A surface charge is an electric charge present on a two-dimensional surface. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m<sup>−2</sup>), is used to describe the charge distribution on the surface. The electric potential is continuous across a surface charge and the electric field is discontinuous, but not infinite; this is unless the surface charge consists of a dipole layer. In comparison, the potential and electric field both diverge at any point charge or linear charge.
In physics, at equilibrium, an ideal conductor has no charge on its interior; instead, the entirety of the charge of the conductor resides on the surface. However, this only applies to the ideal case of infinite electrical conductivity; the majority of the charge of an actual conductor resides within the skin depth of the conductor's surface. For dielectric materials, upon the application of an external electric field, the positive charges and negative charges in the material will slightly move in opposite directions, resulting in polarization density in the bulk body and bound charge at the surface.
In chemistry, there are many different processes which can lead to a surface being charged, including adsorption of ions, protonation or deprotonation, and, as discussed above, the application of an external electric field. Surface charge emits an electric field, which causes particle repulsion and attraction, affecting many colloidal properties.
Surface charge practically always appears on the particle surface when it is placed into a fluid. Most fluids contain ions, positive (cations) and negative (anions). These ions interact with the object surface. This interaction might lead to the adsorption of some of them onto the surface. If the number of adsorbed cations exceeds the number of adsorbed anions, the surface would have a net positive electric charge.
Dissociation of the surface chemical group is another possible mechanism leading to surface charge.
Density
Surface charge density is defined as the amount of electric charge, q, that is present on a surface of given area, A:
<math display="block">\sigma=\frac{q}{A}</math>
Conductors
According to Gauss’s law, a conductor at equilibrium carrying an applied current has no charge on its interior. Instead, the entirety of the charge of the conductor resides on the surface, and can be expressed by the equation:
<math display="block">\sigma = E\varepsilon_0</math>
where E is the electric field caused by the charge on the conductor and <math>\varepsilon_0</math> is the permittivity of the free space. This equation is only strictly accurate for conductors with infinitely large area, but it provides a good approximation if E is measured at an infinitesimally small Euclidean distance from the surface of the conductor.
Colloids and immersed objects
{| class="wikitable sortable" style="float: right;"
|-
! Compound !! Chemical Formula !! Point of Zero Charge
|-
| tungsten(VI) oxide || WO<sub>3</sub> || 0.2–0.5
|-
| silicon carbide (alpha) || SiC || 2–3.5
|-
|manganese(IV) oxide || MnO<sub>2</sub> || 4–5
|-
| thallium(I) oxide || Tl<sub>2</sub>O || 8
|-
| copper(II) oxide|| CuO|| 9.5 This net charge results in a surface potential [L], which causes the surface to be surrounded by a cloud of counter-ions, which extends from the surface into the solution, and also generally results in repulsion between particles. The larger the partial charges in the material, the more ions are adsorbed to the surface, and the larger the cloud of counter-ions. A solution with a higher concentration of electrolytes also increases the size of the counter-ion cloud. This ion/counterion layer is known as the electric double layer.
A solution's pH can also greatly affect surface charge because functional groups present on the surface of particles can often contain oxygen or nitrogen, two atoms which can be protonated or deprotonated to become charged. Thus, as the concentration of hydrogen ions changes, so does the surface charge of the particles. At a certain pH, the average surface charge will be equal to zero; this is known as the point of zero charge (PZC).
Gouy-Chapman
thumb|alt=A diagram of a solid containing a line of positive charge bordering a liquid containing both negative and positive charges|Multiple layers of negative charge accumulate near a positively charged surface to form a double layer.
Gouy-Chapman theory describes the effect of a static surface charge on a surface's potential. "Gouy suggested that interfacial potential at the charged surface could be attributed to the presence of a number of ions of given charge attached to its surface, and to an equal number of ions of opposite charge in the solution." A positive surface charge will form a double layer, since negative ions in solution tend to balance the positive surface charge. Counter ions are not rigidly held, but tend to diffuse into the liquid phase until the counter potential set up by their departure restricts this tendency. The kinetic energy of the counter ions will, in part, affect the thickness of the resulting diffuse double layer. The relation between C, the counter ion concentration at the surface, and <math>C_o</math>, the counter ion concentration in the external solution, is the Boltzmann factor:
<math display="block">C = C_0 e^{-\frac{\psi z e}{k_\mathrm{B} T</math>
where z is the charge on the ion, e is the charge of a proton, k<sub>B</sub> is the Boltzmann constant and ψ is the potential of the charged surface.
This however is inaccurate close to the surface, because it assumes that molar concentration is equal to activity. It also assumes that ions were modeled as point charges and was later modified. An improvement of this theory, known as the modified Gouy-Chapman theory, included the finite size of the ions with respect to their interaction with the surface in the form of a plane of closest approach.
Surface potential
The relation between surface charge and surface potential can be expressed by the Grahame equation, derived from the Gouy-Chapman theory by assuming the electroneutrality condition, which states that the total charge of the double layer must be equal to the negative of the surface charge. Using the one-dimensional Poisson equation and assuming that, at an infinitely great distance, the potential gradient is equal to 0, the Grahame equation is obtained: If these repulsive forces were to be disrupted, perhaps by the addition of a salt or a polymer, the colloidal particles would no longer be able to sustain suspension and would subsequently flocculate.
Electrokinetic phenomena
thumb|right|alt=A positive and negative terminal are placed on opposite ends of a body of water, connected by wires and a voltage source. Between them are two panels of glass containing negative charge; water flows through that glass from the positive to the negative terminal, with the water carrying a positive charge.|Diagram depicting electro-osmosis through a glass capillary submerged in an aqueous solution.
Electrokinetic phenomena refers to a variety of effects resulting from an electrical double layer. A noteworthy example is electrophoresis, where a charged particle suspended in a media will move as a result of an applied electrical field. Electrophoresis is widely used in biochemistry to distinguish molecules, such as proteins, based on size and charge. Other examples include electro-osmosis, sedimentation potential, and streaming potential.
Adhesives/coatings
Charged surfaces are often useful in creating surfaces that will not adsorb certain molecules (for example, in order to prevent the adsorption of basic proteins, a positively charged surface should be used). Polymers are very useful in this respect in that they can be functionalized so that they contain ionizable groups, which serve to provide a surface charge when submerged in an aqueous solution.