Dysonian shape

Figure 29.21 The upper portion shows the EPR lines recorded prior to exposing polyacetylene film to gaseous AsFs and the transformation of a symmetric EPR line shape to a dysonian line for conductive material. The ratio of the low-field to high-field amplitudes is shown in the inset as a function of the composition of the doped film. The lower portion of the curve shows a single line fit to the theoretical dysonian line shape (circles). 

Figure 2(a) shows the ESR signal measured for two temperatures and fits using an assymetric Dysonian line shape. The fit allows us to determine the Lande g factor and the line width (AH) gives us a measurement of the spin scattering time ts using (f//// A//)rs = h. 

On the other hand, if Td is shorter than T2, the diffusion tends to increase the width of the resonance line from T2 to Td When the conductivity, a increases, the skin depth, S decreases and then the diffusion time, Td also decreases according to Eqs. (7.34) and (7.35). As a result, the condition with Td < T2, is realized. The line shape theory by Dyson is then applicable. The exact line shape can be derived as functions of Td, T2, and Tx where Tj is the time it takes for the electron to pass through the sample. Eeher and Kip [49] calculated the line shapes for different ratios of the diffusion time Td to the relaxation time T2, which are shown in Fig. 7.44 in the case of Tx Td, Tj T2. A typical Dysonian line shape is that depicted in the... 

An example of an ESR spectrum of AsFs doped PA is also shown in Fig. 7.48. The excellent agreement between the experimental and calculated spectra indicates that the line shape is Dysonian. The highest doping levels result in a skin depth less than the sample thickness. For a 10 S/cm, the skin depth was calculated... 

Conclusive additional evidence for the metallic nature of PAni and its blends with PMMA is provided by electron spin resonance (ESR) studies with the observation of a Dysonian line shape [104]. In both cases, the asymmetry ratio (A/B) decreases with decreasing temperature. The observed changes in the line shape from Dysonian to Lorentzian are thus seen to be a manifestation of the variation with temperature of the electrical conductivity (Figure 1.46). The g value is calculated as 2.00191 + 0.00005. The g value, which is close to the fi-ee spin value, confirms that the spins are indeed polarons. 

The striking similarity, which in some cases even extends to small asymmetries in line shape, has caused early erroneous assignments of the line as being caused by mobile electrons as observed with ESR in case of metals by Dyson (Dysonian line, [20]). 

Fig. 58. ESR spectra of 150 ppm Mn and 6 ppm Qd in CePdj at 1.5 K and 2.45 K. The experimental results have been fitted using a Dysonian line shape. This is the only example of a well-resolved Mn-hyperflne spectrum in a metal. From Schaeffer and Elschner (1985).

Fig. 60. Line shapes of Gd-ESR experiments in normal and in the superconducting state of CeRuj. Note the strong deviations from a Dysonian lineshape in the sc state. From Baber-schke et al. (1974).

The saturation of spin packets in highly doped polymers decreases significantly due to the increase in spin-spin and spin-lattice interactions. In the ESR spectra of such samples, the Dysonian term normally appears due to the formation of a skin layer with thickness 8. In contrast with the classic ESR signal, the Dyson-like spectrum shape feels both the spin polarons and the spinless bipolarons diffusing through a skin layer. It is possible to determine the intrinsic conductivity Oac of the sample directly from its Dysonian ESR spectrum. If the skin-layer is formed on the surface of a spherical powder particle with radius R, the coefficients A and D in Eq. 5 can be determined from Eqs. 16, ... 

Figure 12 exhibits the temperature dependence of the ac conductivity of some doped RANI samples determined from their Dysonian D-band ESR spectra using Eqs. 5 and 16. The shape of the temperature dependence demonstrates nonmonotonous temperature dependence with a characteristic point 170-200 K. Such a temperature dependence can be a result of two parallel processes the above-mentioned tunneling of charge carriers at T (the semiconducting regime), and their interaction with lattice phonons atT>T (the metallic regime), as desaibed by Eqs. 14 and 15, respectively. 

Oudard et al. [719, 720] recorded ECESR spectra of PPy in a molten salt electrolyte liquid at room temperature. The ESR signal was observed only in a very narrow range of electrode potentials that closely correlate with the electrochemical oxidation current the line shape was not Dysonian, contrary to the observation reported previously. Evaluation of kinetic data implies slow formation of radical cations (polarons) and fast disappearance, most likely by recombination into spinless dications. 

Jg. 11-40 The ESR spectrum of P(MeT) doped with SO3CP3 ion at two levels, (a) P(MeT) (S03CP3)o.3o with a symmetrical Lorentzian line shape and (b) P(MeT) (S03CP3)o.5o with an asymmetrical Dysonian line shape. After Reference [31], reproduced with permission. 

In our first paper [4] we presented a mixture of conductivity and EPR studies. We interpreted the temperature/phase dependence of the EPR line shapes of aluminium trichloride doped HAT6 in terms of Dysonian theory, but this later proved to be incorrect. We later showed that both the g value and the EPR line width are dependent on the orientation of the director relative to the field and this leads to a complex, line shape in powder samples [7], Just as p-doped, hole conductors can be produced by oxidation of discogens with pi excessive cores using aluminium trichloride, aluminium tribromide or NO+X", n-doped, electron conductors can be produced by reduction of discogens with pi deficient cores using alkali metals [8]. 

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