Sean Lubner

A photon thermal diode

A thermal diode is a two-terminal nonlinear device that rectifies energy carriers (for example, photons, phonons and electrons) in the thermal domain, the heat transfer analogue to the familiar electrical diode. Effective thermal rectifiers could have an impact on diverse applications ranging from heat engines to refrigeration, thermal regulation of buildings and thermal logic. However, experimental demonstrations have lagged far behind theoretical proposals. Here we present the first experimental results for a photon thermal diode. The device is based on asymmetric scattering of ballistic energy carriers by pyramidal reflectors. Recent theoretical work has predicted that this ballistic mechanism also requires a nonlinearity in order to yield asymmetric thermal transport, a requirement of all thermal diodes arising from the second Law of Thermodynamics, and realized here using an ‘inelastic thermal collimator’ element. Experiments confirm both effects: with pyramids and collimator the thermal rectification is 10.9±0.8%, while without the collimator no rectification is detectable (<0.3%).

A Micro-Thermal Sensor for Focal Therapy Applications

There is an urgent need for sensors deployed during focal therapies to inform treatment planning and in vivo monitoring in thin tissues. Specifically, the measurement of thermal properties, cooling surface contact, tissue thickness, blood flow and phase change with mm to sub mm accuracy are needed. As a proof of principle, we demonstrate that a micro-thermal sensor based on the supported “3ω” technique can achieve this in vitro under idealized conditions in 0.5 to 2 mm thick tissues relevant to cryoablation of the pulmonary vein (PV). To begin with “3ω” sensors were microfabricated onto flat glass as an idealization of a focal probe surface. The sensor was then used to make new measurements of ‘k’ (W/m.K) of porcine PV, esophagus, and phrenic nerve, all needed for PV cryoabalation treatment planning. Further, by modifying the sensor use from traditional to dynamic mode new measurements related to tissue vs. fluid (i.e. water) contact, fluid flow conditions, tissue thickness, and phase change were made. In summary, the in vitro idealized system data presented is promising and warrants future work to integrate and test supported “3ω” sensors on in vivo deployed focal therapy probe surfaces (i.e. balloons or catheters).

Correspondence: Reply to ‘The experimental requirements for a photon thermal diode’

