Zeta Potential Thick Electrical Double Layers

3 ZETA POTENTIAL THICK ELECTRICAL DOUBLE LAYERS 

We know from Chapter 11 that the potential drops gradually with distance from a charged surface, its range decreasing with increasing electrolyte content. Most of the expressions 

1 Streamlines (which also represent the electric field) around spherical particles of radius Rs. The dashed lines are displaced from the surface of the spheres by the double-layer thickness k. In (a) kRs is small in (b) kRs is large. 

The Poisson equation (see Equation (11.18)) gives the fundamental differential equation for potential as a function of charge density. The Debye-Hiickel approximation may be used to express the charge density as a function of potential as in Equation (11.28) if the potential is low. Combining Equations (11.24) and (11.32) gives 

Remember that e is equal to the product of Cq times e, with Eq = 8.85 10 2 C2 J m for water at 25°C, cr = 78.54. Because of its importance to the present material, we repeat the defining expression for k as given originally by Equation (11.41)  

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Our next task is to relate this mobility to the zeta potential. This requires a number of assumptions, and we focus on the most important of these. We derive the equations for thick electrical double layers (Section 12.3) and for thin double layers (Section 12.4) first and then examine how intermediate cases can be studied (Section 12.5). 

As stated above, the results can be interpreted in terms of potential at the plane of shear, termed the zeta potential ( ). Since the exact location of the shear plane is generally not known, the zeta potential is usually taken to be approximately equal to the potential at the Stern plane. Two simple relations can be used to calculate zeta potentials in limiting cases, one for small particles with thick electric double layers, and one for large particles with thin electric double layers. 

Hiickel Equation A relation expressing the proportionality between electrophoretic mobility and zeta potential for the limiting case of a species that can be considered to be small and that has a thick electric double layer. See also Electrophoresis, Henry Equation, Smoluchowski Equation. 

The microelectrophoretic mobility (jUe) is related to zeta potential ( ) via one of two equations. When the diameter of the particle is small relative to the thickness of the electrical double layer, the Huckel equation applies ... 

The potential in the diffuse layer decreases exponentially with the distance to zero (from the Stem plane). The potential changes are affected by the characteristics of the diffuse layer and particularly by the type and number of ions in the bulk solution. In many systems, the electrical double layer originates from the adsorption of potential-determining ions such as surface-active ions. The addition of an inert electrolyte decreases the thickness of the electrical double layer (i.e., compressing the double layer) and thus the potential decays to zero in a short distance. As the surface potential remains constant upon addition of an inert electrolyte, the zeta potential decreases. When two similarly charged particles approach each other, the two particles are repelled due to their electrostatic interactions. The increase in the electrolyte concentration in a bulk solution helps to lower this repulsive interaction. This principle is widely used to destabilize many colloidal systems. 

It is opportune to mention here that some writers prefer to avoid the use of the concept of the zeta-potential it is true that there must be some form of potential across the double layer, but it is so variable in sign and magnitude that its exact significance is regarded as uncertain. The quantity which is called the zeta-potential is, according to equation (1), proportional to the product of the surface charge density and the thickness of the double layer, i.e., to ad it is, therefore, considered preferable to regard it as a measure of the electric moment per sq. cm. of the double layer. 

Fig.l Schematic representation of the electric double layer at a solid-liquid interface and variation of potential with the distance from the solid surface if/Q, surface potential potential at the Stern plane potential at the plane of share (zeta potential) 8, distance of the Stern plane from the surface (thickness of the Stern layer) k, thickness of the diffuse region of the double layer. 

The Helmholtz-von Smoluchowski equation indicates that under constant composition of the electrolyte solution, the electro-osmotic flow depends on the magnitude of the zeta potential which is determined by many different factors, the most important being the dissociation of the silanol groups on the capillary wall, the charge density in the Stern layer, and the thickness of the diffuse layer. Each of these factors depends on several variables, such as pH, specific adsorption of ionic species in the compact region of the electric double layer, ionic strength, viscosity, and temperature. 

Figure 7.3 Representation of the conditions at a negative surface, with a layer of adsorbed positive ions in the Stern plane. The number of negative ions increases and the number of positive ions decreases (see upper diagram) as one moves away from the surface, the electrical potential becoming zero when the concentrations are equal. The surface potential, and the potential at the Stern plane, are shown. As the particle moves, the effective surface is defined as the surface of shear, which is a little further out from the Stern plane, and would be dependent on surface roughness, adsorbed macromolecules, etc. It is at the surface of shear that the zeta potential, is located. The thickness of double layer is given by 1 /k.

Experimental results showed that treatment of CAJ with a cationic resin decreased the zeta ( surface) potential of the particles, decreased the ionic strength, and consequently increased the thickness of the electrical double layer surrounding the particles (Debye length), but did not change cloud... 

The formation of this electrical double layer gives rise to a potential that falls off exponentially as a function of distance from the capillary surface. This zeta potential (f) has values ranging from 0 to 100 mV. The distance between the Stern layer and a point in the bulk liquid at which the potential is 0.37 times the potential at the interface between Stern and diffuse layer is defined as the thickness of the double layer (5). 

In aqueous media, the pH of the sample is one of the most important parameters that affect the zeta potential. Furthermore, the ion concentration influences the thickness of the electrical double layer. Therefore, the measurement conditions (pH, conductivity) should always defined for a given a zeta potential value. 

The electrical double layer in the phase boimdaries produces the -potential as a result of electrostatic and adsorptive interactions. The zeta potential has a very close relationship to the stability of a sol. The zeta potential of a sol can be very effectively reduced ty addition of elec j-olytes. The electrolytes decrease the zeta potential to a critical value, after which neutralization of the charges takes place resulting in the collapse of the double layer. When this happens, flocculation of the colloid takes place. Various other factors which affect zeta potential are surface charge density, dielectric constant of the medium and thickness of the double layer. 

Ion adsorption at day partides is a dynamic process, so that an exchange of ions can take place readily in response to the changing pH. These changes in pH influence the thickness of the Hehnholtz-Gouy-Chapman electrical double layer, and in turn the value of the so-called zeta potential (Q that behaves inversely to the viscosity (see Figure 2.20). 

Figure 2.18 Potential distribution around a clay particle suspended in a polar liquid (water). The thickness of the Gouy electrical double layer is the sum of the Stern and the diffuse layers. is the zeta potential.

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