Validity of Molecular Dynamics Heat Transfer in Tribochemistry?

Nov. 2, 2011 - PRLog -- Introduction

The 2011 Tribochemistry Conference was held in Hagi Japan prior to the International Tribology Conference in Hiroshima, both of which included discussions of heat transfer simulations by molecular dynamics (MD).  Historically, MD simulations of the bulk were first performed in submicron computation boxes taken from the bulk for analysis. By imposing periodic boundary conditions (PBC) on the computation box, the MD simulations of the bulk [1]  are VALID because the atoms in the MD computation boxes by classical physics have the same thermal heat capacity as those in the bulk being simulated. Indeed, MD based on classical physics assumes atoms have thermal heat capacity or kT energy, i.e., kT > 0, where k is Boltzmann’s constant and T absolute temperature.

Problem

Unlike MD simulations of the bulk, Tribochemistry is the study of rubbing induced chemical reactions in the submicron film between sliding surfaces. Rubbing is unambiguously not periodic, and therefore PBC are not applicable. Nevertheless, MD simulations were presented for rubbing comprising discrete submicron portions of the surfaces and film, the atoms of which assumed to have heat capacity. However, quantum mechanics (QM) requires the atoms in discrete submicron groups of atoms collectively called nanostructures to have zero kT energy, i.e., kT = 0.  What this suggests is QM invalidates MD simulations of heat transfer in Tribochemistry.  

Background
         
QM by the Einstein-Hopf relation for the harmonic oscillator limits the kT energy of the atom depending on temperature T and wavelength w as shown in the thumbnail. Instead of wavelength w, the harmonic oscillator may also be described by frequency f = c/w, where c is the speed of light. For nanostructures with w < 1 micron, the atom is noted having kT = 0. In contrast, SM, MD, and FE simulations based on classical physics assume atoms have kT > 0. SM stands for statistical mechanics and FE for finite element.    

The physical meaning of kT is explained [2] by Feynman. To wit: “When Sir James Jeans was worrying about the specific heats of gases, he noted that motions which have high frequency are “frozen out” as the temperature goes too low.  That is, if the temperature T is too low, if the frequency f too high, the oscillators do not have kT of energy on average. ..kT is the mean energy of the  harmonic oscillator of frequency f at temperature T.  Classically, this is kT, but experimentally, no!-not when the temperature is too low or the oscillator frequency is too high.” Paraphrasing Feynman: At ambient temperature, high oscillator frequency f corresponds to wavelengths w < 1 micron in the thumbnail.
What this means is atoms in discrete nanostructures lack the heat capacity to conserve absorbed EM energy by an increase in temperature. Instead, conservation is proposed [1] to occur by the creation of QED photons that drive chemical reactions by photolysis or by Einstein’s photoelectric effect electrically charge the nanostructure. EM stands for electromagnetic and QED for quantum electrodynamics.  

Discussion

Comments on the presentation of [1] at “Tribochemistry Hagi 2011” are answered as follows.

Phonons as Heat Carriers Phonons were stated to be the source of heat capacity at the nanoscale. However, EM energy conservation is satisfied by QED emission well before the phonons can thermalize the nanostructure. One should remember that QED emission travels at the speed of light compared to phonons moving at acoustic velocities. Indeed, the QED photons conserve absorbed EM energy before the phonons even “think” of moving, e.g., the erroneous reductions in thermal conductivity in thin films based on phonon scattering occurs because QED radiation was excluded from the heat balance. If included, heat flow by conduction does not exist, and therefore thermal conductivity is not even applicable. Hence, reduced conductivity is meaningless as the conductivity simply remains at bulk.

Experiments on Heat Capacity of Nanoparticles Experiments [3,4] of NPs comprising clusters of 70 - 200 sodium atoms that show melting and evaporation upon heating by laser photons question the QM requirement that NPs do not increase in temperature. It should be noted, however, the temperature of the NPs was not measured because of their small size. Instead, the heat capacity was inferred by heating the NPs two ways: (1) by supplying energy thermally and (2) by heating with photons from the laser. That the same internal energy is reached was monitored with a mass spectrometer to assure the same number of atoms are ejected. The experimenters admit [4] the photon-induced excitation is assumed to relax completely to thermal equilibrium before the atoms are ejected, but this was thought unimportant because different photon energies gave the same results.

However, the QED radiation emitted by the NP was not included in the heat balance before the atoms are ejected. See above “Phonons as Heat Carriers”, i.e., the laser photons are conserved by prompt QED emission well before thermal equilibrium is reached irrespective of the photon energy. What this means is the atoms ejected during laser excitation had nothing to do with photons absorbed by the NP, but rather can only be an artifact of the experiment. Simply put, the NPs do not increase in temperature by laser photon absorption, and therefore the atoms in the NPs have kT = 0 consistent with QM.  

Conclusions

1. MD simulations of discrete nanostructures in Tribochemistry and Tribology are invalid by QM. MD validity by QM is restricted to PBC.

2. The source of Tribochemistry is QED photons created in NPs that form by rubbing surfaces together. Chemical reactions in the film occur by photolysis. Charged ions are produced.

3. In Tribology, rubbing produces NPs not electrons. The NPs produce the QED photons that create the electrons. The electrons may then produce UV photons.

4. Redshift of galaxy photons occurs in cosmic dust NPs without any Universe expansion.

References
[1] T. Prevenslik, “The Validity of Heat Transfer by Molecular Dynamics," See “Tribochemistry Hagi 2011,” at  http://www.nanoqed.org
[2] R. P. Feynman, et al., See Lectures in Physics, The Brownian Movement, Equipartition and the quantum oscillator, Vol. 1, Chp. 41-3 (1971)
[3] M. Schmidt, et al., “Irregular variations in the melting point of size-selected atomic clusters,” See http://www.uni-ulm.de/iok/bernhardt/Teaching/ClusterWS07-...
[4]  M. Schmidt, et al., “Experimental determination of the melting point and heat capacity for a free cluster of 139 sodium atoms. See  http://cluster.physik.uni-freiburg.de/lit/preprints/p99_1...

# # #

Classically, thermal EM radiation conserves heat by an increase in temperature. But at the nanoscale, temperature increases are forbidden by quantum mechanics. QED radiation explains how heat is conserved by the emission of nonthermal EM radiation.