Budaev1 correctly identifies a fundamental symmetry error in several crucial experiments in our recent study2, specifically the results presented in Fig. 3c (the three filled and four striped bars, labeled ‘Col. 1’ and ‘Col. 2’, respectively) and Fig. 4. A suitable configuration for those measurements should have included identical (mirror-imaged) collimators at both hot and cold sides, as in Fig. 1a here. However, the actual experiments omitted the cold-side collimator, a choice made for experimental simplicity and which we believed was acceptable at the time based on a simple thermal model3 and the fact that TBBC 4 cTN , where TBBC and TN are the temperatures of the blackbody (BB) cavity and cold-side plate, respectively. However, upon careful reconsideration we now find that thermal model to be flawed, and we believe that omitting the cold-side collimator invalidated several key measurements. We provide a more detailed discussion of that thermal estimate, and the reasons for its failure, elsewhere3. Although we believe the heat flow (Q) measurements in ref. 2 were accurate for all of the configurations presented, due to the symmetry error none of those experimental configurations were actually relevant to the following two major claims, which therefore are invalidated for lack of experimental support: First, that these experiments demonstrated a thermal diode. Second, that the ‘inelastic thermal collimation’ mechanism is a suitable nonlinearity for realizing thermal rectification when combined with asymmetric scattering structures (for example, copper pyramids or etched triangular pores in silicon). The symmetry error1 does not apply to the experiments without thermal collimation, specifically the results presented in Fig. 3c for photons (the six leftmost, unfilled bars) and Supplementary Fig. 12 for phonons. Therefore, the last major conclusion of ref. 2 remains well-supported by the original experiments: Asymmetric scattering alone is insufficient to achieve thermal rectification. The rest of this Reply is devoted to another problem which we have only recently realized: a fundamental issue with the inelastic thermal collimation concept based on absorption, thermalization, and re-emission, as exemplified by the perforated graphite plate approach used in ref. 2. This leads us to now conclude that if it had used a correct two-plate symmetry as depicted here in Fig. 1a, the thermalizing graphite plate scheme as originally conceived2 could not rectify. The essence of the graphite plate approach is radiation absorption and re-emission by a solid plate of infinite thermal conductivity, as exemplified by Supplementary Fig. 4 of ref. 2. The motivating insight is that when analyzed as part of its adjacent BB reservoir, the combined effect of (BBþ collimator) is to convert a local boundary condition into a nonlocal one (or linear into nonlinear in the language originally used in ref. 2). This is depicted here in Fig. 1b, corresponding closely to Supplementary Fig. 5c of ref. 2. This shows how the graphite plate next to BB1 can convert the local equilibrium Bose-Einstein statistics fBE(T1) to a nonlocal, non-equilibrium reservoir boundary condition fNE,1(T1,T2), at the boundary between (BB1þ plate1) and the test section SA, as shown here in Fig. 1b. As noted below Supplementary Equation 5 of ref. 2, this functional form fNE,1(T1,T2) is a necessary condition for the heat transfer response function Q(T1,T2) through the test section SA to be non-symmetric upon the exchange T12T2. Analogous statements hold for the other boundary condition, at the interface between SA and (BB2þ plate2). However, the heat transfer analysis could just as well combine the graphite plates with the pyramids as a larger alternate test section, not considered in ref. 2 but indicated here in Fig. 1c as SB. Because the only distinction between Fig. 1b, c is in how the control volumes are drawn, with no changes to the physical system, clearly both approaches must give the same heat transfer response function Q(T1,T2). Yet because the boundary conditions in Fig. 1c are now ideal blackbodies, SB can be analyzed rigorously using radiation network analysis4, as indicated schematically here in Fig. 2. This network analysis accounts for the direct and indirect radiative exchanges between numerous differential areas which cover all surfaces, including pyramids and graphite plates. The approach can be generalized to handle surfaces with any combination of diffuse (for example, the BBs and graphite plates) and specular (for example, the copper pyramids and sidewalls) character4. The essential point is that the resulting matrix formulation of the heat transfer problem4 is fundamentally a linear relationship in terms of the BB emissive powers Eb,i1⁄4sTi, where s is the DOI: 10.1038/ncomms16136 OPEN

Measurements of the Thermal Conductivity of Sub-Millimeter Biological Tissues

Accurate knowledge of the thermal conductivities of biological tissues is important for thermal bioengineering, including applications in cryopreservation, cryosurgery, and other thermal therapies. The thermal conductivity of biomaterials is traditionally measured with macroscale techniques such as the steady longitudinal heat flow method or embedded thermistor method. These techniques typically require relatively large, centimeter-scale samples, limiting their applicability to finer biological structures. They are also vulnerable to errors caused by thermal contact resistances and parasitic heat losses. In contrast, the thermal conductivity of inorganic solids such as semiconductor wafers and thin films is commonly measured using the “3 omega method” [1–3]. This frequency domain technique is robust against thermal contact resistances and parasitic heat losses. It routinely has sub-millimeter spatial resolution, with theoretical limits down to tens of microns. Here we adapt the 3 omega method for measurements of biological tissues. Thermal conductivity measurements are made on both frozen and un-frozen samples including agar gel, water, and mouse liver, including samples with sub-millimeter thicknesses. The measurement results compare favorably with literature values and span the range from around 0.5 to 2.5 W/m-K. This study demonstrates the promise that this technique holds for thermal measurements of bulk tissues as well as fine sub-millimeter samples.Copyright

Retraction: A photon thermal diode

This corrects the article DOI: 10.1038/ncomms6446.