Stokes-Einstein relationship hydrodynamic radius

Knowing these functions, the mean-square radius of gyration (S2)z and the translational diffusion coefficient Dz can easily be derived eventually by application of the Stokes-Einstein relationship an effective hydrodynamic radius may be evaluated. These five... 

Second, an equivalent hydrodynamic radius can be defined from the diffusion coefficient via a Stokes-Einstein relationship... 

Diffusion coefficients may be converted to the molecular parameters (25.) In dilute solution where each molecule is separated, the diffusion coefficient is the translational diffusion coefficient of individual molecules and is related to the hydrodynamic radius, Rj,by the well-known Stokes-Einstein relationship (20)... 

Even within the group of dynamic methods, one can find in the recent literature entirely different hydration numbers, for instance, those presented in Table 12.2 for biologically important ions [157]. Surprisingly, the fundamental Stokes-Einstein relationship between the hydrodynamic radius and the diffusion coefficient of the ion is being used in several different manners in the calculation of the effective hydrated radius of an ion (compare [158] and [159]). 

The function F(F) is expanded in a power series of r. The first moment (cumulant) in the expansion is the average decay constant Favg, which defines an effective diffusion coefficient A for the particle size distribution. A is converted to the effective hydrodynamic radius using the Stokes-Einstein relationship. 

The Stokes-Einstein relationship then relates the diffusion constant to the hydrodynamic radius of the spherical aggregate, according to equation (15.8). 

The refractive index of the ethane/propane mixture, needed for calculation of the scattering vector, was determined from experimental density measurements and an empirical Lorentz-Lorenz relationship (12). Incorporating the errors from the viscosity and refractive index calculations into the Stokes-Einstein relation results in a maximum error in the hydrodynamic radius of approximately 5%. 

According to the Stokes-Einstein equation, diffusion coefficients have a reciprocal relationship to the dynamic viscosity of the host fluid (rj) and the hydrodynamic radius of the diffusing species (R). 

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