Double electric layer. Mechanism of formation and theory of structure

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MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE

NATIONAL AVIATION UNIVERSITY

INSTITUTE OF ECOLOGICAL SAFETY

DEPARTMENT OF CHEMISTRY AND CHEMICAL TECHNOLOGY

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On the discipline: “Physical and colloid chemistry”

Theme: “Double electric layer. Mechanism of formation and theory of structure”

Done by student of IES 304

Irina Litvin

Checked by Maksimuk M.R.

Kyiv 2014

Content

Introduction

1. Theories of double electrical layer structure

1.1 Helmholtz Theory

1.2 Gouy-Chapman Theory

1.3 Stern Theory

1.4 Grahame Theory

1.5 Bockris/Devanthan/Mьller Theory

1.6 Trasatti/Buzzanca Theory

1.7 Conway Theory

1.8 Marcus Theory

1.9 Modern Theory of Electrical Double Layer

2. Mathematical description

3. Methods of study

References

Introduction

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 body. The DL refers to two parallel layers of charge surrounding the object. The first layer, the surface charge (either positive or negative), comprises ions 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" [1].

Figure 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

Interfacial 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.

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, paint, ink and ceramic and cement slurry.

The 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].

When 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.

In 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.

Simplified illustration of the potential development in the area and in the further course of a Helmholtz double layer is shown on Figure 1.1.

Figure 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.

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 [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].

Figure 1.2. Scheme of Gouy-Chapman construction of double layer

Gouy-Chapman model give such conclusions as:

a) The concentration of counterions decreases with increasing distance from the surfaceand the thickness of the diffusion layer decreases in inverse proportion;

b) 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.

According 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.

Figure 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.

Stern theory provided an explanation for the phenomenon of surface overcharging.

1.4 Grahame Theory

D. 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).

1.5 Bockris/Devanthan/Mьller Theory

In 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].

On Figure 2.4. depicted scheme of DL according Bockris/Devanthan/Mьller theory.

Figure 2.4. 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

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.

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 [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

The 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).

Due 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].

Figure 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.

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 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.

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. It is also denoted as ж-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 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.

Figure3. Detailed illustration of interfacial DL

Zeta potential can be measured using electrophoresis, electroacoustic phenomena, streaming potential, and electroosmotic flow.

The 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.

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 double layers.

The 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 у^d and the Stern potential Ш^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 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.

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 electrophoresis is just one example. The theory of electroacoustic phenomena 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 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.

Secondly, 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.

Information 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.

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