Theory of Electrophoresis

The rate of migration of ions in an electrical field depends on factors such as the (1) net charge of the molecule, (2) size and shape of the molecule, (3) strength of the electric field, (4) properties of the supporting medium, and (5) temperature of operation. The equation expressing the driving force in such a system is given by 

Q = the net charge on the ion EMF = the electromotive force (voltage [V] applied) d the length of die electrophoretic medium (cm) The steady acceleration of the migrating ion is counteracted by a resisting force characteristic of the solution in which migration occurs. This force, expressed by Stokes law, is 

F = the counter force r = the ionic radius of the solute T) = the viscosity of the buffer solution in which migration is occurring n =3.1416 

V - the rate of migration of the solute = velocity, length (/) traveled per unit of time (cm/s) 

The force F counteracts the acceleration that would be produced by F if no counter force were present, and the result of the two forces is a constant velocity. Therefore when 

The movement of a charged molecule subjected to an electric field is represented by Equation 4.1. 

The movement of a charged particle in an electric field is often defined in terms of mobility, /r, the velocity per unit of electric field (Equation 4.2). 

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. 

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A more detailed theory of electrophoresis is found in Refs. 9 and 58. The motion of the ions in the double layer due to the field F and due to the relative motion of the particle, cause a retardation of the electrophoretic motion that must be considered to... 

One must be very careful in reviewing the older, and some more recent, literature in consideration of the tortuosity and constriction factors some work has attempted to separate these two factors however, more modem developments show that they cannot be strictly decoupled. This aspect will be particularly important when reviewing the barrier and tortuous-path theories of electrophoresis, as discussed later. 

Overbeek, JTG Bijsterbosch, BH, The Electrical Double Layer and the Theory of Electrophoresis. In Electrokinetic Separation Methods Righetti, PG van Oss, CJ Vanderhoff, JW, eds. Elsevier/North-Holland Biomedical Press , 1979 1. 

In this section, we shall first give a brief review of the phenomenological theory of these effects.5 -6 26 We shall then show how the methods we have discussed in the previous sections may be extended to derive a microscopic theory of the relaxation effect the microscopic theory of electrophoresis will be considered in the next section. 

VI. MICROSCOPIC THEORY OF ELECTROPHORESIS AN EXAMPLE OF HYDRODYNAMICAL LONG-RANGE... 

We have seen in Section V that the classical theory of electrophoresis is intimately connected with the existence of a velocity field of the fluid around a given moving ion, which in turn contributes to a supplementary friction acting on the Debye atmosphere of this ion. 

Principle and Theory of Electrophoresis of Bent or Kinked Nucleic Acids... 

This section deals with a general theory of electrophoresis of soft particles and approximate analytic expressions for the mobility of soft particles [30-51]. This theory unites the electrophoresis theories of hard particles [1-29] and of polyelec-trolytes [52], since a soft particle tends to a hard particle in the absence of the polymer layer and to a polyelectrolyte in the absence of the particle. 

To estimate x, the decrease in equilibrium adsorption and the actual adsorption rate according to the electrostatic phenomena, have to be considered. The application of Boltzmann s law assumes equilibrium condition of the DL and neglects any transport within the diffuse layer. Thus, the classic Boltzmann law cannot be used to describe the distribution of adsorbing ions within the double layer in non-equilibrium systems. The presence of any ionic flux is connected with a non-equilibrium state of the DL and the approach given by Overbeek (1943) in his theory of electrophoresis has to be considered. In that theory, the non-equilibrium of the DL causes non-linear dependencies of electrophoresis on the electrokinetic potential, in contrast to the theory of Smoluchowski where this effect is not allocated for. The importance of the non-equilibrium state of the DL for many other surface phenomena was emphasised by Dukhin Deijaguin (1974), Dukhin Shilov (1974), and Dukhin (1993). 

The electrokinetic motion of colloidal particles and molecules in solution in response to applied electric fields can be rather complicated, so many approximations have been made in theoretical treatments. The classical theory of electrophoresis, dating back over a century to Smoluchowski, considers homogeneous particles, which are ... 

The classical theory of electrophoresis (particle motion due to electroosmotic flow) assumes that surface charge remains fixed at its equilibrium value, when electric fields (or other perturbations) are applied [1]. For thin electric double layers, the assumption of fixed charge implies that particles of uniform composition all have the same electrophoretic mobility b (velocity/field)... 

A well-known prediction of the classical theory of electrophoresis is that the mobility Eq. 1 only depends on the total charge (or average zeta potential), in the limits of thin double layers, small charge, and weak fields [1]. This remarkable result holds for any size or shape, even if the particle is polarizable and acquires a nonuniform charge (or zeta) profile in response to the applied field. It is not widely appreciated, however, that this follows from the assumption of constant double-layer capacitance, which reduces Eqs. 5 and 6. 

Simonov IN, Dukhin SS (1973) Theory of electrophoresis of solid conducting particles in case of ideal polarization of a thin diffuse double-layer. Colloid 35 191-193... 

Electrophoresis and sedimentation potential also offer a test of predictions of thermodynamics of irreversible processes, provided these are supplemented by classical analysis of the data. Few measurements of sedimentation potential have been reported [1] and the theories due to Kruyt [2], Debye and Huckel [3] and Henry [4] are not in complete agreement. The thermodynamics of irreversible processes [5] may be helpful since the theory does not depend on any model. In the present chapter it is intended (i) to test linear phenomenological relations, (ii) to test the Onsager s reciprocal relation and (iii) to examine the validity of conflicting theories of electrophoresis. 

Levine, S. and O Brien, R.N., A theory of electrophoresis of charged mercury drops in aqueous electrolyte solution, J. Colloid Interface Set, 43, 616, 1973. 

Figure 1 General theory of electrophoresis. Many substances exist in solution as electrically charged species. Ions can be separated in an electrical field where the speed and direction of movement depends on their charge.

The theory of electrophoresis is discussed in detail in another article, but it must be noted here that the rate of protein migration is dependent on such factors as net electric charge of the molecule, size and shape of the molecule, electric field strength, properties of the supporting medium, and the temperature of the operation. 

The theory of electrophoresis has been adequately covered in the excellent textbooks of Giddings [1] and Andrews [2] as well as in specific manuals [3], [4]. For discussion on electrophoresis in free liquid media, e.g., curtain, freeflow, endless belt, field-flow-fractionation, particle, and cell electrophoresis the reader is referred to a comprehensive review by Van Oss [5] and to a book largely devoted to continuous-flow electrophoresis [6], Here the focus is mostly on electrophoresis in a capillary support, i.e, in gel-stabilized media, and discussion is limited to protein applications. 

The classical theory of electrophoresis (particle motion due to electro-osmotic flow) assumes that surface charge remains fixed at its equilibrium value, when electric fields... 

The movement of charged particles (ions) in an electric field is called electrophoresis. The basic theory of electrophoresis is related to ionic mobility u, which is also called electrophoretic mobility. When an ion in solution is moving in the direction of a field E, its velocity v depends on three factors the charge z carried by the ion, the frictional coefficient / arising from the resistance of the solution, and the strength of the field E. The quantity E is defined as... 

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