Hydrodynamic radius

The hydrodynamic radius (also " Stokes radius " according to George Gabriel Stokes ) is the radius of a hypothetical solid sphere that has the same diffusion properties in a solvent as the particle described by the hydrodynamic radius (for example ion , protein , micelle , virus or dust particle ). ${\displaystyle R_{0}}$

The volume of a particle in solution that is relevant for diffusion is not only formed by the atoms of the particle itself, but also by the surrounding solvent molecules. Due to electrostatic interactions, these can interact so tightly with the particle ( Grotthus mechanism ) that this solvation shell remains bound when it moves through the solvent. This total volume determines the diffusion, with a larger volume causing slower diffusion. For non-spherical particles, the shape also determines the diffusion speed and thus the hydrodynamic radius.

Since the real dimensions of the particle cannot be measured directly in solution, the hydrodynamic radius is defined using the Stokes-Einstein equation (the temperature, the viscosity and the diffusion constant can be measured in practice):

${\displaystyle R_{0}={\frac {k_{\mathrm {B} }\cdot T}{6\cdot \pi \cdot \eta \cdot D}}}$

With

• ${\displaystyle k_{B}}$the Boltzmann constant
• ${\displaystyle T}$the temperature
• ${\displaystyle \eta }$the viscosity of the solvent
• ${\displaystyle D}$the diffusion constant .

The hydrodynamic radius can deviate considerably from the real radius of the particle; usually it is smaller than the effective radius of the particle.

In practice, the hydrodynamic radius of proteins and polymers is determined by

• Dynamic light scattering
• Fluorescence Correlation Spectroscopy
• Electron Spin Resonance Spectroscopy (ESR)
• Nuclear Magnetic Resonance Spectroscopy  (NMR) or
• Fluorescence polarization measurements .

The radius is measured, among other things, to check the behavior of polymers towards solvents or to be able to make statements about the structure of proteins .