Tag Archives: molecular dynamics

Materials At The Nanoscale Have Zero Specific Heat

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 Background
Specific heat is thought to be an intensive thermophysical property independent of the amount of the substance. Given the amount of the substance in a body is proportional to its volume, specific heat should therefore be independent of whether the body dimensions are macroscopic or nanoscopic. In contrast, specific heat that depends on the amount of the substance is an extensive property dependent on the dimensions of the body.  See http://en.wikipedia.org/wiki/Specific_heat_capacity

 Classical Specific Heat at the Nanoscale  Currently, specific heat at the nanoscale is considered an intensive property having the same value as for macroscopic bodies. The Debye and Einstein macroscopic theories of specific heat including modifications thereof by Raman are generally assumed in simulating heat transfer in nanostructures. See Thumbnail of “Macroscopic Specific Heat at the Nanoscale?”. What this means is the classical oscillators of statistical mechanics from macroscopic bodies all having the same kT energy are used to model specific heat at the nanoscale. See Ibid.

Specific Heat by Quantum Mechanics Contrarily, quantum mechanics (QM) embodied in the Einstein-Hopf relation for the harmonic oscillator shows the QM states do not have the same kT energy at the nanoscale. At ambient temperature, the average Planck energy of QM states is kT only at thermal wavelengths greater than about 50 microns while at shorter wavelengths is less than kT and vanishes for nanostructures at submicron wavelengths.  See Paper and Presentation at “Zero Specific Heat”, http://www.nanoqed.org , 2010.

Since the Planck energy at a given wavelength is the amount of thermal energy that can be stored in the QM oscillator, and since the only thermal wavelengths that can fit into nanostructures are submicron, QM requires zero specific heat capacity at the nanoscale, the consequence of which is absorbed heat cannot be conserved in nanostructures by an increase in temperature. Conservation may only proceed by the QED induced frequency up-conversion of absorbed heat to non-thermal EM radiation at the fundamental EM confinement frequency of the nanostructure, typically in the UV and beyond. The EM confinement is quasi-bound allowing leakage of QED induced radiation from the nanostructure to be absorbed in the macroscopic surroundings. See Ibid.

But QED emission in the UV and beyond from nanostructures is not readily observed – even by standard photomultipliers because of the UV cut-off, and therefore heat balances of nanostructures do not include QED emissions as heat losses. Hence, thermal conductivity is inferred to be reduced from that of the bulk to be consistent with the measured temperature difference across the body, e.g., as in thin films. If QED emissions are included in heat losses, the bulk conductivity need not be reduced for consistency with temperature differences thereby precluding any modification of Fourier’s theory of heat conduction by the Boltzmann transport equation (BTE). See Ibid.  

 Molecular Dynamics and Periodic Boundaries  Molecular Dynamics (MD) describes the classical solution of atomic motion based on Newton’s equations. To determine bulk transport properties, there are no QM restrictions on kT energy of atoms, i.e., atoms are assumed to have kT energy because the MD solution for the bulk is obtained by imposing periodic boundary conditions on the computational box. Historically, Monte Carlo (MC) preceded MD simulations, however. MC simulations of spherical particles in a submicron computational square with periodic boundaries were used to determine the 2D virial coefficients for the PVT equation of state. See Metropolis et al. Ibid.For a discrete nanostructure, periodic boundaries do not apply, and therefore the atoms in the nanostructure are subject to QM restrictions of zero kT energy.

Heat transfer of discrete nanostructures which are unambiguously not periodic is generally simulated by MD on the invalid assumption the atoms have kT energy. See e.g., http://pubs.acs.org/doi/full/10.1021/ct7002594  Extending specific heat from macroscopic samples to the nanoscale is just as invalid as extending the Dulong-Petit law for specific heat at ambient temperature to low temperatures about 200 years ago. Nevertheless, MD simulations of nanostructures today are proudly displayed in the belief they provide precise atomistic explanations of conduction heat transfer when in fact they are not valid because the simulations are performed on the assumption the atoms have finite kT energy. See Ibid, and http://www.scienceblog.com/cms/blog/8209-quantum-mechanics-questions-molecular-dynamics-submicron-structures-25639.html

Conclusions

1. QM requires zero specific heat capacity at the nanoscale be specified as a new thermophysical property of all materials.

