Models cavity

We will return to the cavity model in Section 8.3, giving a description in terms of the so-called solubility parameter. 

The interpretation of these remarkable properties has excited considerable interest whilst there is still some uncertainty as to detail, it is now generally agreed that in dilute solution the alkali metals ionize to give a cation M+ and a quasi-free electron which is distributed over a cavity in the solvent of radius 300-340 pm formed by displacement of 2-3 NH3 molecules. This species has a broad absorption band extending into the infrared with a maximum at 1500nm and it is the short wavelength tail of this band which gives rise to the deep-blue colour of the solutions. The cavity model also interprets the fact that dissolution occurs with considerable expansion of volume so that the solutions have densities that are appreciably lower than that of liquid ammonia itself. The variation of properties with concentration can best be explained in terms of three equilibria between five solute species M, M2, M+, M and e ... 

Hydration-free enthalpies of different conformers of formamide and allyl vinyl ether were studied using the ellipsoidal cavity model and the BLYP functional170,177. A very good agreement between the MP2/SCRF and the DFT(BLYP)/SCRF results was shown for the... 

Identical olfactory neurons are located in different places in the cavity, and therefore occupy different positions in the flow path. By using a nasal cavity model, we investigated the influence of the dynamic flow on the sensors response14. The responses from identical fiber optic sensors located... 

V. Dillet, D. Rinoldi, and J. L. Rivail, Liquid-state quantum chemistry An improved cavity model, J. Phys. Chem. 98 5034 (1994). 

Fig. 5.1 Four mirror ring cavity model. Left, microcavity and tapered fiber in contact. Light can couple from the fiber into the resonator and back into the fiber. Right, the four mirror ring cavity equivalent. The top mirror is partially transmitting all others have 100% reflectivity. Reprinted from Ref. 3 with permission. 2008 Optical Society of America...

Aguilar, M. A., Olivares del Valle, F. J. and Tomasi, J. Nonequilibrium solvation an ab initio quantum-mechanical method in the continuum cavity model approximation, J.Chem.Phys., 98 (1993), 7375-7384... 

Shear enhancement effects in foam formation can be understood through the modified cavity model. Shear force behaves as catalyst to reduce energy barrier to allow a quik path from stable gas cavity to unstable bubble phase. It can be concluded that both shear rate and viscosity contribute to foam nucleation in the continuous foam extrusion process. Therefore, proper die opening and process conditions will help to optimise the foam product. 11 refs. 

Appendix B Solubility of Organic Molecules in Water Using a Surface Tension-Cavity Model System... 

The redox potential values of all metal atoms, except alkaline and earth-alkaline metals [60], are higher than that of °(H20/eaq) = —2.87 V he- However, some complexed ions are not reducible by alcohol radicals under basic conditions and thus ii°(M L/ M°L)< —2.1 Vnhe (Table 2). The results were confirmed by SCF calculations of Ag L and Ag L structures associated with the solvation effect given by the cavity model for L = CN [61] or NH3 [47], respectively. 

Figure 18. The reaction cavity model as presented by Cohen. Reaction cavity before and after the reaction is shown as full lines. Transition state requirements for a reaction are shown as broken lines. Case I represents a favorable and case II an unfavorable reaction. [Reproduced with permission from M. D. Cohen, Angew. Chem. Int. Ed. Eng. 14, 386 (1975).]...

In discussions to this point, no significant interaction between a guest and its medium has been considered. This is probably the case in the reaction cavity model of Cohen [13] as well, since product selectivity was attributed mainly to the presence or absence of free volume within the cavity. The analogy of guests in hosts to balls in boxes is very deficient, but is really not different from the situation in the kinds of crystal systems which first inspired the Cohen nomenclature. Interatomic attraction and repulsion was important in analyzing those systems and was even critical to the crystal engineering used to assemble some of the systems used in the studies by Schmidt and his co-workers [1,48,89]. In addition to being stiff or flexible, cavity walls must... 

The importance of the size of the enclosure (reaction cavity) on a reaction course has been a subject of investigation in several laboratories. On the basis of the proposed mechanistic scheme for DBK fragmentation and on the basis of the effective reaction cavity model presented in Section III, the following predictions can be made (a) a relationship will exist between the cage effect and the reaction cavity size (b) the cage effects observed for singlet and triplet benzyl radical pairs will be different (assuming very similar diffusion rates)... 

Over the last decade, a large number of examples (in the crystalline state) have corroborated the reaction cavity model due to Cohen and have brought out elegantly the need to have free volume within reaction cavities for the occurrence of solid state reactions. Even quantitative correlations have been attempted. Scheffer, Trotter, and co-workers have examined free volumes within reaction cavities to gain insight into the mechanism of intramolecular photorearrangements of enones [126,127]. They have shown that the course of a solid state reaction is influenced profoundly by certain specific... 

Several authors have discussed how C(r) can be calculated from the Onsager cavity model. Briefly, we need to consider the time-dependent reaction field, which was related above (Eqs. (12) and (15)) to C(t). For simplicity we consider the case of a probe with ps = 0 and 0. If the probe... 

The physical meaning of the relationship described in the previous subsection becomes apparent when we consider the popular special case of the Onsager cavity model that arises if we assume that the solvent s dielectric properties are well described by a Debye form. 

These results allow a test of the Onsager cavity model for a uniform dielectric continuum solvent with a dielectric response that is well modeled by Eq. (24). Our group recently tested this model for methanol. In this case, both high frequency (co) data (see Barthel et al. [Ill]) and short time resolution C(t) data [32] exist. 

The energy curves in Figure 22 are closely related to the Marcus-Hush theory for electron transfer. The formalism we employ emphasizes a dipole model for the solute solvent interaction, i.e., an Onsager cavity model. However, a Born charge model based on ion solvation as something in between [135] would be essentially equivalent because we do not attempt to calculate Bop and Bor but rather determine them empirically. 

Simple cavity models have been used to study solvated electrons in liquid ammonia. In that case the dominant interactions arise from long range polarization effects, so that the energy of the localized state is not very sensitive to the fluid deformation in the vicinity of the localized charge. In the case of an excess electron in liquid helium, however, the electron-fluid interaction arises mainly from short range electron-atom interactions, and we shall show that the localized excess electron in a cavity in liquid helium lies lower in energy than the quasi-free electron. 

While the conductivity decrease may be explained adequately by the Becker, Lindquist, and Alder model (2), and while the magnetic features may be explained adequately by the cavity model proposed by Ogg (19), neither model will serve to explain all the properties of these solutions. 

The spectra of dilute solutions of lithium, sodium, potassium, calcium, and barium in liquid deutero-ammonia indicate that the absorbing species is the same in each case. The dependence of the shape, intensity, and energy of the absorption band on temperature was investigated for sodium-ND3 solutions. The data are discussed in terms of the electron-in-a-cavity model. No spectral evidence was found for the presence of new species in ND3 solutions containing mixtures of sodium and sodium iodide. 

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