Liquid cage theory

The rectangular approximation (7.6) of dependence E(r) implies that ts = 0. This simplification being valid only for non-adiabatic interaction, exact knowledge of the time-dependence V(t) is not obligatory. Random walk approximation is quite acceptable. The value Ro/R is a free parameter of the model ( Ro/R < 1) and makes it possible to vary the ratio of times 0 < tc/to < oo. This interval falls into two regions one of them corresponds to impact theory (0 < tc/to < 1), and the other (1 <, tc/t0 < oo) to the fluctuating liquid cage. In the first case non-adiabaticity of the process is provided by the condition... 

In the so-called cage theory, a liquid molecule is supposed to be surrounded by a cluster of about twelve other molecules, which act as a batrier in preventing its free translatory motion. i The theory of liquids has formed the subject of many recent papers, but it is not ripe for summarising in a systematic treatise, as distinguished from a... 

Tmskett and Dill (2002) proposed a two-dimensional water-like model to interpret the thermodynamics of supercooled water. This model is consistent with model (1) for liquid water. Cage-like and dense fluid configurations correspond to transient structured and unstructured regions, observed in molecular simulations of water (Errington and Debenedetti, 2001). Truskett and Dill s model provides a microscopic theory for the global phase behavior of water, which predicts the liquid-phase anomalies and expansion upon freezing. 

The model was recently tested to determine whether it was able to model analyte retention in the presence of novel and unusual IPRs (see Chapter 7) such as chaotro-pic salts and ionic liquids. Chaotropes that break the water structure around them and lipophilic ions (classical IPRs and also ionic liquids) that produce cages around their alkyl chains, thereby disturbing the ordinary water structure, are both inclined to hydrophobic ion-pairing since both are scarcely hydrated. This explains the success of the theory, that is predictive in its own right, when neoteric IPRs are used [64]. Recently a stoichiometric model (vide supra) was put forward to describe retention of analytes in the presence of chaotropic IPRs in eluents [18] but its description of the system is not adequate [64]. 

This more sophisticated way shows a [arge distribution of residence times for water molecules in the cage formed by the neighboring molecules, which is a more realistic view than the sharp separation of water molecules into two classes, according to their mobility [49]. Short time dynamics resuits about hydrated myoglobin have recently been interpreted by using this same theory of kinetic glass transition in dense supercooled liquids [73]. 

With the intensive development of ultrafast spectroscopic methods, reaction dynamics can be investigated at the subpicosecond time scale. Femtosecond spectroscopy of liquids and solutions allows the study of sol-vent-cage effects on elementary charge-transfer processes. Recent work on ultrafast electron-transfer channels in aqueous ionic solutions is presented (electron-atom or electron-ion radical pairs, early geminate recombination, and concerted electron-proton transfer) and discussed in the framework of quantum theories on nonequilibrium electronic states. These advances permit us to understand how the statistical density fluctuations of a molecular solvent can assist or impede elementary electron-transfer processes in liquids and solutions. 

A full discussion of the mechanism of hot atom reactions is beyond the scope of this chapter. Wolfgang (24) has reviewed the hot atom chemistry of gas-phase systems and uses a theoretical approach analogous to that of nuclear reactions to describe hot atom reactions with others he has developed a kinetic theory of hot reactions also known as Wolfgang s Adiabatic Theory. The theory is believed to be applicable to liquid and solid phases as well, with some diflFerences due to cage and steric eflFects. 

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