2. The classification of specific heat as an intensive thermophysical property of a body should be changed to an extensive property depending on the dimensions of the body.

3. Nanoscale heat transfer based on the assumption of macroscopic specific heat is likely to produce unphysical results, e.g., reduced thermal conductivity in thin films.

4.  There is no need for the BTE to determine the thermal conductivity in thin films as bulk conductivity may be assumed without any loss in accuracy.

5. Macroscopic Debye and Einstein theories should be revised to include zero specific heat at the nanoscale.

6. Lacking specific heat at the nanoscale, absorbed EM energy is not conserved by an increase in temperature, but rather by the emission of non-thermal QED induced EM radiation.

7. MD and MC simulations of bulk thermal conductivity based on full kT energy of atoms in submicron computational boxes under periodic boundary conditions are consistent with QM.

8. Zero specific heat is required for atoms in MD and MC simulations of discrete nanostructures without periodic constraints.

9. Absorbed EM energy in discrete nanostructures may be a priori assumed to be emitted as high frequency EM radiation that is absorbed in the macroscopic surroundings, thereby obviating any need to perform MD and MC simulations of the nanostructure itself.

Nanocars are powered by electrostatic forces from QED induced charges

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Nanocars comprising fullerene spherical wheels on hydrocarbon axles are shown to move on substrates by electrostatic forces from charges produced by quantum electrodynamics (QED)

Background
Nanocars evolved from research that began over a decade ago. At the IBM Zurich Research Laboratory, synthetic molecules (S-molecules) on a metal substrate were moved in a controlled and repeatable manner by pushing them with the tip of a scanning tunneling microscope (STM). See http://domino.watson.ibm.com/comm/wwwr_thinkresearch.nsf … .

The S-molecules included an organic molecule called porphyrin comprising a ring of atoms about 1.5 nanometers in diameter with a metal atom at its center. Groups of hydrocarbons were added to the porphyrin to provide four leg supports. The function of the legs was thought to allow the S-molecule to grip the surface to stabilize random thermal motion. Friction between the legs and the substrate could not have been significant because upon nudging with the STM tip the S-molecules appeared as though they were on rollers.

Quantum Mechanics Explanation
The S-molecule motion may be explained by quantum mechanics (QM). The Einstein-Hopf relationship for the QM harmonic oscillator shows the thermal kT energy of an atom at ambient temperature resides in the far infrared (FIR) beyond 50 microns. Here, k is Boltzmann’s constant and T is absolute temperature. But the S-molecule by its size excludes all thermal radiation beyond a few nanometers, and therefore lacks the heat capacity to conserve the FIR heat absorbed from the contact of the legs with the substrate by an increase in temperature. Upon contact of the legs with the substrate, the S-molecule becomes a part of a macroscopic body that by QM is allowed to have kT energy. But in moving, the S-molecule breaks contact to be momentarily isolated from the substrate, and therefore has excess kT energy above the vanishing small amount allowed by QM.

Lacking heat capacity, the S-molecule cannot conserve the excess kT energy by an increase in temperature. Conservation therefore may only proceed by the QED induced frequency up-conversion of the excess kT energy in the FIR to the electromagnetic (EM) confinement frequency of the S-molecule, which at ultraviolet (UV) levels and beyond has the Planck energy to charge the S-molecule by the photoelectric effect.

The QED induced charge only produces momentary electrostatic interactions. Nevertheless, the S-molecule is held to the substrate by momentary electrostatic attraction instead of by gripping as initially thought. Lateral motion depends on the momentary electrostatic interaction with its neighbors. In a random arrangement of S-molecules, the electrostatic interactions are not symmetric and on that basis alone may initiate motion. Moreover, lateral motion over the substrate occurs by intermittent stick-slip, but small friction at contacts makes it appear as though the S-molecule is on rollers. Regardless, contact neutralizes the charge on the S-molecule and allows the kT energy to be reacquired from the substrate to allow subsequent breaking of contact to produce QED charge. During stick-slip motion, the intermittent QED induced charge occurs very rapidly and may be difficult to detect.

