Recent claims based on classical heat transfer that nanotrumpets produce sound from temperature fluctuations caused by Joule heating in passing electrical current through thin films are refuted by quantum mechanics.
Recently, the journal Nature published an article entitled Nanotherm Trumpets that claimed sound was produced from temperature fluctuations in passing electrical current through an array of nanometer thick aluminum films. The claim is based on classical heat transfer theory that assumes films under Joule heating increase in temperature to heat the surrounding air and produce the pressure in propagating the sound. High thermal conductivity of the films is thought to allow the Joule heat to be lost to the substrate, and therefore not contribute to the large temperature fluctuations necessary to produce sound. To avoid loss of Joule heat, reductions in bulk thermal conductivity are viewed as an important feature of the Nanotrumpets. Required reductions in thin film thermal conductivity are supported by scattering of electrons in the Boltzmann transport equation (BTE). See “Nature Article” under http://www.nanoqed.org, “Thermophone” at “Nanotrumpet Update”, 2010.
Classical Heat and QM Transfer
Quantum mechanics (QM) trumps the classical heat transfer theory claims that sound is produced from temperature fluctuations in nanometer thick films. QM precludes any fluctuations in the film temperatures because the specific heat given by the heat capacity of the atom vanishes in submicron films, and therefore there can be no heat flow through the thin film. Without heat flow, bulk conductivity may be retained in temperature solutions by Fourier’s heat conduction theory yielding isothermal temperatures without gradients. Hence, there are no temperature fluctuations in the film to heat the surrounding air and produce sound. Conversely, sound by QM is produced without temperature fluctuations by conserving the Joule heat by the emission of non-thermal electromagnetic (EM) radiation from the surfaces of the thin film. Pressure fluctuations producing the sound are caused by the absorption of the EM radiation in the surrounding air. The validity of classical heat transfer theory in thin films having submicron thicknesses was the subject of an earlier critique of the BTE. See http://www.prlog.org/10321896-thermophones-produce-sound…
QED induced EM Radiation
In general, QM precludes nanostructures of any form from conserving absorbed EM energy by an increase in temperature. See http://www.nanoqed.org, 2009 and 2010. Instead, the absorbed EM energy is conserved by creating photons inside the nanostructure at its fundamental EM confinement frequency, the process called QED induced EM radiation. QED stands for quantum electrodynamics. The QED process is consistent with QM that asserts photons of wavelength L are spontaneously created upon supplying EM energy U to a QM box with walls separated by L/2. It is important to emphasize the QED photons are created inside the solid nanostructure where the velocity c of light is reduced by the refractive index n of the solid. For a thin film, the QED photons created in the thickness direction are under EM confinement at wavelength L = 2nT, where T is its thickness. The number N of QED photons created having Planck energy E is N = U/E, where E = hc/2nT and h is Planck’s constant. See Ibid.
With regard to the verification of QED radiations, the EM emission may be difficult to detect. Submicron thin films create QED photons having Planck energies in the ultraviolet (UV) and beyond, and therefore are beyond the typical cut-off of most photomultipliers. But verification is possible with thicker films, e.g., QED radiation in the near infrared (NIR) is emitted from films having supramicron thicknesses. Since Joule heat is typically low frequency EM radiation in the far infrared (FIR), thin films may be considered frequency up-conversion devices converting FIR to EM radiation from the NIR to the UV or beyond.
Comments on Nanotrumpet Claims
Reduced Conductivity Requirement The Nature article cites a recent paper by Niskanen et al. showing an array of 3 micron wide x 30 nm thick x 200 micron long aluminum wires (sic films) suspended above a silicon substrate by an air gap g of 1-2 microns. The claim that reducing the bulk conductivity Kal of aluminum is required to reduce heat loss to the substrate is unlikely because the air film insulates the film from the substrate. In fact, the thermal resistance R between the outer film surface and the substrate is the sum of R1 and R2, where R1 = T / Kal is the resistance of the thin aluminum film and R2 = g / Kair that of the air gap. For bulk aluminum and air, Kal = 240 W/mK wile air has Kair = 0.026 W/mK. The R1 and R2 resistances are then 1.25e-10 and 5e-5 sq-m K/W. Hence, the air gap and not the aluminum film limit the heat loss to the substrate. Even if the bulk conductivity of aluminum is reduced to 70W/mK as claimed by BTE theory, the resistance of the air film still controls the heat loss to the substrate. The conductivity of the thin film is therefore inconsequential to the sound produced by the Nanotrumpet.
BTE and Reduced Conductivity In support of the claim that the BTE reduces the bulk conductivity of aluminum, thereby reducing the heat loss to the substrate and enhancing the sound, the Nature article cites the BTE paper by Jin et al. that claims reductions in bulk conductivity of aluminum to 70 W/mK for a 30 nm thick film is close to that found in experiments. But this claim is unlikely because the reduced conductivities were computed based on an assumed 10K temperature difference across the thin film which is precluded by QM. Isothermally there is no temperature difference across the film, and therefore the BTE is consistent with QM by predicting no reduction in bulk conductivity. The BTE is therefore also inconsequential in producing sound from the Nanotrumpet.
1. Classical heat transfer that includes finite specific heat in thin films is not applicable to Nanotrumpets. Sound cannot be produced by temperature fluctuations that are precluded by QM.
2. Instead of producing temperature fluctuations, QM allows the Nanotrumpets to conserve the Joule heat by the emission of EM radiation that upon absorption in the surrounding air produces the sound.