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Flexible Thermoelectric Polymers and Systems. Группа авторовЧитать онлайн книгу.

Flexible Thermoelectric Polymers and Systems - Группа авторов


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lattice thermal conductivity is given by the Debye equation,

      (1.25)kappa Subscript upper L Baseline equals one third c Subscript normal p Baseline v l comma

      where c p, v, and l are the specific heat capacity, the phonon velocity, and the phonon mean free path, respectively. The phonon mean free path of polymers is usually extremely small due to the scattering by other phonons, defects, and grain boundaries. Thus, polymers usually have a thermal conductivity much lower than metals and semiconductors. For example, the values of c p, v, and l are 1.8 × 106 J (K−1 m−3), 1.58 × 103 m s−1, and 0. nm, respectively, for PEDOT:PSS. The κ L value of PEDOT:PSS is thus ~0.3 W (m−1 K−1). The lattice thermal conductivity is related to the crystallinity of polymers. The higher the crystallinity, the higher the thermal conductivity.

      The electronic thermal conductivity is related to the electrical conductivity by the Wiedemann–Franz law,

      (1.26)kappa Subscript normal e Baseline equals upper L sigma upper T comma

      (1.27)upper L 0 equals StartFraction pi squared k Subscript upper B Superscript 2 Baseline Over 3 e squared EndFraction period

      One important reason for the thermoelectric application of polymer nanocomposites is their low thermal conductivity. The thermal conductivity of a composite with polymer matrix and fillers depends on its microstructure [30]. A composite has the highest thermal conductivity when its structure is modeled with two components in parallel and the lowest thermal conductivity when it is modeled with the two components in series.

      The thermal conductivity (κ c) of a composite by the parallel model is given by

      (1.28)kappa Subscript c Baseline equals chi Subscript alpha Baseline kappa Subscript alpha Baseline plus chi Subscript beta Baseline kappa Subscript beta Baseline comma

      where χ α and χ β are the volume fractions of the two phases, respectively, and κ α and κ β are the thermal conductivities of the two phases, respectively. The parallel model usually overestimates the contribution of the fillers to the overall thermal conductivity of the composites.

      The thermal conductivity of a composite by the series model is given by

      (1.29)StartFraction 1 Over kappa Subscript c Baseline EndFraction equals StartFraction chi Subscript alpha Baseline Over kappa Subscript alpha Baseline EndFraction plus StartFraction chi Subscript beta Baseline Over kappa Subscript beta Baseline EndFraction period

      The thermal conductivity of composites with nano‐fillers dispersed in polymers is between that by the parallel model and series model, and it is usually close to the value by the series model.

      A more precise equation for the thermal conductivity of composites with fillers in matrix is given by the Maxwell–Garnett equation,

      (1.30)kappa Subscript c Baseline equals kappa Subscript m Baseline left-bracket 1 plus StartFraction 3 chi Subscript f Baseline left-parenthesis delta minus 1 right-parenthesis Over 2 plus delta minus chi Subscript f Baseline left-parenthesis delta minus 1 right-parenthesis EndFraction right-bracket comma

      (1.31)chi Subscript m Baseline StartFraction kappa Subscript m Baseline minus kappa Subscript c Baseline Over kappa Subscript m Baseline plus 2 kappa Subscript c Baseline EndFraction plus chi Subscript f Baseline StartFraction kappa Subscript f Baseline minus kappa Subscript c Baseline Over kappa Subscript f Baseline minus 2 kappa Subscript c Baseline EndFraction equals 0 period

      There is an interface between the polymer matrix and fillers in composites. Phonons can be scattered at this interface if the interfacial coupling between the matrix and fillers is weak. If the fillers are small and the separation between the fillers is large, the thermal conductivity of the composites is low.

      1.2.1 Dependence of Thermoelectric Efficiency on ZT

      The most important application for thermoelectric materials is the energy conversion between heat and electricity. It is important to understand the heat transfer, drift electrical current and thermoelectric current in thermoelectric generators. The Seebeck effect is exploited to convert heat into electricity in thermoelectric generator. Assume that the p‐type and n‐type thermoelectric materials have the same ZT value, the thermoelectric conversion efficiency depends on the ZT value of the thermoelectric materials,

      where η c is the Carnot efficiency for the temperature difference at the hot (T H) and cold ends (T C),

      (1.33)eta Subscript normal c Baseline equals StartFraction upper T Subscript normal upper H Baseline minus upper T Subscript normal upper C Baseline Over upper T Subscript normal upper H Baseline EndFraction comma

      and upper T overbar is the mean value of the operation temperatures,

      (1.34)upper T overbar equals StartFraction upper T Subscript normal upper H Baseline plus upper T Subscript normal upper C Baseline Over 2 EndFraction period

Schematic illustration of dependence of thermoelectric generation <hr><noindex><a href=Скачать книгу
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