When thermoelectric systems meet the Feymann ratchet: harmonic response and feedback Christophe Goupil, Henni Ouerdane, Yann Apertet, Philippe Lecoeur.

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Transcription de la présentation:

When thermoelectric systems meet the Feymann ratchet: harmonic response and feedback Christophe Goupil, Henni Ouerdane, Yann Apertet, Philippe Lecoeur Advanced thermoelectrics at nanoscale: from materials to devices

Feynman ratchet model T hot T cold torque spring energy escape frequency Strong coupling configuration effective « current » Energy taken from hot side Energy delivered to the cold side Velasco at al. J. Phys. D: Appl. Phys.34 (2001) 1000–1006 gear wheel Spring pawl pulley blades R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics I Addison-Wesley, Reading, (1963), Chap. 46.

Linearization & thermoelectric model T hot T cold R V0V0 R load Apertet et al. PRE 2014

Power budget T hot T cold R in V0V0 R load dissipative resistance Apertet et al. PRE 2014 « entropy per tooth » (Seebeck like:  FR )

Extension to non-linear model In the non linear case the dissipative resistance and the linear resistance do not coincide. Apertet et al. PRE 2014 Efficiency at maximum power Linear System Supra-Linear System Sub-Linear System

General model: Onsager description - + v oc K hot K TE (I) K cold TE R T hot T cold LOADLOAD I  T TE T hTE T cTE  V TE K0K0 Y. Apertet, H. Ouerdane, O. Glavatskaya, C. Goupil et Ph. Lecoeur, EPL 97 (2012) Conduction Convection

General model: resulting picture The feedback comes from K c No R TE if the coupling is perfect, K c =>∞. T hot Y. Apertet, et al. EPL 97 (2012) - + v ’ oc K hot K TE (I) K cold TEG R TE R T cold LOADLOAD I  T TE  V TE K0K0 T hTE T cTE TT Thevenin model

1rst order harmonic response C hot C cold - + v ’ oc K hot K TE (I) K cold TEG R TE R T hot T cold LOADLOAD I  T TE  V TE K0K0 T hTE T cTE C th

Small signal analysis + -  TE KCKC R LOADLOAD i(t)  T TE  v TE K0K0 CC i i

Small signal analysis Total ouput impedance Maximal output power if impedance matching => non zero frequency?

Complete analysis Low frequency approximation:

Conclusion Feynman’s ratchet as a system model for thermoelectricity. The entropy per tooth generalizes the entropy per carrier concept. Thermoelectric resistance: R TE Thermoelectric capacitance: C TE 1rst order dynamic response:  TE  =R TE C TE Impedance spectroscopy is a powerful tool for ZT evaluation!