Cage models

Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],...

The fluctuating cage model presented in Chapter 7 is an alternative. The idea came from comparison of the different kinds of absorption spectra of HC1 found in liquid solutions (Fig. 0.5). In SFg as a solvent the rotational structure of the infrared absorption spectrum of HC1 is well resolved [15, 16], while in liquid He it is not resolved but has... 

The Hubbard relation in the frames of the liquid cage model 251... 

The liquid phase cage model accounts for appearance in the spectrum of resolved rotational components by effective isotropization of the rapidly fluctuating interaction. This interpretation of the gas-like spectral manifestations seems to be more adequate to the nature of the liquid phase, than the impact description or the hypothesis of over-barrier rotation. Whether it is possible to obtain in the liquid cage model triplet IR spectra of linear rotators with sufficiently intense Q-branch and gas-like smoothed P-R structure has not yet been investigated. This investigation requires numerical calculations for spectra at an arbitrary value of parameter Vtv. 

This brief analysis explains why it is very important to know whether the Hubbard relation is reproduced in the liquid cage model. The existence of the Hubbard limit means that orientational relaxation is insensitive to the precise details of the interaction. Below, it is shown that this is the case. 

The Hubbard relation in the frames of the liquid cage model 257 existence of an inverse operator for the right f is sufficient to obtain... 

The present appendix represents a detailed derivation of the kinetic equations of the fluctuating liquid cage model in the classical formalism. A natural generalization is done for the case of partially ordered media, e.g. nematic liquid crystals. One of the simplest ways to take into account the back reaction is demonstrated, namely to introduce friction. 

Serebrennikov Y. A., Temkin S. I., Burshtein A. I. Infrared and Raman spectra of a linear rotator in the fluctuating liquid cage model, Chem. Phys. 81, 31-40 (1983). 

Temkin S. I., Abdrakhmanov B. M. Does the Hubbard relation hold in the liquid cage model Phys. Lett. A155, 43-8 (1991). 

Here the vector rj represents the centre of mass position, and D is usually averaged over several time origins to to improve statistics. Values for D can be resolved parallel and perpendicular to the director to give two components (D//, Dj ), and actual values are summarised for a range of studies in Table 3 of [45]. Most studies have found diffusion coefficients in the 10 m s range with the ratio D///Dj between 1.59 and 3.73 for calamitic liquid crystals. Yakovenko and co-workers have carried out a detailed study of the reorientational motion in the molecule PCH5 [101]. Their results show that conformational molecular flexibility plays an important role in the dynamics of the molecule. They also show that cage models can be used to fit the reorientational correlation functions of the molecule. 

The Values of Er and Eor for Bimolecular Reactions of Nitroxyl Radicals with Phenols Calculated According to the Rigid Cage Model for Reaction in a Polymer Matrix (Equation (19.7)) [7,9,14,15,21]... 

For an infinitely thin rodlike polymer for which d/L = de/Le = 0, we have fi = F 0 = Fx0 = D 0/D = 1, and Eq. (46) reduces to Teraoka and Hay-aka wa s original expression [107] of Dx for rodlike polymers. At high concentrations, the results from the Green function method approach the one from the cage model [107], Teraoka [110] calculated stochastic geometry and probability of the entanglement for infinitely thin rods by use of the cage model, and evaluated px to be... 

In the infinitely thin rod limit, Eq. (50) reduces to Teraoka and Hayakawa s original expression of Dr for rodlike polymers [108]. The latter approaches the equation of Dr derived on the cage model [108, 111] at high concentrations. Teraoka et al. [Ill] estimated pr from calculations of stochastic geometry and probability of the entanglement for infinitely thin rods with the cage model, and obtained... 

Clathrate-Cage Model. The final water model which is of major interest is based on clathrate hydrate cage structures. It was originally proposed by Pauling (116), who noted the existence of clathrate hydrates of many inert gases and suggested, by analogy to the chlorine hydrate,... 

An obvious difficulty in the cage model approach is the fact that there ought to be geometric limitations on the type of solutes which may enter the cages. Frank and Quist s theory should work well for small, nonpolar solutes, but larger solute molecules would present a difficulty. However, these authors do not imply that only specific, complete, pentagonal dodecahedra are involved in the cage formation in solution, but... 

For outer subshells of the encaged atom, the ionization thresholds of which vary from a few eV to a few tens eV, the dynamical-cage model is required. The photoionization cross section of the encaged atom in the dynamical-cage approximation will be marked with a tilde sign 5 s and... 

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