Electrophoretic theory migration velocity

In 1809, Reuss observed the electrokinetic phenomena when a direct current (DC) was applied to a clay-water mixture. Water moved through the capillary toward the cathode under the electric field. When the electric potential was removed, the flow of water immediately stopped. In 1861, Quincke found that the electric potential difference across a membrane resulted from streaming potential. Helmholtz first treated electroosmotic phenomena analytically in 1879, and provided a mathematical basis. Smoluchowski (1914) later modified it to also apply to electrophoretic velocity, also known as the Helmholtz-Smoluchowski (H-S) theory. The H-S theory describes under an apphed electric potential the migration velocity of one phase of material dispersed in another phase. The electroosmotic velocity of a fluid of certain viscosity and dielectric constant through a surface-charged porous medium of zeta or electrokinetic potential (0, under an electric gradient, E, is given by the H-S equation as follows ... 

The photomicrographic measurements refer directly to polymer motion under the influence of an external force. However, measurements of migration velocity v as a function of applied electrical field E show that some of these electrophoretic measurements were made in a low-field linear regime, in which the electrophoretic mobility jx is independent of E. Linear response theory and the fluctuation-dissipation theorem are then applicable they provide that the modes of motion used by a polymer undergoing electrophoresis in the linear regime, and the modes of motion used by the same polymer as it diffuses, must be the same. This requirement on the equality of drag coefficients for driven and diffusive motion was first seen in Einstein s derivation of the Stokes-Einstein equation(16), namely thermal equilibrium requires that the drag coefficients / that determine the sedimentation rate v = mg/f and the diffusion coefficient D = kBT/f must be the same. 

One of the most successful models for gel electrophoresis is the reptation theory of Lumpkin and Zimm for the migration of double-stranded DNA (Lumpkin, 1982). An in-depth discussion can be found in Zimm and Levene (1992) for a synopsis see Bloomfield et al. (2000). The velocity v of a charged particle in a solution with an electric field E depends on the electrical force Fei = ZqE, in which Z is the number of charges and q is the charge of a proton, and the frictional force l fr = —fv, in which/is the frictional coefficient. At steady state, these forces balance and the velocity is v = ZqE/f. The electrophoretic mobility fi is the velocity relative to the field strength, fi = vE = Zq/f. 

In the case of conductance studies, the ions move under the influence of the electric field. Because the field is uniform this means that the ions migrate at a constant velocity. This will become relevant in the section on ionic mobilities (Section 11.17), and when discussing the relaxation and electrophoretic effects in the theories of conductance (see Sections 12.1, 12.2 and 12.4). 

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