Arrhenius carrier transport

As described in the previous section, both electronic and ionic conductions take place in mesophases when the material contains trace amounts of chemical impurities. These types of conduction exhibit different charge carrier transport properties, as demonstrated by the transient photocurrents the different mesophases measured under the same conditions as shown in Fig. 2.10. In these transient photocurrents, the fast transit times are shifted to shorter times as the molecular order in the mesophases is increased from SmA to SmE and from Coin to the plastic phase, while the slow transits stay in the same time range of 1,000 (xs irrespective of the mesophase in both smectics and discotics. Figiue 2.11 shows Arrhenius plots of the mobilities for fast and slow transits of the 2-phenylnaphthalene derivative 8PNP-012. The mobility for the fast transit hardly depends on the temperature, while the mobility for the slow transit does depend on temperature, with an activation energy... 

However, one should be cautious about overinterpreting the field and temperature dependence of the mobility obtained from ToF measurements. For instance, in the analyses of the data in [86, 87], ToF signals have been considered that are dispersive. It is well known that data collected under dispersive transport conditions carry a weaker temperature dependence because the charge carriers have not yet reached quasi-equilibrium. This contributes to an apparent Arrhenius-type temperature dependence of p that might erroneously be accounted for by polaron effects. 

On average, a carrier located at can continue its motion only after thermal excitation. If all carriers were located at and a transport level existed at e = 0, the center of the DOS, the temperature dependence of the mobility should follow a non-Arrhenius dependence of the form exp[-(a/ 7)-2]. This temperature dependence has been recovered by both EMA studies and Monte Carlo simulations, although with a constant in the exponent of less than unity that accounts for the statistics of occupational energies. The predicted temperature dependence of the zero-field mobility is... 

Transit Pulse Shapes. Figure 3 displays the current-mode hole transit pulse shapes in PVK and in Br-substituted PVK from 264 to 490 K, together with the corresponding Arrhenius plots of mobility (34). For brominated PVK, the transit pulses remain relatively featureless over the entire experimentally accessed range. For PVK, however, the transit pulses display a well-developed shoulder above 414 K, which is characteristic of nondisper-sive transport of the photoinjected carrier sheet. 

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. 

The dependence of the dc conductivities and the parameters derived thereof show that there are distinct differences between the ion dynamics in PDADMAC-rich and PSS-rich PEC. In both cases, however, the Arrhenius dependence of clearly shows that the ion dynamics in PEC materials is determined by the thermally activated hopping processes of the mobile ions. The fact that the isothermal dc conductivity increases continuously with NaPSS content indicates that the chloride ions do not dominate the ion transport, even in PEC materials with an excess of polycations and thus Cl as the most abundant mobile charge carrier. Otherwise, aac as a function of x should pass through a minimum, which is obviously not seen experimentally. The conductivity measured for PEC with x < 0.50 could therefore be either due to residual Na ions or protons. To shed more light on this aspect, PEC in which the sodium ions were replaced by lithium or cesium ions were studied. These results are discussed in the following section. 

Some polymer electrolytes show conductivity temperature dependence that falls outside the three types described above, with neither the Arrhenius law nor the VTF (or WLF) law being followed in the temperature ranges studied." Here, if there are no phase changes, effects associated with ionic aggregate equilibria are likely, superimposed on the simple variation in ionic mobility. In all cases, it is important to consider not only this parameter, but also the number and types of charge carriers, which are influenced by the ionic association that probably exists in ionic transport. ... 

Fig. 2.11 Arrhenius plot of carrier mobility for negative carriers in various phases of a 2-phenylnaphthalene derivative, 6-(4 -octylphenyl)-2-dodecyloxynaphthalene. Two transits, i.e., fast and slow transits are observed in the SmA and SmB phases the fast transit is attributed to electron transport and the slow one to anion transport the ionic mobility is enhanced by 5 mol%-dilution with dodecane, while electron mobility remains unchanged or is slightly decreased...

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