Sedimentation equilibrium in a suspension of different particles, such as molecules, exists when the rate of transport of each material in any one direction due to sedimentation equals the rate of transport in the opposite direction due to diffusion.
It was discovered for colloids by Jean Baptiste Perrin for which he received the Nobel Prize in Physics in 1926.
[1] In a colloid, the colloidal particles are said to be in sedimentation equilibrium if the rate of sedimentation is equal to the rate of movement from Brownian motion.
For dilute colloids, this is described using the Laplace-Perrin distribution law:
is the colloidal particle volume fraction as a function of vertical distance
is the colloidal particle volume fraction at reference point
is the standard acceleration due to gravity,
is the difference in mass density between the colloidal particles and the suspension medium, and
The Laplace-Perrin distribution law can be rearranged to give the sedimentation length
The sedimentation length describes the probability of finding a colloidal particle at a height
above the reference point, the concentration of colloidal particles decreases by a factor of
If the sedimentation length is much greater than the diameter
), the particles can diffuse a distance greater than this diameter, and the substance remains a suspension.
), the particles can only diffuse by a much shorter length.
They will sediment under the influence of gravity and settle to the bottom of the container.
The substance can no longer be considered a colloidal suspension.
between the colloidal particles of mass density
and the medium of suspension of mass density
, and the diameter of the particles, have an influence on the value of
is the mass density of polyethylene, which is approximately on average 920 kg/m3 [3] and
is the mass density of water, which is approximately 1000 kg/m3 at room temperature (293K).
is larger than the diameter, and the particles will be able to diffuse.
is negative the particles will cream, and the substance will no longer be a colloidal suspension.
Consider a colloid with particles much denser than polyethylene, for example silicon with a mass density of approximately 2330 kg/m3.
For example, if the particles had a diameter of 10 μm the sedimentation length would be 5.92×10−4 μm, one order of magnitude smaller than for polyethylene particles.
Modern applications use the analytical ultracentrifuge.
The theoretical basis for the measurements is developed from the Mason-Weaver equation.
The advantage of using analytical sedimentation equilibrium analysis for Molecular Weight of proteins and their interacting mixtures is the avoidance of need for derivation of a frictional coefficient, otherwise required for interpretation of dynamic sedimentation.
Sedimentation equilibrium can be used to determine molecular mass.
It forms the basis for an analytical ultracentrifugation method for measuring molecular masses, such as those of proteins, in solution.