Wiedemann–Franz law at boundaries

Mahan, G. D.; Bartkowiak, M.

doi:10.1063/1.123420

Cited by 131 publications

(73 citation statements)

References 10 publications

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“…As Equation (1) shows, an optimized thermoelectric material should have high Seebeck coefficient and electrical conductivity, but at the same time low thermal conductivity. However, such properties cannot be achieved easily, due to the fact that all three parameters are interrelated, especially the electrical and thermal conductivity are coupled though the Wiedemann-Franz Law [10]. As a result, researchers in the past were primarily focus on semiconductor based materials, such as bismuth telluride ((Bi2Te3) [11], and antimony telluride (Sb2Te3) [12].…”

Section: S(t) Is the Seebeck Coefficient σ(T) Is The Electrical Condmentioning

confidence: 99%

Study on the thermoelectric properties of PVDF/MWCNT and PVDF/GNP composite foam

Sun

Terakita

Tseng

et al. 2015

Smart Mater. Struct.

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Always cite the published version, so the author(s) will receive recognition through services that track citation counts, e.g. Scopus. If you need to cite the page number of the author manuscript from TSpace because you cannot access the published version, then cite the TSpace version in addition to the published version using the permanent URI (handle) found on the record page. Abstract. Thermoelectric effect is defined as the revisable translation between thermal and electrical energy. In this paper, we investigate the properties of p-type poly(vinylidene fluoride) (PVDF) based polymer composite foams that can be used in next generation energy harvesting applications. The composites were created via continuous melt blending method. Multi-walled carbon nanotubes (MWCNTs) and graphene nano-platelets (GNPs) were used as secondary phases to strengthen the electrical conductivity of the composites. Foam structures were later generated via super-critical carbon dioxide saturation method. We study the material properties between solid and foam samples; the results indicate a dramatic increase in overall thermoelectric properties for GNP foamed samples. We also report at least an order decreased in thermal conductivity which is in favor of thermoelectric effect. An unexpected drop in electrical conductivity was observed after the foaming process and can be explained by large volumetric expansion of the foam. Finally we report the Seebeck coefficient for both types of composite foams: 11 μV/K for 5 wt% MWCNT/PVDF foam and 58 μV/K for 15 wt% GNP/PVDF foam. IntroductionThermoelectric (TE) effect is known as the direct conversion between electrical and thermal energy and such effect can be explained by three different phenomena: Seebeck effect, Peliter effect, and Thomson effect. When a temperature gradient is applied to a circuit that consists of two different electric conductors, a small current can be observed which is called the Seebeck effect. The opposite phenomenon is called the Peliter effect, of which the junctions of the two conductors may either absorb or release heat when a voltage is supplied to the circuit. Lastly, the Thomson Effect states that when an electric current is passing through a conductor, certain amount of heat (Thomson heat) would be released or absorbed by the material and such heat is does not include the non-reversible Joule heating which is generated from the electric resistance nature of the material [1]. Seebeck effect is currently being implemented in verity types of temperature sensors or thermocouples [2] while the Peliter effect can be applied in different types of heat engines and coolers [3]. Other than temperature sensors, Seebeck effect also being widely researched for energy harvesting

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Section: S(t) Is the Seebeck Coefficient σ(T) Is The Electrical Condmentioning

confidence: 99%

Study on the thermoelectric properties of PVDF/MWCNT and PVDF/GNP composite foam

Sun

Terakita

Tseng

et al. 2015

Smart Mater. Struct.

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“…Furthermore, we use the Wiedemann-Franz Law [45][46][47] to estimate the relative contribution of electrons and phonons to heat conduction along the nanotube and at the contacts. In its classical form this states that the part of the thermal conductivity owed to electrons is proportional to the electrical conductivity σ, the absolute temperature, and the Lorenz constant…”

Section: Electrical and Thermal Contact Resistancementioning

confidence: 99%

Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates

Pop

Mann

Goodson

et al. 2007

Journal of Applied Physics

319

307

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We analyze transport in metallic single-wall carbon nanotubes (SWNTs) on insulating substrates over the bias range up to electrical breakdown in air. To account for Joule self-heating, a temperature-dependent Landauer model for electrical transport is coupled with the heat conduction equation along the nanotube.The electrical breakdown voltage of SWNTs in air is found to scale linearly with their length, approximately as 5 V/µm; we use this to deduce a thermal conductance between SWNT and substrate g ≈ 0.17 ± 0.03 WK -1 m -1 per tube length, which appears limited by the SWNT-substrate interface rather than the thermal properties of the substrate itself. We examine the phonon scattering mechanisms limiting electron transport, and find the strong temperature dependence of the optical phonon absorption rate to have a remarkable influence on the electrical resistance of micron-length nanotubes. Further analysis reveals that unlike in typical metals, electrons are responsible for less than 15% of the total thermal conductivity of metallic nanotubes around room temperature, and this contribution decreases at high bias or higher temperatures. For interconnect applications of metallic SWNTs, significant self-heating may be avoided if power densities are limited below 5 µW/µm, or if the SWNT-surrounding thermal interface is optimized.Contact: epop@stanfordalumni.org, hdai@stanford.edu 2

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“…The comparison the value η with obtained earlier boundary conditions [8,9] allows to conclude that η is the surface thermal conductivity.…”

Section: General Boundary Conditionmentioning

confidence: 96%

Boundary conditions in theory of photothermal processes

Logvinov¹,

Cruz‐Irisson²,

Lashkevych³

et al. 2006

Braz. J. Phys.

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The general boundary conditions for the thermal diffusion equation are obtained. It is shown that in the general case of a nonstationary photothermal process these boundary conditions must include both the surface thermal conductivity and surface thermal capacity. One more parameter, the surface capacity thermal impedance, appears in the boundary conditions when the photothermal process is the thermal wave propagation.

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Wiedemann–Franz law at boundaries

Cited by 131 publications

References 10 publications

Study on the thermoelectric properties of PVDF/MWCNT and PVDF/GNP composite foam

Study on the thermoelectric properties of PVDF/MWCNT and PVDF/GNP composite foam

Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates

Boundary conditions in theory of photothermal processes

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