Disorder model

The key parameter of the disorder formalism is the width of the hopping site manifold. There is considerable evidence that a is dependent on the dipole moment of the dopant molecule, as well as the polymer repeat unit, and/or polar additives. This has been described by an argument based on dipolar disorder, originally due to Borsenberger and Bassler (1991). Stated simply, the argument 

Young (1995) analyzed the same problem described by Dieckmann et al. Young s model was derived analytically while the model of Dieckmann et al. was by simulations. Further, Young s model is based on point dipoles while Dieckmann et al. used pairs of charges. Young s expression for the dipolar component is 

Equation (18) yields values of Oj that are approximately a factor of 2 larger than those derived from the expression of Dieckmann et al. In agreement with Dieckmann et al., Young s results show that the main portion of the DOS is Gaussian. At low concentrations, Young s results show that the DOS can deviate significantly from the Gaussian that fits the central portion 

For other treatments of dipolar disorder, see Sugiuchi and Nishizawa (1993), Richert and Loring (1995), Dunlap et al. (1996), Dunlap (1996), Gartstein and Conwcll (1996). and Parris (1996). 

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The De Wolff disorder model has been extended to the cation vacancy model for /-Mn02 and -Mn02 by Ruetschi [42]. In this model the occurrence of manganese cation vacancies and the non stoichiometry of electrochemical Mn02 have been taken into account. Furthermore, the vacancy model deals with the explanation of the different water contents of manganese dioxide. Ruetschi makes some simple assumptions ... 

Crystalline forms corresponding to limiting ordered or disordered models, with equal lattice geometry, can be obtained with different procedures and can present dif-... 

The difference electron density map following the last cycle of least squares refinement did not show evidence for a simple disorder model to explain the anomalously high B for the hydroxyl oxygen. Attempts to refine residual peaks with partial oxygen occupancies did not significantly improve the agreement index. 

Disordered structures belonging to the class (i) are interesting because, in some cases, they may be characterized by disorder which does not induce changes of the lattice dimensions and of the crystallinity, and a unit cell may still be defined. These particular disordered forms are generally not considered as mesomorphic modifications. A general concept is that in these cases the order-disorder phenomena can be described with reference to two ideal structures, limit-ordered and limit-disordered models, that is, ideal fully ordered or fully disordered models. 

The real crystalline forms are generally intermediate between the limit-ordered and limit-disordered models, the amount of disorder being dependent on the condition of crystallization and thermal and mechanical treatments of the samples. A condition to have more or less disordered modifications, corresponding to the same unit cell, is the substantial equality of steric hindrances in the space regions where a statistical substitution is achieved (Figure 2.29b). 

Figure 2.29 (a) Limit-ordered model (space group Ibca or P2i/a) and (b) limit-disordered model (space group Bmcm) for crystal structure of form I of sPP172 (R = right-handed helix, L = left-handed helix). 

Fig. 2. Classes of structural models of amyloid-like fibrils. The Refolding models propose that a native protein (circle) partially or completely unfolds to attain a new fold (rectangle) in the fibril (stack of rectangles). In contrast, the Gain-of-Interaction models propose that only part of the native protein changes and takes on a new structure in the fibril. The remainder of the protein (partial circle) retains its native structure. The Natively Disordered models begin with disordered proteins or protein fragments, and these become ordered in the fibril. PolyQ refers to polyglutamine.

The pH dependence of could be due to changes in A-B loop disorder rates, perhaps the chemical exchange phenomenon observed for NPl-ImH (Section ll,E,2,b), or to changes in ligand bond strength. The change in lies in the off-rates (Tables I-Ill) consistent with the loop disorder model. Plots of vs pH display an excellent fit with the equation for a titration curve (Fig. 21), indicating that the transition... 

Table 2 Results of data fits to the Gaussian disorder model of charge transport in EHO-...

A (which means the superimposed carbon atoms are only 0.058 A apart), the disorder contribution is as small as 0.0008 A2, which does not allow one to discard a possible / -disordered model on experimental grounds even at very low temperature. 

Despite the success of the disorder model concerning the interpretation of data on the temperature and field dependence of the mobility, one has to recognize that the temperature regime available for data analysis is quite restricted. Therefore it is often difficult to decide if a In p vs or rather a In p vs representation is more appropriate. This ambiguity is an inherent conceptual problem because in organic semiconductors there is, inevitably, a superposition of disorder and polaron effects whose mutual contributions depend on the kind of material. A few representative studies may suffice to illustrate the intricacies involved when analyzing experimental results. They deal with polyfluorene copolymers, arylamine-containing polyfluorene copolymers, and c-bonded polysilanes. 

Fig. 8 Temperature dependence of the zero field hole mobility in the low carrier density limit in a polyfluorene copolymer. The data are inferred from space-charge-limited current experiments and analyzed in terms of the extended Gaussian disorder model (see Sect. 4.1). From [90] with permission. Copyright (2008) by the American Institute of Physics...

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