This work reports experimental studies on radiative heat flux between two parallel glass surfaces. Small polystyrene particles are used as spacers to maintain a micron-sized gap between two optical flats. By carefully choosing the number of particles and performing the measurement in a high-vacuum environment, the experiment is designed to ensure that the radiative heat flux is the dominant mode of heat transfer. The experimental results clearly demonstrate that the radiative heat flux across micron-sized gaps can exceed the far-field upper limit given by Planck’s law of blackbody radiation. The measured radiative heat flux shows reasonable agreement with theoretical predictions

Chen, Gang

Chen, Xiaoyuan

Hu, Lu

Narayanaswamy, Arvind

Columbia University Academic Commons

Near-field thermal radiation between two closely spaced glass platesexceeding Planck’s blackbody radiation lawLu Hu, Arvind Narayanaswamy, Xiaoyuan Chen, and Gang Chen  Citation: Appl. Phys. Lett. 92, 133106 (2008); doi: 10.1063/1.2905286 View online: http://dx.doi.org/10.1063/1.2905286 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v92/i13 Published by the American Institute of Physics.  Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors Downloaded 03 Apr 2013 to 128.59.161.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissionsNear-field thermal radiation between two closely spaced glass platesexceeding Planck’s blackbody radiation lawLu Hu,1 Arvind Narayanaswamy,2 Xiaoyuan Chen,1 and Gang Chen1,a1Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA2Columbia University, New York, New York 10027, USAReceived 5 February 2008; accepted 14 March 2008; published online 1 April 2008This work reports experimental studies on radiative heat flux between two parallel glass surfaces.Small polystyrene particles are used as spacers to maintain a micron-sized gap between two opticalflats. By carefully choosing the number of particles and performing the measurement in ahigh-vacuum environment, the experiment is designed to ensure that the radiative heat flux is thedominant mode of heat transfer. The experimental results clearly demonstrate that the radiative heatflux across micron-sized gaps can exceed the far-field upper limit given by Planck’s law ofblackbody radiation. The measured radiative heat flux shows reasonable agreement with theoreticalpredictions. © 2008 American Institute of Physics. DOI: 10.1063/1.2905286At a finite temperature, electrons and ions in any matterare under constant thermal agitation, acting as the randomcurrent source for thermal emission. The thermally excitedelectromagnetic waves have two forms: the propagatingmodes that can leave the surface of the emitter and radiatefreely into the space and the nonpropagating modes evanes-cent modes that do not radiate.1,2 The contribution from thepropagating modes to the radiative heat flux is well knownand its maximum is governed by Planck’s law of blackbodyradiation.3 The nonpropagating modes do not propagate andthus do not carry energy in the direction normal to the sur-face, unless a second surface is brought close to the first toenable photon tunneling. The contribution from the non-propagating modes to radiative heat flux is the near-field ra-diative flux.Theoretical study of the radiative flux between closelyspaced parallel surfaces has been carried out by variousresearchers.1–8 Most of the theoretical studies are based onthe fluctuating electrodynamics approach pioneered by Rytovet al.6 and Polder and van Hove.5 These theoretical studiesshow that, when the distance between two parallel surfaces issmall compared to the dominant thermal radiation wave-length, the near-field radiative heat flux can exceed the far-field upper limit imposed by Planck’s law of blackbody ra-diation. Experiments have followed to measure the near-fieldradiative heat flux. Domoto et al. measured radiative heattransfer between two metallic surfaces at cryogenic tempera-tures, reporting a value only 129 of the upper limit for gapsbetween 50 m and 1 mm.9 Hargreaves extended the mea-surements to gaps as small as 1 m between two chromiumsurfaces, which gave a radiative heat transfer rate at 50% ofthe blackbody upper limit.10 Xu