CENTER FOR NONLINEAR AND COMPLEX SYSTEMS. Como - Italy

Transcription

1 CENTER FOR NONLINEAR AND COMPLEX SYSTEMS Como - Italy

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3 Providing a sustainable supply of energy to the world s population will become a major societal problem for the 21 st century as fossil fuel supplies decrease and world demand increases. Thermoelectric phenomena are expected to play an increasingly important role in meeting the energy challenge of the future. a newly emerging field of low-dimensional thermoelectricity, enabled by materials nanoscience and nanotechnology. Dresselhaus et al: Adv. Mater. 2007

4 A central issue in physics What are the fundamental limits that thermodynamics imposes on the efficiency of thermal machines? This problem is becoming more and more practically relevant in the future society due to the need of providing a sustainable supply of energy and to strong concerns about the environmental impact of the combustion of fossil fuels

5 Sadi Carnot, Reflexions Sur la Puissance Motrice du Feu et Sur Les Machines Propres a` Developper Cette Puissance (Bachelier, Paris, 1824).

6 Sadi Carnot, Reflexions Sur la Puissance Motrice du Feu et Sur Les Machines Propres a` Developper Cette Puissance (Bachelier, Paris, 1824). In a cycle between two reservoirs at temperatures T 1 and T 2 (T 1 >T 2 ), the efficiency, is bounded by the so-called Carnot efficiency

7 Sadi Carnot, Reflexions Sur la Puissance Motrice du Feu et Sur Les Machines Propres a` Developper Cette Puissance (Bachelier, Paris, 1824). In a cycle between two reservoirs at temperatures T 1 and T 2 (T 1 >T 2 ), the efficiency, is bounded by the so-called Carnot efficiency The Carnot efficiency is obtained for a quasistatic transformation which requires infinite time and therefore the extracted power, in this limit, reduces to zero.

8 Efficiency at maximum power Curzon -Ahlborn upper bound

9 INTRODUCTORY REMARKS Can we control the heat current?

10 INTRODUCTORY REMARKS Can we control the heat current? Towards thermal diodes and thermal transistors M. Terraneo, M. Peyrard and G.C. p.r.l. 88, (2002)

11 QUESTION: Can one derive the Fourier law of heat conduction from dynamical equations of motion without any statistical assumptions? Normal transport

12 J. B. FOURIER Attempt to explain the thermal gradient inside the earth

13 It seems there is no problem in modern physics for which there are one record as many false starts and as many theories which overlook some essential features as in the problem of the thermal conductivity of non conducting crystals R. E. PEIERLS

14 REMARK: Randonmnes is an essential ingredient of thermal conductivity deterministically random systems are tacitly required by the transport theory

15 THE DING-A -LING MODEL

16 THE DING-A -LING MODEL

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20 Nature, 7 june 1984

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24 Plane waves solutions Dispersion relations Phonon band

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28 INTERNAL TEMPERATURE PROFILE

29 In nonlinear systems the position of the band depends on the temperature

30 p.r.l. 88, (2002)

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32 For uniform mass distribution, thermal conduction is symmetric

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34 All measurements showed that a higher thermal conductance was observed when heat flowed from the high-mass region to the low -mass region

35 A wave diode: asymmetric wave propagation in nonlinear systems

36 A wave diode: asymmetric wave propagation in nonlinear systems G.C., S. Lepri, prl. 106, (2011) Layered photonic( phononic) crystal

37 The transmission is large for the left incoming packet G.C., S. Lepri, prl. 106, (2011)

38 POWERFUL HEAT How to increase efficiency of thermopower generation and refrigeration? A dynamical systems approach

39 A.Volta (Como) Volta effect: an electric potential difference is developed by the contact of two different metals at the same temperature.

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42 A.Volta (Como) Seebeck In 1822, the Estonian German physicist Thomas Johann Seebeck discovered that if heat is applied across the junction of two wires, a current is generated.

43 Thermoelectricity concerns the conversion of temperatures differencies into electrical potential or viceversa It can be used to perform useful electrical work or to pump heat from cold to hot place, thus performing refrigeration

44 Abram Ioffe, 1950s : doped semiconductors have large thermoelectric effect The initial excitement about semiconductors in 1950 was due to their promise, not in electronics but in refrigeration. The discovery that semiconductors can act as efficient heat pumps led to expectations of environmentally benign solid state home refrigerators and power generators

45 During this period, the thermoelectric field received little attention from the worldwide scientific research community. Nevertheless, the thermoelectric industry grew slowly and steadily, by finding niche applications: space missions laboratory equipment medical applications where cost and energy efficiency were not as important as energy availability, reliability, predictability, and the quiet operation of equipment.

46 Thermoelectric devices provide on board power to operate radio signal trasmitters, on board computers, gyros and navigational systems, spectrometers and many other scientific instruments. These power generating systems can operate unattended, maintenance free, for many years NASA uses thermoelectric because key advantages include high reliability, small size and no noise.

47 New Horizon spacecraft to Pluto (The RTG is the black, cylindrical finned object at lower left). Radioisotope Thermoelectric Generators (RTGs) is the only technology (so far) capable of providing electrical power for deep-space missions including: - Voyagers I and II, -Galileo, Cassini, and the New Horizons mission to Pluto.

