Thermopower

The standard Mott equation for diffusion thermopower 5a in metallic systems is a function of the first derivative of the density of states at the Fermi level, and it is expressed as 

In undoped conducting polymers [cr(300 K) 10-6 S/cm], S (300 K) 1 mVK-1. This value decreases upon doping, and in fully doped systems S (300 K) 10 pV K-1. Although conducting polymers are intrinsically quasi-ID and highly disordered, a remarkable linear S(T) has been observed in high quality metallic samples down to 10 K [16,21]. This indicates that the thermal current carried by phonons is less impeded by insulating barriers 

The anisotropic MR in oriented metallic samples can be used to probe the microscopic level correlation between the orientation of chains and transport properties. 

Acknowledgements. The author would like to thank Mr. A.K. Mukherjee for his help with the preparation of figures. 

Nalwa (Ed.) Handbook of Organic Conductive Molecules and Polymers, Vols. 1-4 (Wiley, New York, 1997) 

The effect of fast neutron fluence on thermal conductivity and thermopower has been determined by Uher and Huang (70). For fluences to 3 x 1018 n/cm2 Tc decreases in Y-Ba-Cu-O to a temperature of 86 K, the thermal conductivity decreases and is without a peak above Tc and the thermopower starts from a negative value and approaches zero and becomes positive. As will be seen below the more usual value of thermopower is positive in the superconducting material but these authors note the variability dependent on sample preparation conditions. 

The thermopower or thermoelectric power is the electrostatic potential difference between the high and low temperature regions of a material with an impressed thermal gradient and zero electric current flow. The sign gives an indication of the sign of the charge carriers - positive for hole carriers. 

Measurements in the La-Ba-Cu-O material were reported by Maeno et al. (71). At the optimum Ba concentration (0.15) the 

Theoretical interpretation is incomplete early measurements on La-Sr-Cu-O by Hundley et al. (76) were suggested to indicate a phonon drag to explain some features although more recently a narrow band Hubbard model has been developed by Fisher (77). 

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A novel modification of the STM supplements images with those due to the thermopower signal across the tip-sample temperature gradient [49]. Images of guanine on graphite illustrate the potential of this technique. 

Heremans J. and Beetz, C.P.,. Thermal conductivity and thermopower of vapor-grown graphite fibers J. Phys. Rev.B 32, 1985, p.l981... 

After briefly introducing the main electronic features of CNTs (Sec. 2) and some general aspects of electronic conduction and transmission (Sec.. 1), we will show how complex electrical measurements to perform on such tiny entities are (Sec. 4). Then we will present the main experimental results obtained on the electrical resistivity of MWCNT and SWCNT and the very recent data relative to the thermopower of SWCNT bundles (Sec. 5). We will also discuss the effect of intercalation on the electrical resistivity of SWCNT bundles (Sec. 6). Finally, we will present some potential applications (Sec. 7). 

In conclusion, wc have shown the interesting information which one can get from electrical resistivity measurements on SWCNT and MWCNT and the exciting applications which can be derived. MWCNTs behave as an ultimate carbon fibre revealing specific 2D quantum transport features at low temperatures weak localisation and universal conductance fluctuations. SWCNTs behave as pure quantum wires which, if limited in length, reduce to quantum dots. Thus, each type of CNT has its own features which are strongly dependent on the dimensionality of the electronic gas. We have also briefly discussed the very recent experimental results obtained on the thermopower of SWCNT bundles and the effect of intercalation on the electrical resistivity of these systems. 

The interest of physicists in the conducting polymers, their properties and applications, has been focused on dry materials 93-94 Most of the discussions center on the conductivity of the polymers and the nature of the carriers. The current knowledge is not clear because the conducting polymers exhibit a number of metallic properties, i.e., temperature-independent behavior of a linear relation between thermopower and temperature, and a free carrier absorption typical of a metal. Nevertheless, the conductivity of these specimens is quite low (about 1 S cm"1), and increases when the temperature rises, as in semiconductors. However, polymers are not semiconductors because in inorganic semiconductors, the dopant substitutes for the host atomic sites. In conducting polymers, the dopants are not substitutional, they are part of a nonstoichiometric compound, the composition of which changes from zero up to 40-50% in... 

Nagels and Krikor143 studied the effect of y-irradiation on the electrical properties of fraws-polyacetylene. They reported a marked decrease of the conductivity and a slight increase of the thermopower after y-irradiation of 10 kGy (1 Mrad). Their study showed that no essential structural changes occur during irradiation. 

The Seebeck coefficient is frequently called the thermoelectric power or thermopower, and labeled Q or S. Neither of these alternatives is a good choice. The units of the Seebeck coefficient are not those of power. The symbol Q is most often used to signify heat transfer in materials. The designation S can easily be confused with the entropy of the mobile charge carriers, which is important because the Seebeck coefficient is equivalent to the entropy per mobile charge carrier (see Supplementary Material S3). 

Figure 6.48 (a) Effect of doping on the electrical conductivity (solid line) and thermopower (broken line) of polyacetylene. (Following Etemad et al, 1982.) (b) solitons in trans-polyacetylene (i) neutral, (ii) positive and (iii) negative solitons. Arrow marks the boundary between the two symmetric configurations. A, acceptor D, donor. (Following Subramanyam Naik, 1985.)... 

We shall in this book use the concept of a degenerate gas of small—or at any rate heavy—polarons. Clearly we should not expect these to be formed unless the number of carriers is considerably less than the number of sites. We also remark, as mentioned earlier, that in all metals, at temperatures less than B phonons lead to a certain mass enhancement, of order less than 2. A treatment is given by Ashcroft and Mermin (1976, p. 520). This affects the thermopower some results for an amorphous alloy (Ca AlJ from Naugle (1984) are shown in Fig. 2.2. A theoretical treatment of the range between this situation and the polaron gas has not yet been given. 

Fig. 2J2 Thermopower 5 of metallic glasses Cax. Al, as a function of temperature. Since S is proportional to kBT/EF, these show an increase of p(=i 2k2/meff) above about...

In crystalline materials a characteristic of polaron motion is a difference between E the activation for conduction, and s, that for the thermopower written as S=(kB/e) (EsjkBT+ const). We expect that Ea=Ec—EF+WH and Es=Ec-Ef, where Ee is the extremity of the band in which the carriers move. 

Our model for the density of states is thus as in Fig. 4.7. The total density of states is mainly due to spin fluctuations, and has a maximum for n=1, where n is the number of electrons per atom. The curve for current carriers needs to be used for calculating thermopower and resistance the experimental evidence discussed in the following chapters suggests, however, that the Hall coefficient RH is given by the classical formula 1 jnec. 

This material, which has the corundum structure, is a semiconductor at low temperatures, the optical band gap being 0.2 eV (Lucovsky et al. 1979). We should probably consider it to be an intrinsic semiconductor, but the activation energy in the conductivity does not appear to be constant. The thermopower (Chandrasekhar et al. 1970) is about 900pVK 1 at 100K and 500pVK 1 at 200 K this would suggest an activation energy of about 0.06 eV, or less than half the band gap.f This makes it likely that one of the carriers is a small polaron the... 

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