Electrophoresis and sedimentation potential

In electrophoresis we consider the motion of charged particles in electric fields (in contrast, the movement of ions is treated in electrochemistry under the keyword ionic conductivity ). Electrophoresis is of great practical importance in biochemistry because it is used to isolate proteins. 

As an example, we consider the motion of a spherical particle. C, is the potential at a distance 6 from the particle surface. The distance U I S is the hydrodynamic radius of the particle. It can be larger than the particle radius due to the binding of liquid molecules or ions. Up to this distance the surface charge density amounts to ag. The entire charge of the particle is Q = 47t(R + 5)2ag 4TtR2ag. An electric field of strength E causes a force QE. At constant drift velocity, v0, the force is compensated by the friction force 

This is Stokes5 law of hydrodynamic friction. Equating the two expressions leads to 

This simple equation is, however, only valid for R Xp- If the radius is not much larger than the Debye length we can no longer treat the particle surface as an almost planar surface. In fact, we can no longer use the Gouy-Chapman theory but have to apply the theory of Debye and Hiickel. Debye and Hiickel explicitly considered the electric double layer of a sphere. A result of their theory is that the total surface charge and surface potential are related by 

5 Sir George Gabriel Stokes, 1819-1903. British mathematician and physicist, professor in Cambridge. 

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. 

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The electrokinetic processes can actually be observed only when one of the phases is highly disperse (i.e., with electrolyte in the fine capillaries of a porous solid in the cases of electroosmosis and streaming potentials), with finely divided particles in the cases of electrophoresis and sedimentation potentials (we are concerned here with degrees of dispersion where the particles retain the properties of an individual phase, not of particles molecularly dispersed, such as individual molecules or ions). These processes are of great importance in particular for colloidal systems. 

Of the four electrokinetic phenomena, two (electroosmotic flow and the streaming potential) fall into the region of membrane phenomena and will thus be considered in Chapter 6. This section will deal with the electrophoresis and sedimentation potentials. 

In classical electrokinetic phenomena, the forces and fluxes are independent of time. Electroacoustic effects are analogs of electrophoresis and sedimentation potential in which the forces and fluxes are variable in time. Alternating forces induce alternating fluxes of the same frequency, with a time delay. The phenomenological coefficients between the force and coupled flux can be used to calculate the potential. The phase shift is a source of additional information about the system. The electric sonic amplitude (ESA) is the amplitude of the ultrasonic field... 

In the case of mobile charged particles (electrophoresis and sedimentation potential Figure 5.66c and 5.66d), we should identify 7, as the flux of particles, Jp, and F, as the gravity force, F Then, the Onsager relations read... 

Exhaustive experimental studies on electrophoresis and sedimentation potential have been reported by Rastogi and Mishra [7] with a view to test the thermodynamic theory of the phenomena. The experimental setup involving (i) sedimentation column and (ii) optical assembly are shown in Figs. 6.1 and 6.2. Both sedimentation potential and electrophoretic velocity were measured with these setups. 

FIGURE 31.2 Schematic design of cells for studying electrophoresis (a) and sedimentation potentials (b). 

The movement of a charged particle with respect to an adjacent liquid phase is the basic principle underlying four electrokinetic phenomena electrophoresis, electroosmosis, sedimentation potential, and streaming potential. 

Because so much of the behavior of suspensions is determined or modified by charge associated with the solid phases, ZPC may be inferred from a wide variety of experiments involving pH as a master variable. For example, coagulation and sedimentation rates are maximum at the ZPC, and anion and cation exchange capacities (measured with nonspecific, symmetrical electrolytes) are equal and minimum at the ZPC. More direct and less ambiguous are electrophoresis and streaming potential, in any of their modifications. One can estimate the IEP(s) by measuring adsorption of H+ and OH" if one is certain that no specific adsorption of other species occurs. 

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],... 

Electrophoresis has the greatest practical applicability of these electrokinetic phenomena and has been studied extensively in its various forms, whereas electro-osmosis and streaming potential have been studied to a moderate extent and sedimentation potential rarely, owing to experimental difficulties. 

It could be argued, of course, that the differences and similarities cited above stem from the fact that solvent extraction is essentially a steady-state (equilibrium) process while electrophoresis and sedimentation are transient (rate) processes. However, such an argument would overlook the fact (to be explained later) that the different forms of the chemical potential profile determine which systems can be run successfully in the steady-state mode and which in the transient mode. Thus the chemical potential profile and associated flow structure emerge as dominant influences that should be classified at the very beginning of any attempt to organize separation phenomena into a cohesive discipline. 

The spatial charge distribution in the electrical double layer is exactly what causes the electrokinetic phenomena, namely the mutual displacement of the phases in contact in an applied external electric field (electrophoresis and electroosmosis) or the charge transfer that occurs upon the mutual motion of phases (streaming and sedimentation potentials and currents). The following consideration, the simplest consistent with the Helmholtz model, establishes the relationship between the rate of the phase shift, e.g. that of electroosmosis, and the strength of the external electric field, E, directed along the surface3. 

