Diffuse-trap model

Thomann and co-workers have reported that all of the spins are localized in 99% C enriched trans- and cis-(accurate composition is cisIQ. -tmnslO.l) polyacetylene, studied by the multiple quantum NMR (MQNMR) detected by the ESE-technique [165,186]. This is, however, clear experimental evidence demonstrating the validity of the difFuse/trap model [6,82]. 

It is important to know that tlie result firom proton NMR is consistent with that from ESR. If we lake into account a quantitative large ambiguity induced Irom the diffuse/trap model (especially in proton NMR, almost the entire temperatuve dependence is governed by the trapping effect), this consistency is satisfactory and suggests that both methods delected the same phenomenon, in spite of the criticism that l/ /oJ dependence observed by proton NMR could come from a relaxation... 

The topic of neutral soliton dynamics has been controversial for many years. The reasons have been due to a lack of definite data and a lot of different interpretations from a variety of bases for many experimental data. In this review, we tried to explain most of the important experimental results in terms of a diffuse/trap model based on observations of the ESR linewidth as functions of temperature and frequency. Anomalous broadening observed only in (CH) but not in (CD), at frequencies lower than 6 MHz was explained in a clear-cut way by this model, giving a consistent value of the maximum spin density of the neutral soliton, 0.15-0.17 in comparison with 0.17 determined by the ENDOR technique. These successes represented in the finally obtained diffusion rates which are found to be consistent between NMR and ESR seem to settle the controversy. 

However, the nuclear relaxation rate T decreases at low temperature, while it is scarcely affected in the presence of oxygen. The latter result shows that the data could not all be accounted for just by introducing a diffusion coefficient dependent on both temperature and oxygen content. A comprehensive explanation of the data has been proposed in terms of a two-spin species model [56], also called the diffusive-trap model," as follows. In a pure ideal (CH)v chain we would be dealing with diffusive solitons with a diffusion coefficient D( T) that will be discussed later. In the presence of impurities such as adsorbed oxygen, traps are created in which the solitons can be temporarily pinned and thus localized. The total number of solitons, n, is thus = + /Ji., where... 

Using the previous equations we can derive the microscopic structure (/. e., the kinds of defects and their concentrations) from the experimentally determined lifetimes and intensities if the problem is homogeneous. This premise, however, does not hold for RPV steels completely. In inhomogeneous problems, the diffusion of positrons from the various implantation sites to the trapping centres must also be considered [125,130]. However, the mathematical difficulties associated with the corresponding diffusion-trapping model (DTM) [73] have so far prevented exact solutions from being obtained for all but the simplest problems [116,117], Thus, it is impossible to qualitatively analyse the very detailed experimental results obtained with a pulsed positron beam. 

B. G. Pound, Evaluation of a Diffusion/Trapping Model for Hydrogen Ingress in High-Strength Alloys, Final Report to the Office of Naval Research, Contract N00014-86-C-0233, 1990. 

Table 10.4 lists the values of trap density and binding energy obtained in the quasi-ballistic model for different hydrocarbon liquids by matching the calculated mobility with experimental determination at one temperature. The experimental data have been taken from Allen (1976) and Tabata et ah, (1991). In all cases, the computed activation energy slightly exceeds the experimental value, and typically for n-hexane, 0/Eac = 0.89. Some other details of calculation will be found in Mozumder (1995a). It is noteworthy that in low-mobility liquids ballistic motion predominates. Its effect on the mobility in n-hexane is 1.74 times greater than that of diffusive trap-controlled motion. As yet, there has been no calculation of the field dependence of electron mobility in the quasi-ballistic model. 

An important question concerning energy trapping is whether its kinetics are limited substantially by (a) exciton diffusion from the antenna to RCs or (b) electron transfer reactions which occur within the RC itself. The former is known as the diffusion limited model while the latter is trap limited. For many years PSII was considered to be diffusion limited, due mainly to the extensive kinetic modelling studies of Butler and coworkers [232,233] in which this hypothesis was assumed. More recently this point of view has been strongly contested by Holzwarth and coworkers [230,234,235] who have convincingly analyzed the main open RC PSII fluorescence decay components (200-300 ps, 500-600 ps for PSII with outer plus inner antenna) in terms of exciton dynamics within a system of first order rate processes. A similar analysis has also been presented to explain the two PSII photovoltage rise components (300 ps, 500 ps)... 

Two types of models have been suggested, namely, a diffusion approach and a random trap model. The measurements of Dahan s and Bawendi s groups [5,7], which show the universal power law a = 0.5, are consistent with the diffusion model (see details below). The fact that all dots are found to be similar [5] seems not to be consistent with models of quenched disorder [4,9,10] since these support the idea of a distribution of a . However, some experiments show deviations from the a+ a 0.5 and may support a distribution of a . It is possible that preparation methods and environments lead to different mechanisms of power-law blinking, along with different exponents [6]. More experimental work in this direction is needed in particular, experimentalists still have to investigate the distribution of a and need to show whether and under what conditions are all the dots statistically identical. We discuss the diffusion model below different aspects of the tunneling and trapping model can be found in Refs. 4, 6, and 10. 

Validation of the Model. Outputs from the various models were compared to observations of blood concentrations reported from studies of oral gavage or intravenous exposures of rats to di- -butyl phthalate (NIEHS 1994, 1995). Based on the comparisons of model outputs to observed time courses for blood mono- -butyl phthalate concentrations from NIEHS (1994, 1995), Keys et al. (2000) concluded that the diffusion-limited, pH-trapping model more closely represents the empirical data. However, it is difficult to interpret this finding if the same data were used in the model optimization (see Table 4 of Keys et al. 2000). The diffusion-limited, pH-trapping model simulated reasonably well the time courses for blood concentrations of mono- -butyl phthalate reported by NIEHS (1994, 1995). A log-likelihood ratio test was used to compare the fit of the various augmented models to that of the flow-limited model. The diffusion-limited, pH-trapping model gave a better statistical fit to the empirical data than the other four models, with the next best fit achieved with enterohepatic circulation model. However, the latter model appeared to underestimate peak mono- -butyl phthalate plasma concentrations, which would be an important limitation for its use in risk assessment. 

Urayama et al. [119-121] tested the diffused constraint model using both uniaxial compression and equibiaxial elongation data for end-linked PDMS networks in which trapped entanglements were dominant in number relative to chemical crosslinks. The parameter k was used as an empirical fitting parameter, and the best-fit procedure yielded k = 2.9. The structural parameters (v, jj., /)... 

Hydrogen diffusion in amorphous gQ 20 apparently does not involve a continuous distribution of hydrogen jump rates, but consists of two well-separated classes of jump rates. A two state trapping model allows a semi-quantitative description of our quasielastic neutron scattering data. 

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