Electrophoretic migration theory

Although CE separations can be reasonable well described by the classical theoretical relationships for electrophoretic migration, slight deviations from the theory occur in the case of many classes of solutes. Thus, it has been reported that the CE separation of oligosaccharides follow the general rule [124], while the description of the separation of DNA in polymer solutions necessitated a new mathematical model. The drag forces were expressed by... 

The classical theory of electrophoretic migration has also been successfully applied to the description of the behaviour of human growth hormone peptides. According to the classical theory, the mobility (ju) of a peptide can be described by... 

In theory, if the net charge, q, on a molecule is known, it should be possible to measure / and obtain information about the hydrodynamic size and shape of that molecule by investigating its mobility in an electric field. Attempts to define /by electrophoresis have not been successful, primarily because Equation 4.3 does not adequately describe the electrophoretic process. Important factors that are not accounted for in the equation are interaction of migrating molecules with the support medium and shielding of the molecules by buffer ions. This means that electrophoresis is not useful for describing specific details about the shape of a molecule. Instead, it has been applied to the analysis of purity and size of macromolecules. Each molecule in a mixture is expected to have a unique charge and size, and its mobility in an electric field will therefore be unique. This expectation forms the basis for analysis and separation by all electrophoretic methods. The technique is especially useful for the analysis of amino acids, peptides, proteins, nucleotides, nucleic acids, and other charged molecules. 

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. 

Charged particles migrate in solution when an electric field is applied this phenomenon was described in the middle of the nineteenth century and from this early work, Kohlrausch (K12) developed a theory of ionic migration that can be used to describe all electrophoretic principles. However, it was not until 1923 that isotachophoresis was first used to separate rare earth metals and some simple acids (K3). 

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). 

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 ... 

Estimates of E and E in dilute solution can be obtained using Debye-Huckel theory in its simplest form. Assume the electrolyte to be point charges interacting via coulomb forces only. Ignore the molecular structure of both solvent and ions. Since the electrophoretic effect is due to the migration of the ion cloud through the fluid, the reduction in ion mobility can be calculated using Stokes law (3.21)... 

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. 

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