Double layer (surface science)
In surface science, 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 media. The DL refers to two parallel layers of Electric charge surrounding the object. The first layer, the surface charge (either positive or negative), consists of 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 Electromagnetism 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 (respectively) on the scale of micrometres to nanometres. However, DLs are important to other phenomena, such as the electrochemical behaviour of .
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
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.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, 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
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 (Cytochrome Cytochrome c and c1) 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 Photosystem.
Stern
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 , assumes dielectric permittivity to be constant throughout the double layer, and that fluid viscosity is constant plane.
Grahame
Bockris/Devanathan/Müller (BDM)
Trasatti/Buzzanca
Conway
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.
Marcus
Mathematical description
As stated by Lyklema, "...the reason for the formation of a "relaxed" ("equilibrium") double layer is the non-electric affinity of charge-determining ions for a surface..."Lyklema, J. "Fundamentals of Interface and Colloid Science", vol.2, page.3.208, 1995 This process leads to the buildup of an electric surface charge, expressed usually in C/m2. This surface charge creates an electrostatic field that then affects the ions in the bulk of the liquid. This electrostatic field, in combination with the thermal motion of the ions, creates a counter charge, and thus screens the electric surface charge. The net electric charge in this screening diffuse layer is equal in magnitude to the net surface charge, but has the opposite polarity. As a result, the complete structure is electrically neutral.
The diffuse layer, or at least part of it, can move under the influence of tangential stress. There is a conventionally introduced slipping plane that separates mobile fluid from fluid that remains attached to the surface. Electric potential at this plane is called electrokinetic potential or zeta potential (also denoted as ζ-potential).
The electric potential on the external boundary of the Stern layer versus the bulk electrolyte is referred to as Stern potential. Electric potential difference between the fluid bulk and the surface is called the electric surface potential.
Usually zeta potential is used for estimating the degree of DL charge. A characteristic value of this electric potential in the DL is 25 mV with a maximum value around 100 mV (up to several volts on electrodesV.S. Bogotsky, Fundamentals of Electrochemistry, Wiley-Interscience, 2006.). The chemical composition of the sample at which the ζ-potential is 0 is called the point of zero charge or the iso-electric point. It is usually determined by the solution pH value, since protons and hydroxyl ions are the charge-determining ions for most surfaces.
Zeta potential can be measured using electrophoresis, electroacoustic phenomena, streaming potential, and electroosmotic flow.
The characteristic thickness of the DL is the Debye length, κ−1. It is reciprocally proportional to the square root of the ion concentration C. In aqueous solutions it is typically on the scale of a few nanometers and the thickness decreases with increasing concentration of the electrolyte.
The electric field strength inside the DL can be anywhere from zero to over 109 V/m. These steep electric potential gradients are the reason for the importance of the DLs.
The theory for a flat surface and a symmetrical electrolyte is usually referred to as the Gouy-Chapman theory. It yields a simple relationship between electric charge in the diffuse layer σd and the Stern potential Ψd:
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