Ions and dipoles

The electric field-jump method is applicable to reactions of ions and dipoles. Application of a powerful electric field to a solution will favor the production of ions from a neutral species, and it will orient dipoles with the direction of the applied field. The method has been used to study metal ion complex formation, the binding of ions to macromolecules, and acid-base reactions. 

FIGURE 5.1 The distance dependence of the potential energy of the interaction between ions (red, lowest line), ions and dipoles (brown), stationary dipoles (green), and rotating dipoles (blue, uppermost line). 

In principle, the distribution of ions and dipoles at the M/s interface is different from that at the free M and s surfaces. Therefore the Galvani potential may also be written, in the absence of specific adsorption, as the sum of the charge and dipole components ... 

As mentioned in Section 2.1, Earnshaw s theorem establishes that there can be no stable static equilibrium arrangement of classical ions and dipoles. Nevertheless, quantum mechanics allows numerous stable arrangements of ions, such as those... 

Figure 17.5 An ensemble of hard sphere ions and dipoles in contact with a metal.

Figure 17.6 Distribution of the electrostatic potential for an ensemble of hard sphere ions and dipoles in contact with a hard wall the straight line is the prediction of the Gouy-Chapman theory. Data taken from Ref. 8.

Interest within the physical organic community on the mechanism for the formation and reaction of ion-pair and ion-dipole intermediates of solvolysis peaked sometime in the 1970s and has declined in recent years. The concepts developed during the heyday of this work have stood the test of time, but these reactions have not been fuUy characterized, even for relatively simple systems. Richard and coworkers have prepared a short chapter that summarizes their recent determinations of absolute rate constants for the reactions of these weak association complexes in water. This work provides a quantitative basis for the formerly largely qualitative discussions of competing carbocation-nucleophile addition and rearrangement reactions of ion and dipole pairs. 

The interfacial solution layer contains h3 ated ions and dipoles of water molecules. According to the hard sphere model or the mean sphere approximation of aqueous solution, the plane of the center of mass of the excess ionic charge, o,(x), is given at the distance x. from the jellium metal edge in Eqn. 5-31 ... 

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 ... 

The least distance to which the ion and dipole can approach each other is equal to the sum of the radii of the two. If a value of 3 A is assumed for this, then the energy is... 

Because of the complexity of the forces operating in the covalent bond, it is not possible to write a simple potential energy function as for the electrostatic forces such as ion—ion and dipole-dipole. Nevertheless, it is possible to describe the covalent energy qualitatively as a fairly short-range force (as the atoms are forced apart, the overlap decreases). 

This countercharge can accumulate in the electrolyte side of the interface by coulombic non-specific interactions as well as by specifically adsorbed ions and dipoles and it can extend, to some degree, into the electrolyte, especially at low ionic concentrations. 

The high electrical field across the interface and localized in a small distance as a consequence of the high capacitance of the electrode-solution interface also affects the adsorption phenomena considerably. Mutual interaction of adsorbed ions and dipoles is possible at the electrochemical interface. 

Gibbs energy of ion and dipole transfer — The standard -> Gibbs energy of ion transfer (see also -> ion transfer at liquid-liquid interfaces) can be represented as the difference of two -> solvation energies A Gf = A acGA -... 

Ion-dipole interaction — One of the intermolecular interactions, which acts between an ion and dipoles such as water molecules. The ion-dipole interaction shows a significant stabilizing effect on the hydration or - solvation of ions (see -> hydrated ion). The interaction energy 1/i d between a dipole and an ion placed at a distance r from the dipole center is approximately given by... 

Camie and Chan30 treated an ensemble of hard-sphere ions and dipoles in contact with a hard wall. Specifically, they considered solvent molecules of radius rw with a point dipole at their center, and two kinds of ions, positive and negative, both with the same radius r,. One kind of ion can be adsorbed on the surface of the hard wall by a potential proportional to a Dirac delta function. Charge transfer between the metal (i.e. the hard wall) and the adsorbate was not... 

The elementary reactions of carbocationic polymerizations can be separated into three types. Deactivation of carbenium ions with anions and transfer to counteranion are ion-ion reactions, propagation and transfer to monomer are ion-dipole reactions, and ionization is a dipole-dipole reaction [274]. Ion-ion and dipole-dipole reactions with polar transition states experience the strongest solvent effects. Carbocationic propagation is an ion-dipole reaction in which a growing carbenium ion adds electro-philically to an alkene it should be weakly accelerated in less polar solvents because the charge is more dispersed in the transition state than in the ground state [276]. However, a model addition reaction of bis(p-methoxyphenyl)carbenium ions to 2-methyl- 1-pentene is two times faster in nitroethane (e = 28) than in methylene chloride (e = 9) at - 30° C [193]. However, this is a minor effect which corresponds to only ddG = 2 kJ morit may also be influenced by specific solvation, polarizability, etc. [276,277]. 

The effect of ionic strength on iou-dipole reactions, aside from specific interactions, can be guessed intuitively from considerations of the interactions of the ion atmosphere with the dipole moment of the reactant molecule in the free state and in the complex. For positive interactions of the ion and dipole (0 > 90 ) we may expect the ion field to reduce the dipole... 

The problem is to calculate the interaction energy between a dipole and an ion placed at a distance r from the dipole center, the dipole being oriented at an angle 0 to the line joining the centers of the ion and dipole G ig. A2.2.1). (By convention, the direction of the dipole is taken to be the direction from the negative end to the positive end of the dipole.)... 

Interaction of ions and dipoles, hydrogen bonded systems Minimum Appropriate for relative stabilities and geometries counterpoise correction should be tested... 

An electrode interface has a layered structure in which a nonunifomi electric field (potential slope) is generated by polarization of the electrode. An extremely strong electric field of around 10 Vcm in the innermost layer, the so-called electron transfer layer, which is very thin, 10 A or less, might cause a variety of polar effects. Since not only the electron transfer step but also adsorption and some of the chemical steps involved in an electrolytic reaction take place in the electron transfer layer, the electrochemical reaction should be strongly influenced by polar factors. The orientation of polar adsorbed species, such as ions and dipoles, is electrostatically influenced, and consequently the stereochemistry of their reactions is also controlled by this kind of electrostatic factor. 

Single-ion activity coefficients at higher ionic strength are estimated by using an empirical approach in which complex ion and dipole interactions are accounted for by direct laboratory measurements. One such experimentally based approach that can be applied to seawater is the mean salt method (MSM). This procedure is based upon measurements... 

The electrostatic part of the chemical potentials for ions and dipoles is expressed as,... 

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