Electrokinetic theory

Electrokinetic phenomena are only directly related to the nature of the mobile part of the electric double layer and may, therefore, be interpreted only in terms of the zeta potential or the charge density at the surface of shear. No direct information is given about the potentials tf/0 and //d (although, as already discussed, the value of may not differ substantially from that of 0d), or about the charge density at the surface of the material in question. 

Electrokinetic theory involves both the theory of the electric double layer and that of liquid flow, and is quite complicated. In this section the relation between electrokinetically determined quantities (particularly electrophoretic mobility) and the zeta potential will be considered. 

For curved surfaces the shape of the double layer can be described in terms of the dimensionless quantity 1ko which is the ratio of radius of curvature to double-layer thickness. When tea is small, a charged particle may be treated as a point charge when tea is large, the double layer is effectively flat and may be treated as such. 

Consider kq to be small enough for a spherical particle to be treated as a point charge in an unperturbed electric field, but let the particle be large enough for Stokes law to apply. Equating the electrical force on the particle with the frictional resistance of the medium, 

The zeta potential is the resultant potential at the surface of shear due to the charges + QE of the electrokinetic unit and -Qe of the mobile part of the double layer - i.e. 

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In the following sections an account of the origin and measurement of electroosmosis is elicited, Furthermore, it is shown how to employ its measurement as a characterization technique. The discussion will focus on the measurement of electro-osmosis in cylindrical chambers and in a novel rectangular chamber whereby electro-osmosis can be measured at small sample plates. Examples of using the measurement of electro-osmosis as a surface characterization technique are discussed in terms of interpretation of the source of electro-osmosis according to classical electrokinetic theory. 

In this chapter, we extend the electrokinetic theory of soft particles (Chapter 21), which is applicable for dilute suspensions, to cover the case of concentrated suspensions [1-3] on the basis of Kuwabara s cell model [4], which has been applied to theoretical studies of various electrokinetic phenomena in concentrated suspensions of hard colloidal particles [5-23]. 

The current-voltage curves corresponding to these processes are depicted in Fig. 5.1. As the net current across the metal/solution interface is zero the potential Ep assumed by the particle under stationary conditions is given by the point of intersection of the two i(E) curves. At this potential the anodic and cathodic currents are equal and their value corresponds to iR. The latter defines the overall reaction rate. Both the mixed potential Ep and the reaction current iR may be evaluated from electrokinetic theory. Application of the Butler-Volmer equation to reaction (5.2) gives for the reaction rate V the expression... 

Alternative models for the calcium effects have been advanced by Hubbard, Jones, and Landau and by Katz and Miledi. These workers believe that the reaction of calcium with sites on the vesicle or on the presynaptic membrane controls the rate of discharge of synaptic vesicles. The effect of depolarization is then either (a) to facilitate the transport of Ca + to these specific absorption sites by opening channels for ionic transport, or (b) to facilitate the transport of the calcium complex through the membrane. To what extent can the calcium effect on MEPP be understood within the framework of the basic electrokinetic theory without such new ad hoc assumptions, namely, by means of an effect of [Ca +] on the free energy of activation AC ... 

Brooks and coworkers [136,141] measured drop electrophoretic mobilities in ATPSs. They were surprised to discover that the sign of the droplet mobilities was opposite to that predicted from the phosphate partition and the Donnan potential. They also found mobility to be directly proportional to drop radius, which is a contradiction of standard colloid electrokinetic theory [144]. Levine [140] and Brooks et al. [141] hypothesized that a dipole potential at the phase boundary oriented in a way that reverses the potential gradient locally is responsible for the paradox of the sign of electrophoretic mobilities of ATPS droplets. 

The theories describing micellar electrokinetic chromatography (MEKC), capillary zone electrophoresis (CZE), and capillary gel electrophoresis (CGE) separations of small molecules and biopolymers are described in other chapters of this book and will not be discussed here. Here, we will briefly touch upon the theoretical aspects of the electrophoretic mobility of organelles, foregoing an in depth discussion of electrokinetic theory that can be found elsewhere in original publications and comprehensive reviews. The electrophoretic mobility (/ue) is defined as... 

D. S. Fensom, "The Bioelectric Potentials of Plants and Their Functional Significance. I An Electrokinetic Theory of Transport, Can. J. Botany 35, 573-582 (1957). 

Based on the nonlinear electrokinetic theory, the electric field induces surface charge when... 

The first microvalve was introduced by Terry [1], in 1979, which was the first magnetic MEMS microvalve. After that, microvalves were improved in several ways. Around the year 2000 a revolution in fabrication of microvalves happened [2—4] which solved the problems of the various MEMS-based microvalves. However, many problems (such as (i) using moving parts that causes additional problems and difficulties, (ii) external actuation means, (iii) complex fabrication and installation processes, (iv) resistible flow and pressure, (v) considerable dead volume, (vi) long respmise time, (vii) leakage, and (viii) stability) remain unsolved when classical electrokinetic theory is used to design a microvalve. 

