A
double layer is a structure that appears on the surface of an object when it is placed into a liquid. 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 chargeSurface charge is the electric charge present at an interface. There are many different processes which can lead to a surface being charged, including adsorption of ions, protonation/deprotonation, and the application of an external electric field...
(either positive or negative), comprises ions adsorbed directly onto the object due to a host of 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, because it is made of free ions which move in the fluid under the influence of
electric attractionElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and thermal motion rather than being firmly anchored. It is thus called the
diffuse layer.
InterfacialAn interface is a surface forming a common boundary among two different phases, such as an insoluble solid and a liquid, two immiscible liquids or a liquid and an insoluble gas. The importance of the interface depends on which type of system is being treated: the bigger the quotient area/volume,...
DL is usually most apparent in systems with a large ratio of surface area to volume, such as
colloidA colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...
or porous bodies with particles or pores (respectively) on the scale of micrometres to nanometres. However, the importance of DLs extends to other systems, e.g., DL is fundamental to the electrochemical behavior of
electrodeAn electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...
s.
The DL plays a fundamental role in many everyday substances. For instance, milk exists only because fat droplets are covered with a DL that prevent their coagulation into butter. DLs exist in practically all heterogeneous fluid-based systems, such as blood, paints, inks, ceramic slurries and cement slurries.
The DL is closely related to
electrokinetic phenomenaElectrokinetic phenomena are a family of several different effects that occur in heterogeneous fluids or in porous bodies filled with fluid. The term heterogeneous here means a fluid containing particles...
and
electroacoustic phenomenaElectroacoustic 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 electroacoustic phenomena. Fluid might be a simple...
.
The earliest model of the electrical DL is usually attributed to Helmholtz. Helmholtz treated the DL mathematically as a simple capacitor, based on a physical model in which a single layer of ions is adsorbed at the surface.
Later
Louis Georges GouyLouis Georges Gouy was a French physicist who was born at Vals-les-Bains, Ardèche in 1854 and died January 27 1926. He is the namesake of the Gouy balance, the Gouy-Chapman electric double layer model and the ....
and
David ChapmanDavid Chapman may refer to:*David Chapman , writer/producer covering video games, comic books, and other pop culture interests*David Chapman English physical chemist...
made significant improvements by introducing a diffuse model of the electrical DL, in which the
electric potentialIn classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...
decreases exponentially away from the surface to the fluid bulk.
The Gouy-Chapman model fails for highly charged DLs. In order to resolve this problem Stern suggested the combination of the Helmholtz and Gouy-Chapman models, giving an internal
Stern layer (i.e. Helmholtz layer), and an outer diffuse layer (i.e. Gouy-Chapman layer).
The combined Gouy-Chapman-Stern model is most commonly used. It still has some limitations, such as
- ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s are effectively modeled as point charges
- the only significant interactions in the diffuse layer are Coulombic
- dielectric permittivity is assumed constant throughout the double layer
- the viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
of fluid is constant above slipping plane.
There are more recent theoretical developments that seek to overcome the limitations of the Gouy-Chapman-Stern model. They are reviewed in J. Lyklema's
Fundamentals of Interface and Colloid Science.
Mathematical description
There are detailed descriptions of the interfacial DL in many books on colloid and interface science and microscale fluid transport. There is also a recent IUPAC technical report on the subject of interfacial double layer and related
electrokinetic phenomenaElectrokinetic phenomena are a family of several different effects that occur in heterogeneous fluids or in porous bodies filled with fluid. The term heterogeneous here means a fluid containing particles...
.
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..." This process leads to the build up of an
electric surface chargeElectric surface charge practically always appears on an object surface when it is placed into a fluid. All fluids contain ions, positive and negative . These ions interact with the object surface. This interaction might lead to the adsorption of some of them on the surface...
, expressed usually in C/m
2. 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
stressIn continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
. 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 potentialZeta potential is a scientific term for electrokinetic potential in colloidal systems. In the colloidal chemistry literature, it is usually denoted using the Greek letter zeta, hence ζ-potential...
