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Temperatures do not exist at the Nanoscale
Claims that a thermal platform allows nanoscale samples to be tested at extreme temperatures of 4000 K may be safely dismissed as quantum mechanics precludes the atom from conserving heat by an increase in temperature.
Measuring the thermal properties of nanoscale samples at any temperature, let alone temperatures of 4000 K is, to say the least, quite controversial. Nevertheless, a few years ago claims  were made that a thermal test platform was developed that is capable of operating at extreme temperatures as high as 4000 K while allowing local temperatures to be inferred with nanoscale resolution.
The thermal test platform comprises a suspended membrane on which are placed gold NPs and the nanoscale sample of interest, say a MWNT. NP stands for nanoparticle and MWNT for multi-walled nanotube. The NPs act as thermometers that are distributed over the membrane, say Si3N4. Gold NPs (<10 nm diameter) are thought to allow local temperatures of the MWNT to be inferred because they evaporate  immediately upon melting, e.g., 6 nm NPs are considered to melt at 1275 K. Therefore, temperatures at a point on the platform at the instant the evaporating NPs disappear are inferred to be 1275 K, while upon disintegration of the Si3N4 membrane temperatures of 2173 K are assumed. See PR at http://users.soe.ucsc.edu/~
In the test platform, temperatures at times the NPs are not disappearing are inferred from FE simulations assuming the classical transient Fourier equation for heat conduction. FE stands for fine element. The thumbnail (a) shows the FE solution for MWNT temperatures are 300 K everywhere under zero electrical bias voltage conditions. As the bias is increased, the Joule heat raises the temperature (b) and the NP thermometers near the center are the first to evaporate as noted by light colored spots. Higher bias voltage (c) shows evaporation of NPs to move into the surroundings. Eventually, the Si3N4 membrane begins to disintegrate, the temperature corresponding to 2173 K. At extreme temperatures, the MWNT (d) is thought to catastrophically fail at 3200 K.
Claims the thermal platform allows the extreme temperature response of nanoscale samples to be inferred from the evaporation gold NPs may be dismissed by QM. QM stands for quantum mechanics. Yet, the QM restrictions are not limited to the instant thermal platform based on temperatures for the vaporization of NPs, but rather to the wide spread use of classical physics in nanotechnology.
1. Classical Physics and QM In classical physics, the heat capacity of the atom is constant at kT from the macroscale to the nanoscale. Here, k is Boltzmann’s constant and T absolute temperature. The instant thermal platform that infers temperature from the vaporization of gold NPs is therefore consistent with classical physics, but unfortunately not QM. In fact, QM by the Einstein-Hopf relation for the atoms in the NPs and MWNT as harmonic oscillators requires the heat capacity to vanish in nanoscale samples. See Paper “Zero Specific Heat” and Presentation at http://www.nanoqed.org , 2010.
2. Validity of FE Simulations Unlike FE simulations of the macroscale where atoms have heat capacity, QM precludes atoms in NPs and nanoscale samples to have heat capacity and allow the conservation of heat by an increase in temperature. What this means FE including MD simulations of nanoscale samples by the classical modes of heat transfer – convection, radiation, and conduction that depend on temperature have no meaning. MD stands for molecular dynamics. The FE simulations of the thermal platform temperatures based on the Fourier equation are therefore simply not valid. See Ibid, “Validity of Heat Transfer in Molecular Dynamics,” 2013
QED Heat Transfer
At the nanoscale, heat may only be conserved by QED induced EM radiation. QED stands for quantum electrodynamics and EM for electromagnetic. Indeed, absorbed EM energy of any kind in a nanoscale sample cannot be conserved by an increase in temperature because QM requires the atom to have vanishing heat capacity under its own TIR confinement. TIR stands for total internal reflection. Instead, conservation proceeds by the creation of non-thermal EM radiation at the TIR resonant frequency of the nanoscale sample. Lacking heat capacity by QM, QED conserves the Joule heat at the TIR frequency of the NP or MWNT by creating excitons (holon and electron pairs) that charge the nanostructure or upon recombination are emitted to the surroundings as QED radiation. See diverse QED applications at Ibid, 2009 to 2014.
In the thermal platform, QED converts the Joule heat to ionizing EM radiation that charges the atoms in the NPs and MWNT and induces Coulomb repulsion between atoms, thereby ejecting charged atoms to the surroundings. What this means is the Joule heat does not increase the nanoscale sample temperature to vaporize the gold NPs. Instead, the NPs vaporize by a Coulomb explosion from the ionization of atoms within the NPs. Simply put, Joule heat in nanoscale samples does not increase temperature, but rather only induces Coulomb repulsion.
1. QM precludes the thermal platform from the evaluation of the extreme temperature response of nanoscale MWNT samples by vaporization of NP thermometers. Temperature changes of any magnitude simply do not occur in nanoscale samples.
2. Instead, QED conserves the Joule heat dissipated in the NP thermometers by the creation of charge from EM radiation that ionizes the gold atoms or is lost to the surroundings. Ionized atoms undergo Coulomb repulsion inducing them to be ejected to the surroundings that has been mis-interpreted as vaporization at high temperatures. Indeed, the claim of measuring extreme temperatures may be safely dismissed as the observed disappearance of NPs has nothing to do with temperature.
3. FE simulations based on classical physics of the thermal platform are not valid at the nanoscale. Instead, the heat transfer may be determined by QED induced radiation
 G. E. Begtrup, et al., “Probing Nanoscale Solids at Thermal Extremes,” PRL 99, 155901 (2007).
 K. Koga, et al, “Size and Temperature Dependent Structural Transitions in Gold Nanoparticles,”