Electrokinetic Phenomena. Electrokinetic motion occurs when the mobile part of the EDL is sheared away from the inner layer (charged surface). There are four types of electrokinetic measurements, electrophoresis, electroosmosis, streaming potential, and sedimentation potential, of which the first finds the most use in industrial practice. Good descriptions of practical experimental techniques in electrophoresis and their limitations can be found in references 18-20. 

The potential may be obtained from measurements of particle mobility using electrokinetic techniques, such as electrophoresis or sedimentation potential [70]. Electrophoresis, the standard technique for submicrometer particles, is based on the movement of charged particles in response to an applied electrical field. Optical scattering methods are used to measure the distribution of particle velocities for a given field strength, and may then be calculated using the Henry equation. 

There are four electrokinetic phenomena (electrophoresis, electroosmosis, streaming potential, and sedimentation potential), all of which involve both the theory of the electric double layer and that of liquid flow. Among them electrophoresis has the greatest practical applicability to the study of biomolecules and biocell surface porperties. In this section, the relation between electrophoretic mobility and its related electrokinetic potential C will be discussed. 

Particle charge plays a major role on the stabilization of colloidal systems. Especially when nanoparticles are stabilized by an adsorption layer of polyelectrolytes, zeta potential measurements are very useful. The stabilization of the nanoparticles results from a combination of ionic and steric contributions. The zeta potential can be detected by means of electro-osmosis, electrophoresis, streaming potential, and sedimentation potential measmements. The potential drop across the mobile part of electric donble layer can be determined experimentally, whenever one phase is made... 

The zeta potential of a particle is calculated from electro kinetic phenomena such as electrophoresis, streaming potential, electro-osmosis and sedimentation potential. Each of these phenomena and the determination of zeta potential by using each technique will be discussed briefly in this section. 

Electrokinetic phenomena refers to dynamic processes that occur when viscous or electrical forces are applied to a charged interface. The most common of these phenomena are electrophoresis, electroosmosis, streaming potential and sedimentation potential. 

The classic experimental approach when measuring electrokinetic phenomena is to measure either the velocity of the respective phases, in the case of electrophoresis and electroosmosis, or the strength of the induced electric field under relative phase motion, in the case of streaming potential and sedimentation potential. A number of experimental set-ups can be used to measure electrokinetic phenomena. However, the appropriate experimental set-up for a given system is usually determined by the size, shape and state of the substrate of interest. The following provides a discussion of some common experimental regimes for measurement of electrokinetic effects. 

The most popular and straightforward way to determine zeta potential is to apply an electric field to a colloidal suspension. In the case of neutral particles nothing happens, while particles carrying surface charges will have an oriented motion dependent on the direction of the electric field. Several phenomena (collectively known as electrokinetic effects) are observed i.e., electrophoresis, electroosmosis, streaming potential, and sedimentation potential. In this chapter we will discuss the first two effects. 

There are four related electrokinetic phenomena which are generally defined as follows electrophoresis—the movement of a charged surface (i.e., suspended particle) relative to astationaiy hquid induced by an applied ectrical field, sedimentation potential— the electric field which is crested when charged particles move relative to a stationary hquid, electroosmosis—the movement of a liquid relative to a stationaiy charged surface (i.e., capiUaty wall), and streaming potential—the electric field which is created when liquid is made to flow relative to a stationary charged surface. The effects summarized by Eq. (22-26) form the basis of these electrokinetic phenomena. 

The streaming potential (Dorn effect) relates to a movement of liquid that generates electric potential, and electroosmosis occurs when a direct electric potential causes movement of the liquid. The sedimentation potential relates to sedimentation (directed movement) of charged particles that generates electric potential, and electrophoresis occurs when a direct electric potential causes a movement of charged particles. 

Good descriptions of practical experimental techniques in conventional electrophoresis can be found in Refs. [81,253,259]. For the most part, these techniques are applied to suspensions and emulsions, rather than foams. Even for foams, an indirect way to obtain information about the potential at foam lamella interfaces is by bubble electrophoresis. In bubble microelectrophoresis the dispersed bubbles are viewed under a microscope and their electrophoretic velocity is measured taking the horizontal component of motion, since bubbles rapidly float upwards in the electrophoresis cells [260,261]. A variation on this technique is the spinning cylinder method, in which a bubble is held in a cylindrical cell that is spinning about its long axis (see [262] and p.163 in Ref. [44]). Other electrokinetic techniques, such as the measurement of sedimentation potential [263] have also been used. 

Zeta potential was the first, experimentally available value characterizing edl. The potential of the solid particles in the electrolyte solutions may be determined on the basis of one of the four following phenomena microelectrophoresis, streaming potential, sedimentation potential and electroosmosis. The most popular of them and the best described theoretically and methodically is the electrophoresis. Other papers, concerning the electrophoretic mobility, stationary level determination and the theory of the charged particles transportation in the electric field are still published. 

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