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 A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant d ...

, or a porous body. The DL refers to two parallel layers of charge surrounding the object. The first layer, 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 dis ...

(either positive or negative), consists of ions

adsorbed Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which ...

onto the object due to chemical interactions. The second layer is composed of ions attracted to the surface charge via the

Coulomb force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventio ...

, electrically screening the first layer. This second layer is loosely associated with the object. It is made of free ions that move in the fluid under the influence of electric attraction and thermal motion rather than being firmly anchored. It is thus called the "diffuse layer". Interfacial DLs are most apparent in systems with a large surface area to volume ratio, such as a

colloid A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others exten ...

or porous bodies with particles or pores (respectively) on the scale of micrometres to nanometres. However, DLs are important to other phenomena, such as the

electrochemical Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outco ...

behaviour of

electrode An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte, a vacuum or air). Electrodes are essential parts of batteries that can consist of a variety of materials ...

s. DLs play a fundamental role in many everyday substances. For instance, homogenized milk exists only because fat droplets are covered with a DL that prevents their

coagulation Coagulation, also known as clotting, is the process by which blood changes from a liquid to a gel, forming a blood clot. It potentially results in hemostasis, the cessation of blood loss from a damaged vessel, followed by repair. The mechanis ...

into butter. DLs exist in practically all

heterogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...

fluid-based systems, such as blood, paint, ink and ceramic and cement

slurry A slurry is a mixture of denser solids suspended in liquid, usually water. The most common use of slurry is as a means of transporting solids or separating minerals, the liquid being a carrier that is pumped on a device such as a centrifugal p ...

. The DL is closely related to

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 ...

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 e ...

Development of the (interfacial) double layer

Helmholtz

When an ''electronic'' conductor is brought in contact with a solid or liquid ''ionic'' conductor (electrolyte), a common boundary (

interface Interface or interfacing may refer to: Academic journals * ''Interface'' (journal), by the Electrochemical Society * '' Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics'' * '' Int ...

) among the two phases appears.

Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Associatio ...

was the first to realize that charged electrodes immersed in electrolyte solutions repel the co-ions of the charge while attracting counterions to their surfaces. Two layers of opposite

polarity Polarity may refer to: Science * Electrical polarity, direction of electrical current * Polarity (mutual inductance), the relationship between components such as transformer windings * Polarity (projective geometry), in mathematics, a duality of o ...

form at the interface between electrode and electrolyte. In 1853 he showed that an electrical double layer (DL) is essentially a

molecular A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

dielectric and stores charge electrostatically. Below the electrolyte's decomposition voltage, the stored charge is linearly dependent on the voltage applied. This early model predicted a constant

differential capacitance Differential capacitance in physics, electronics, and electrochemistry is a measure of the voltage-dependent capacitance of a nonlinear capacitor, such as an electrical double layer or a semiconductor diode. It is defined as the derivative of char ...

independent from the charge density depending on the

dielectric constant The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...

of the electrolyte

solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...

and the thickness of the double-layer.Srinivasan S. (2006) Fuel cells, from Fundamentals to Applications, Springer eBooks,
Chapter 2, Electrode/electrolyte interfaces: Structure and kinetics of charge transfer.
(769 kB) This model, with a good foundation for the description of the interface, does not consider important factors including diffusion/mixing of ions in solution, the possibility of

adsorption Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which ...

onto the surface, and the interaction between solvent dipole moments and the electrode.

Gouy–Chapman

Louis Georges Gouy Louis Georges Gouy (February 19, 1854 – January 27, 1926) was a French physicist. He is the namesake of the Gouy balance, the Gouy–Chapman electric double layer model (which is a relatively successful albeit limited model that describes the ...

in 1910 and

David Leonard Chapman David Leonard Chapman FRS (6 December 1869 – 17 January 1958) was an English physical chemist, whose name is associated with the Chapman-Jouguet treatment (on the theory of detonation in gases) and the Gouy-Chapman layer (the surface layer ...

in 1913 both observed that capacitance was not a constant and that it depended on the applied potential and the ionic concentration. The "Gouy–Chapman model" made significant improvements by introducing a

diffuse Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...

model of the DL. In this model, the charge distribution of ions as a function of distance from the metal surface allows

Maxwell–Boltzmann statistics In statistical mechanics, Maxwell–Boltzmann statistics describes the distribution of classical material particles over various energy states in thermal equilibrium. It is applicable when the temperature is high enough or the particle density ...

to be applied. Thus the

electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...

decreases exponentially away from the surface of the fluid bulk.

Stern

The Gouy-Chapman model fails for highly charged DLs. In 1924,

Otto Stern :''Otto Stern was also the pen name of German women's rights activist Louise Otto-Peters (1819–1895)''. Otto Stern (; 17 February 1888 – 17 August 1969) was a German-American physicist and Nobel laureate in physics. He was the second most n ...

suggested combining the Helmholtz model with the Gouy-Chapman model: in Stern's model, some ions adhere to the electrode as suggested by Helmholtz, giving an internal Stern layer, while some form a Gouy-Chapman diffuse layer. The Stern layer accounts for ions' finite size and consequently an ion's closest approach to the electrode is on the order of the ionic radius. The Stern model has its own limitations, namely that it effectively treats ions as point charges, assumes all significant interactions in the diffuse layer are

Coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary ch ...

ic, assumes dielectric permittivity to be constant throughout the double layer, and that fluid viscosity is constant plane.

Grahame

Electric double-layer (BMD model) NT-int

D. C. Grahame modified the Stern model in 1947. He proposed that some ionic or uncharged species can penetrate the Stern layer, although the closest approach to the electrode is normally occupied by solvent molecules. This could occur if ions lose their

solvation shell A solvation shell or solvation sheath is the solvent interface of any chemical compound or biomolecule that constitutes the solute. When the solvent is water it is called a hydration shell or hydration sphere. The number of solvent molecules sur ...

as they approach the electrode. He called ions in direct contact with the electrode "specifically adsorbed ions". This model proposed the existence of three regions. The inner Helmholtz plane (IHP) passes through the centres of the specifically adsorbed ions. The outer Helmholtz plane (OHP) passes through the centres of solvated ions at the distance of their closest approach to the electrode. Finally the diffuse layer is the region beyond the OHP.

Bockris/Devanathan/Müller (BDM)

In 1963 J. O'M. Bockris, M. A. V. Devanathan and Klaus Müller proposed the BDM model of the double-layer that included the action of the solvent in the interface. They suggested that the attached molecules of the solvent, such as water, would have a fixed alignment to the electrode surface. This first layer of solvent molecules displays a strong orientation to the electric field depending on the charge. This orientation has great influence on the

permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more i ...

of the solvent that varies with field strength. The IHP passes through the centers of these molecules. Specifically adsorbed, partially solvated ions appear in this layer. The solvated ions of the electrolyte are outside the IHP. Through the centers of these ions pass the OHP. The diffuse layer is the region beyond the OHP.

Trasatti/Buzzanca

Further research with double layers on ruthenium dioxide films in 1971 by Sergio Trasatti and Giovanni Buzzanca demonstrated that the electrochemical behavior of these electrodes at low voltages with specific adsorbed ions was like that of capacitors. The specific adsorption of the ions in this region of potential could also involve a partial charge transfer between the ion and the electrode. It was the first step towards understanding pseudocapacitance.

Conway

Between 1975 and 1980 Brian Evans Conway conducted extensive fundamental and development work on

ruthenium oxide Ruthenium oxide may refer to either of the following: * Ruthenium(IV) oxide, RuO2 * Ruthenium(VIII) oxide, RuO4 {{Short pages monitor