Double electric layer. Mechanism of formation and theory of structure
MINISTRY
OF EDUCATION AND SCIENCE OF UKRAINEAVIATION UNIVERSITYOF ECOLOGICAL SAFETYOF
CHEMISTRY AND CHEMICAL TECHNOLOGY
TASKthe
discipline: “Physical and colloid chemistry”: “Double electric layer. Mechanism
of formation and theory of structure”
Done by student of IES
304Litvinby Maksimuk M.R.
2014
Content
Introduction
1. Theories of double
electrical layer structure
1.1 Helmholtz Theory
.2 Gouy-Chapman Theory
1.3 Stern Theory
1.4 Grahame
Theory
.5 Bockris/Devanthan/Mьller
Theory
.6 Trasatti/Buzzanca
Theory
.7 Conway Theory
.8 Marcus Theory
1.9 Modern Theory of
Electrical Double Layer
. Mathematical description
3. Methods of study
References
Introduction
1. Schematic of
double layer in a liquid at contact with a negatively-charged solid. Depending
on the nature of the solid, there may be another double layer (unmarked on the
drawing) inside the solid
DL is most apparent in systems with
a large surface area to volume ratio, such as colloid or porous bodies with
particles or pores (respectively) on the scale of micrometres to nanometres.
However, DL is important to other phenomena, such as the electrochemical
behavior of electrodes.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, paint, ink and ceramic and
cement slurry.DL is closely related to electrokinetic phenomena and
electroacoustic phenomena.
1.
Theories of double electrical layer structure
1.1 Helmholtz theory
First quantitative theory of the
electric double layer was developed by Helmholtz in 1879. At that time the
existence of ions in solution was not known and Helmholtz consider double layer
as a capacitor, outer armature of which is positioned in liquid parallel to the
surface at a distance of the molecular order from it [2].an electronic
conductor is brought in contact with a solid or liquid ionic conductor
(electrolyte), a common boundary (interface) among the two phases appears.
Hermann von Helmholtz was the first to realize that charged electrodes immersed
in electrolytic solutions repel the coions of the charge while attracting
counterions to their surfaces. Two layers of opposite polarity form at the
interface between electrode and electrolyte. 1853 he showed that an electrical
double layer (DL), that is essentially a molecular dielectric, stored charge
electrostatically. Below the electrolyte's decomposition voltage the stored
charge is linearly dependent on the voltage applied.illustration of the potential
development in the area and in the further course of a Helmholtz double layer
is shown on Figure 1.1.
1.1. Simplified
illustration of the potential development in the area and in the further course
of a Helmholtz double layer
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. 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
[1].
1.2 Gouy-Chapman
theory
Louis Georges Gouy in 1910 and David
Leonard Chapman in 1913 independently observed that capacitance was not a
constant and that it depended on the applied potential and the ionic
concentration. According to this theory counterions that are not strongly bound
to the surface, unlike the potential-determining ions, form not a plane but
diffuse layer. The "Gouy-Chapman model" made significant improvements
by introducing a diffuse model of the double layer. 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 (Figure 1.2)
[1].
1.2. Scheme of
Gouy-Chapman construction of double layer
Gouy-Chapman model give such
conclusions as:) The concentration of counterions decreases with
increasing distance from the surfaceand the thickness of the diffusion layer
decreases in inverse proportion;) Ions, which is more have greater effect
on increasing the thickness of the diffusion layer at the same concentration
[3].
1.3 Stern Theory
Gouy-Chapman model fails for highly
charged double layers. In 1924 Otto Stern suggested theory combining Helmholtz
with Gouy-Chapman. 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. to Stern theory formation of a counterions layer
determined not only by their electrostatic interaction with the charged
surface, but also by adsorption. The theory also takes into account that no
matter how small counterions are, they still have a finite size and
consequently ions' closest approach to the electrode is on the order of the
ionic radius [3]. The ratio between the electrostatic and adsorption forces
determines the concentration and even charge of the ion at the surface.
Electric double layer structure in accordance with the theory of Stern shown in
Figure 1.3.
1.3. Electric
double layer structure according to the theory of Stern
The Stern model had its own
limitations, effectively modeling ions as point charges, assuming all
significant interactions in the diffuse layer are Coulombic, assuming
dielectric permittivity to be constant throughout the double layer and that
fluid viscosity is constant above the slipping plane. theory provided an
explanation for the phenomenon of surface overcharging.
.4 Grahame Theory
. C. Grahame modified Stern theory
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 outer Helmholtz plane (OHP).
.5 Bockris/Devanthan/Mьller Theory
1963 J. O'M. Bockris, M. A. V.
Devanthan and K. Alex Mьller 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 inner Helmholtz plane (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 outer Helmholtz plane (OHP). The diffuse layer is the
region beyond the OHP. The BDM model now is most commonly used [1].Figure 2.4.
depicted scheme of DL according Bockris/Devanthan/Mьller theory.
