Models of ions

Rashin A A and B Honig 1985. Reevaluation of the Bom Model of Ion Hydration. Journal of Physici Chemistry 89 5588-5593. 

The first simulation studies of full double layers with molecular models of ions and solvent were performed by Philpott and coworkers [51,54,158] for the NaCl solution, using the fast multipole method for the calculation of Coulomb interactions. The authors studied the screening of a negative surface charge by free ions in several highly concentrated NaCl solutions. A combination of (9-3) LJ potential and image charges was used to describe the metal surface. 

Another quasi-thermodynamical model of ion transport in polymers is based on the concept of minimum configurational entropy required for rearrangement of the polymer, giving practically identical o—T and D — T dependences as the preceding model. 

In order to probe cation occupation in the active site in the absence of Mg2+ ions, we examined Na+ distributions in the reactant and activated precursor (deprotonated 20H nucleophile) states. It has been noted in the recent literature that the modeling of ions in highly charged systems such as HHR affords tremendous challenges with regard to simulation time scales [129], This section presents the results of series of five 300 ns simulations of the full length HHR, in both the reactant and activated precursor states, in order to ascertain the cation occupation requirement of the active site to maintain catalytic integrity. 

Roux, B., Theoretical and computational models of ion channels, Curr. Opin. Struct. Biol. 2002,12, 182-189. 

For example, the investigations of the current-generating mechanism for the polyaniline (PANI) electrode have shown that at least within the main range of potential AEn the "capacitor" model of ion electrosorption/ desorption in well conducting emeraldine salt phase is more preferable. Nevertheless, the possibilities of redox processes at the limits and beyond this range of potentials AEn should be taken into account. At the same time, these processes can lead to the fast formation of thin insulation passive layers of new poorly conducting phases (leucoemeraldine salt, leucoemeraldine base, etc.) near the current collector (Figure 7). The formation of such phases even in small amounts rapidly inhibits and discontinues the electrochemical process. 

A recent success in the detection of H species has been that of the molecular ion H3+. All of the models of ion-molecule chemistry in hydrogen-dominated regions are controlled by reactions of H3+ but until recently the H2+ molecular ion had not been detected. However, the modes of vibration of H3"1" provide for an allowed IR transition at 3.668 pin used for its detection. These ro-vibrational transitions have now been observed in a number of places, including the interstellar medium and in the aurorae of Jupiter. Not all astronomical detection and identification problems have been solved, however, and the most annoying and compelling of these is the problem of diffuse interstellar bands. 

In this chapter, we consider several simple models of ion sorption and exchange that can be applied within the context of a geochemical model. These models include distribution coefficients, Freundlich and Langmuir isotherms, and ion exchange theory. In the following chapter (Chapter 10), we consider surface com-plexation theory, which is more complicated but in some ways more robust than the models presented here. 

Tipping E., 1994, WHAM - a chemical equilibrium model and computer code for waters, sediments and soils incorporating a discrete site/electrostatic model of ion-binding by humic substances. Computers and Geosciences 20,973-1023. 

However, if we consider a model of ion solvation that uses the electrostatic potential at nucleus ... 

The use of electrostatic potentials, defined in the context of DFT, for the calculation of ion solvation energies has been reviewed. It has been shown that physically meaningful ionic radii may be obtained from this methodology. In spite of the fact that the electrostatic potentials for cations and anions display a quite different functional dependence with the radial variable, we have shown that it is still possible in both cases to build up a procedure consistent with the Bom model of ion solvation. 

Sposito, G. (1990), "Molecular Models of Ion Adsorption on Mineral Surfaces", in M. F. Hochella Jr. and A. F. White, Eds., Mineral-Water Interface Geochemistry, Mineralogical Society of America, Washington, D.C., pp. 261 -279. 

The theoretical model that best describes regulation of transepithelial transport is derived from the Ussing-Zerahn equivalent electrical circuit model of ion transport theory [57] (Figure 15.1B). The model predicts that epithelia are organized as a layer(s) of confluent cells, where plasma membranes of neighboring cells come into close contact and functionally occlude the intercellular space. Accordingly, molecules can move across epithelia either through the cells... 

