Lattice polaron

It is shown below that the soliton lattice is always the most stable lattice configuration. This is not surprising since the system is restricted to one chain, i.e., it is one-dimensional. For onedimensional systems, the Peierls effect results in an opening of a gap in the electronic spectrum 

The characteristic width of the polaron is determined by lp=V21s and M=0.623 Ip [39], where 1 is the soliton width. The soliton width is estimated to ls=3 by fitting a tanh function to the optimized order parameter (see Ref. 26 and below). This length is very close to the value obtained from ab inlto, extended basis set Hartree-Fock calculations for a single soliton in the presence of a screened sodium counterion [40], 

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The origin of paramagnetism in the conducting state of polyaniline has been attributed to a polaron lattice [89] which forms at 50% protonation,... 

Figure 12 Formation of a polaron lattice according to Ref. 89 (a) emeraldine salt in bipolaron form (b) dissociation of the bipolaron into two polarons (c) rearrangement of the charges into a polaron lattice. ...

Experimental Evidences of Polarons, Lattice-Charge Segregation, and the Isotope Effect The Role of JT Distortions... 

FIGURE 5.1 The doping of emeraldine base with protons to form the conducting emeral-dine salt form of polyaniline (a polaron lattice). 

However, the most significant dependence of the conductivity of PAn is on the proton-doping level.19 The maximum conductivity occurs when PAn is 50% doped by protons, to give the polaron lattice structure shown in Figure 5.1. Under these conditions, the conduction mechanism is similar to that for the other polymers described, with the polaron states overlapping to form midgap bands. The electrons are thermally promoted at ambient temperatures to the lower energy-unfilled bands that permits conduction.20... 

Internal redox reaction Polaron lattice formation... 

The optical properties of the different forms of PANI have been extensively studied in the literature and a good agreement exists about the assignment of most of the transitions, overall in the insulating forms. The controversy which always exists on a point as fundamental as the existence of either bi-polarons or a polaron lattice, is accompanied by divergences in the interpretation of some features in the optical spectrum of the conducting form. Moreover, in an ideal form with two electrons in a four ring unit, the situation of polarons remains questionable are they solely on the imine sites Are amine sites also protonated ... 

When EB is protonated leading to ES, a continuous shift of the exciton band from 2 to 1.5 eV is observed, together with the growth of the polaron band, due to the formation of within-gap new defects levels. The polaron state with unpaired spin, (that is to say the isolated polaron) has been determined by Electron Spin Resonance at 2.75 eV when the level of protonation increases up to the formation of two associated polarons, the spin resonance disappears, while the peak shifts up to 3.1 eV [51]. In ES, beside the polaron lattice peak at (on an average) 2.9 eV, a new absorption centred at 1.0 eV attributed to intrachain ffee-carrier excitation appears also [52]. The near-UV absorption weakens, since the metallic character of ES is inconsistent with the keeping of a 7t —> tt transition. 

Finally, in protonated pemigraniline, the band at 3.8 eV disappears completely and a polaron lattice character was assumed for fully oxidized protonated PANl, with two bands at 2.2 and 4.3 eV [55] but the reality of this kind of structure is not demonstrated. 

All energies are between the two values given in the literature for a single polaron and a polaron lattice. The value of 2.75 eV for isolated polarons in leucomer-aldine salt was found [78] by determination of the... 

Figure 14.22 Decomposition of the OMA polaron band during the PANI/Sn02 film polarization at 450 mV in a pH 3 solution in two sub-bands at 3.16 eV (bipolaron) and 2.88 eV (isolated polaron/polaron lattice).

As noted above, the free carrier contribution which extrapolates to the measured a(0) must be in the far-IR below 450 cm"1.15 Nevertheless, most of the 7C-electron oscillator strength remains in the broad absorption band above 0.2 eV. An alternative which appears to be in agreement with the essential experimental facts is that polyacetylene is an example of a polaronic metal. The polaron lattice with a half-filled polaron band is certainly consistent with the observed susceptibility, hi the case of a polaron lattice, the IRAV modes are expected, and would be r -shifted from the Raman modes provided that the pinning is weak. Although the intensity of the IRAV modes was initially csdculated to be much too weak, this calculation ignored the effect of the counter-ions the counter-ion Coulomb potentials may lead to sufficient nonuniformity in the charge density, to yield the observed IRAV mode intensities.For the polaron lattice, a((o) would have two contributions with a "gap" in between ... 

Jozefowicz, M.E., R. Laversanne, H.H.S. Javadi, A.J. Epstein, J.P. Pouget, X. Tang, and A.G. MacDiarmid. 1989. Multiple lattice phases and polaron-lattice spinless-defect competition in polyaniline. Phys Rev B 39 12958. 

Illustration of delocalization (polaron lattice) of the emeraldine state ... 

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