1.6 Trasatti/Buzzanca
Theory
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 [1].
1.7
Conway Theory
Between 1975 and 1980 Brian Evans
Conway conducted extensive fundamental and development work on ruthenium
oxideelectrochemical 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. "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 [1].
1.8 Marcus Theory
The physical and mathematical basics
of electron charge transfer absent chemical bonds leading to pseudocapacitance
was developed by Rudolph A. Marcus. Marcus Theory explains the rates of
electron transfer reactions-the rate at which an electron can move from one
chemical species to another. It was originally formulated to address outer
sphere electron transfer reactions, 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 of Henry Eyring's transition
state theory which was derived for reactions with structural changes. Marcus
received the Nobel Prize in Chemistry in 1992 for this theory [1].
colloid chemistry
adsorption disperse
1.9
Modern Theory of Electrical Double Layer
main contribution to the development
of modern theory made works of G. Gelmgolts (1879), J. Guy (1910), D. Chapman
(1913), A. Stern (1924) and David Graham (1947-58). to thermal motion of the
ions adsorbed on the electrode only by the action of the Coulomb force is distributed
near the surface like the gas molecules in the atmosphere and form a part of
the diffuse electric double layer. Boundary of the diffuse part is a so-called
Outer Helmholtz plane (OHP), (x2 on Figure 2.5), to which can reach electrical
centers of ions involved in the thermal motion. Between the OHP and metal
surface located dense part of the electric double layer, which is characterized
by the permittivity significantly smaller than in the volume of solution. In
the dense layer is localized dipole electric double layer formed by oriented
dipoles of solvent and solute. In addition, the dense part of the electric
double layer consists of specifically adsorbed ions; thus their electrical
centers form a so-called Inner Helmholtz plane (x1 on Figure 2.5) [4].
2.5. Scheme of the
potential distribution in the electric double layer: 1 - when | q1 | <| q |;
2 - at | q1 |> | q |
2.
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 phenomena.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 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. Figure 3 showed detailed
illustration of interfacial double layer.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. It is also denoted as ж-potential.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.zeta
potential is used for estimating the degree of double layer 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 ж-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.
. Detailed
illustration of interfacial DL
potential can be measured using
electrophoresis, electroacoustic phenomena, streaming potential, and
electroosmotic flow.characteristic thickness of the DL is the Debye length, к−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.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 double layers.theory for a flat surface and a symmetrical electrolyte[20]
is usually referred to as the Gouy-Chapman theory. It yields a simple
relationship between electric charge in the diffuse layer уd
and the Stern potential Шd:
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 double
layers. 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 Ш
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.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 electrophoresis is
just one example. The theory of electroacoustic phenomena is another example. 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.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.last
model introduces "overlapped DLs". This is important in concentrated
dispersions and emulsions when distances between particles become comparable
with the Debye length.double layers have an additional parameter defining their
characterization: differential capacitance. Differential capacitance, denoted
as C, is described by the equation below:
where у
is the surface charge and ш
is the electric surface potential [1].
3.
Methods of study
For the study of double electric
layer use mainly three groups of methods. Firstly, the adsorption methods,
which are based on the fact that the formation of the electrical double layer
is due to the adsorption of various components of the solution and causes a
change in their concentration. Specifically, adsorption methods are widely used
to study the electric double layer formed on the fine particles in colloidal
systems., methods based on electrocapillary phenomena. Their essence is, that
the formation of the electric double layer reduces the work required for
creating a new surface interface and thereby leads to dependence of interfacial
tension from electrode potential. The use of electrocapillary methods is
limited by interfaces between the liquid phases on which possible direct
measurement of the interfacial tension; for solid electrodes, these methods
provide only qualitative information on the structure of the electric double
layer. Third, methods, recording the amount of electricity spent on creating a
certain electrode charge (charging the electric double layer). These include
various galvanostatic and potentiostatic impulse techniques, as well as a
method for measuring the electrical capacitance of the electric double layer
using sinusoidal alternating current. For the successful application of these
methods requires that all electricity supplied to the electrode was spent only
on the electric double layer charging and not spent on electrochemical
reaction. Electrodes satisfying this requirement is called ideally
polarizable.about the structure of the electric double layer at the interface
solution| insulator can be obtained through the study of electrokinetic
phenomena. Electric double layer is also studied by optical methods
(ellipsometry, different variants of electroreflection of light, Raman
scattering in the adsorbed layer, etc.). Based on these techniques we can
determine the charge of the electrode surface q, its dependence on the
potential of the electrode E, the potential of zero charge Eq = 0, the
capacitance of the electric double layer equal dq / dE, and the surface excess
(adsorption) of the various components of the solution, depending on E (or q)
and the volume concentration [4].
References
1. Д.А. Фридрихсберг. Курс
коллоидной химии. - Л.: Химия, 1984. - 181с.
2. В.Н. Захарченко. Коллоидная
химия. - М.: Высшая школа, 1989. -
89-92c.