Polarons in solid

A complete treatment must also include formation of neutral atomic clusters A and negative ion clusters A. These species are stabilized by the presence of an ionized electron. They are the fluid state analogues of the polarons in solids described in Sec. 2.3.3(c). The idea that negative clusters affect the optical, dielectric, and thermoelectric properties of dense metal vapors close to the critical point has been put forward by a number of authors (Khrapak and lakubov, 1970 Hefner and Hensel, 1982 Hernandez, 1982 Hefner et al., 1982). We discuss this in relation to the transport properties of mercury in chapter 4. 

Gartstein YN, Conwell EM (1994) High-field hopping mobility of polarons in disordered molecular-solids - a Monte-Carlo study. Chem Phys Lett 217 41... 

Bipolaron — Bipolarons are double-charged, spinless quasiparticles introduced in solid state physics [i]. A bipolaron is formed from two -> polarons (charged defects in the solid). For chemists the double-charged states mean dications or dianions, however, bipolarons are not localized sites, they alter and move together with their environment. By the help of the polaron-bipolaron model the high conductivity of -> conducting polymers can be explained. 

Soliton — Solitons (solitary waves) are neutral or charged quasiparticles which were introduced in solid state physics in order to describe the electron-phonon coupling. In one-dimensional chainlike structures there is a strong coupling of the electronic states to conformational excitations (solitons), therefore, the concept of soliton (-> polaron, - bipolaron) became an essential tool to explain the behavior of - conducting polymers. While in traditional three-dimensional -> semiconductors due to their rigid structure the conventional concept of - electrons and -> holes as dominant excitations is considered, in the case of polymers the dominant electronic excitations are inherently coupled to chain distortions [i]. 

By comparing the result of w /w for the infinite-site system obtained by VED [96] (see. Fig. 2), we are confident that the two-site calculation provides a reasonably good result for m /m in the whole range of g at least in the anti-adiabatic region of t/a>o. The relevance of the two-site calculation has also been seen in the Holstein model [78]. Thus we can expect that the same is true for the r (g) t JT polaron. In Fig. 3, we show the result of m/m for the T (g) r system solid curve) which is obtained in the anti-adiabatic region by implementing an... 

Fig. 3 Inverse of the mass enhancement factor, mim, as a function of g

The PL quantum yield r)pl. While r]pl of many dyes is close to 100% in solution, in almost all cases that yields drops precipitously as the concentration of the dye increases. This well-known concentration quenching effect is due to the creation of nonradiative decay paths in concentrated solutions and in solid-state. These include nonradiative torsional quenching of the SE,148 fission of SEs to TEs in the case of rubrene (see Sec. 1.2 above), or dissociation of SEs to charge transfer excitons (CTEs), i.e., intermolecular polaron pairs, in most of the luminescent polymers and many small molecular films,20 24 29 32 or other nonradiative quenching of SEs by polarons or trapped charges.25,29 31 32 In view of these numerous nonradiative decay paths, the synthesis of films in which r]PL exceeds 20%, such as in some PPVs,149 exceeds 30%, as in some films of m-LPPP,85 and may be as high as 60%, as in diphenyl substituted polyacetylenes,95 96 is impressive. 

A polaron is an electron attached to, and moving with, the polarization induced by it in a polar environment. This concept is used mostly in solid state physics the liquid analog is the solvated electron. 

An electron in a solid behaves as if its mass [CGS units are used in this review the exception is for the tabulation of effective masses, which are scaled by the mass of an electron (m0), and lattice constants and radii associated with trapped charges, which are expressed in angstroms (1A = 10 8 cm)] were different from that of an electron in free space (m0). This effective mass is determined by the band structure. The concept of an effective mass comes from electrical transport measurements in solids. If an electron s motion is fast compared to the lattice vibrations or relaxation, then the important quantity is the band effective mass (mb[eff]). If the electron moves more slowly (most cases of interest) and carries with it lattice distortions, then the (Frohlich) polaron effective mass (tnp[eff]) is appropriate [11]. The known band effective and polaron effective masses for electrons in the silver halides are listed in Table 1. The polaron and band effective masses are related to a... 

Figure 6.28. Spin density distribution of the polaron in PPV calculated by PPP model [132] Reprinted from Solid st. Commun. 95 (1995) 137-41.

Second, canonical transformation methods may be employed to diagonalize the system-bath Hamiltonian partially by a transformation to new ( dressed ) coordinates. Such methods have been in wide use in solid-state physics for some time, and a large repertoire of transformations for different situations has been developed [101]. In the case of a linearly coupled harmonic bath, the natural transformation is to adopt coordinates in which the oscillators are displaced adiabatically as a function of the system coordinates. This approach, known in solid-state physics as the small-polaron transformation [102], has been used widely and successfully in many contexts. In particular, Harris and Silbey demonstrated that many important features of the spin-boson system can be captured analytically using a variationally optimized small-polaron transformation [45-47]. As we show below, the effectiveness of this technique can be broadened considerably when a collective bath coordinate is first included in the system directly. 

It is clear that the polaron shifts, fj, directly reduce the linear TLS-bath couplings, so that F would vanish entirely for fj = gf, this is the traditional (nonvariational) small-polaron transformation used in solid-state physics [102]. This choice is not generally optimal, however, because it leads to larger F+ and F couplings. In calculations presented below, the fj are always variationally optimized. 

In solid state physics, polarons are electrostatically induced local lattice distortions caused by an electron in a ionic crystal. In conducting polymers radical cations (lone electrons associated with positively charged holes) have a similar effect. 

These radical cations are termed polarons based on the physical description of similar states in solid state physics. Their relevance to the electronic conduction mechanism in these films has been discussed elsewhere [86]. 

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