The Stokes radius or Stokes–Einstein radius of a solute is the radius of a hard sphere that diffuses at the same rate as that solute. Named after
George Gabriel Stokes
Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish migration to Great Britain, Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University ...
, it is closely related to solute mobility, factoring in not only size but also solvent effects. A smaller ion with stronger hydration, for example, may have a greater Stokes radius than a larger ion with weaker hydration. This is because the smaller ion drags a greater number of water molecules with it as it moves through the solution.
Stokes radius is sometimes used synonymously with effective hydrated radius in solution.
Hydrodynamic radius
The hydrodynamic radius of a macromolecule or colloid particle is R_. The macromolecule or colloid particle is a collection of N subparticles. This is done most commonly for polymers; the subparticles would then be the units of the polymer. R_ ...
, ''R''
''H'', can refer to the Stokes radius of a polymer or other macromolecule.
Spherical case
According to
Stokes’ law, a perfect sphere traveling through a viscous liquid feels a drag force proportional to the frictional coefficient
:
where
is the liquid's
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
,
is the sphere's
drift speed, and
is its radius. Because
ionic mobility
Electrical mobility is the ability of charged particles (such as electrons or protons) to move through a medium in response to an electric field that is pulling them. The separation of ions according to their mobility in gas phase is called ion ...
is directly proportional to drift speed, it is inversely proportional to the frictional coefficient:
where
represents ionic charge in integer multiples of electron charges.
In 1905,
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
found the diffusion coefficient
of an ion to be proportional to its mobility constant:
where
is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
and
is
electrical charge
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
. This is known as the
Einstein relation. Substituting in the frictional coefficient of a perfect sphere from Stokes’ law yields
which can be rearranged to solve for
, the radius:
In non-spherical systems, the frictional coefficient is determined by the size and shape of the species under consideration.
Research applications
Stokes radii are often determined experimentally by gel-permeation or gel-filtration chromatography.
They are useful in characterizing biological species due to the size-dependence of processes like enzyme-substrate interaction and membrane diffusion.
The Stokes radii of sediment, soil, and aerosol particles are considered in ecological measurements and models.
They likewise play a role in the study of polymer and other macromolecular systems.
See also
*
Born equation
The Born equation can be used for estimating the electrostatic component of Gibbs free energy of solvation of an ion. It is an electrostatic model that treats the solvent as a continuous dielectric medium (it is thus one member of a class of method ...
*
Capillary electrophoresis
Capillary electrophoresis (CE) is a family of electrokinetic separation methods performed in submillimeter diameter capillaries and in micro- and nanofluidic channels. Very often, CE refers to capillary zone electrophoresis (CZE), but other electr ...
*
Dynamic light scattering
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using ...
*
Equivalent spherical diameter
The equivalent spherical diameter of an irregularly shaped object is the diameter of a sphere of equivalent geometric, optical, electrical, aerodynamic or hydrodynamic behavior to that of the particle under investigation.
The particle size of a pe ...
*
Einstein relation (kinetic theory)
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works ...
*
Ionic radius
Ionic radius, ''r''ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the catio ...
*
Ion transport number
*
Molar conductivity
The molar conductivity of an electrolyte solution is defined as its conductivity divided by its molar concentration.
: \Lambda_\text = \frac,
where:
: ''κ'' is the measured conductivity (formerly known as specific conductance),
: ''c'' is the mol ...
References
{{DEFAULTSORT:Stokes Radius
Fluid dynamics