The interfacial electric double layer is represented by a combination of the improved jeUium model on the metal side and the hard sphere model of ions and dipoles on the aqueous solution side. Then, the electric capacity, Ch, of the compact layer is given by Eqn. 5-34 ... 

Davis, S.C. Natoli, V. Neumann, G.M. Derrick, P.J. A Model of Ion Evaporation Tested Through Field Desorption Experiments on Glucose Mixed With Alkali Metal Salts. Int. J. Mass Spectrom. Ion Proc. 1987, 78, 17-35. 

The elder model of ion formation, the charged-residue model (CRM), assumes the complete desolvation of ions by successive loss of all solvent molecules from droplets that are sufficiently small to contain just one analyte molecule in the end of a cascade of Coulomb fissions. [9,42,84] The charges (protons) of this ultimate droplet are then transferred onto the molecule. This would allow that even large protein molecules can form singly charged ions, and indeed, CRM is supported by this fact. [23]... 

The first half of this chapter concentrates on the mechanisms of ion conduction. A basic model of ion transport is presented which contains the essential features necessary to describe conduction in the different classes of solid electrolyte. The model is based on the isolated hopping of the mobile ions in addition, brief mention is made of the influence of ion interactions between both the mobile ions and the immobile ions of the solid lattice (ion hopping) and between different mobile ions. The latter leads to either ion ordering or the formation of a more dynamic structure, the ion atmosphere. It is likely that in solid electrolytes, such ion interactions and cooperative ion movements are important and must be taken into account if a quantitative description of ionic conductivity is to be attempted. In this chapter, the emphasis is on presenting the basic elements of ion transport and comparing ionic conductivity in different classes of solid electrolyte which possess different gross structural features. Refinements of the basic model presented here are then described in Chapter 3. 

Extraction processes that proceed according to the model of ion-pair extraction are described by a formalism different from that presented in section 16.4.2, and are based on partition of single ions and their association in the organic phase [76] (see also section 2.6). The Born equation has been widely used to describe the transfer of an ion of the charge q and radius r from vacuum to the liquid (water) of the dielectric constant e ... 

Figure 9. (a) Batrachotoxin (BTX) docked into the KcSA X-ray structure. Residue positions superimposed in green correspond to those implicated in the sodium channel Navi.4 and (b) its display as projected on the generic logical model of ion channels and predicted interaction with an ion channel Theme. 

The crystal structures observed in ternary fluorides of the transition metals may be explained to a first approximation by reasons of geometry, i. e. by the relative sizes and charges of their constituent ions. The underlying hard sphere model of ions proves to be surprisingly useful. 

Figure 1. Space-filling model of ion pair diastereomer [10a ...

The theory of Frank and Wen (54) for ion hydration involves the notion that some water molecules intimately contact the ion under consideration and subject to the strong centrosymmetric force field, are highly ordered. Beyond this area is a region of disorder, beyond which, in dilute solutions, unaffected water prevails. Typical literature values for primary hydration numbers range from 2-8 water molecules. For divalent ions, primary hydration numbers range from 10-20 water molecules while some authors have suggested hydration numbers for trivalent ions (based on compressibility data) between 20 and 30 water molecules per ion. Many attempts have been made to extend theories of this type to account better for the hydration of ions. Thus, Azzam (7, 8) and Horne and Birkett (80) have proposed a multilayer model of ion hydration. 

The proper treatment of ionic fluids at low T by appropriate pairing theories is a long-standing concern in standard ionic solution theory which, in the light of theories for ionic criticality, has received considerable new impetus. Pairing theories combine statistical-mechanical theory with a chemical model of ion pair association. The statistical-mechanical treatment is restricted to terms of the Mayer/-functions which are linear in / , while the higher terms are taken care by the mass action law... 

A theoretical approach for explaining the relationship between S and the characteristics of the electrolyte was provided by Onsager on the basis of the model of ions plus ionic cloud developed in the Debye-Hiickel theory, obtaining [4]... 

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