48 Thermoelectric coolers/heaters by Amerigon (USA)

49 Efforts are underway to replace alternator in cars with a thermoelectric generator mounted on the exhaust stream

50 Vehicle waste heat is redirected to a thermoelectric generator to produce electricity rather than using drive train power and an alternator. More drive train power is available to move the vehicle and electricity is still available. Plan is to improve overall fuel economy by 10% and aims to reach production in the 2014

51 New funding. In the early 1990s DARPA and the Office of Naval Research initiated support for basic thermoelectric materials research: thermoelectric coolers are used for night vision, sensors, guidance systems, etc. and even modest efficiency gains might make TE air conditioning practical in submarines (TE cooling is quiet) and enhance the existing DoD applications. USS DOLPHIN AGSS 555 Test for Silent Running

52 The suitability of a thermoelectric material for energy conversion or electronic refrigeration is evaluated by

53 The ZT figure of merit The suitability of a thermoelectric material for energy conversion or electronic refrigeration is evaluated by

54 In linear response regime:

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56 A. Majumdar Science 303, 777(2004) In five decades the ZT of semiconductors has increased only marginally, from about 0.6 to 1

57 A ZT value > 3 would make solid state home refrigerators economically competitive with compressor-based refrigerators

58 A ZT value > 3 would make solid state home refrigerators economically competitive with compressor-based refrigerators Metals are poor thermoelectric materials because of low Seebeck coefficient and large electronic contribution to thermal conductivity.

59 A ZT value > 3 would make solid state home refrigerators economically competitive with compressor-based refrigerators Metals are poor thermoelectric materials because of low Seebeck coefficient and large electronic contribution to thermal conductivity. Insulators have large Seebeck coefficient but have too few carriers which result in large electrical resistivity

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62 The only thermodynamic restrictions to the Onsager coefficients come from the positivity of the entropy production, which is a quadratic form in the generalized forces: and The only restriction:

63 ZT diverges iff the Onsager matrix is ill- conditioned that is the condition number: diverges In such case the system is singular:

64 Consider a two dimensional gas with circular scatterers (Lorentz gas model)

65 Consider a two dimensional gas with circular scatterers (Lorentz gas model) ZT =1.5

66 1-d non interacting gas Particles current: energy distribution of particles from reservoir transmission prob. for a particle with energy to transit from one hand to the other.

67 Assuming Maxwell-Boltzmann distribution for particles in the baths: (Injection rates) Particles current: Heat current:

68 If transmission is possible only inside a tiny energy window then

69 Carnot efficiency Delta-like energy-filtering mechanism; Mahan et al (1996), Humphrey et al (2002)

70 Interacting system Consider a one dimensional gas of elastically interacting particles with unequal masses: m M G.C., Lei Wang, T. Prosen: J. of Stat. Mech. (2009)

71 There is no sign of narrowing of D(E) with increasing system size L A different mechanism for increase of ZT!?

72 A new challenge: Break time-reversal symmetry

73 A new challenge: Break time-reversal symmetry Onsager

74 A new challenge: Break time-reversal symmetry Onsager however

75 Maximum efficiency and efficiency at maximun power depend on two parameter x and y G. Benenti, K. Saito and G.C. prl (2011) (x=1 implies y=zt) The second, asymmetry parameter, x offers an additional freedom for efficiency of thermoelectric devices

76 G. Benenti, K. Saito and G.C. prl (2011)

77 For non interacting systems S(B) = S(-B) due to symmetry properties of the scattering matrix

78 For non interacting systems S(B) = S(-B) due to symmetry properties of the scattering matrix Accurate numerical simulations of two terminal interacting dynamical systems which violate time-reversal symmetry sistematically failed to find a non symmetric thermopower S(B) S(-B) why?

79 For non interacting systems S(B) = S(-B) due to symmetry properties of the scattering matrix Accurate numerical simulations of two terminal interacting dynamical systems which violate time-reversal symmetry sistematically failed to find a non symmetric thermopower S(B) S(-B) why? Inelastic scattering introduced e.g. by a, selfconsistent, third terminal, leads to non-symmetric thermopower K. Saito, G. Benenti, G.C., T. Prosen PRB (2011)

80 For non interacting systems S(B) = S(-B) due to symmetry properties of the scattering matrix Accurate numerical simulations of two terminal interacting dynamical systems which violate time-reversal symmetry have shown a non symmetric thermopower S(B) S(-B) Inelastic scattering introduced e.g. by a, selfconsistent, third terminal, leads to non-symmetric thermopower K. Saito, G. Benenti, G.C., T. Prosen PRB (2011) How to increase asymmetry x??

81 -A large number of complex materials are now available At issue are some fundamental scientific challenges, which could be overcome by deeper understanding of heat and charge transport.

82 Thermal diodes and wave diodes Phys Rev Lett (2002) Phys Rev Lett (2004) Chaos (2005) Phys Rev Lett (2007) Phys Rev Lett (2011) Thermoelectric Phys Rev Lett (2008) J Stat Mech L03004 (2009) Phys Rev E (2009) Phys Rev E (2009) Chem. Phys. 375, 508 (2010) Phil. Trans. R. Soc.A 369, 466 (2011) J Stat Mech (2011) Phys Rev B (2011) Phys Rev Lett (2011)