Quotations 

 Thought for us

Penetrating so many secrets, we cease to believe in the unknowable.

But there it sits nevertheless, calmly licking its chops.

                                                                              

                                                                                        H L Mencken

Validity of Molecular Dynamics in Heat Transfer 

Molecular Dynamics (MD) is commonly used in computational heat transfer to determine the thermal response of nanostructures. MD is based on classical statistical mechanics with the thermal energy of the atom related to its momentum by the equipartition theorem. Momenta of atoms in an ensemble are determined by solving Newton’s equations with inter-atomic forces derived from Lennard-Jones potentials.  Statistical mechanics implicitly assumes the atom has heat capacity as otherwise the temperature of the atom cannot be related to its thermal energy.  Moreover, statistical mechanics assumes atoms in nanostructures have the same heat capacity as at the macroscale.

For bulk materials, MD heat transfer based on atoms in submicron computation boxes having macroscopic heat capacity is valid provided periodic boundary conditions are imposed in the MD solution. The statistical mechanics requirement of macroscopic heat capacity is satisfied because the atoms in submicron boxes under periodic boundary conditions are equivalent to atoms in the bulk that do indeed have heat capacity.

In contrast, quantum mechanics (QM) precludes atoms in submicron nanostructures from having the capacity to conserve heat by an increase in temperature.  Nevertheless, MD simulations are commonly performed by assuming atoms in discrete or non-periodic nanostructures have heat capacity. Although consistent with statistical mechanics, MD of discrete nanostructures is unequivocally invalid by QM. By QM, atoms in discrete nanostructures lacking heat capacity cannot conserve heat by an increase in temperature, and therefore Fourier’s heat conduction equation that depends on temperature has no meaning. Instead, conservation in discrete nanostructures proceeds by the creation of QED induced non-thermal EM radiation that charges the nanostructure by the photoelectric effect. QED stands for quantum electrodynamics and EM for electrodynamics. Examples of MD simulations that by QM are valid or invalid are presented and recommendations made for how MD heat transfer simulations of discrete nanostructures may be made consistent with QM.  See Paper and Press Release
 

QED Induced Heat Transfer 

 Over the past century, Fourier’s transient heat conduction equation including the notions of heat capacity of Lavosier and Laplace .have served well in our understanding heat transfer in macroscopic systems. Modern day heat transfer assumes phonons are the heat carriers solids based on theories formulated by Einstein and Debye at the time systems were macroscopic. Today, the heat transfer systems are no longer typically macroscopic, but include the nanoscale. Macroscopic heat capacity in Fourier’s equation is routinely applied in heat transfer simulations at the nanoscale, the consequence of which has led to unphysical results, e.g. standard mixing rules are violated for nanofluids; thermal conductivity of thin films is reduced depending on thickness; the memristor is thought necessary to complete symmetry to the circuit elements of resistor, capacitor, and inductor; molecular polymers in nanoscale electronics have thermal conductivity; unlikely molecular signaling by the lock and key mechanism olfaction, and so forth.
 
Unphysical observations from application of classical heat transfer to nanostructures may be traced back to Einstein’s and Debye’s theories of heat capacity based on phonons. In contrast, nanoscale heat transfer based on QED by Planck’s photons avoids the unphysical, i.e. thin film conductivity remains at bulk as thickness decreases, nanofluids obey mixing rules, the memristor is a quantum size effect, molecular conductivity is meaningless, olfaction reduces to signaling of the odorant molecule by its unique vibration spectrum, etc. QED stands for quantum electrodynamics. Supporting QED physics is based on quantum mechanics from the Einstein-Hopf relation for the harmonic oscillator in terms of temperature and EM confinement. Both Einstein and Debye phonon theories based on classical statistical mechanics permit the atom at the nanoscale to have the heat capacity necessary to conserve absorbed EM energy by an increase in temperature. But quantum mechanics requires the heat capacity to vanish thereby precluding conservation by a temperature increase at the nanoscale. Instead, conservation proceeds by the creation of non-thermal photons inside the nanostructure by the QED induced frequency up-conversion of absorbed EM energy to the TIR confinement of the nanostructure. TIR stands for total internal reflection. The TIR confinement of the QED photons occurs because the high surface to volume ratio of nanostructures naturally concentrates the absorbed EM energy in the TIR mode, thereby effectively supporting photon confinement. The QED photons may excite phonons, but the absorbed EM energy is primarily conserved by the prompt creation of QED photons that may be converted to electric charge by Einstein‘s photoelectric effect, or lost to the surroundings. Examples of QED physics are presented to illustrate the fact the QED physics extends far beyond nanoscale heat transfer. See Press Release and Presentation

Invalidity of Near-Field Heat Transfer

Over the past decade, extensive research in near-field heat transfer has suggested the EM radiation at submicron distances < 100 nm from a surface is orders of magnitude larger than the limit given by Planck's theory of BB radiation. BB stands for blackbody. But Planck never stated his theory set an upper limit on radiative heat transfer, although he was surely aware bringing BB surfaces close together does not increase their thermal energy. 

However, experimental support for near-field enhancement is limited to micron and not nanoscale gaps, and therefore support for claims that near-field enhancement in submicron gaps exceeds the  Planck limit relies almost entirely on classical EM analysis of evanescent waves by the Maxwell equations.But near-field enhancement based on Maxwell’s equations is refuted because temperature fluctuations in the surfaces of nanoscale gaps as required by the FDT are precluded by QM. FDT stands for the fluctuation-dissipation theorem and QM for quantum mechanics.

The FDT that relates the strength of the oscillations of the dipoles inside a body to the temperature fluctuations cannot be assumed in the solution of Maxwell’s equations because QM precludes atoms in the surfaces of nanoscale gaps to respond to absorption of heat by changes in temperature. Solutions of Maxwell’s equations for  by evanescent waves showing Planck theory is exceeded are unphysical because the FDT is no longer valid at the nanoscale.

Given that the thermal energy of a body is not increased by bringing it close to another body, near–field enhancement by tunneling of evanescent waves simply does not exist. Instead, conservation of EM energy proceeds by QED induced heat transfer, and therefore Planck’s theory is indeed an upper bound to near-field radiative heat transfer at the nanoscale.   See Press Release, Paper, and Presentation

Johnson-Nyquist Noise 

 The validity of Maxwell's solutions in near-field heat transfer by tunneling of evanescent waves through nanoscale gaps is of great importance in the hope a breakthrough of a large enhancement in energy harvesting can be realized. However, atoms in the surface of nanoscale gaps are under high EM confinement that by QM are precluded from having the heat capacity necessary to conserve heat flow by a change in temperature, and therefore the temperature fluctuations required by the FDT do not occur in nanoscale gaps suggesting solutions of Maxwell's equations that rely on temperature fluctuations are invalid. See above "Invalidiity of Near-Field Heat Transfer," 2012.

One way of assessing whether the FDT is satisfied is to estimate the effect of EM confinement on the strength of the Johnson-Nyquist (J-N) noise signals from a hypothetical resistor in the surface atoms of nanoscale gaps. See Press Release and Paper.

The  J-N signals of V(f) under EM frequencies > 3E+15 Hz ( Gap < 50 nm) show the noise is at least 100 orders of magnitude less than that of a surface free of EM confinement. See above Plot. Since Maxwell solutions require gaps of about 10 nm to achieve enhancements consistent with breakthorughs in energy havesting, the tunneling of evanescent waves through nanoscale gaps is likely to be difficult to achieve in practice.  

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