Wikipedia / Sedimentation equilibrium
Wikipedia / Sedimentation equilibrium
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. Sedimentation is due to an external force, such as gravity or centrifugal force in a centrifuge.
It was discovered for colloids by Jean Baptiste Perrin for which he received the Nobel Prize in Physics in 1926.
Colloid
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:
where
is the colloidal particle volume fraction,
,
is the buoyant mass of the colloidal particles,
is the standard acceleration due to gravity,
is the Boltzmann constant,
is the absolute temperature,
is the sedimentation length.
is the radius of the colloidal particle).
Sedimentation length
. The sedimentation length describes the probability.
), 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. It may become a colloidal suspension again if an action to undertaken to suspend the colloidal particles again, such as stirring the colloid.
Example
. As an example, consider a colloidal suspension of polyethylene.
is the mass density of polyethylene, which is approximately on average 920kg/m3 is the mass density of water, which is approximately 1000kg/m3 at room temperature (293K). is -80kg/m3. is negative the particles will cream, and the substance will no longer be a colloidal suspension.
is relatively small. Consider a colloid with particles much denser than polyethylene, for example silicon with a mass density of approximately 2330kg/m3. will be 1330kg/m3 increases. For example, if the particles had a diameter of 10 μm the sedimentation length would be 5.92×10−4 is positive and the particles will sediment.
Ultracentrifuge
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.