Retrapping

Concerning the nature of electronic traps for this class of ladder polymers, we would like to recall the experimental facts. On comparing the results of LPPP to those of poly(para-phenylene vinylene) (PPV) [38] it must be noted that the appearance of the maximum current at 167 K, for heating rates between 0.06 K/s and 0.25 K/s, can be attributed to monomolecular kinetics with non-retrapping traps [26]. In PPV the density of trap states is evaluated on the basis of a multiple trapping model [38], leading to a trap density which is comparable to the density of monomer units and very low mobilities of 10-8 cm2 V-1 s l. These values for PPV have to be compared to trap densities of 0.0002 and 0.00003 traps per monomer unit in the LPPP. As a consequence of the low trap densities, high mobility values of 0.1 cm2 V-1 s-1 for the LPPPs are obtained [39]. 

As stated already in the introductory section, main feature of the carrier transport in the polymer is known to be the multitrapping process of the hole carrier. So, the fundamental equation due to Haering and Adams [6 of the fast retrapping limit (equation (i)) will be used to analyze the results ... 

All TSRs involve the release of trapped charge carriers into either the conduction band or valence band and their subsequent capture by recombination centers and recapture by other traps (retrapping). Their experimental investigation is undertaken with the goal of determining the characteristic properties (parameters) of traps cap-tnre cross sections, thermal escape rates, activation energies, concentration of traps. 

A carrier thermally released from the trap into the transport band may be either retrapped by the same species of traps or a different one and, under the influence of an electric field, may contribute to an externally measurable current. It may either be swept out of the region being probed or recombined with a recombination center. Some of the electrons may even overcome the work function barrier and leave the solid. The traffic of these carriers from traps to the recombination centers or out of the material can be monitored at various stages, and thus, information on the thermal emission rates can be obtained indirectly. 

After the decay of the excess free carriers due to recombination and trapping transitions, the solid is in the so-called excited state, which is characterized by the perturbation of the statistical equilibrium. The concentration of the remaining free carriers is now determined by the balance between thermal emission of carriers from the traps, retrapping transitions, and capture by recombination centers. 

Analytic solntions for a(T) were reported by Simmons and Taylor [12] for the case that retrapping can be neglected in a thin sample at high electric fields. They considered the presence of several trap levels of density A and demonstrated the snperposi-tion of the individnal glow peaks when the thermal ionization energies of these levels are very close to each other (Fig. 1.3). 

Detailed solutions have not been discussed in the literature so far. The time dependence of the rate equations (2.4) and (2.5) is replaced by the temperature dependence via the heating program, which is taken to be linear T(f) = Tq + v t, where Vt = dr/dt is the heating rate. Retrapping can be neglected in a sample at high electric fields. From equations (2.5) and (2.6), we have... 

Initially, we will assume that as the electrons are released from the trap, they quickly are captured at recombination centers and are not retrapped, i.e., r"1 (Nt — ni)ff iv . Then the average n in the conduction band will remain small and Eq. (47) becomes... 

Several further trap-trap distillations between flasks 2 and 3 yield successively smaller crops of crystalline trimethylindium which are in each case retrapped into the bulk of the product contained in flask 1. 

The product, which at this point is bright yellow due to traces of dissolved base, is retrapped at room temperature, in vacuo, from one storage flask to another. If the product is now not completely colorless, the retrapping process is repeated. Yield 72 g (96% based on adduct, 93% based on cadmium dichloride). 

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