Surface conductivity is an additional

conductivity Conductivity may refer to: *Electrical conductivity, a measure of a material's ability to conduct an electric current **Conductivity (electrolytic), the electrical conductivity of an electrolyte in solution **Ionic conductivity (solid state), elec ...

of an

electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...

in the vicinity of the charged interfaces.ISO International Standard 13099, Parts 1,2 and 3, “Colloidal systems – Methods for Zeta potential determination", (2012)
/ref> Surface and volume conductivity of liquids correspond to the electrically driven motion of

ions An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...

in an

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

. A layer of

counter ion 160px, Polystyrene sulfonate, a cation-exchange resin, is typically supplied with as the counterion.">cation-exchange_resin.html" ;"title="Polystyrene sulfonate, a cation-exchange resin">Polystyrene sulfonate, a cation-exchange resin, is typical ...

s of the opposite polarity to the surface charge exists close to the interface. It is formed due to attraction of counter-ions by the

surface charge Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge di ...

s. This layer of higher ionic concentration is a part of the interfacial double layer. The concentration of the ions in this layer is higher as compared to the ionic strength of the liquid bulk. This leads to the higher electric conductivity of this layer. Smoluchowski was the first to recognize the importance of surface conductivity at the beginning of the 20th century. There is a detailed description of surface conductivity by Lyklema in "Fundamentals of Interface and Colloid Science" The Double Layer (DL) has two regions, according to the well established Gouy-Chapman-Stern model. The upper level, which is in contact with the bulk liquid is the

diffuse layer A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...

. The inner layer that is in contact with interface is the

Stern layer The stern is the back or aft-most part of a ship or boat, technically defined as the area built up over the sternpost, extending upwards from the counter rail to the taffrail. The stern lies opposite the bow, the foremost part of a ship. Or ...

. It is possible that the lateral motion of ions in both parts of the DL contributes to the surface conductivity. The contribution of the Stern layer is less well described. It is often called "additional surface conductivity". The theory of the surface conductivity of the diffuse part of the DL was developed by Bikerman.Bikerman, J.J. Z.Physik.Chem. A163, 378, 1933 He derived a simple equation that links surface conductivity κ^σ with the behaviour of ions at the interface. For symmetrical electrolyte and assuming identical ions diffusion coefficients D⁺=D⁻=D it is given in the reference: :

^ = \frac\left(\cosh\frac-1\right)

where :F is the

Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...

:T is the

absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wor ...

:R is the

gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...

:C is the ionic concentration in the bulk fluid :z is the

ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...

valency :ζ is the

electrokinetic potential Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface. Zeta potential is a scientific term for electrokinetic potential in coll ...

The parameter ''m'' characterizes the contribution of

electro-osmosis Electroosmotic flow (or electro-osmotic flow, often abbreviated EOF; synonymous with electroosmosis or electroendosmosis) is the motion of liquid induced by an applied potential across a porous material, capillary tube, membrane, microchannel, or an ...

to the motion of ions within the DL: :

m = \frac

The

Dukhin number The Dukhin number () is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous sy ...

is a dimensionless parameter that characterizes the contribution of the surface conductivity to a variety of

electrokinetic phenomena Electrokinetic phenomena are a family of several different effects that occur in heterogeneous fluids, or in porous bodies filled with fluid, or in a fast flow over a flat surface. The term heterogeneous here means a fluid containing particles. Part ...

, such as,

electrophoresis Electrophoresis, from Ancient Greek ἤλεκτρον (ḗlektron, "amber") and φόρησις (phórēsis, "the act of bearing"), is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric fie ...

and

electroacoustic phenomena Electroacoustic phenomena arise when ultrasound propagates through a fluid containing ions. The associated particle motion generates electric signals because ions have electric charge. This coupling between ultrasound and electric field is called el ...

.Dukhin, A. S. and Goetz, P. J. ''Characterization of liquids, nano- and micro- particulates and porous bodies using Ultrasound'', Elsevier, 2017 This parameter and, consequently, surface conductivity can be calculated from the electrophoretic mobility using appropriate theory. Electrophoretic instrument by

Malvern Malvern or Malverne may refer to: Places Australia * Malvern, South Australia, a suburb of Adelaide * Malvern, Victoria, a suburb of Melbourne * City of Malvern, a former local government area near Melbourne * Electoral district of Malvern, an e ...

and electroacoustic instruments by

Dispersion Technology Dispersion Technology Inc is a scientific instrument manufacturer located in Bedford Hills, New York. It was founded in 1996 by Philip Goetz (former Chairman, retired in 2010) and Dr. Andrei Dukhin (current CEO). The company develops and sells ...

contain software for conducting such calculations.

Surface Science

Surface conductivity may refer to the electrical conduction across a solid surface measured by surface probes. Experiments may be done to test this material property as in the n-type surface conductivity of p-type. Additionally, surface conductivity is measured in coupled phenomena such as

photoconductivity Photoconductivity is an optical and electrical phenomenon in which a material becomes more electrically conductive due to the absorption of electromagnetic radiation such as visible light, ultraviolet light, infrared light, or gamma radiation. Wh ...

, for example, for the metal oxide semiconductor ZnO. Surface conductivity differs from bulk conductivity for analogous reasons to the electrolyte solution case, where the

charge carrier In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is used ...

s of holes (+1) and electrons (-1) play the role of ions in solution.

References

{{DEFAULTSORT:Surface Conductivity Chemical mixtures Colloidal chemistry Surface science Matter Soft matter

See also

Surface Science

References