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# Surface charge

Surface charge is the electric charge present at an interface, for instance on the surface of a semiconductor material, or for example, on the surface of a protein in water.

There are multiple factors generating surface charge.

First of all, surface charge appears practically always on an object surface when it is placed into a fluid. All fluids contain ions, positive (cations) and negative (anions). These ions interact with the object surface. This interaction might lead to adsorption some of them on the surface. If number of adsorbed cations exceeds number of adsorbed anions, surface would gain total positive electric charge. This mechanism is important for colloids and other fluid based heterogeneous systems.

There is another possible mechanism leading to surface charging in fluids. It is dissociation or Differential Solubility of the surface chemical group. The two ionic components of crystals like CaCO3, AgBr, BaSO4, and CaC2O4 always obey the bulk solubility equilibrium. E.g. for AgI Ksp = [Ag+][I-]

The thermodynamic parameter used to describe charged surfaces is the surface potential.The surface potential,y0 , of an ionic crystal is related to the bulk concentration of a potential-determining ion by

y0=(RT/zF)ln(c/cpzc)

where z is the valence (including sign) of the potential-determining ion i, whose concentration is cpzc at the point of zero charge , c is the concentration of the potential detrming ion, R is the gas constant,F is the Faraday constant and T is the temperature.

This equation relates the (chemical potentials) concentrations in the bulk, electrically neutral solution to that in the crystal.

i.e. AgI(s) can be precipitated by mixing aqueous solutions of AgNO3 and KI in any ratio. The equilibrium concentrations of [Ag+] and [I-] need not be equal. For mre details of the electric surfface charge description and its relation to the surface chemistry are given by Lyklema in "Fundamentals of Interface and Colloid Science" [1],

Other important example is charging of semiconductors, which originates from a disrupted lattice structure. The presence of surface charge also alters the distribution of charge in the near-surface region of the semiconductor.

In conductors of uniform resistivity at equilibrium, there can be no free charges in the bulk, instead all the charge density is on the surface.

In the case of conducting macroscopic bodies surface charge can be measured using electrostatic fieldmeters or voltmeters can also be used.

In the case of colloids and similar heterogeneous fluid based systems, direct measurement of the surface charge is impossible due to small sizes of the objects. Instead, zeta potential measurement yields information for calculation surface charge. Another method is titration with appropriate surface active chemical. Some details are given in the book [2]

The average surface charge density σ is given by

$\sigma=q/A \!$,

where q is the net amount of charge and A is the surface area of the interface.

The measurement of surface charge density has applications in:

## References

1. ^ Lyklema, J. “Fundamentals of Interface and Colloid Science”, vol.2, page.3.208, 1995
2. ^ Dukhin, A.S. and Goetz, P.J "Ultrasound for characterizing colloids", Elsevier, 2002