Polaronic relaxation

While experimental evidence for polaronic relaxation is extensive, other experiments render the polaron models problematic (i) the use of the Arrhenius relation to describe the temperature dependence of the mobility (see above) leads to pre-factor mobilities well in excess of unity, and (ii) the polaron models cannot account for the dispersive transport observed at low temperatures. In high fields the electrons moving along the fully conjugated segments of PPV may reach drift velocities well above the sound velocity in PPV.124 In this case, the lattice relaxation cannot follow the carriers, and they move as bare particles, not carrying a lattice polarization cloud with them. In the other limit, creation of an orderly system free of structural defects, like that proposed by recently developed self-assembly techniques, may lead to polaron destabilization and inorganic semiconductor-type transport of the h+,s and e s in the HOMO and LUMO bands, respectively. 

Yet another advantage of higher-MW materials over small molecules is their smaller polaron relaxation energies [99], so that the turn-over from polaron-like to band-Uke transport should, in principle, occur at a lower degree of interchain order. This provides an additional explanation of the higher mobilities in higher-MW polymers, as compared to more crystalline, but lower-MW materials longer chains tolerate more disorder. 

Such renormalization can be obtained in the framework of the small polaron theory [3]. Scoq is the energy gain of exciton localization. Let us note that the condition (20) and, therefore, Eq.(26) is correct for S 5/wo and arbitrary B/ujq for the lowest energy of the exciton polaron. So Eq.(26) can be used to evaluate the energy of a self-trapped exciton when the energy of the vibrational or lattice relaxation is much larger then the exciton bandwidth. 

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

The electrical conductivity in the solid state is determined by the product of the carrier concentration and the carrier mobility. In conjugated polymers both entities are material dependent and, i.e., are different for electrons and holes. Electrons or holes placed on a conjugated polymer lead to a relaxation of the surrounding lattice, forming so-called polarons which can be positive or negative. Therefore, the conductivity, o, is the sum of both the conductivity of positive (P+) and negative polarons (P ) ... 

Later we will describe both oxidation and reduction processes that are in agreement with the electrochemically stimulated conformational relaxation (ESCR) model presented at the end of the chapter. In a neutral state, most of the conducting polymers are an amorphous cross-linked network (Fig. 3). The linear chains between cross-linking points have strong van der Waals intrachain and interchain interactions, giving a compact solid [Fig. 14(a)]. By oxidation of the neutral chains, electrons are extracted from the chains. At the polymer/solution interface, positive radical cations (polarons) accumulate along the polymeric chains. The same density of counter-ions accumulates on the solution side. 

The realization of the polaronic nature of polyene radical cations leads naturally to the question, to what extent the pronounced relaxation of polyenes upon ionization affects their excited-state energies. Such changes can be assessed by comparing the ionization energy differences I) —I] obtained from PE spectra with the positions of the band maxima in the radical cation s EA spectra which measure the same quantities at the radical cation... 

The hopping energy is thus one-half of the energy released when a polaron is formed. For this so-called adiabatic case, when the electron goes backwards and forwards several times during the period of excitation, the chance per unit time that the electron will have moved from one site to another after the system has relaxed is given by (3), where co is the attempt-to-escape frequency. The diffusion coefficient D is thus... 

Above the Curie or Neel point, a spin polaron will move by a diffusive process. A moment on the periphery of the polaron will reverse its direction in a time t (the relaxation time for a spin wave). Each time it does so, the polaron can be thought to diffuse a distance (a/R)3R, so the diffusion coefficient is... 

We investigated the ultrafast dynamics in a Na-NaBr melt at 1073 K by fs pump probe absorption spectroscopy. A simple model was used to simulate the dynamics of polaron-, bipolaron- and Drude-type electrons. The relaxation times for polarons and bipolarons are 210 fs and 3 ps, respectively. The existence of an isosbestic point at 1.35 eV indicates an inter-conversion between bipolarons and Drude-type electrons. 

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