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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] |
Equivalent Electrical Circuit
In electrical engineering and science, an equivalent circuit refers to a theoretical electrical network, circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that simplifies calculation, and more broadly, that is a simplest form of a more complex circuit in order to aid analysis. In its most common form, an equivalent circuit is made up of linear, passive elements. However, more complex equivalent circuits are used that approximate the nonlinear behavior of the original circuit as well. These more complex circuits often are called ''macromodels'' of the original circuit. An example of a macromodel is the Boyle circuit for the 741 operational amplifier. Examples Thévenin and Norton equivalents One of linear circuit theory's most surprising properties relates to the ability to treat any two-terminal circuit no matter how complex as behaving as only a source and an impedance, which have either of two simple equivalent c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. The concept of diffusion is widely used in many fields, including physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas, and price values). The central idea of diffusion, however, is common to all of these: a substance or collection undergoing diffusion spreads out from a point or location at which there is a higher concentration of that substance or collection. A gradient is the change in the value of a quantity, for example, concentration, pressure, or temperature with the change in another variable, usually distance. A change in c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dielectric 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] |
Emil Warburg
Emil Gabriel Warburg (; 9 March 1846 – 28 July 1931) was a German physicist who during his career was professor of physics at the Universities of Strassburg, Freiburg and Berlin. He was president of the Deutsche Physikalische Gesellschaft 1899–1905. His name is notably associated with the Warburg element of electrochemistry. Among his students were James Franck (Nobel Prize in Physics, 1925), Eduard Grüneisen, Robert Pohl, Erich Regener and Hans von Euler-Chelpin (Nobel Prize in Chemistry, 1929). He carried out research in the areas of kinetic theory of gases, electrical conductivity, gas discharges, heat radiation, ferromagnetism and photochemistry. He was a member of the Warburg family, and the father of Otto Heinrich Warburg (Nobel Prize in Physiology, 1931). He was a friend of Albert Einstein. See also *Magnetic refrigeration Magnetic refrigeration is a cooling technology based on the magnetocaloric effect. This technique can be used to attain extremely low tem ... [...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] |
Charge Transfer Complex
In chemistry, a charge-transfer (CT) complex or electron-donor-acceptor complex describes a type of supramolecular assembly of two or more molecules or ions. The assembly consists of two molecules that self-attract through electrostatic forces, i.e., one has at least partial negative charge and the partner has partial positive charge, referred to respectively as the electron acceptor and electron donor. In some cases, the degree of charge transfer is "complete", such that the CT complex can be classified as a salt. In other cases, the charge-transfer association is weak, and the interaction can be disrupted easily by polar solvents. Examples Electron donor-acceptor complexes A number of organic compounds form charge-transfer complex, which are often described as electron-donor-acceptor complexes (EDA complexes). Typical acceptors are nitrobenzenes or tetracyanoethylene. The strength of their interaction with electron donors correlates with the ionization potentials of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double-layer Capacitance
Double-layer capacitance is the important characteristic of the electrical double layer which appears, for example, at the interface between a conductive electrode and an adjacent liquid electrolyte. At this boundary two layers of charge with opposing polarity form, one at the surface of the electrode, and one in the electrolyte. These two layers, electrons on the electrode and ions in the electrolyte, are typically separated by a single layer of solvent molecules that adhere to the surface of the electrode and act like a dielectric in a conventional capacitor. The amount of electric charge stored in double-layer capacitor depends on the applied voltage. The unit of capacitance is the farad. The double-layer capacitance is the physical principle behind the electrostatic double-layer type of Supercapacitors. History * Development of the double layer and pseudocapacitance model see Double layer (interfacial) * Development of the electrochemical components see Supercapacitors Cap ... [...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] |
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] |
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] |
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] |
