Electrophoresis surface conductivity

In this chapter these phenomena will be systematically discussed. Related phenomena such as surface conduction and dielectric relaxation of sols will be included. In view of the fact that the rigorous theory is both physically and mathematically extremely involved, we shall discuss the phenomena in two steps. First, elementary theory will be presented. For electrophoresis this leads to the Huckel-Onsager and Helmholtz-Smoluchowskl equations. It gives the leading term for a number of simple conditions regarding potential and particle size and shape. Thereafter, more advanced theoretical treatments will follow. 

As a later generalization we present a more rigorous derivation of the Helmholtz-Smoluchowski equation for high yq, in which the curvature of the field is explicitly taken into account. This method, given by Anderson and Prleve l, may be considered as an elaboration of the Smoluchowski theorem for the case of electrophoresis of large spheres. Surface conduction is still Ignored. 

Other simplifications included the disregarding of surface conduction (i.e. only the case Du = 0 was considered) and the limitation to very simple geometries (spheres, capillaries, etc.) without double layer overlap. Inclusion of all these features is physically and mathematically extremely dlfiicult and as yet only rigorously solved under limiting conditions. In order to identify the various problems we shall, in the present section, retain the restrictions to simple geometries (emphasizing electrophoresis of spheres) and absence of double layer overlap but do automatically consider double layer polarization (i.e. the relaxation retardation, force in sec. 4.3a(i)) and always take surface... 

Table 4.2. Electrokinetic potentials of negative polystyrene latex particles obtained from electro-osmosis, electrophoresis and conductivity. In the conversion of mobilities surface conduction behind the slip plane was ignored. (Data from A.G. van der Put, PhD. thesis. Agricultural University Wagenlngen. NL (1980) as elaborated by O Brlen, J. CoOoid Interface Set 110 (1986) 477.)...

In other experiments electrokinetic consistency could be achieved without consideration of conduction behind the plane of shear. Examples include streaming potentials and conduction for charged mlcroporous membranes and diffuslophoresls and electrophoresis of latices K Obviously, the role of surface conduction depends on the nature of the system and on the way of measurement. 

The anomalous surface conduction was studied extensively by O Brien and by Hunter, and they could show that the Stem layer conduction is about thirty times larger than the diffuse layer conduction at low salt concentration. This explains substantial discrepancies between the electrophoresis and the conductance estimates of zeta potential. For thin double-layer systems such as this, the zeta potential is usually calculated from the electrophoretic mobility using Smoluchowski s formula, which in O Brien s case corresponds to a zeta potential of 50 mV [8]. Complex conductivity measurements result in f = —160 mV. 

HENRY, D.C. 1948. The electrophoresis of suspended particles. IV. The surface conductivity effect. Trans. Faraday Soc. 44, 1021-1026. 

Consider now the case of a double layer with the finite thickness Ad- Here we should distinguish between three effects [48-51], due to which the velocity of electrophoresis will differ from the Huckel (9.17) and the Helmholtz-Smoluchowski (9.20) equations electrophoresis retardation surface conductivity relaxation. Consider them successively. 

There are three commonly used methods to measure the zeta potential, which involves pressure-driven flow, electrophoresis, and electroosmotic-driven flow, respectively. For the measurement of the specific surface conductivity, there are primarily two methods involving pressure-driven flow and electroosmotic-driven flow. In this entry, we will focus on the electrical current monitoring methods which can be used to measure the zeta potential, specific surface conductivity, volumetric flow rate, and electroosmotic mobility by employing electroosmotic flow with a solution displacement process. 

Like in the case of electrophoresis, the Smoluchowski equation is only valid for particles with thin double layers and negligible surface conductance (low zeta potentials). The theory was later generalized to arbitrary Ka values by Booth [43] for low zeta potentials, and was developed for arbitrary by Stigter [44], Considering the fact that rather concentrated suspensions are often used in sedimentation potential determinations, theories have also been elaborated to include these situations [45-47]. 

In the case of electrophoresis, the retardation and relaxation effects are influenced by surface conduction. In Equations 10.10 and 10.25, K p, the specific electric conductivity of the bulk solution should be replaced by a term accounting for the excess conduction at the surface as well. Taking the streaming potential as an example, the expression for Equation 10.24, should be modified to contain a contribution from the surface. Hence,... 

Another effect which is important in a discussion of the conductivity of colloidal systems is the surface conduction, i.e. a conductivity contribution from the double-layers. This contribution is important when the electrolyte content is relatively low in the bulk phase. The surface conductance is also important when measurements of electrokinetic phenomena (electrophoresis, electro-osmosis, etc.) need to be evaluated. Recently, it... 

Surface conductance also has pronounced effects on the usual electrophoretic mobUity it can lead to a large drop in the mobUity and therefore to a large error in the reported zeta potential obtained using standard electrophoresis formulae. To determine the true zeta potential in these systems it is necessary to determine the surface conductance. The electroacoustic technique provides the most convenient method for doing this. 

A. In the frame of Von Smoluchowski s treatment of electrophoresis deviations may result from the surface conductance of the particle In this case the electric current is concentrated in the neighbourhood of the particle In order to prevent an accumulation of electricity at the limits between the highly conducting surface layer and the weakly conducting bulk of the liquid, a counter E M F is generated and the electrophoretic velocity is decreased. 

The objective of comparing values of f determined from electrophoresis with those determined by other electrokinetic methods was stated at the beginning of Section 12.6. Enough experiments have been conducted in which at least two of the electrokinetic methods we have discussed are compared to leave no doubt as to the self-consistency of f as determined by these different methods. There is no guarantee, however, that self-consistent f potentials are correct. Consistency means only that f has been extracted from experimental quantities by a self-consistent set of approximations. It should be emphasized, however, that the existence of a potential at the surface of shear —which is the common component in all the electrokinetic analyses we have discussed —is more than amply confirmed by these observations. 

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