Born ion

Arnold F and Viggiano A A 1986 Review of rocket-borne ion mass spectrometry in the middle atmosphere Middie Atmosphere Program Handbook, Voi. 19 ed R A Goldberg (Urbana, IL SCOSTEP)... 

Fig. 1. Born ion self energy and the problem of inorganic ion passage through a lipid barrier.

This solution, formally expressed as Equation (1.131), is essentially nonlocal in space, although the problem is originally formulated in terms of local Equations (1.119). The spatial nonlocality arises from boundary conditions on S. Simple solutions are available only for spherically symmetrical cases (Born ion or Onsager point dipole). The equilibrium solvation energy is expressed as... 

Here p(A) is the Fourier transform of p(R). This Born ion is considered as a conducting sphere with its charge Q being smeared over the surface of its cavity p(R) = (Q/4Tra2)8(R - a), p(k) = Qsm(ka)/ka. Outside the cavity the electrostatic field created by this charge is fully equivalent to the field due to the point charge Q considered earlier. By this means for R > a... 

In order to obtain the matrix equations above, one must decide how to construct, and subsequently discretize, the cavity surface. The most widely used methods take the cavity to be a union of atom-centered spheres [77], as suggested in Fig. 11.1(a). The electrostatic solvation energy is quite sensitive to the radii of these spheres (it varies as in the Born ion model), and highly parameterized constructions that exploit information about the bonding topology [6] or the charge states of the atoms [31] are sometimes employed. The details of these parameterizations are beyond the scope of the present work, especially given that careful reconsideration of these parameters is probably necessary for classical biomolecular electrostatics calculations. 

The Born ion is the simplest model of solvation It considers the solvation energy of a spherical, nonpolarizable (sp = 1) solute of radius R with a single point charge of magnitude z at its center. In this case, an analytical expression is available for the solvation energy ... 

All water contains some dissolved oxygen and is therefore somewhat corrosive. The rate of corrosion depends on many factors including the water s pH, electrical conductivity, oxygen concentration, and temperature. In addition to corrosion, metals dissolve when the water is extremely low in dissolved salts and in the presence of certain water-borne ions. 

The insoluhilily of ionic compounds in nonpolar solvents is a similar phenomenon. The solvalion energies are limited to those born ion-induced dipole forces, which are consideiahly weaker than ion-dipolc forces and not large enough to overcome the very strong ion-ion forces of the lattice. 

Schlager H and Arnold F 1985 Balloon-borne fragment ion mass spectrometry studies of stratospheric positive ions unambiguous detection of H (CH3CN), (H20)-clusters Pianet. Space Sc/. 33 1363-6... 

The enthalpies for the reactions of chlorine and fluorine are shown graphically in Figure 11.2 as the relevant parts of a Born-Haber cycle. Also included on the graph are the hydration energies of the two halogen ions and hence the enthalpy changes involved in the reactions... 

Consider an alchemical transformation of a particle in water, where the particle s charge is changed from 0 to i) (e.g., neon sodium q = ). Let the transformation be performed first with the particle in a spherical water droplet of radius R (formed of explicit water molecules), and let the droplet then be transferred into bulk continuum water. From dielectric continuum theory, the transfer free energy is just the Born free energy to transfer a spherical ion of charge q and radius R into a continuum with the dielectric constant e of water ... 

Using a set of (partial) atomic charges is often called the generalized Born model. It can be noted that the Born model predicts equal solvation for positive and negative ions of the same size, which is not the observed behaviour in solvents like H2O. 

The overall lattice energies of ionic solids, as treated by the Born-Eande or Kaputin-sldi equations, thus depends on (i) the product of the net ion charges, (ii) ion-ion separation, and (iii) pacldng efficiency of the ions (reflected in the Madelung constant, M, in the Coulombic energy term). Thus, low-melting salts should be most... 

A criterion for the presence of associated ion pairs was suggested by Bjerrum. This at first appeared to be somewhat arbitrary. An investigation by Fuoss,2 however, threw light on the details of the problem and set up a criterion that was the same as that suggested by Bjerrum. According to this criterion, atomic ions and small molecular ions will not behave as strong electrolytes in any solvent that has a dielectric constant less than about 40. Furthermore, di-divalent solutes will not behave as strong electrolytes even in aqueous solution.2 Both these predictions are borne out by the experimental data. 

The high-purity water thus produced typically has a conductance of about 0.5 x 10-6fi-1cm-1 (0.5juScm-1) and is suitable for use under the most stringent requirements. It will meet the purity required for trace-element determinations and for operations such as ion chromatography. It must however be borne in mind that such water can readily become contaminated from the vessels in which it is stored, and also by exposure to the atmosphere. For the determination of organic compounds the water should be stored in containers made of resistant glass (e.g. Pyrex), or ideally of fused silica, whereas for inorganic determinations the water is best stored in containers made from polythene or from polypropylene. 

The following facts must be borne in mind. All strong electrolytes are completely dissociated hence only the ions actually taking part or resulting from the reaction need appear in the equation. Substances which are only slightly ionised, such as water, or which are sparingly soluble and thus yield only a small concentration of ions, e.g. silver chloride and barium sulphate, are, in general, written as molecular formulae because they are present mainly in the undissociated state. 

The Hamiltonian for this system should include the kinetic and potential energy of the electron and both of the nuclei. However, since the electron mass is more than a thousand times smaller than that of the lightest nucleus, one can consider the nuclei to be effectively motionless relative to the quickly moving electron. This assumption, which is basically the Born-Oppenheimer approximation, allows one to write the Schroedinger equation neglecting the nuclear kinetic energy. For the Hj ion the Born-Oppenheimer Hamiltonian is... 

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