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Cole–Davidson Equation
The Cole-Davidson equation is a model used to describe dielectric relaxation in glass-forming liquids. The equation for the complex permittivity is : \hat(\omega) = \varepsilon_ + \frac, where \varepsilon_ is the permittivity at the high frequency limit, \Delta\varepsilon = \varepsilon_-\varepsilon_ where \varepsilon_ is the static, low frequency permittivity, and \tau is the characteristic relaxation time of the medium. The exponent \beta represents the exponent of the decay of the high frequency wing of the imaginary part, \varepsilon''(\omega) \sim \omega^. The Cole–Davidson equation is a generalization of the Debye relaxation keeping the initial increase of the low frequency wing of the imaginary part, \varepsilon''(\omega) \sim \omega. Because this is also a characteristic feature of the Fourier transform of the stretched exponential function The stretched exponential function f_\beta (t) = e^ is obtained by inserting a fractional power law into the exponential function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Chemical Physics
''The Journal of Chemical Physics'' is a scientific journal published by the American Institute of Physics that carries research papers on chemical physics."About the Journal" from the ''Journal of Chemical Physics'' website. Two volumes, each of 24 issues, are published annually. It was established in 1933 when '''' editors refused to publish theoretical works. The editors have been: *2019-present: Tim Lian *2008–2018: *2007–2008: [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dielectric Constant
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivity is a material's property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum. Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric. Relative permittivity is also commonly known as the dielectric constant, a term still used but deprecated by standards organizations in engineering as well as in chemistry. Definition Relative permittivity is typically denoted as (sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permittivity
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor. In the simplest case, the electric displacement field D resulting from an applied electric field E is :\mathbf = \varepsilon \mathbf. More generally, the permittivity is a thermodynamic function of state. It can depend on the frequency, magnitude, and direction of the applied field. The SI unit for permittivity is farad per meter (F/m). The permittivity is often represented by the relative permittivity ''ε''r which is the ratio of the absolute permittivity ''ε'' and the vacuum permittivity ''ε''0 :\kappa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relaxation Time
In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of time ''t'' is an exponential law (exponential decay). In simple linear systems Mechanics: Damped unforced oscillator Let the homogeneous differential equation: :m\frac+\gamma\frac+ky=0 model damped unforced oscillations of a weight on a spring. The displacement will then be of the form y(t) = A e^ \cos(\mu t - \delta). The constant T (=2m/\gamma) is called the relaxation time of the system and the constant μ is the quasi-frequency. Electronics: RC circuit In an RC circuit containing a charged capacitor and a resistor, the voltage decays exponentially: : V(t)=V_0 e^ \ , The constant \tau = RC\ is called the ''relaxation time'' or RC time constant of the circuit. A nonlinear oscillator circuit which generates a repeating waveform by the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debye Relaxation
In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation. Because of dielectric polarisation, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field (for example, if the field is moving parallel to the positive ''x'' axis, the negative charges will shift in the negative ''x'' direction). This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stretched Exponential Function
The stretched exponential function f_\beta (t) = e^ is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments between 0 and +∞. With , the usual exponential function is recovered. With a ''stretching exponent'' ''β'' between 0 and 1, the graph of log ''f'' versus ''t'' is characteristically ''stretched'', hence the name of the function. The compressed exponential function (with ) has less practical importance, with the notable exception of , which gives the normal distribution. In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution. The stretched exponential is also the characteristic function, basically the Fourier transform, of the Lévy symmetric alpha-stable distribution. In physics, the stretched exponential function is often used as a phenomenological description of relaxation in disordered systems. It was first introduced by Rudo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glass
Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of the molten form; some glasses such as volcanic glass are naturally occurring. The most familiar, and historically the oldest, types of manufactured glass are "silicate glasses" based on the chemical compound silica (silicon dioxide, or quartz), the primary constituent of sand. Soda–lime glass, containing around 70% silica, accounts for around 90% of manufactured glass. The term ''glass'', in popular usage, is often used to refer only to this type of material, although silica-free glasses often have desirable properties for applications in modern communications technology. Some objects, such as drinking glasses and eyeglasses, are so commonly made of silicate-based glass that they are simply called by the name of the material. Despite bei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liquids
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. Water is by far the most common liquid on Earth. The density of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid are both termed condensed matter. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
