Nikiya Anton Bettey 2021: 09-27-2021-2032 - time–temperature superposition principle polymer rubber glass

Tuesday, September 28, 2021

09-27-2021-2032 - time–temperature superposition principle polymer rubber glass

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The time–temperature superposition principle is a concept in polymer physicsand in the physics of glass-forming liquids.^[1]^[2]^[3]^[4] This superposition principle is used to determine temperature-dependent mechanical properties of linear viscoelastic materials from known properties at a reference temperature. The elastic moduli of typical amorphous polymers increase with loading rate but decrease when the temperature is increased.^[5] Curves of the instantaneous modulus as a function of time do not change shape as the temperature is changed but appear only to shift left or right. This implies that a master curve at a given temperature can be used as the reference to predict curves at various temperatures by applying a shift operation. The time-temperature superposition principle of linear viscoelasticity is based on the above observation.^[6]

https://en.wikipedia.org/wiki/Time–temperature_superposition

A superglass is a phase of matter which is characterized (at the same time) by superfluidity and a frozen amorphous structure.^[1]

J.C. Séamus Davis theorised that frozen helium-4 (at 0.2 K and 50 Atm) may be a superglass.^[1]^[2]^[3]

https://en.wikipedia.org/wiki/Superglass

Supercooling,^[1] also known as undercooling,^[2] is the process of lowering the temperature of a liquid or a gasbelow its freezing point without it becoming a solid.

https://en.wikipedia.org/wiki/Supercooling

Spontaneous glass breakage is a phenomenon by which toughened glass (or tempered) may spontaneously break without any apparent reason.

https://en.wikipedia.org/wiki/Spontaneous_glass_breakage

Devitrification is the process of crystallization in a formerly crystal-free (amorphous) glass.^[1] The term is derived from the Latin vitreus, meaning glassyand transparent.

https://en.wikipedia.org/wiki/Devitrification

A nickel sulfide inclusion, (also abbreviated to NiS), occurs during the process of manufacturing float glass (normal window glass).

https://en.wikipedia.org/wiki/Nickel_sulfide_inclusion

https://en.wikipedia.org/wiki/Float_glass

https://en.wikipedia.org/wiki/Soda–lime_glass

Solar gain (also known as solar heat gain or passive solar gain) is the increase in thermal energy of a space, object or structure as it absorbs incident solar radiation. The amount of solar gain a space experiences is a function of the total incident solar irradiance and of the ability of any intervening material to transmit or resist the radiation.

https://en.wikipedia.org/wiki/Solar_gain

Low emissivity (low e or low thermal emissivity) refers to a surface condition that emits low levels of radiant thermal (heat) energy. All materials absorb, reflect, and emit radiant energy according to Planck's law but here, the primary concern is a special wavelength interval of radiant energy, namely thermal radiation of materials. In common use, especially building applications, the temperature range of approximately -40 to +80 degrees Celsius is the focus, but in aerospace and industrial process engineering, much broader ranges are of practical concern.

https://en.wikipedia.org/wiki/Low_emissivity

In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium.

https://en.wikipedia.org/wiki/Kirchhoff%27s_law_of_thermal_radiation

Negative luminescence is a physical phenomenon by which an electronic device emits less thermal radiation when an electric current is passed through it than it does in thermal equilibrium (current off). When viewed by a thermal camera, an operating negative luminescent device looks colder than its environment.

https://en.wikipedia.org/wiki/Negative_luminescence

The electron–hole pair is the fundamental unit of generation and recombination in inorganic semiconductors, corresponding to an electron transitioning between the valence band and the conduction band where generation of electron is a transition from the valence band to the conduction band and recombination leads to a reverse transition.

https://en.wikipedia.org/wiki/Carrier_generation_and_recombination

The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation in all frequency ranges, emitting more energy as the frequency increases. By calculating the total amount of radiated energy (i.e., the sum of emissions in all frequency ranges), it can be shown that a black body is likely to release an arbitrarily high amount of energy. This would cause all matter to instantaneously radiate all of its energy until it is near absolute zero – indicating that a new model for the behaviour of black bodies was needed.

https://en.wikipedia.org/wiki/Ultraviolet_catastrophe

In physics, a photon gas is a gas-like collection of photons, which has many of the same properties of a conventional gas like hydrogen or neon – including pressure, temperature, and entropy. The most common example of a photon gas in equilibrium is the black-body radiation.

