edl wikipedia

8/12/2019 EDL Wikipedia

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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 liquiddroplet,or aporous body.The DL refers to two parallel layers of charge surrounding

the object. The first layer, thesurface charge(either positive or negative), comprises

ionsadsorbedonto the object due to chemical interactions. The second layer is composed of ions

attracted to the surface charge via thecoulomb force,electricallyscreeningthe 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 ofelectric attractionandthermal motionrather than being firmly anchored. It is thus

called the "diffuse layer".

InterfacialDL is most apparent in systems with a large surface area to volume ratio, such ascolloidor

porous bodies with particles or pores (respectively) on the scale of micrometres to nanometres.

However, DL is important to other phenomena, such as theelectrochemicalbehavior ofelectrodes.

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 theircoagulationinto butter. DLs exist in practically

allheterogeneousfluid-based systems, such as blood, paint, ink and ceramic and cementslurry.

The DL is closely related toelectrokinetic phenomenaandelectroacoustic phenomena.

Contents

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1 Development of the double layer modelo 1.1 Helmholtzo 1.2 Gouy-Chapmano 1.3 Stern
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o 1.4 Grahameo 1.5 Bockris/Devanthan/Mllero 1.6 Trasatti/Buzzancao 1.7 Conwayo 1.8 Marcus

2 Mathematical description 3 Electrical double layers

o 3.1 Differential capacitance 4 See also 5 References 6 External links

Development of the double layer model[edit]

Helmholtz[edit]

Simplified illustration of the potential development in the area and in the further course of a

Helmholtz double layer.

When a electronicconductor is brought in contact with a solid or liquid ionicconductor (electrolyte), a

common boundary (interface)among the twophasesappears.Hermann von Helmholtz[1]was the

first to realize thatchargedelectrodes immersed in electrolytic solutions repel thecoionsof the

charge while attracting counterions to their surfaces. Two layers of oppositepolarityform at the

interface between electrode and electrolyte. In 1853 he showed that an electrical double layer (DL)
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layerareCoulombic,assumingdielectric permittivityto be constant throughout the double layer and

that fluid viscosity is constant above the slipping plane.[8]

Grahame[edit]

Schematic representation of a double layer on an electrode (BMD) model. 1. Inner Helmholtz plane,

(IHP), 2. Outer Helmholtz plane (OHP), 3. Diffuse layer, 4. Solvated ions (cations) 5. Specifically

adsorbed ions (redox ion, which contributes to the pseudocapacitance), 6. Molecules of the

electrolyte solvent

D. C. Grahame modified Stern in 1947.[9]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 (IHP) plane 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/Devanthan/Mller[edit]

In 1963J. O'M. Bockris,M. A. V. Devanthan andK. Alex Mller[10]proposed the BDM model of the

double-layer that included the action of the solvent in the interface. They suggested that the attached
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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 thepermittivityof 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. The BDM

model now is most commonly used.

Trasatti/Buzzanca[edit]

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.[4]

Conway[edit]

Ph.D., Brian Evans Conway within theJohn BockrisGroup At Imperial College, London 1947

Between 1975 and 1980Brian Evans Conwayconducted extensive fundamental and development

work onruthenium oxideelectrochemical capacitors. In 1991 he described the difference between

Supercapacitor and Battery behavior in electrochemical energy storage. In 1999 he coined the term
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supercapacitor to explain the increased capacitance by surface redox reactions with faradaic charge

transfer between electrodes and ions.[11][12]

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[edit]

The physical and mathematical basics of electron charge transfer absent chemical bonds leading to

pseudocapacitance was developed byRudolph A. Marcus.Marcus Theoryexplains the rates of

electron transfer reactionsthe rate at which an electron can move from one chemical species to

another. It was originally formulated to addressouter sphere electron transferreactions, in which two

chemical species change only in their charge, with an electron jumping. For redox reactions without

making or breaking bonds, Marcus theory takes the place ofHenry Eyring'stransition state

theorywhich was derived for reactions with structural changes. Marcus received theNobel Prize in

Chemistryin 1992 for this theory.[citation needed]

Mathematical description[edit]

There are detailed descriptions of the interfacial DL in many books on colloid and interface

science[13][14][15]and microscale fluid transport.[16][17]There is also a recent IUPAC technical

report[18]on the subject of interfacial double layer and relatedelectrokinetic phenomena.
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detailed illustration of interfacial DL

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..."[19]This process leads to the build

up of anelectric 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 oftangentialstress.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 calledelectrokinetic potentialorzeta potential.It is

also denoted as -potential.
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The electric potential on the external boundary of the Stern layer versus the bulk electrolyte is

referred to asStern potential.Electric potential difference between the fluid bulk and the surface is

called the electric surface potential.

Usuallyzeta potentialis 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[17][20]). The chemical composition of the sample at which the -potential is 0 is called

thepoint of zero chargeor theiso-electric point.It is usually determined by the solution pH value,

since protons and hydroxyl ions are the charge-determining ions for most surfaces .[19][17]

Zeta potential can be measured usingelectrophoresis,electroacoustic phenomena,streaming

potential,andelectroosmotic flow.

The characteristic thickness of the DL is theDebye length,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 9V/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 [19]is usually referred to as the Gouy-

Chapman theory. It yields a simple relationship between electric charge in the diffuse layer dand the

Stern potential 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
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holds. It yields the following expression for electric potential in the spherical DL as a function

of the distance rfrom 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

ofelectrophoresisis just one example.[21]The theory ofelectroacoustic phenomenais

another example.[22]

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".[22]This is important in concentrated

dispersions and emulsions when distances between particles become comparable

with the Debye length.
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Electrical double layers[edit]

The electrical double layer(EDL) is a structure which describes the variation

ofelectric potentialnear a surface, and has a significant influence on the behaviour

ofcolloidsand other surfaces in contact withsolutionsor solid-statefast ion

conductors.

The primary difference between a DL on an electrode and one on an interface is the

mechanisms ofsurface chargeformation. 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 thedouble layerinplasma.

Differential capacitance[edit]

Main article:Differential capacitance

EDLs have an additional parameter defining their characterization:differential

capacitance.Differential capacitance, denoted as C, is described by the equation

below:

where is thesurface chargeand is theelectric surface potential.
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