick’s law diffusion coefficient for mutual binary diffusion in terms of the mobility tensors. The relationship between the concentration dependence of the solute chemical potential, sedimentation rate and mutual diffusion coefficient D is proved. A distinction is made between D and the mean self‐diffusion coefficient Ds for solute molecules, thus allowing interpretation of results obtained using different experimental techniques. An argument is presented which indicates that quasielastic light scattering is suitable for the determination of Ds and higher moments of the self diffusion coefficient distribution for a monodisperse solution of macromolecules. The normalized second moment of this distribution is calculated for a solution of spherical macromolecules in terms of the solute volume fraction. It is concluded that quasielastic light scattering may be used to determine the value of a dimensionless parameter which is dependent solely on the shape of the hydrodynamic particle corresponding to a solvated macromolecule.