Thermodynamics of a black body photon gas[edit]

In a classical ideal gas with massive particles, the energy of the particles is distributed according to a Maxwell–Boltzmann distribution. This distribution is established as the particles collide with each other, exchanging energy (and momentum) in the process. In a photon gas, there will also be an equilibrium distribution, but photons do not collide with each other (except under very extreme conditions, see two-photon physics), so the equilibrium distribution must be established by other means. The most common way that an equilibrium distribution is established is by the interaction of the photons with matter. If the photons are absorbed and emitted by the walls of the system containing the photon gas, and the walls are at a particular temperature, then the equilibrium distribution for the photons will be a black-body distribution at that temperature.

A very important difference between a Bose gas (gas of massive bosons) and a photon gas with a black-body distribution is that the number of photons in the system is not conserved. A photon may collide with an electron in the wall, exciting it to a higher energy state, removing a photon from the photon gas. This electron may drop back to its lower level in a series of steps, each one of which releases an individual photon back into the photon gas. Although the sum of the photon energies of the emitted photons are the same as the absorbed photon, the number of emitted photons will vary. It can be shown that, as a result of this lack of constraint on the number of photons in the system, the chemical potential of the photons must be zero for black-body radiation.

The thermodynamics of a black-body photon gas may be derived using quantum mechanical arguments. The derivation yields the spectral energy density u which is the energy per unit volume per unit frequency interval, given by Planck's law:

u(\nu ,T)={\frac {8\pi h\nu ^{3}}{c^{3}}}~{\frac {1}{e^{\frac {h\nu }{kT}}-1}}

where h is Planck's constant, c is the speed of light, ν is the frequency, k is Boltzmann's constant, and T is temperature.

Integrating over frequency and multiplying by the volume, V, gives the internal energy of a black-body photon gas:

U=\left({\frac {8\pi ^{5}k^{4}}{15(hc)^{3}}}\right)VT^{4}

.^[1]

The derivation also yields the (expected) number of photons N:

N=\left({\frac {16\pi k^{3}\zeta (3)}{(hc)^{3}}}\right)VT^{3}

where $\zeta (n)$ is the Riemann zeta function. Note that for a particular temperature, the particle number N varies with the volume in a fixed manner, adjusting itself to have a constant density of photons.

If we note that the equation of state for an ultra-relativistic quantum gas (which inherently describes photons) is given by

U=3PV

then we can combine the above formulas to produce an equation of state that looks much like that of an ideal gas:

PV={\frac {\zeta (4)}{\zeta (3)}}NkT\approx 0.9\,NkT

The following table summarizes the thermodynamic state functions for a black-body photon gas. Notice that the pressure can be written in the form $P=bT^{4}$ , which is independent of volume (b is a constant).

Thermodynamic state functions for a black-body photon gas $(\hbar =h/2\pi )$
	State function (T, V)
Internal energy	$U=\left({\frac {\pi ^{2}k^{4}}{15c^{3}\hbar ^{3}}}\right)\,VT^{4}$
Particle number	$N=\left({\frac {2k^{3}\zeta (3)}{\pi ^{2}c^{3}\hbar ^{3}}}\right)\,VT^{3}$ ^[2]
Chemical potential	$\mu =0\,$
Pressure	$P={\frac {1}{3}}\,{\frac {U}{V}}=\left({\frac {\pi ^{2}k^{4}}{45c^{3}\hbar ^{3}}}\right)\,T^{4}$ ^[1]
Entropy	$S={\frac {4U}{3T}}=\left({\frac {4\pi ^{2}k^{4}}{45c^{3}\hbar ^{3}}}\right)\,VT^{3}$ ^[1]
Enthalpy	$H={\frac {4}{3}}\,U$ ^[1]
Helmholtz free energy	$A=-{\frac {1}{3}}\,U$
Gibbs free energy	$G=0\,$

Isothermal transformations[edit]

As an example of a thermodynamic process involving a photon gas, consider a cylinder with a movable piston. The interior walls of the cylinder are "black" in order that the temperature of the photons can be maintained at a particular temperature. This means that the space inside the cylinder will contain a blackbody-distributed photon gas. Unlike a massive gas, this gas will exist without the photons being introduced from the outside – the walls will provide the photons for the gas. Suppose the piston is pushed all the way into the cylinder so that there is an extremely small volume. The photon gas inside the volume will press against the piston, moving it outward, and in order for the transformation to be isothermic, a counter force of almost the same value will have to be applied to the piston so that the motion of the piston is very slow. This force will be equal to the pressure times the cross sectional area (A ) of the piston. This process can be continued at a constant temperature until the photon gas is at a volume V₀ . Integrating the force over the distance (x ) traveled yields the total work done to create this photon gas at this volume