Electrophoretic theory

While polyelectrolyte behavior is generally not within the remit of this work, Stellwagen, et a/. s use of capillary electrophoresis to examine a fundamental physico-chemical issue is worthy of note(49). Their interest was a vexing question, namely whether or not zwitterions contribute to the ionic strength / of a solution. Many would assert that the theoretical studies of Kirkwood are substantially definitive, but some doubts remain(50,51). Stellwagen, etal. noted that the Debye-Hueckel-Onsager electrophoretic theory requires pi [Pg.57]

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... 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

Electroultrafiltration has been demonstrated on clay suspensions, electrophoretic paints, protein solutions, oil—water emulsions, and a variety of other materials. Flux improvement is proportional to the appHed electric field E up to some field strength E where particle movement away from the membrane is equal to the Hquid flow toward the membrane. There is no gel-polarization layer and (in theory) flux equals the theoretical permeate flux. It... 

The Dehye-Hbckel theory of electrolytes based on the electric field surrounding each ion forms the basis for modern concepts of electrolyte behavior (16,17). The two components of the theory are the relaxation and the electrophoretic effect. Each ion has an ion atmosphere of equal opposite charge surrounding it. During movement the ion may not be exacdy in the center of its ion atmosphere, thereby producing a retarding electrical force on the ion. 

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

Theory of Electrophoretic Motion. The study of the mechanics of electrophoresis focuses on the basis of electric potential on the surface of an object, and the relation of the electric potential to the velocity of the particle. Whereas research has been generally limited to nonmolecular particles of weU-defined geometry and is not strictly apphcable to molecules such as proteins and DNA fragments, this work is useful for understanding the physics of electrophoretic motion. 

An important reason for this lack of experimental work is that the zeta-potential cannot be easily determined independent of the electrophoretic mobility [284] however, in the case of proteins (as well as some other charged colloids), the intrinsic charge obtained by titration is a parameter that can be measured independent of the electrophoretic mobility. The charge obtained from electrophoretic measurements (i.e., the net charge) via the preceding theories is generally not the same as the charge obtained from titration (i.e., the in-... 

The tortuous-path and barrier theories consider the effects of the media on the electrophoretic mobility in a way similar to the effect of media on diffusion coefficients discussed in a previous section of this chapter. The tortuons-path theory seeks to determine the effect of increased path length on electrophoretic mobility. The barrier theory considers the effects of the barrier or media conductivity on the electrophoretic mobility. 

Boyack, JR Giddings, JC, Theory of Electrophoretic Mobility in Stabilized Media, Archives of Biochemistry and Biophysics 100, 16, 1963. 

Muthukumar, M, Theory of Electrophoretic Mobility of Polyelectrolyte Chains, Macromolec-ular Theory and Simulations 3, 61, 1994. 

Norden, B Elvingson, C Jonsson, M Akerman, B, Microscopic Behavior of DNA Duing Electrophoresis Electrophoretic Orientation, Quarterly Reviews of Biophysics 24, 103,1991. Nozad, I Carbonell, RG Whitaker, S, Heat Conduction in Multiphase Systems—I Theory and Experiment for Two-Phase Systems, Chemical Engineering Science 40, 843, 1985. 

Overbeek, JTG Wiersema, PH, The Interpretation of Electrophoretic Mobilities. In Electrophoresis, Theory, Methods and Applications Bier, M, ed. Academic Press New York, 1967 1. 

SaviUe, D Palusinski, OA, Theory of Electrophoretic Separations Part 1 Eormulation of a Mathematical Model, AIChE Journal 32, 207, 1986. 

These rules are based on the theory of conductivity of strong electrolytes accounting for the electrophoretic effect only (the relaxation effect terms outbalance each other). 

Righetti, P.G., Stoyanov, A., Zhukov, M. Y. (2007). The Proteome revisited Theory and Practice of All Relevant Electrophoretic Steps. Elsevier, Amsterdam, pp. 275-378. 

By hydrolysis under very mild alkaline conditions (with a boiling suspension of barium carbonate), ribonucleic acids have been shown to yield small quantities of cyclic phosphates as well as the normal nucleotides.96 These materials were identical electrophoretically with synthetic cyclic phosphates and were readily hydrolyzed to mixtures of 2- and 3-phosphates. Their formation in this way constitutes strong support for Brown and Todd s theory. The precise way in which the alkaline hydrolysis of the polynucleotide occurs has been studied using isotopically labeled water, and the results are in agreement202 with the scheme outlined above. 

As soon as the concentration of the solute becomes finite, the coulombic forces between the ions begin to play a role and we obtain both the well-known relaxation effect and an electrophoretic effect in the expression for the conductivity. In Section V, we first briefly recall the semi-phenomenological theory of Debye-Onsager-Falkenhagen, and we then show how a combination of the ideas developed in the previous sections, namely the treatment of long-range forces as given in Section III and the Brownian model of Section IV, allows us to study various microscopic... 

It is well-known that the electrophoretic effect involves the hydrodynamical properties of the solvent in a very crucial way for this reason, the theory of this effect is rather difficult. However, using a Brownian approximation for the ions, we have been able to obtain recently a microscopic description of this effect. This problem, together with the more general question of long-range hydrodynamical correlations, is discussed in Section VI. 

However, the present formulation has the advantage of furnishing a mathematically rigorous foundation to the classical theory and is readily extended to other physical situations, like plasmas32 and semiconductors. Also, it allows us to give a microscopic foundation to the theory of the electrophoretic effect, which is much more delicate because it involves the difficult question of long-range hydrodynamical correlations this point will be the object of Section VI. 

Our discussion of Section V has indicated that the electrophoretic effect has to be found in the Ta term defined in Eq. (301) (see also Eq. (312)) moreover we have already found a diagram (Fig. 14a) in which the solvent is transmitting the wave number —k from ion /S to ion a, as we expect to find from the classical theory. This term was not calculated in Section V because it gives a contribution of order ei to while the relaxation term is of order e6 it will be considered presently. 

We begin with a short introduction to provide polymer chemists who may be new to the field of electrophoresis with a brief background concerning electrophoretic separation and characterization. Those who wish to obtain an in-depth understanding of the theory or detailed practical techniques are referred to textbooks/monographs on this subject [1-6]. Next, the advantages of gel electrophoresis as an analytical tool, and the structural requirements regarding dendrimers as electrophoretic analytes are discussed. Finally, studies directed at... 

The surface potential is not accessible by direct experimental measurement it can be calculated from the experimentally determined surface charge (Eqs. 3.1 - 3.3) by Eqs. (3.3a) and (3.3b). The zeta potential, calculated from electrophoretic measurements is typically lower than the surface potential, y, calculated from diffuse double layer theory. The zeta potential reflects the potential difference between the plane of shear and the bulk phase. The distance between the surface and the shear plane cannot be defined rigorously. 

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... 

The CE theories briefly discussed above can be applied to the prediction of the electrophoretic mobility of natural pigments and synthetic dyes too, and for the design of a CE system for their optimal separation. 

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