Rosen et al. [107], Simonova and Shilov [108], and Zukoski and Saville [109,110] were among the first in modifying, in a quantitative manner, the classical electrokinetic theories to account for... 

Zukoski IV, C.F. and SaviUe, D.A., An experimental test of electrokinetic theory using measurements of electrophoretic mohiUty and electrical conductivity, J. Colloid Interface Sci., 107, 322, 1985. 

Figure 19.7. The dependence of zeta potential on charge and electrolyte concentration for a 1 1 electrolyte according to the Guoy-Chapman model of the interface (Figure 19.1) and classical electrokinetic theory...

Edwards [105] has extended the macrotransport method, originally developed by Brenner [48] and based upon a generalization of Taylor-Aris dispersion theory, to the analysis of electrokinetic transport in spatially periodic porons media. Edwards and Langer [106] applied this methodology to transdermal dmg delivery by iontophoresis and electroporation. 

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. 

Altria, K.D. (2000). Background theory and applications of microemulsion electrokinetic chromatography. J. Chromatogr. A 892 171-186. 

In addition to the interphase potential difference V there exists another potential difference of fundamental importance in the theory of the electrical properties of colloids namely the electro-kinetic potential, of Freundlich. As we shall note in subsequent sections the electrokinetic potential is a calculated value based upon certain assumptions for the potential difference between the aqueous bulk phase and some apparently immobile part of the boundary layer at the interface. Thus represents a part of V but there is no method yet available for determining how far we must penetrate into the boundary layer before the potential has risen to the value of the electrokinetic potential whether in fact f represents part of, all or more than the diffuse boundary layer. It is clear from the above diagram that bears no relation to V, the former may be in fact either of the same or opposite sign, a conclusion experimentally verified by Freundlich and Rona. 

The coupling of two different electrokinetic ratios (Estr/p and V/I) through Equation (65) is an illustration of a very general law of reciprocity due to L. Onsager (Nobel Prize, 1968). The general theory of the Onsager relations, of which Equation (65) is an example, is an important topic in nonequilibrium thermodynamics. 

Throughout most of this chapter the emphasis has been on the evaluation of zeta potentials from electrokinetic measurements. This emphasis is entirely fitting in view of the important role played by the potential in the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability. From a theoretical point of view, a fairly complete picture of the stability of dilute dispersions can be built up from a knowledge of potential, electrolyte content, Hamaker constants, and particle geometry, as we discuss in Chapter 13. From this perspective the fundamental importance of the f potential is evident. Below we present a brief list of some of the applications of electrokinetic measurements. 

Chapters 11 and 12 in the present edition focus exclusively on the theories of electrical double layers and forces due to double-layer interactions (Chapter 11) and electrokinetic phenomena (Chapter 12). Chapter 11 includes expressions for interacting spherical double layers, and both chapters provide additional examples of applications of the concepts covered. 

Equation (2.1.3a) has been studied extensively in different mathematical and physical contexts ranging from differential geometry to reaction-diffusion, electrokinetics, colloid stability, theory of polyelectrolytes, etc. In... 

The reproducibility of the electrokinetic injection is poorer than that of the dynamic pressure injection and strongly depends on the ionic strength. Internal standards are usually added to improve the accuracy and precision [44]. For a stacking injection, a mathematical model has been developed to account for the increase in the migration time with increasing sample injection time a good agreement with the theory has been found [45]. 

If a liquid moves tangential to a charged surface, then so-called electrokinetic phenomena arise [101]. Electrokinetic phenomena can be divided into four categories Electrophoresis, electro-osmosis, streaming potential, and sedimentation potential [102], In all these phenomena the zeta potential plays a crucial role. The classic theory of electrokinetic effects was proposed by Smoluchowski2 [103],... 

An enantioselective dynamic electrokinetic chromatography technique was used by Trapp et al. for determination of rate constants, enantiomerization barriers (AG (298 K) = 100.9 + 0.5 kJ mol ) and activation parameters [AH (298K) = 89.5+ 2.0 kJ mol AS (298K) = -42+10J mol 1 K ] of 1 at pH 2.2 (02CEJ3629). Introduction of a permanent positive charge in TB 1 significantly decreased the enantiomerization, which is not in conflict with the iminium-based theory. 

Finally we shall argue that present-day theories of the nonprimitive models of the electric double layer have considerable difficulty in treating properly ion adsorption in the Stern inner region at metal-aqueous electrolyte interfaces and we suggest that this region is a useful concept which should not be dismissed as unphysical. Indeed Stern-like inner region models continue to be used in colloid and electrochemical science, for example in theories of electrokinetics and aqueous-non-metallic (e.g., oxide) interfaces. 

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