A Review of Near-Field Radiative Heat Transfer

June 6, 2012 - PRLog -- Background
In 2011, the validity of claims that near-field heat transfer by evanescent waves exceeded Planck’s BB radiation by 3-4 orders of magnitude were openly questioned. Maxwell solutions for evanescent waves and experimental data were shown to support the argument that the Stefan-Boltzmann (S-B) equation is still valid in the near field.  In summary:

A. Maxwell equations were considered invalid because QM by negating the heat capacity of the atom under EM confinement in surfaces of nanoscale gaps precludes the temperature fluctuations necessary to satisfy the FDT. QM stands for quantum mechanics, EM for electromagnetic, and FDT for the fluctuation dissipation theorem.

B. Experiments of nanoscale heat transfer between (1) flat surfaces, and (2) a sphere and a flat surface were considered invalid because the temperature of surface atoms in the gap were not measured, but rather assumed to be at bulk temperature. In fact, QM requires the heat capacity of surface atoms to vanish, the consequence of which is the temperature difference across the gap also vanishes.
 
See PR at http://www.prlog.org/11759939-invalidity-of-near-field-he...

NANORAD 2012
The International Workshop on Nano-Micro Thermal Radiation held on 23-25, May 2012 at Matsushima allowed researchers to present their work on near-field heat transfer. Supporters of the near-field radiative transfer by evanescent waves presented arguments of the status quo.  In contrast, the argument was made that QED conserves the BB radiation that otherwise is excluded from near-field gaps by creating standing wave photons that tunnel S-B radiation across the gap.  QED stands for quantum electrodynamics. In this way, Planck’s BB radiation is still valid in the near-field. See PPT presentation at  NANORAD 2012 “Invalidity of Near Field Heat Transfer,”  http://www.nanoqed.org/, 2012.

Discussion

Certainly, Planck’s theory [1] of BB radiation by the Einstein-Hopf relation for the QM oscillator giving the dispersion of thermal kT energy of the atom with wavelength (or frequency) at temperature that has stood the test of time for over a century is not the problem.

The problem is near-field heat transfer based on classical physics is not valid at the nanoscale.

Absent other surfaces, atoms on a surface freely emit BB radiation. However, if surfaces are brought within a close distance d of each other, the BB radiation is no longer freely emitted and the atom in the Einstein-Hopf description is said to be under EM confinement at a wavelength W = 2d. Indeed, the near-field is distinguished from the far-field in this way, i.e., the near-field is defined for gaps d < W/2 , where W is the wavelength of the BB radiation.  

Under EM confinement at wavelength W, classical physics allows the atom to have the same kT energy in the near-field as in the far-field, but not QM. In fact, the thermal kT energy of the atom given by Einstein-Hopf for the QM oscillator vanishes for W < 1 micron.  Lacking thermal kT energy, the atom by QM simply does not have the heat capacity to conserve absorbed EM energy in gap surfaces by an increase in temperature. What this means is solutions of Maxwell’s equations [3,4] in the near-field are not valid because the FDT cannot be satisfied, i.e., dipole oscillations in nanoscale gap surfaces have nothing to do with temperature. The fact that QM has been around for over a century begs the question how the FDT formulated from classical physics by Rytov [2] for near-field heat transfer by evanescent waves has survived to the present day?

Similarly, QM questions the validity of experiments in support of near-field heat transfer. In radiative heat transfer between: (1) flat surfaces [3] , and (2) a sphere and a flat surface [3,4], the temperatures of gap surfaces are not measured. Instead, bulk temperatures removed from the gap are assumed for respective gap surfaces. Since measuring temperatures in nanoscale gaps is next to impossible, heat transfer analysis is performed. However, classical heat transfer analysis is also questionable because QM that accounts for the lack of heat capacity in surface atoms as well as other submicron regions adjacent the gap is not used in the heat transfer simulations.

AFM measurement [3] of heat transfer between a sphere and a flat surface is ambiguous.  The laser is not directed onto the sphere, but rather on the edge of the cantilever tip.  Therefore, the magnitude of the heat absorbed causing the cantilever bending cannot be accurately calculated. The heat absorbed in [4] is not ambiguous because the hot surface is placed directly adjacent the sphere. Regardless, QM requires some of the heat absorbed to be loss as QED radiation to the surroundings. Neither [3] or[4] consider the QM heat loss, although  both cite reduced heat transfer vs. gap curves as the sphere at the tip of the cantilever is reduced in size.

Barnes et al. [5] describe the AFM cantilever calorimeter that has been adopted as the standard in heat transfer between a sphere and a flat surface. Again, QM is excluded from the heat transfer analysis, e.g., the equipartition theorem of classical physics is used instead of QM. High sensitivity of heat flux is claimed because of the overall micro size of the sensor, but this is exactly what causes QM to trump classical physics in heat transfer at the nanoscale. Indeed, the cantilever thickness is 0.6 microns, and therefore QM requires some QED radiation to be lost to the surroundings. In fact, Barnes et al. admit a loss of sensitivity consistent with “there being some other heat loss mechanism.”  Regardless, the precise amount of heat causing the cantilever deflection cannot be accurately calculated, although claims [3-5]  to the contrary are made.

Temperature measurements of gap surfaces would resolve the issue for imprecise estimates of absorbed heat, but cannot be made. Therefore, near-field heat transfer by evanescent waves requires testing of prototypes before the promise of near–field radiative heat transfer may be known.  

Conclusions

The problems with near-field heat transfer by evanescent waves may be avoided with QED induced standing waves as the tunneling mechanism. The heat flowing by conduction between bulk hot and cold temperatures is conserved by QED inducing the surface atoms to create standing wave photons having Planck energy E = hc/W, where h is Planck’s constant and c is the speed of light.  A single QED photon therefore transfers EM power across the gap d by q = E*c/W, the number N of QED photons are determined from the S-B power Q = sigma*A(T_H⁴ –T_C⁴) by N = Q/q.  QED does not enhance near-field heat transfer above S-B, but allows broadband BB radiation to be converted to EM radiation at a single frequency. In TPV cells, all of the BB radiation emitted from a hot surface may be converted by QED to standing wave photons that are tuned to the wavelength of the peak cell sensitivity, e.g.,a TPV cell having a peak sensitivity at 0.67 eV or W = 1.85 microns absorbs all BB radiation from a hot surface by selecting  the gap d = W/2 ~ 0.9 microns - a much more practical solution than evanescent waves requiring nanoscale gaps.

References

[1] M. Planck, The Theory of Heat Radiation (Dover, New York, 1991)
[2] Rytov, S.M., “Correlation Theory of Thermal Fluctuations in an Isotropic Medium,”   Soviet Physics JETP, Vol. 6, No. 1, pp 130-140 (1958).
[3] A. Narayanaswamy et al., “Breakdown of the Planck blackbody radiation law at nanoscale gaps,” Appl Phys A, 96: 357–362  (2009).  
[4]  E. Rousseau, et al., “Radiative heat transfer at the nanoscale,” Nature Photonics Letters, vol. 3, pp. 514-517, September  (2009).
[5]  J. R. Barnes, et al., “A femtojoule calorimeter using micromechanical sensors,” Rev. Sci. Instrum., vol. 65, pp. 3793-3798 (1994).