Charge transfer coefficient, and symmetry factor (symbols ''α'' and ''β'', respectively) are two related parameters used in description of the
kinetics
Kinetics (, ''movement'' or ''to move'') may refer to:
Science and medicine
* Kinetics (physics), the study of motion and its causes
** Rigid body kinetics, the study of the motion of rigid bodies
* Chemical kinetics, the study of chemical ...
of
electrochemical reaction
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 (typica ...
s. They appear in the
Butler–Volmer equation
In electrochemistry, the Butler–Volmer equation (named after John Alfred Valentine Butler and Max Volmer), also known as Tibor Erdey-Grúz, Erdey-Grúz–Volmer equation, is one of the most fundamental relationships in electrochemical kinetics. I ...
and related expressions.
The symmetry factor and the charge transfer coefficient are
dimensionless
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...
.
According to an
IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
definition, for a reaction with a single rate-determining step, the charge transfer coefficient for a cathodic reaction (the cathodic transfer coefficient, ''α
c'') is defined as:
:
The anodic transfer coefficient (''α
a'') is defined by analogy:
:
where:
*
:
stoichiometric number
Stoichiometry () is the relationships between the masses of reactants and products before, during, and following chemical reactions.
Stoichiometry is based on the law of conservation of mass; the total mass of reactants must equal the total m ...
, i.e., the number of
activated complex
In chemistry, an activated complex represents a collection of intermediate structures in a chemical reaction when bonds are breaking and forming. The activated complex is an arrangement of atoms in an arbitrary region near the saddle point
...
es formed and destroyed in the overall reaction (with ''n'' electrons)
*
:
universal gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature, temperature ...
*
:
absolute temperature
Thermodynamic temperature, also known as absolute temperature, is a physical quantity which measures temperature starting from absolute zero, the point at which particles have minimal thermal motion.
Thermodynamic temperature is typically expres ...
*
: number of electrons involved in the electrode reaction
*
:
Faraday constant
In physical chemistry, the Faraday constant (symbol , sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge () by the amount () of elementary charge carriers in any given sample of matter: it ...
*
:
electrode potential
An electrode is an electrical conductor used to make contact with a nonmetallic part of a Electronic circuit, circuit (e.g. a semiconductor, an electrolyte, a vacuum or a gas). In electrochemical cells, electrodes are essential parts that can c ...
*
:
partial cathodic (anodic) current[IUPAC. ''ELECTRODE REACTION ORDERS, TRANSFER COEFFICIENTS AND RATE CONSTANTS. APPLICATION OF DEFINITIONS AND RECOMMENDATIONS FOR PUBLICATION OF PARAMETERS.'' Pure & Appi. Chern., Vol. 52, pp.233—240, 1979]
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Significance
The charge transfer coefficient signifies the fraction of the interfacial potential at an electrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte, a vacuum or a gas). In electrochemical cells, electrodes are essential parts that can consist of a varie ...
-electrolyte
An electrolyte is a substance that conducts electricity through the movement of ions, but not through the movement of electrons. This includes most soluble Salt (chemistry), salts, acids, and Base (chemistry), bases, dissolved in a polar solven ...
interface that helps in lowering the free energy barrier
In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (''E''a) of a reaction is measured in kilojoules per mole (k ...
for the electrochemical reaction. The electroactive ion
An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convent ...
present in the interfacial region experiences the interfacial potential and electrostatic work is done on the ion by ''a part'' of the interfacial electric field. It is charge transfer coefficient that signifies ''this part'' that is utilized in activating the ion to the top of the free energy barrier.
Batteries and fuel cells
In operating batteries and fuel cell
A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen fuel, hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most bat ...
s, charge transfer coefficient is the parameter that signifies the fraction of overpotential
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 r ...
that affects the current density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ...
. This parameter has had a mysterious significance in electrochemical kinetics for over three quarters of the previous century. It can also be said that charge transfer coefficient is the heart of electrode kinetics.
Symmetry factor
The symmetry factor (or barrier symmetry factor) is a coefficient similar to the transfer coefficient, but applicable only to single-step reactions.
The sum of anodic symmetry factor and cathodic symmetry factor is equal to one:
:
References
{{Reflist
Dimensionless numbers of chemistry
Electrochemistry