The Zeta Potential and the Electric Double Layer

 

The electric double layer theory deals with the between-phase boundary as a layer of finite dimensions. If ions of one sign are part of, or absorbed by, one phase then the resulting electric field will attract ions of the opposite sign which, will accumulate as another adjacent layer. The second layer will still exhibit Brownian movement. The static charges on one phase and the attracted ion layer form the other phase constitute the electric double layer.

 

The total charge of the double layer is zero, but as the charges are spatially oriented and not randomly organized, they give rise to an electrical potential. The potential at any point on the double layer being defined (form the study of static electricity) as the work done in bringing unit charge from infinity to that point. The double layer for a spherical particle is depicted in figure 2. The charge (Q) can be considered situated at the centre or evenly distributed over the sphere surface.

 

 

Figure 2. The Electrical Double Layer Formed Round a Spherical Particle

 

The charged layer on the particle surface is depicted by the red circle (positive charge) and that adsorbed from the solvent depicted by the blue circle (negative charge). The second layer is bound so firmly to the inner layer that, under electrophoresis, it is moved with the particle providing a sheer-surface separate from but directly associated with the particle.

 

From electrostatic theory the potential () at the surface is given by,

 

 

Where (a) is the radius of the spherical particle,

    And () is the dielectric constant of the medium.

 

The potential at the surface of the particle, will however be different from the potential at the surface of the shear (at a position () where the adsorbed ions exist) and () is the average thickness of the adsorbed shell.

 

It is the potential at the shear boundary that provides the electrophoretic mobility and is called the electrokinetic potential or the zeta potential.

 

Surrounding the positively charged spherical particle there is a static accumulation of negatively charged counter-ions falling to random levels at an infinite distance from the sphere. The function describing the potential () at any point (x) decrease as (x) increases and has been shown to be described by the following equation,

 

 

where (k) is given by the following equation,

 

 

where, (e) is the electronic charge,

            () is the bulk concentration of each ion,

            (z) is the valency of the ion,

     and () is the Boltzman Constant

 

The ratio (l/k) is often referred to as the “thickness of the double layer. The zeta potential and the double layer thickness fall rapidly as the concentration or the valency of the ions increase. Unfortunately, the zeta potential of a electrophoretic system cannot be measured directly and only a theoretical value can be calculated.