Abraham model

Sprunger, L. et al., Characterization of room temperature ionic liquids by the Abraham model cation-specific and anion-specific equation coefficients, /. Chem. Info. Model, 47,1123,2007. 

S. L. Post, J. Abraham Modeling the outcome of drop-drop collisions in Diesel sprays, Int. J. Multiphase Flow 28, 997-1019 (2002). 

S. L. Post and J. Abraham. Modeling the outcome of drop-drop collisirais in diesel sprays. International Journal of Multiphase Plow, 28 997—1019, 2002. 

Acree, W.E., Jr. Abraham, M.H. (2006). The analysis of solvation in ionic liquids and organic solvents using the Abraham model linear free energy relationship. /. Chem. Technol Biotechnol., 81,1441-1446. 

The Miller-Abrahams model is illustrated in Figure 5(c), with the energy difference equal to AE = Ei,. i The rate of... 

When the temperature inaeases, the probability of charge carrier transfer to the nearest neighbor increases, in spite of the energy difference, as shown in Figure 5(b). In such a case a more appropriate description of charge transport is offered by the Miller-Abrahams model descrihed in Section 2.33.2.3.2.2. 

Palmer R G, Stein D L, Abrahams E and Anderson P W 1984 Models of hierarohioally oonstrained dynamios for glassy relaxation Phys. Rev. Lett. 53 958-61... 

In a series of papers published throughout the 1980s, Colin Poole and his co-workers investigated the solvation properties of a wide range of alkylammonium and, to a lesser extent, phosphonium salts. Parameters such as McReynolds phase constants were calculated by using the ionic liquids as stationary phases for gas chromatography and analysis of the retention of a variety of probe compounds. However, these analyses were found to be unsatisfactory and were abandoned in favour of an analysis that used Abraham s solvation parameter model [5]. 

A celebrated derivation of the temperature dependence of the mobility within the hopping model was made by Miller and Abrahams 22. They first evaluated the hopping rate y,y, that is the probability that an electron at site i jumps to site j. Their evaluation was made in the case of a lightly doped semiconductor at a very low temperature. The localized states are shallow impurity levels their energy stands in a narrow range, so that even at low temperatures, an electron at one site can easily find a phonon to jump to the nearest site. The hopping rate is given by... 

We note a temperature dependence of the zero field mobility as exp[—( F()/F)2], a behavior which is indeed encountered in real organic semiconductors, and differs from both Millers-Abrahams fixed range and Moll s variable range hopping models. 

Williamson, V. M., Abraham, M. R. (1995). The efiects of computer animation on the particulate mental models of college chemistry students. Journal of Research in Science Teaching, 32(5), 521-534. 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

The nonlinear character of log has not often been discussed previously. Nevertheless, Jorgensen and Duffy [26] argued the need for a nonlinear contribution to their log S regression, which is a product of H-bond donor capacity and the square root of H-bond acceptor capacity divided by the surface area. Indeed, for the example above their QikProp method partially reflects for this nonlinearity by predichng a much smaller solubility increase for the indole to benzimidazole mutation (0.45 versus 1.82 [39, 40]). Abraham and Le [41] introduced a similar nonlinearity in the form of a product of H -bond donor and H -bond acceptor capacity while all logarithmic partition coefficients are linear regressions with respect to their solvation parameters. Nevertheless, Abraham s model fails to reflect the test case described above. It yields changes of 1.8(1.5) and 1.7(1.7) [42] for the mutations described above. 

Stephen Rossnagel and Abraham Ulman, Modeling of Film Deposition for Microelectronic Applications, Volume 22, 1996. 

The modification by method 2 is more acceptable. Although several types of modifications have been reported, Abraham and Liszi [15] proposed one of the simplest and well-known modifications. Figure 2(b) shows the proposed one-layer model. In this model, an ion of radius r and charge ze is surrounded by a local solvent layer of thickness b — r) and dielectric constant ej, immersed in the bulk solvent of dielectric constant ),. The thickness (b — r) of the solvent layer is taken as the solvent radius, and its dielectric constant ej is supposed to become considerably lower than that of the bulk solvent owing to dielectric saturation. The electrostatic term of the ion solvation energy is then given by... 

On the assumption that = 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the above-mentioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene-water and 1,2-dichloroethane-water interfaces. 

FIG. 2 (a) The Born model [1], (b) The one-layer model proposed by Abraham and Liszi [15]. (From Ref. 10. Copyright the Japan Society for Analytical Chemistry.)... 

In an excellent paper, Zhao et al. [29] assembled a carefully reviewed literature set of human absorption data on 241 drugs. They showed that a linear regression model built with 5 Abraham descriptors could fit percent human absorption data reasonably well (r2 = 0.83, RMSE = 14%). The descriptors are excess molar refraction (E), polarizability (S), hydrogen bond acidity (A), hydrogen bond basicity (B), and McGowan volume (V), all related to lipophilicity, hydrophilicity, and size. In a follow-on paper, data on rat absorption for 151 drugs was collected from the literature and modeled using the Abraham descriptors [30]. A model with only descriptors A and B had r2 = 0.66, RMSE = 15%. 

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