Molecular theory of the translational Stokes-Einstein relation

A molecular-statistical derivation is presented for the Stokes-Einstein expression for the translational diffusion constant for a Brownian (large) particle. The friction constant is expressed in terms of a correlation function of the forces on the particle, and this correlation function is related to the correlation function of pressure fluctuations in a volume equal to that of the particle. Whereas the forces are those on the particle surface, the pressure fluctuations are a property of the liquid solvent. The amplitude of the pressure fluctuations can be obtained from fluctuation theory and the time dependence can be obtained from hydrodynamics, which in turn can be derived from molecular-statistical considerations. Although the exact numerical factors cannot be obtained, the linear dependence of the friction constant on the radius of the Brownian particle is derived. Finally, a discussion of the diffusion constant for small diffusing particles is presented.