Polaron, in polyacetylene

Because the extension of the polaron in polyene radical cations is finite (10-20 double bonds depending on the type of calculation), its electronic structure is independent of the number of double bonds attached to either side of it, so that the two lines in Figure 29 must bend at some point to meet the abscissa horizontally, as indicated by the dashed curves. Apparently, the point of inflection has not been reached for n = 15, but it is of interest that the curve for the first excited state could well extrapolate to 0.35 eV, which happens to be where the absorption of a polaron in polyacetylene has been observed300. If this is true, a second, more intense absorption band should occur between 0.5 and 0.7 eV, but the corresponding experiments have not yet been carried out. 

We use these equations first to study formation of the polaron in the absence of an electric field, i.e., with A=0 [65]. Because only small motions of the sites are involved in the formation, the results should be approximately correct even for DNA in solution. To begin with we find the static undistorted solution (y =0) for a stack of AT base pairs with 2N n electrons. Using this solution as the initial condition for t=0, we integrate Eqs. 15 and 16 numerically for the case of 2N-1 n electrons on the stack. The parameters used were fo=0.3 eV, a=0.6 eV/A, and fC=0.85 eV/A. The result for the sequence given at the bottom of the figure is shown in Fig. 5. It is seen that the polaron is fully formed at 4 ps. The time of formation is much longer than was found for polarons in polyacetylene. The calculations of Su and Schrieffer... 

Fig. 9.12 Energy level schemes of solitons and polarons in polyacetylene (a) soliton, (b) anti-soliton, (c) negative soliton, (d) positive soliton, (e) negative polaron and (f) positive polaron.

Anderson SM and Krinsky NI (1973) Protective action of carotenoid pigments against photodynamic damage to Uposomes. Photochem Photobiol 18 403 08 Badger B and Brocklehurst B (1969) Absorption spectra of dimer cations. Trans Faraday Soc 65 2576-2581 Bally T, Roth K, Tang W, Schrock RR, Knoll K and Park LY (1992) Stable polarons in polyacetylene oligomers Optical spectra of long polyene radical cations. J Amer Chem Soc 114 2440-2446... 

J.L. Bredas, R.R. Chance, and R. Silbey, Comparative theoretical study of the doping of conjugated pol3Tners Polarons in polyacetylene and polyparaphenylene, Phys. Rev. B. Condens. Matter., 26, 5843 5854 (1982). 

D. S. Boudreaux, R. R. Chance, J. L. Bredas, R. Silbey, Solitons and polarons in polyacetylene - self-consistent-field calculations of the effect of neutral and charged defects on molecular-geometry, Physical Review B 1983, 28, 6927. 

Photoexcitation is one of the most powerful methods for the investigation of the nature of defects such as solitons and polarons in polyacetylene. For a consistent... 

Fesser K, Bishop AR, Campbell DK (1983) Optical-absorption from polarons in a model of polyacetylene. Phys Rev B 27 4804... 

As pointed out above, the most accurate and reliable information obtained by ENDOR is the resonance frequency that directly gives the hyperfine coupling con.stant. In this respect, the firequency-derivative ENDOR spectra obtained by cw-ENDOR detection by employing the frequency modulation scheme, are particularly important because of high-frequency resolution. Combined with ENDOR-induced ESR, the maximum ENDOR frequency, important in identifying the peak value of the spin density distribution, can be determined very accurately [7]. Specific examples are discussed in the cases of solitons in polyacetylene and polarons in poly(paraphenylene vinylene) in Sections 3.2 and 3.3. 

However, simple band theory is not sufficient to explain the electrical behavior of conducting polymers. For example, simple band theory cannot explain why the charge carriers, usually electrons and holes, in polyacetylene and polypyrrole are spinless. In order to overcome these and other difficulties, the concepts of solitons, polarons, and bipolarons have been used since the 1980s to explain the electronic behavior of conductive polymers [21]. 

FIGURE 2 (a) Polaron in polythiophene, (b) bipolaron in polythiophene, and (c) soliton in polyacetylene. 

There could also be polarons in c/5-poIyacetylene, and these could be mobile. Even without interchain interaction there is a soliton-antisoliton attraction in cis-polyacetylene because of the energy difference between the cw-transoid and the trans-cisoid structure. Figure 1.32 shows polarons and bipolarons in cw-polyacety-lene. In polyaraphenylene the situation is very similar... 

The radical cations of polyenes are models of a positive polaron in traw-polyacetylene. The electronic absorption spectra of the radical cations of a,w-dibutyloligoenes have been reported [114]. The observed absorption maxima of the radical cations [114] of dibutyloligoenes are listed in Table XIII. Each radical cation gives... 

C. W. Spangler and K. O. Havelka, Polaron and bipolaron stabilization via substituent effects and increasing conjugation length in polyacetylene oligomers, Polym. Prepr. 3l(l) 396 (19W). 

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