The Tafel equation is an equation in electrochemical kinetics relating the rate of an electrochemical reaction to the overpotential. [1] The Tafel equation was first deduced experimentally and was later shown to have a theoretical justification. The equation is named after Swiss chemist Julius Tafel.
It describes how the electrical current through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for a simple, unimolecular redox reaction. [2] [ circular reference ]
Where an electrochemical reaction occurs in two half reactions on separate electrodes, the Tafel equation is applied to each electrode separately. On a single electrode the Tafel equation can be stated as:
(1) |
where
A verification plus further explanation for this equation can be found here. [6] The Tafel equation is an approximation of the Butler–Volmer equation in the case of .
"[ The Tafel equation ] assumes that the concentrations at the electrode are practically equal to the concentrations in the bulk electrolyte, allowing the current to be expressed as a function of potential only. In other words, it assumes that the electrode mass transfer rate is much greater than the reaction rate, and that the reaction is dominated by the slower chemical reaction rate ". [7] [ circular reference ]
Also, at a given electrode the Tafel equation assumes that the reverse half reaction rate is negligible compared to the forward reaction rate.
The exchange current is the current at equilibrium, i.e. the rate at which oxidized and reduced species transfer electrons with the electrode. In other words, the exchange current density is the rate of reaction at the reversible potential (when the overpotential is zero by definition). At the reversible potential, the reaction is in equilibrium meaning that the forward and reverse reactions progress at the same rates. This rate is the exchange current density.
The Tafel slope is measured experimentally. It can, however, be shown theoretically that when the dominant reaction mechanism involves the transfer of a single electron that
where A is defined as
(2) |
where
In a more general case,
The following derivation of the extended Butler–Volmer equation is adapted from that of Bard and Faulkner and Newman and Thomas-Alyea. [8] [ circular reference ] [ ... ] the current is expressed as a function not only of potential (as in the simple version), but of the given concentrations as well. The mass-transfer rate may be relatively small, but its only effect on the chemical reaction is through the altered (given) concentrations. In effect, the concentrations are a function of the potential as well. [7]
The Tafel equation can be also written as:
(3) |
where
As seen in equation ( 1 ), so: as seen in equation ( 2 ) and because . because [9] [ circular reference ] [10] [ circular reference ] due to the electrode mass transfer [11] [ circular reference ], which finally yields equation ( 3 ).
An other equation is applicable at low values of polarization . In such case, the dependence of current on polarization is usually linear (not logarithmic):
This linear region is called polarization resistance due to its formal similarity to Ohm's law.
The pace at which corrosion develops is determined by the kinetics of the reactions involved, hence the electrical double layer is critical.
Applying an overpotential to an electrode causes the reaction to move in one direction, away from equilibrium. Tafel's law determines the new rate, and as long as the reaction kinetics are under control, the overpotential is proportional to the log of the corrosion current. [12]
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference and identifiable chemical change. These reactions involve electrons moving via an electronically-conducting phase between electrodes separated by an ionically conducting and electronically insulating electrolyte.
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit. Electrodes are essential parts of batteries that can consist of a variety of materials depending on the type of battery.
In electrochemistry, electrode potential is the voltage of a galvanic cell built from a standard reference electrode and another electrode to be characterized. By convention, the reference electrode is the standard hydrogen electrode (SHE). It is defined to have a potential of zero volts. It may also be defined as the potential difference between the charged metallic rods and salt solution.
In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction from the standard electrode potential, absolute temperature, the number of electrons involved in the redox reaction, and activities of the chemical species undergoing reduction and oxidation respectively. It was named after Walther Nernst, a German physical chemist who formulated the equation.
A galvanic cell or voltaic cell, named after the scientists Luigi Galvani and Alessandro Volta, respectively, is an electrochemical cell in which an electric current is generated from spontaneous oxidation–reduction reactions. A common apparatus generally consists of two different metals, each immersed in separate beakers containing their respective metal ions in solution that are connected by a salt bridge or separated by a porous membrane.
A solid oxide fuel cell is an electrochemical conversion device that produces electricity directly from oxidizing a fuel. Fuel cells are characterized by their electrolyte material; the SOFC has a solid oxide or ceramic electrolyte.
Dielectric spectroscopy measures the dielectric properties of a medium as a function of frequency. It is based on the interaction of an external field with the electric dipole moment of the sample, often expressed by permittivity.
