Double layer (surface science)
In surface science, a double layer 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 DL refers to two parallel layers of charge surrounding the object. The first layer, the surface charge, consists of ions which are adsorbed onto the object due to chemical interactions. The second layer is composed of ions attracted to the surface charge via the Coulomb force, 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 or porous bodies with particles or pores on the scale of micrometres to nanometres. However, DLs are important to other phenomena, such as the electrochemical behaviour of electrodes.
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 into butter. DLs exist in practically all heterogeneous fluid-based systems, such as blood, paint, ink and ceramic and cement slurry.
The DL is closely related to electrokinetic phenomena and electroacoustic phenomena.
Development of the (interfacial) double layer
Helmholtz
When an electronic conductor is brought in contact with a solid or liquid ionic conductor, a common boundary among the two phases appears. Hermann von Helmholtz 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 form at the interface between electrode and electrolyte. In 1853, he showed that an electrical double layer is essentially a molecular 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 independent from the charge density depending on the dielectric constant of the electrolyte solvent and the thickness of the double-layer.
This model, while 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 onto the surface, and the interaction between solvent dipole moments and the electrode.
Gouy–Chapman
in 1910 and David Leonard Chapman 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 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 to be applied. Thus the electric potential decreases exponentially away from the surface of the fluid bulk.Gouy-Chapman layers may bear special relevance in bioelectrochemistry. The observation of long-distance inter-protein electron transfer through the aqueous solution has been attributed to a diffuse region between redox partner proteins that is depleted of cations in comparison to the solution bulk, thereby leading to reduced screening, electric fields extending several nanometers, and currents decreasing quasi exponentially with the distance at rate ~1 nm−1. This region is termed "Gouy-Chapman conduit" and is strongly regulated by phosphorylation, which adds one negative charge to the protein surface that disrupts cationic depletion and prevents long-distance charge transport. Similar effects are observed at the redox active site of photosynthetic complexes.
The Gouy-Chapman model fails for highly charged double layers as it predicts impossibly high ion densities. For large potential differences such as induced at an ideally polarizable electrode, it predicts a capacitance that unphysically rises exponentially with bias voltage up to extreme values.
Stern
In 1924, Otto Stern 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 Coulombic, assumes dielectric permittivity to be constant throughout the double layer, and that fluid viscosity is constant plane.
Bikerman
In 1942, Bikerman introduced an alternative approach which is to include a maximum density in the continuum thermodynamic assumptions, including an over-crowding entropy term instead of simply using the ideal gas entropy. In this way the density of ions as a continuum is naturally capped, and characteristically the differential capacitance does not saturate to a plateau but instead has a 'hump' after which it falls as.Friese improved Bikerman's work by allowing for various ions of different sizes. This model was recently refined by Kornyshev. There is a short overview of this model most essential features in the book published Elsevier in 2025
Various Bikerman-type models exist that induce a maximum density in different ways, e.g. a lattice gas or a hard sphere model.
Grahame
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 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 passes through the centres of the specifically adsorbed ions. The outer Helmholtz plane 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 K.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 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.This model was invoked for explaining two paradoxical effects.
The first one is electrokinetics at high ionic strength when charge separation should not exist according to classical EDL model. There is an overview of experiments conducted by 5 different groups with 5 different methods reporting observation of electrokinetic phenomena at ionic strength exceeding 1 mol/l. The BDM model offers an explanation of these experiments as discussed in the said review.
The other effect is paradoxical longevity of nanobubbles, which has been observed by many different groups. There is a paper presenting overview of these experiments and explanation based on BDM model
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 electrochemical capacitors. In 1991, he described the difference between 'Supercapacitor' and 'Battery' behavior in electrochemical energy storage. In 1999, he coined the term supercapacitor to explain the increased capacitance by surface redox reactions with faradaic charge transfer between electrodes and ions.His "supercapacitor" stored electrical charge partially in the Helmholtz double-layer and partially as the result of faradaic reactions with "pseudocapacitance" charge transfer of electrons and protons between electrode and electrolyte. The working mechanisms of pseudocapacitors are redox reactions, intercalation and electrosorption.