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Sedimentation equilibrium in a suspension of different particles, such as
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s, exists when the rate of transport of each material in any one direction due to
sedimentation Sedimentation is the deposition of sediments. It takes place when particles in suspension settle out of the fluid in which they are entrained and come to rest against a barrier. This is due to their motion through the fluid in response to the ...
equals the rate of transport in the opposite direction due to
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
. Sedimentation is due to an external force, such as
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
or
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...
in a centrifuge. It was discovered for colloids by
Jean Baptiste Perrin Jean Baptiste Perrin (30 September 1870 – 17 April 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids ( sedimentation equilibrium), verified Albert Einstein’s explanation of this ...
for which he received the
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
in 1926.


Colloid

In a
colloid A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
, the colloidal
particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...
s are said to be in sedimentation equilibrium if the rate of sedimentation is equal to the rate of movement from
Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...
. For dilute colloids, this is described using the Laplace-Perrin distribution law: \Phi(z) = \Phi_0\exp\biggl(-\fracz\biggr)=\Phi_0e^ where \Phi(z) is the colloidal particle volume fraction as a function of vertical distance z above reference point z=0, \Phi_0 is the colloidal particle volume fraction at reference point z=0, m^* is the
buoyant mass Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pr ...
of the colloidal particles, g is the standard acceleration due to gravity, k_Bis 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, ...
, T is the absolute
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
, and l_g is the sedimentation length. The buoyant mass is calculated using m^*=\Delta\rho V_P=\frac\pi\Delta\rho R^3 where \Delta\rho is the difference in mass density between the colloidal particles and the suspension medium, and V_P is the colloidal particle volume found using the volume of a sphere (R is the radius of the colloidal particle).


Sedimentation length

The Laplace-Perrin distribution law can be rearranged to give the sedimentation length l_g. The sedimentation length describes the
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
of finding a colloidal particle at a height z above the point of reference z=0. At the length l_g above the reference point, the concentration of colloidal particles decreases by a factor of e. l_g=\frac If the sedimentation length is much greater than the diameter d of the colloidal particles (l_g>>d), the particles can diffuse a distance greater than this diameter, and the substance remains a suspension. However, if the sedimentation length is less than the diameter (l_g), 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

The difference in mass density \Delta\rho between the colloidal particles of mass density \rho_1 and the medium of suspension of mass density \rho_2, and the diameter of the particles, have an influence on the value of l_g. As an example, consider a colloidal suspension of
polyethylene Polyethylene or polythene (abbreviated PE; IUPAC name polyethene or poly(methylene)) is the most commonly produced plastic. It is a polymer, primarily used for packaging ( plastic bags, plastic films, geomembranes and containers including bo ...
particles in water, and three different values for the diameter of the particles: 0.1 μm, 1 μm and 10 μm. The volume of a colloidal particles can be calculated using the volume of a sphere V=\frac\pi R^3. \rho_1 is the mass density of polyethylene, which is approximately on average 920 kg/m3 and \rho_2 is the mass density of water, which is approximately 1000 kg/m3 at room temperature (293K). Therefore \Delta\rho=\rho_1-\rho_2 is -80 kg/m3. {, class="wikitable" , +l_g for different sizes of polyethylene and silicon particles !Diameter d (μm) !l_g for polyethylene particles (μm) !l_g for silicon particles (μm) , - , 0.01 , -9.84×106 , 5.92×105 , - , 0.1 , -9840 , 592 , - , 1 , -9.84 , 0.592 , - , 10 , -9.84×10−3 , 5.92×10−4 Generally, l_g decreases with d^3. For the 0.1 μm diameter particle, l_g is larger than the diameter, and the particles will be able to diffuse. For the 10 μm diameter particle, l_g is much smaller than the diameter. As l_g is negative the particles will cream, and the substance will no longer be a colloidal suspension. In this example, the difference is mass density \Delta\rho is relatively small. Consider a colloid with particles much denser than polyethylene, for example
silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
with a mass density of approximately 2330 kg/m3. If these particles are suspended in water, \Delta\rho will be 1330 kg/m3. l_g will decrease as \Delta\rho increases. 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. Also, because the particles are more dense than water, l_gis positive and the particles will sediment.


Ultracentrifuge

Modern applications use the
analytical ultracentrifuge An ultracentrifuge is a centrifuge optimized for spinning a rotor at very high speeds, capable of generating acceleration as high as (approx. ). There are two kinds of ultracentrifuges, the preparative and the analytical ultracentrifuge. Both cla ...
. 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 Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
, otherwise required for interpretation of dynamic
sedimentation Sedimentation is the deposition of sediments. It takes place when particles in suspension settle out of the fluid in which they are entrained and come to rest against a barrier. This is due to their motion through the fluid in response to the ...
. Sedimentation equilibrium can be used to determine
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
. It forms the basis for an analytical ultracentrifugation method for measuring molecular masses, such as those of
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
s, in solution.


References


External links




Reversible Associations in Structural and Molecular Biology
Biochemistry methods