Nanocars
Today, nanocars moving on substrates are more complex than the S-molecules, but the QED charging is the same. Currently, many research groups are engaged in nanocar research typified by Rice University. See http://news.cnet.com/Here-come-the-nanocars/2100-11395_3 ….

In QED charging, nanocars like S-molecules are powered by converting EM energy into mechanical motion. The EM energy may take various forms of heating including light, thermal, Joule, and electron beams. Indeed, nanocars have been shown to move by simply heating the substrate, the form of heat being the same thermal kT energy driving the earlier S-molecules. In effect, nanocars act as FIR to higher frequency up-conversion devices that charge the nanocars by producing momentary electrostatic repulsive forces that produce the observed nanocar motions. Similar arguments allow QED charges to explain the motions of molecular motors under Joule and electron beam heating. See http://www.nanoqed.org at “Nanocars by Quantum Mechanics”, 2010.

Molecular Dynamics
Unfortunately, the QED charging by which thermal kT energy is converted into powering the nanocar is not included in a conventional MD solution that implicitly assumes atoms have kT energy at the nanoscale. Valid MD simulations in heat transfer need to specify vanishing kT energy in the MD computational algorithms, and if so included would give isothermal temperature solutions. The invalidity of MD in heat transfer at the nanoscale is widespread, e.g., in tribology, see http://www.scienceblog.com/cms/blog/8209-quantum-mechanics-questions-molecular-dynamics-submicron-structures-25639.html ; whereas, in nanocars, see http://pubs.acs.org/doi/full/10.1021/ct7002594

MD is not needed for heat transfer at the nanoscale because temperature solutions are, a priori known to be isothermal. However, QED induced charging in nanostructures can and should be included in MD simulations of dynamic response, at least within the restrictions of Newton’s equations.

Conclusions

1. Nanostructures including S-molecules, nanocars, CNT motors and the like act as frequency up-conversion devices that are charged from QED radiation by the photoelectric effect, thereby allowing pair-wise interactions by momentary electrostatic repulsion.

2. MD simulations of heat transfer in nanocars are precluded by QM. At ambient temperature, the thermal heat capacity resides in the FIR beyond 50 microns, and therefore nanocars by their size exclude the heat capacity necessary for heat transfer. MD simulations of heat transfer in nanostructures are simply meaningless.

3. Unlike heat transfer, MD simulations are valid if directed to deriving the dynamic response of nanostructures on substrates under momentary QED induced charges.

Quantum Mechanics Questions the Molecular Dynamics of Submicron Structures

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In the 1950s, Metropolis and Teller pioneered molecular dynamics (MD) as a method to derive the thermodynamic and transport properties of bulk molecular liquids. Submicron ensembles comprising a few hundred atoms with periodic boundary conditions were used to derive the bulk liquid properties. Even though the ensembles were submicron, the periodic boundary conditions allowed the heat capacity of the atom at wavelengths longer than the dimensions of the ensemble to be included in the MD simulations.

Today, MD simulations have been extended almost entirely to discrete submicron structures. See WTC IV The implicit assumption in the later MD simulations was there is no difference between the thermal heat capacity of the atoms in the discrete submicron structures and those ensembles in MD simulations with periodic boundary conditions.

However, quantum mechanics (QM) as embodied in the Einstein-Hopf relation shows the thermal heat capacity of the atom as given by the Planck energy of the harmonic oscillator depends on dispersion with wavelength. At ambient temperature, most of the thermal heat capacity of the atom is available at wavelengths > 100 microns where the thermal kT energy is about 25.8 meV. But the thermal emission from atoms in submicron structures is confined to wavelengths < 1 micron, and therefore excludes almost all of the heat capacity of the atom. Alternatively, atoms in discrete submicron structures in MD simulations lack the heat capacity necessary to conserve absorbed EM energy by an increase in temperature.

MD simulations of discrete submicron ensembles may proceed as usual provided the QM restriction on the heat capacity of the atoms is properly simulated. One such method is the theory of QED induced radiations. See QED radiations Lacking the heat capacity to conserve absorbed EM energy by an increase in temperature, the absorbed EM energy is frequency up or down-converted by QED to the EM confinement frequency of the submicron structure. Subsequently, the absorbed EM energy is conserved by the emission of non-thermal EM radiation.