Equilibrium sedimentation - diffusion

Describe the relation between sedimentation/diffusion equilibrium and the barometric equation. 

When a state of sedimentation-diffusion equilibrium has been reached, the molecular or particle mass can, therefore, be evaluated without a knowledge of the diffusion coefficient (and, hence, independently of shape and solvation) by determining relative concentrations at various distances from the axis of rotation. Molecules as small as sugars have been studied by this technique. 

Scholte, Th. G., "Determination of Thermodynamic Parameters of Polymer-Solvent Systems from Sedimentation-Diffusion Equilibrium in the Ultracentrifuge," J. Polym. Sci., Part A-2, 8, 841 (1970b). 

Sedimentation-diffusion equilibrium in an ultracentrifuge gives also a virial series ... 

After the sedimentation process has finished, the diffusion is still present and leads to a fuzzy interface between the sediment and the particle-free supernatant. The thickness of this layer depends on particle size. It may even extend over the whole vessel (cuvette), which means that the particles are not separated, but obey an sedimentation-diffusion equilibrium, which is characterised by an exponential concentration profile (cf. Sect. 3.1.2) ... 

Jean-Baptiste Perrin (1870-1942). .. was a French physicist who worked on various subjects, for instance, on cathode rays, fluorescence, sound propagation, and the decay of radium. A major part of his scientiflc life was dedicated to colloids. His investigations on the Brownian motion of colloids by means of the previously developed ultramicroscope verified Einstein s statistic explanation of this phenomenon and thereby confirmed the atomic nature of matter. Moreover, Perrin was able to closely limit the possible range of Avogadro s number and he discovered the sedimentation-diffusion equilibrium. For his work on the discontinuous structure of matter and especially for his discovery of sedimentation equilibrium he received 1926 the Nobel Prize in Physics. 

Thermodynamic data from the ultracentrifuge experiment ean be obtained either from flie sedimentation velocity (sedimentation coefficient) or from the sedimentation-diffusion equilibrium since the centrifugal forces are balanced by the activity gradient. The determination of sedimentation and diffusion coefficients yields the virial coefficients by ... 

An alternative analytical method, based upon a detailed analysis of phase relatkmships, is still in an early stage of development. Being an absolute procedure it cotdd be useful for supporting other absolute ta, e.g. those obtained from the sedimentation-diffusion equilibrium in the ultracentrifr e. 

Biesheuvel, P. M., and Lyklema, J. (2005). Sedimentation-diffusion equilibrium of binary mixtures of charged colloids including volume effects. J. Phys. Condens. Matter 17, 6337. 

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