Voltammetry is a category of electroanalytical methods used in analytical chemistry and various industrial processes. In voltammetry, information about an analyte is obtained by measuring the current as the potential is varied. The analytical data for a voltammetric experiment comes in the form of a voltammogram, which plots the current produced by the analyte versus the potential of the working electrode.
The saturated calomel electrode (SCE) is a reference electrode based on the reaction between elemental mercury and mercury(I) chloride. It has been widely replaced by the silver chloride electrode, however the calomel electrode has a reputation of being more robust. The aqueous phase in contact with the mercury and the mercury(I) chloride (Hg2Cl2, "calomel") is a saturated solution of potassium chloride in water. The electrode is normally linked via a porous frit (sometimes coupled to a salt bridge) to the solution in which the other electrode is immersed.
In electrochemistry, overpotential is the potential difference (voltage) between a half-reaction's thermodynamically determined reduction potential and the potential at which the redox event is experimentally observed. The term is directly related to a cell's voltage efficiency. In an electrolytic cell the existence of overpotential implies that the cell requires more energy than thermodynamically expected to drive a reaction. In a galvanic cell the existence of overpotential means less energy is recovered than thermodynamics predicts. In each case the extra/missing energy is lost as heat. The quantity of overpotential is specific to each cell design and varies across cells and operational conditions, even for the same reaction. Overpotential is experimentally determined by measuring the potential at which a given current density is achieved.
In electrochemistry, the Butler–Volmer equation, also known as Erdey-Grúz–Volmer equation, is one of the most fundamental relationships in electrochemical kinetics. It describes how the electrical current through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for a simple, unimolecular redox reaction, considering that both a cathodic and an anodic reaction occur on the same electrode:
The gaseous detection device (GDD) is a method and apparatus for the detection of signals in the gaseous environment of an environmental scanning electron microscope (ESEM) and all scanned beam type of instruments that allow a minimum gas pressure for the detector to operate.
In electrochemistry, exchange current density is a parameter used in the Tafel equation, Butler–Volmer equation and other electrochemical kinetics expressions. The Tafel equation describes the dependence of current for an electrolytic process to overpotential.
Charge transfer coefficient, and symmetry factor are two related parameters used in description of the kinetics of electrochemical reactions. They appear in the Butler–Volmer equation and related expressions.
In electrochemistry, the Randles–Ševčík equation describes the effect of scan rate on the peak current ip for a cyclic voltammetry experiment. For simple redox events such as the ferrocene/ferrocenium couple, ip depends not only on the concentration and diffusional properties of the electroactive species but also on scan rate.
In chemistry, ion transport number, also called the transference number, is the fraction of the total electric current carried in an electrolyte by a given ionic species i:
Electrochemical kinetics is the field of electrochemistry that studies the rate of electrochemical processes. This includes the study of how process conditions, such as concentration and electric potential, influence the rate of oxidation and reduction (redox) reactions that occur at the surface of an electrode, as well as an investigation into electrochemical reaction mechanisms. Two accompanying processes are involved in the electrochemical reaction and influence the overall reaction rate:
In electrochemistry, protein film voltammetry is a technique for examining the behavior of proteins immobilized on an electrode. The technique is applicable to proteins and enzymes that engage in electron transfer reactions and it is part of the methods available to study enzyme kinetics.
The Virtual breakdown mechanism is a concept in the field of electrochemistry. In electrochemical reactions, when the cathode and the anode are close enough to each other, the double layer of the regions from the two electrodes is overlapped, forming a large electric field uniformly distributed inside the entire electrode gap. Such high electric fields can significantly enhance the ion migration inside bulk solutions and thus increase the entire reaction rate, akin to the "breakdown" of the reactant(s). However, it is fundamentally different from the traditional "breakdown".
Electro-oxidation(EO or EOx), also known as anodic oxidation or electrochemical oxidation (EC), is a technique used for wastewater treatment, mainly for industrial effluents, and is a type of advanced oxidation process (AOP). The most general layout comprises two electrodes, operating as anode and cathode, connected to a power source. When an energy input and sufficient supporting electrolyte are provided to the system, strong oxidizing species are formed, which interact with the contaminants and degrade them. The refractory compounds are thus converted into reaction intermediates and, ultimately, into water and CO2 by complete mineralization.