. It is 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 potentialZeta potential is a scientific term for electrokinetic potential in colloidal systems. In the colloidal chemistry literature, it is usually denoted using the Greek letter zeta, hence ζ-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 electrodes). 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
electrophoresisElectrophoresis, also called cataphoresis, is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss , who noticed that the application of a constant electric...
,
electroacoustic phenomenaElectroacoustic 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 electroacoustic phenomena. Fluid might be a simple...
, streaming potential, and electroosmotic flow.
The characteristic thickness of the DL is the
Debye lengthIn plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge...
, 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 10
9 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 σ
d and the Stern potential Ψ
d:
There is no general analytical solution for mixed electrolytes, curved surfaces or even spherical particles. There is an asymptotic solution for spherical particles with low charged DLs. In the case when electric potential over DL is less than 25 mV, the so-called Debye-Huckel approximation holds. It yields the following expression for electric potential
Ψ in the spherical DL as a function of the distance
r from the particle center:
There are several asymptotic models which play important roles in theoretical developments associated with the interfacial DL.
The first one is "thin DL". This model assumes that DL is much thinner than the colloidal particle or capillary radius. This restricts the value of the Debye length and particle radius as following:
This model offers tremendous simplifications for many subsequent applications. Theory of
electrophoresisElectrophoresis, also called cataphoresis, is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss , who noticed that the application of a constant electric...
is just one example. The theory of
electroacoustic phenomenaElectroacoustic 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 electroacoustic phenomena. Fluid might be a simple...
is another example.
The thin DL model is valid for most aqueous systems because the Debye length is only a few nanometers in such cases. It breaks down only for nano-colloids in solution with ionic strengths close to water.
The opposing "thick DL" model assumes that the Debye length is larger than particle radius:
This model can be useful for some nano-colloids and non-polar fluids, where the Debye length is much larger.
The last model introduces "overlapped DLs". This is important in concentrated dispersions and emulsions when distances between particles become comparable with the Debye length.
Electrical double layers
The
electrical double layer (
EDL) is a structure which describes the variation of
electric potentialIn classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...
near a surface, and has a significant influence on the behaviour of
colloidA colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...
s and other surfaces in contact with
solutionIn chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is dissolved in another substance, known as a solvent. The solvent does the dissolving.- Types of solutions :...
s or solid-state fast ion conductors.
The primary difference between a DL on an electrode and one on an interface is the mechanisms of
surface chargeSurface charge is the electric charge present at an interface. There are many different processes which can lead to a surface being charged, including adsorption of ions, protonation/deprotonation, and the application of an external electric field...
formation. With an electrode, it is possible to regulate the surface charge by applying an external electric potential. This application, however, is impossible in colloidal and porous DLs, because for colloidal particles, one does not have access to the interior of the particle to apply a potential difference.
EDLs are analogous to the
double layerA double layer is a structure in a plasma and consists of two parallel layers with opposite electrical charge. The sheets of charge cause a strong electric field and a correspondingly sharp change in voltage across the double layer. Ions and electrons which enter the double layer are accelerated,...
in
plasmaIn physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
.
Differential capacitance
EDLs have an additional parameter defining their characterization:
differential capacitanceDifferential 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...
. Differential capacitance, denoted as
C, is described by the equation below:
where σ is the
surface chargeSurface charge is the electric charge present at an interface. There are many different processes which can lead to a surface being charged, including adsorption of ions, protonation/deprotonation, and the application of an external electric field...
and ψ is the electric surface potential.
See also
- Depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an...
(structure of semiconductor junction)
- Electroosmotic pump
An electroosmotic pump , or EO pump, is used for generating flow or pressure by use of an electric field. One application of this is removing liquid flooding water from channels and gas diffusion layers and direct hydration of the proton exchange membrane in the membrane electrode assembly of the...
- Interface and colloid science
Interface and colloid science is an interdisciplinary intersection of branches of chemistry, physics, nanoscience and other fields dealing with colloids, heterogeneous systems consisting of a mechanical mixture of particles between 1 nm and 1000 nm dispersed in a continuous...
- Nanofluidics
Nanofluidics is the study of the behavior, manipulation, and control of fluids that are confined to structures of nanometer characteristic dimensions...
External links