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Randles Circuit
In electrochemistry, a Randles circuit is an equivalent electrical circuit that consists of an active electrolyte resistance in series with the parallel combination of the double-layer capacitance and an impedance () of a faradaic reaction. It is commonly used in electrochemical impedance spectroscopy (EIS) for interpretation of impedance spectra, often with a constant phase element (CPE) replacing the double layer capacity. The Randles equivalent circuit is one of the simplest possible models describing processes at the electrochemical interface. In real electrochemical systems, impedance spectra are usually more complicated and, thus, the Randles circuit may not give appropriate results. Explanation Figure 1 shows the equivalent circuit initially proposed by John Edward Brough Randles for modeling of interfacial electrochemical reactions in presence of semi-infinite linear diffusion of electroactive particles to flat electrodes. A simple model for an electrode immersed i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randles Circuit
In electrochemistry, a Randles circuit is an equivalent electrical circuit that consists of an active electrolyte resistance in series with the parallel combination of the double-layer capacitance and an impedance () of a faradaic reaction. It is commonly used in electrochemical impedance spectroscopy (EIS) for interpretation of impedance spectra, often with a constant phase element (CPE) replacing the double layer capacity. The Randles equivalent circuit is one of the simplest possible models describing processes at the electrochemical interface. In real electrochemical systems, impedance spectra are usually more complicated and, thus, the Randles circuit may not give appropriate results. Explanation Figure 1 shows the equivalent circuit initially proposed by John Edward Brough Randles for modeling of interfacial electrochemical reactions in presence of semi-infinite linear diffusion of electroactive particles to flat electrodes. A simple model for an electrode immersed i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant Phase Element
In electronics, a constant phase element is an equivalent electrical circuit component that models the behaviour of a double layer, that is an imperfect capacitor (see double-layer capacitance). Constant phase elements are also used in equivalent circuit modeling and data fitting of electrochemical impedance spectroscopy data. A constant phase element also currently appears in modeling the imperfect dielectrics' behavior. The generalization in the fields of imperfect electrical resistances, capacitances, and inductances leads to the general "phasance" concept: http://fr.scribd.com/doc/71923015/The-Phasance-Concept General equation The electrical impedance can be calculated: :Z_=\frac=\frace^ where the CPE admittance is: Y_=Q_0(\omega i)^n and Q0 and n (0 [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randles Spectrum
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Angular Frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (for example, in rotation) or the rate of change of the phase of a sinusoidal waveform (for example, in oscillations and waves), or as the rate of change of the argument of the sine function. Angular frequency (or angular speed) is the magnitude of the pseudovector quantity angular velocity.(UP1) One turn is equal to 2''π'' radians, hence \omega = \frac = , where: *''ω'' is the angular frequency (unit: radians per second), *''T'' is the period (unit: seconds), *''f'' is the ordinary frequency (unit: hertz) (sometimes ''ν''). Units In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. The unit hertz (Hz) is dimensionally equivalent, but by convention it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imaginary Unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is 2+3i. Imaginary numbers are an important mathematical concept; they extend the real number system \mathbb to the complex number system \mathbb, in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1: and -i, just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter is ambiguous or problematic, the letter or the Greek \iota is sometimes used instead. For example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warburg Coefficient
The Warburg coefficient (or Warburg constant; denoted or ) is the diffusion coefficient of ions in solution, associated to the Warburg element, . The Warburg coefficient has units of /\sqrt= s^ The value of can be obtained by the gradient of the Warburg plot, a linear plot of the real impedance () against the reciprocal of the square root of the frequency (/\sqrt). This relation should always yield a straight line, as it is unique for a Warburg. Alternatively, the value of can be found by: A_W\frac where * is the ideal 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 increment per ...; * is the thermodynamic temperature; * is the Faraday constant; * is the valency; * is the diffusion coefficient of the species, where subscripts and stand for the oxidized and reduced s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warburg Element
The Warburg diffusion element is an equivalent electrical circuit component that models the diffusion process in dielectric spectroscopy. That element is named after German physicist Emil Warburg. A Warburg Electrical impedance, impedance element can be difficult to recognize because it is nearly always associated with a charge-transfer resistance (see charge transfer complex) and a double-layer capacitance, but is common in many systems. The presence of the Warburg element can be recognised if a linear relationship on the log of a Bode plot ( vs. ) exists with a slope of value –1/2. General equation The Warburg diffusion element () is a constant phase element (CPE), with a constant phase of 45° (phase independent of frequency) and with a magnitude inversely proportional to the square root of the frequency by: : = \frac+\frac : = \sqrt\frac where * is the Warburg coefficient (or Warburg constant); * is the imaginary unit; * is the angular frequency. This equation assum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charge Transfer Resistance
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Electrochemical Impedance Spectroscopy
Dielectric spectroscopy (which falls in a subcategory of impedance spectroscopy) measures the dielectric properties of a medium as a function of frequency.Kremer F., Schonhals A., Luck W. Broadband Dielectric Spectroscopy. – Springer-Verlag, 2002. It is based on the interaction of an external field with the electric dipole moment of the sample, often expressed by permittivity. It is also an experimental method of characterizing electrochemical systems. This technique measures the impedance of a system over a range of frequencies, and therefore the frequency response of the system, including the energy storage and dissipation properties, is revealed. Often, data obtained by electrochemical impedance spectroscopy (EIS) is expressed graphically in a Bode plot or a Nyquist plot. Impedance is the opposition to the flow of alternating current (AC) in a complex system. A passive complex electrical system comprises both energy dissipater (resistor) and energy storage (capacitor) eleme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outcome of a particular chemical change, or vice versa. These reactions involve electrons moving via an electronically-conducting phase (typically an external electrical circuit, but not necessarily, as in electroless plating) between electrodes separated by an ionically conducting and electronically insulating electrolyte (or ionic species in a solution). When a chemical reaction is driven by an electrical potential difference, as in electrolysis, or if a potential difference results from a chemical reaction as in an electric battery or fuel cell, it is called an ''electrochemical'' reaction. Unlike in other chemical reactions, in electrochemical reactions electrons are not transferred directly between atoms, ions, or molecules, but via the af ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faradaic Current
The faradaic current is the current generated by the reduction or oxidation of some chemical substance at an electrode. The net faradaic current is the algebraic sum of all the faradaic currents flowing through an indicator electrode or working electrode. Limiting current The limiting current in electrochemistry is the limiting value of a faradaic current that is approached as the rate of charge transfer to an electrode is increased. The limiting current can be approached, for example, by increasing the electric potential or decreasing the rate of mass transfer to the electrode. It is independent of the applied potential over a finite range, and is usually evaluated by subtracting the appropriate residual current from the measured total current. A limiting current can have the character of an adsorption, catalytic, diffusion, or kinetic current, and may include a migration current. Migration current The difference between the current that is actually obtained, at any particular val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. In general, it depends upon the frequency of the sinusoidal voltage. Impedance extends the concept of resistance to alternating current (AC) circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude. Impedance can be represented as a complex number, with the same units as resistance, for which the SI unit is the ohm (). Its symbol is usually , and it may be represented by writing its magnitude and phase in the polar form . However, Cartesian complex number representation is often more powerful for circuit analysis purposes. The notion of impedance is useful for perf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
