Electrical forces key parameters Debye length and zeta potential

6 Electrical forces key parameters (Debye length and zeta potential) 

The complex but rather accurate Gouy-Chapman theory (see Appendix 10.2 for a brief discussion) provides the distribution of potential and the ion concentration as a function of the distance from the surface. The potential decreases exponentially with the distance and also with decreasing Debye length. 

The exact expression for the repulsive potential energy (Vr) depends on the proximity of the particles or surfaces and their shape (see e.g. Equation 10.4). 

There are various expressions for describing the electrostatic (typically) repulsive forces between colloidal particles but all of them indicate that the potential energy decreases exponentially with the distance and increases with increasing Debye length, relative permittivity and surface potential (see Table 10.5). Thus the key properties appearing in the various mathematical expressions are  

A potential is simply the work done in bringing a point charge from infinity to the particle surface. Potentials are always relative to ground (i.e. at an infinite distance from the surface). The surface potential is very important and is approximated by the so-called zeta potential, which can be estimated by (micro)electrophoresis experiments, at least for some special cases (small and large particles via the so-called Hiickel and Smoluchowski equations). In the general case, the zeta potential is calculated from values of the electrophoretic mobility, using graphical solutions or the Henry equation, which requires a correction factor. 

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