Onsager theory solids

Figure 4 Photogeneration quantum efficiencies for hole and electron generation in compound 1. The solid lines are Onsager theory fittings with parameters listed in the figure. (Reprinted from Ref. 27. Copyright 2000 The American Physical Society.)...

The effect of the TTA concentration of the transport layer on the field dependencies is shown in Fig. 4. The solid lines were calculated from the Onsager theory with r Q = 0.60 and different values of rQ. The results show that rQ increases with increasing TTA concentration while r Q remains constant. The most likely explanation of this is that the photogeneration efficiency is determined by the probability of a donor molecule being in contact with the photoexcited aggregate phase, as proposed by Umeda and Hashimoto (1992). 

The wavelength was 580 run. The solid lines were calculated from the Onsager theory. The efficiency of the dual-layer structure is in excess of an order-of-magnitude greater than the generation layer. The authors attributed this to a... 

Figure 25 The low-field slope-to-intercept ratio for a dispersion of /J-F Pc for different delay times between the exposure and the application of a collection field. The exposures were 500-550 nm strobe illumination (open circles) and 532 nm laser exposures (solid circles). The solid line represents the theoretical value derived from the Onsager theory.

Fig. 8.4 Photogeneration efficiency in TP A (40 wt % in polycarbonate) as a function of electric field. The solid line is calculated from the Onsager theory using Vq = 0.25 nm and

Fig. 2. Electrical conductance of 1 1 electrolyte solutions at 298.15 K (data taken from Lobo, 1990). The solid lines and the dashed lines represent, respectively, the predictions of a cube-root linear law (pseudolattice theory) and a square-root linear law in concentration (Debye-Hiickel-Onsager theory).

Various explanations have been given for deviations from the Debye-Hiickel-Onsager equations. A common type of behavior is for the negative slopes of the A versus /c plots to be greater than predicted by the equation that is, the experimental conductivities are lower than predicted by the theory. This has been explained in terms of ion pairing, a concept which was developed by the Danish physical chemist Niels Bjerrum (1879-1958) in 1926. Although most salts, such as sodium chloride, are present in the solid state and in solution as ions and not as covalent species, there is a tendency for them to come together from time to time to form ion pairs. 

Solid electrolytes are not usually solutions of a conducting solute in a solvent matrix. Liquid electrolyte solutions are often sufficiently dilute (1-10 millimolar) to be described by the textbook theories of Debye-Hiickel or Onsager and oppositely charged ions are sufficiently dispersed for interaction between anions and cations to be minimized. By contrast, molten salts are very concentrated (typically 2-20 molar), ion-ion interactions are pronounced, and alternative theories such as that of Fuoss [105] are required. Polymer electrolytes typically have [repeat unit] [cation] ratios, n, in the range 8 to 30, corresponding to 0.7 to 2.5 molar for PEOn LiC104 [106], and ion clustering is an important feature of their behaviour. To account for both the ion-polymer and ion-cluster interactions, Ratner and Nitzan have developed dynamic percolation theory [107]. 

Fig. 1—Theoretical and experimental values of the nematic order para-meters and solid line, theoretical results of simple mean field theory dashed line, HJL theory crosses, Onsager-Lakatos theory filled circles, Raman measurements open circles, NMR data on partially deuterated MBBA squares, relative values obtained from measurements of the optical anisotropy and triangles, relative values obtained from measurements of the diamagnetic anisotropy/ (Reprinted from Ref. [3].)...

Figure 3 Experimental and theoretical osmotic pressure, II, of PBLG in DMF versus solute volume fraction, b is the molecular volume. The datapoints are taken from Refs. 27 and 28 (data set B), and encompass measurements between 15°C and 45°C. Solid line theory based on the Khokhlov-Semenov approach to flexibility in combination with the decoupling approximation and the dimensional separation approach based on Eq. (8) [29]. Upper dotted line extension of isotropic branch. Lower dotted line extension of nematie branch. Dashed-dotted line result for completely rigid molecules. Dashed line Onsager s second virial coefficient-approximation for rigid rods.

Braun [22] extended Onsager s theory to the case that the dissociating e-h pair is the lowest excited state of the system, such as the charge transfer (CT) state in a binary molecular solid, for instance a charge transfer crystal composed by donor-acceptor moieties or a molecular solid doped with either donors or acceptors. The essential new element in Braun s theory is the notion that the e-h pair has a finite lifetime, determined by its nonradiative decay. This implies that an initially optically... 

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