et al. conducted measure-ment of radiation heat transfer between two metallic surfacesfor reduced gap sizes between 50 and 200 nm, but the expla-nation of their experimental data is hindered by the sensitiv-ity of the experimental technique.11 More recently, Kittel etal. measured near-field radiative transfer between a scanningthermal microscope tip and a flat substrate.12The previous experiments were done with conductingsurfaces, which made gap control possible based on measur-ing the electrical capacitance or tunneling current. Aroundroom temperature 300 K, the peak wavelength of thermalradiation is approximately 10 m Wien’s displacementlaw,13 where metals are not good candidates for the purposeof exceeding the Planck blackbody radiation law and ex-tremely small gaps are required to obtain high radiativeflux.14 In this work, we report measurements on near-fieldradiative heat transfer between two glass surfaces, whichsupports surface phonon polaritons in the infrared region ofthe electromagnetic spectrum.1 The resonant wavelength ofsurface phonon polaritions in glass is well aligned with thepeak wavelength of thermal radiation in the temperaturerange of interest, leading to higher radiative heat transfereven with moderate gap sizes. Our experimental data dem-onstrate breakdown of Planck’s blackbody radiation law inthe near field.To guide the experimental design, we analyze the near-field radiative heat transfer between the two parallel flatglass surfaces using Green’s dyadic15 and the fluctuation-dissipation theorem.6 The frequency-dependent optical con-stant of glass fused quartz is taken from Ref. 16. TheLorentizan model17 is used to interpolate the data points be-tween 26.67 and 100 m because no data are available inthis range. The gap dependent heat transfer coefficient isdefined as hr=qr / Th−Tc and plotted in Fig. 1a, where qris the radiative heat flux and Th and Tc are the temperaturesof the hot surface and the cold surface Th=50 °C and TcaElectronic mail: gchen2@mit.edu.FIG. 1. a Gap-size dependent heat transfer coefficient. b Calculated spec-tral radiative heat flux between two glass surfaces.APPLIED PHYSICS LETTERS 92, 133106 20080003-6951/2008/9213/133106/3/$23.00 © 2008 American Institute of Physics92, 133106-1Downloaded 03 Apr 2013 to 128.59.161.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions=24 °C, respectively. As the gap decreases below 5 m, theheat transfer coefficient starts to exceed the blackbody limit.As the gap shrinks even more, the coefficient continues togrow, owing to enhanced tunneling of the surface waves.Around 1 m, the coefficient is more than 50% higher thanthe blackbody limit, which is readily measurable without theneed to shrink the gap further. Figure 1b shows the wave-length dependent radiative heat flux between the two sur-faces, assuming the hot side and cold side temperatures to be50 and 24 °C, respectively, and a gap of 1 m. The figureclearly reveals two dominant peaks at 8.7 and 20.2 m,which are the resonance wavelengths of surface phonon po-laritons in glass,1 indicating the radiative heat transfer acrossa 1 m gap is primarily due to the contribution from thesurface phonon polaritons.Figure 2a shows the schematic drawing of the experi-mental setup. Two identical precision glass optical flats /20 accuracy are used as an emitter hot side and a re-ceiver cold side. The diameter of the glass optical flats is0.5 in. 1.27 cm and the thickness is 0.25 in. 0.635 cm.The surface flatness of the optical flats is better than0.05 m. To maintain a gap between the emitter and thereceiver, polystyrene microspheres Fig. 2b are placed be-tween the two surfaces as spacers. We decide to set the gapto be 1 m and, thus, choose the nominal diameter of thespheres to be d=1 m. Polystyrene is selected because itsthermal conductivity is low, with a reported value at0.18 W /mK.18 Assuming a cross-section area of d2 /4 forheat conduction and a radiative heat transfer coefficient of5 W /m2 K, the heat conducted through a polystyrene sphereis 14500 of the far-field radiative heat flux. Note that in a realmeasurement situation, the heat conduction leakage is aneven smaller fraction of the radiative flux because a contactarea of