The size of the sedimentation coefficient depends on the mass and shape of the particle as well as its interaction with the medium in which the particle sediments . It can therefore be used when using a medium with known properties to determine the nature of the particle, in particular its mass. Mainly in biology the masses of very small particles are determined by means of analytical ultracentrifugation , for example ribosomes , virions or protein molecules . In order to obtain a sufficient centrifugal field with such small particles, ultracentrifuges are usually used.
In the context of a centrifugation experiment with angular velocity ω , several forces act on a particle of mass and density , which is located in a solvent with density in the radius position with respect to the axis of rotation . The sum of all relevant forces can be set up with particle acceleration as:
as well as the friction force according to Stokes ' law , with particle velocity and the coefficient of friction , which depends on the shape, size and hydration of the particle and the viscosity of the medium. :
Since all the forces considered only act in the radial direction, the basis vector is not considered in the following .
Assuming that the forces involved are immediately in equilibrium, the result is
If you divide the sedimentation speed by the strength of the centrifugal field, you get the sedimentation coefficient , which only depends on the nature of the particle and the solvent:
The description of the sedimentation properties of a particle by the sedimentation coefficient offers the advantage of a radius and speed-independent consideration.
It can also be seen directly from the definition of the sedimentation coefficient that the sedimentation speed increases in the context of an experiment for sedimenting particles. This is due to the fact that the sum of centrifugal force and counteracting buoyancy force increases with higher radius positions. In the case of an instantaneous equilibrium of forces at every radius position, however, this is not a contradiction to the assumption .
The dimension of results from
In general, the sedimentation coefficient depends on the size, shape and density of the particles examined. For the special case of spherical particles, if the particle density , solvent density and viscosity are known, the following can be determined directly from the diameter :
If the particles are non-spherical, a corresponding equivalent diameter can be calculated.
When determining the mass of particles from their sedimentation coefficient, it must be taken into account that two particles of the same mass can have different sedimentation coefficients if they have different densities (influence on the buoyancy and thus on the effective mass) or shapes (influence on the friction coefficient). In addition, when two particles come together, their sedimentation coefficients cannot simply be added because, firstly, the contact surfaces do not contribute to friction and, secondly, the friction increases more slowly than the surface, see Stokes' law . For example, a complex ribosome from bacteria consisting of two ribosomal subunits of 30 S and 50 S has a sedimentation coefficient of only 70 S.
From the definition of sedimentation the particle path can be achieved by integration with the radius position of the particle at the time , and at the time , calculated. This means that by observing the movement of the sedimentation band, conclusions can be drawn about the sedimentation coefficient. This technique is used, for example, to determine the particle size by means of photo sedimentation in the earth's gravity field or by means of the disc centrifuge . Depending on the material system investigated, sedimentation coefficient and particle size distributions can be determined by using locally fixed detectors.
Other methods for determining the sedimentation coefficient are based on the spatial and temporal recording of the entire sedimentation process by means of analytical ultracentrifugation .
While local and temporal derivations of the sedimentation bands were used at the beginning of the development of the technology, later numerical solutions of the Lamm equation could be used for data evaluation. By modeling all the data available during the sedimentation process, it is possible to determine sedimentation coefficient distributions adjusted for diffusion broadening even for small particles. In addition, the diffusion information for the sedimentation coefficient can contain information that is complementary to the sedimentation coefficient, which, for example, enables the determination of the molar mass of proteins using the Svedberg equation .
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