d2 /4 between the sphere and the glass surface isoverestimated. The spherical particles are diluted in de-ionized water as liquid suspension. Small droplets of the liq-uid suspension are dispensed with a pipette over the surfaceof the cold side to obtain a uniform spatial distribution of theparticles. A total of about 80 particles are deposited betweenthe two optical flats, thus, limiting the conduction heat fluxto be less than 2% of the radiative heat flux. After the waterin the droplets evaporates, the emitter is placed on top of thereceiver with the particles serving as spacers to separate thetwo objects. We carefully conduct all the operations in alaminar flow workstation to eliminate dust particles in theair.As illustrated in Fig. 2a, a heating pad is attached onthe top surface of the emitter. The temperature of the heatingpad Th0 is monitored with a platinum resistance temperaturedetector, which feeds the signal to a temperature controller.With the feedback control, the temperature of the heating padcan be set to a value with variations within 1 °C. The sidesurfaces of the optical flats are wrapped with aluminum foilto minimize radiative heat exchange with the environment. A11 in.2 heat flux meter is positioned between the receiverand the heat sink. A copper heat spreader 11 in.2 is sand-wiched between the receiver and the heat flux meter to ho-mogenize temperature over the surface. Thermal grease isapplied to the interfaces for good thermal contact. To ensurethat the heat flux meter measures only the radiative flux, theentire setup is placed in a vacuum chamber pumped down to8.510−3 Pa. The vacuum level limits heat conductionthrough the rarefied air19 in the small gap to be less than0.05% of the radiation flux.To test the experimental system, we measured the far-field radiation. The emitter was clamped to a sample holderfor the far-field measurement and the gap between the twosurfaces was set to be 2 mm. We then proceeded to the near-field measurement using the particles as the spacers. Thetemperature of the bottom surface of the receiver Tc0 wasrecorded by a K-type thermocouple inserted in between thecopper spreader and the flux meter. For each measurement,we made sure that the reading from the heat flux meterstabilized before the data were taken. Note that even at thesteady state, the temperatures inside the optical flats is notuniform due to a nonzero one-dimensional 1D heat fluxalong the cylinder axis direction of the optical flats. From thetemperature reading Th0 on the heating pad and the heatflux data, we can derive the temperature Th on the lowersurface of the emitter by solving a 1D heat conduction prob-lem. The lower surface temperature is given by Th=Th0−qrdglass /kglass, where qr is the measured flux and dglass andkglass are the thickness and thermal conductivity of the opticalflat, respectively. Similarly, the temperature Tc on the uppersurface of the receiver is given by Tc=T0+qrdglass /kglass. Thetemperatures Th and Tc are the effective temperatures forthermal emission because the electromagnetic penetrationdepth in glass is much less than 1 mm and thermal radiationis essentially a surface phenomenon in the wavelengths ofinterest.The measured heat flux data are presented in Fig. 3,which has been adjusted by taking into account a heatspreading factor of 16 / between the circular optical flat andthe square flux meter. The variation of the temperature Tc0 onthe bottom surface of the receiver is less than 0.5 °C duringthe experiment and the average value is 23.7 °C. The far-field upper limit of the radiative heat flux is given by qb=Th4−Tc4, where  is the Stefan–Boltzmann constant. NoteFIG. 2. Color online a A schematic drawing of the experiment setup. bA scanning electron microscope image of polystyrene particles.FIG. 3. Measured radiative heat flux between the two optical flats.133106-2 Hu et al. Appl. Phys. Lett. 92, 133106 2008Downloaded 03 Apr 2013 to 128.59.161.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissionsthat Th and Tc are derived based on the 1D heat conductionmodel. As the temperature of the hot surface increases, boththe near-field and far-field radiative fluxes increase. Whilethe far-field heat flux stays below the upper limit, the near-field heat flux clearly exceeds the blackbody upper limit bymore than 35% in the entire temperature range. Also shownin Fig. 3 is the calculated far-field radiative heat flux. Thefar-field curve agrees reasonably well with the experimentaldata.Figure 4 compares theoretical predictions and experi-mental data for the temperature dependent heat transfer co-efficient. The measured data agree well with the theoreticalprediction for a 1.6 m gap. This larger-than-expected gap ismost likely because the polystyrene particles have a devia-tion in diameters, as shown in Fig. 2b. The gap is deter-mined by the larger particles. Another factor that affects thefitting of experimental data is the accuracy of the optical datawe used for the theoretical calculation. Nevertheless, the dataclearly show that the radiative heat transfer exceeds theblackbody radiation flux. The heat transfer coefficient in-creases as the temperature of the hot side rises. An increaseof 19% is found for the temperature range. In the same tem-perature range, the thermal conductivity of polymer typicallydecreases and that of glass20 increase at much lower rate,excluding the possibility that the origin of the measured heatflux is conductive in nature.In summary, we conducted experimental study on thenear-field thermal radiation between two closely spaced glasssurfaces. The measured radiative heat flux exceeds the black-body radiation for more than 35% in the entire temperaturerange, and agrees reasonably well with the calculation re-sults. From theoretical considerations, we attribute the pri-mary contribution to the heat transfer to surface phonon po-laritions at the interface between glass and vacuum.The authors would like to thank Dr. Shuo Chen at MITfor taking the SEM image. This work is supported byDE-FG02-02ER45977 and ONR N00014-03-1-0835.1J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, Microscale Ther-mophys. Eng. 6, 209 2002.2J. B. Pendry, J. Phys.: Condens. Matter 11, 6621 1999.3M. Planck, The Theory of Heat Radiation Dover, New York, 1991.4E. G. Cravalho, C. L. Tien, and R. P. Caren, J. Heat Transfer 89, 3511967.5D. Polder and M. van Hove, Phys. Rev. B 4, 3303 1971.6S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarski, Principles of StatisticalRadiophysics Springer, Berlin, 1987, Vol. 3.7A. Narayanaswamy and G. Chen, Appl. Phys. Lett. 82, 3544 2003.8C. F. Fu and Z. M. Zhang, Int. J. Heat Mass Transfer 49, 1703 2006.9G. A. Domoto, R. F. Boehm, and C. L. Tien, Trans. ASME, Ser. C: J. HeatTransfer 92, 412 1970.10C. M. Hargreaves, Philips Res. Rep., Suppl. 5, 1 1973.11J.-B. Xu, K. Lauger, R. Moller, K. Dransfeld, and I. H. Wilson, J. Appl.Phys. 76, 7209 1994.12A. Kittel, W. Muller-Hirsch, J. Parisi, S.-A. Biehs, D. Reddig, and M.Holthaus, Phys. Rev. Lett. 95, 224301 2005.13M. F. Modest, Radiative Heat Transfer Academic, Boston, 2003.14P.-O. Chapuis, S. Volz, C. Henkel, K. Joulain, and J.-J. Greffet, Phys. Rev.B 77, 035431 2008.15L. Tsang, J. A. Kong, and K. H. Ding, Scattering of ElectromagneticWaves Wiley, New York, 2000.16Handbook of Optical Constants of Solids, edited by E. D. Palik Aca-demic, Orlando, 1985.17C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light bySmall Particles Wiley, New York, 1983.18G. Pezzotti, I. Kamada, and S. Miki, J. Eur. Ceram. Soc. 20, 1197 2000.19G. S. Springer, in Advances in Heat Transfer, edited by T. F. Irvine and J.P. Hartnett Academic, New York, 1971, p. 163.20Thermophysical Properties of Matter, edited by Y. S. Touloukian, R. W.Powell, C. Y. Ho, and P. G. Klemens IFI/Plenum, New York, 1970.FIG. 4. Temperature dependent heat transfer coefficient. The temperature isthe average of the hot surface and cold surface temperatures.133106-3 Hu et al. Appl. Phys. Lett. 92, 133106 2008Downloaded 03 Apr 2013 to 128.59.161.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions

Near-field Thermal Radiation Between Two Closely Spaced Glass Plates Exceeding Planck’s Blackbody Radiation Law

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Near-field Thermal Radiation Between Two Closely Spaced Glass Plates Exceeding Planck’s Blackbody Radiation Law

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