Ion and solvent

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

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. 

Since the term hydration refers to aqueous solutions only, the word solvation was introduced as a general term for the process of forming a solvate in solution. The terms solvation and heat of solvation were introduced at a time when little or nothing was known about polar molecules. We know now that, when an atomic ion is present in a solvent, the molecular dipoles are subject to the ionic field, whose intensity falls off in 1/r2. We cannot draw a sphere round the ion and say that molecules within this sphere react with the ion to form a solvated ion, while molecules outside do not. The only useful meaning that can now be attached to the term solvation is the total interaction between ion and solvent. As already mentioned, this is the sense in which the term is used in this book. 

Chemical models of electrolytes take into account local structures of the solution due to the interactions of ions and solvent molecules. The underlying information stems from spectroscopic, kinetic, and electrochemical experiments, as well as from dielectric relaxation spectroscopy. The postulated structures include ion pairs, higher ion aggregates, and solvated and selectively solvated ions. 

Exchange of counter-ions (and solvent) between the polymer and the solution in order to keep the electroneutrality in the film. In a compacted or stressed film, these kinetics are under conformational relaxation control while the structure relaxes. After the initial relaxation, the polymer swells, and conformational changes continue under counter-ion diffusion control in the gel film from the solution. 

Otero and co-workers208,212 have visually observed nuclei of oxidized polymer in thin polypyrrole films on electrodes. They attribute these to sites of counter-ion and solvent ingress. A nucleation model based on the growth of ionically conductive zones provides good agreement with experimental chronoamperometric responses. 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

The expressions for the rates of the electrochemical reactions given in Section II. A have not taken into account the detailed structure of the interfacial region. In general, the solution adjacent to the electrode will consist of at least two regions. Immediately adjacent to the metal there will be a compact layer of ions and solvent molecules which behaves as a capacitor. A potential difference will be established between... 

The exchange of ions and solvent between a swollen ionic network and the surrounding electrolyte is represented in Fig. 136, where the fixed ion is taken to be a cation. It is apparent that the equilibrium between the swollen ionic gel and its surroundings closely resembles Donnan membrane equilibria. 

Ionic solvation is interaction between ions and solvent molecules that leads to the formation of relatively strong aggregates, the solvated ions. In aqueous solutions the terms ionic hydration and hydrated ions are used as weU. 

A more general theory of solutions would require detailed notions of solution structure and of all types of interactions between the particles (ions and solvent molecules) in the solution. Numerous experimental and theoretical studies have been carried out, and some progress has been made, but a sufficiently universal theory that could describe all properties in not very dilute electrolyte solutions has not yet been developed. 

The third term, Uqt, in Eq. (27) is due to the partial electron transfer between an ion and solvents in its immediate vicinity. The model Hamiltonian approach [33], described in Section V, has shown that Uqt (= AW in Ref. 33) per primary solvent molecule, for an ion such as the polyanion, can also be expressed as a function of E, approximately a quadratic equation ... 

In this manner AG[ r° (SR) is given approximately by a quadratic equation of E. The coefficients Tj, T2, and T3 are related to various molecular properties of the ion and solvents [see Eqs. (32)-(34) and Eqs. (37)-(39)]. To estimate theoretically these coefficients using an appropriate model may not be impossible, but rather difficult at the present stage, because there is insufficient information on the above-mentioned molecular properties (in particular, the charge-transfer properties). Consequently, coefficients T], T2, and T3 in Eq. (36) have been determined empirically, as shown below. 

Most authors have accounted for the mutual influence of ions and solvent molecules only by assuming a firmly bound solvent sheath around the ion. The structure of the bulk solvent and the influence of electrolyte concentration on this structure are not taken into consideration. 

When a multiply charged ion solvated by several solvent molecules is subjected to heating or to vibrational excitation due to collisions with inert neutrals, ion desolvation occurs by successive loss of single solvent molecules, as illustrated below, for a double-charged ion and solvent molecules SI ... 

The ionic profile of the metal was modeled as a step function, since it was anticipated that it would be much narrower than the electronic profile, and the distance dx from this step to the beginning of the water monolayer, which reflects the interaction of metal ions and solvent molecules, was taken as the crystallographic radius of the metal ions, Rc. Inside the metal, and out to dl9 the relative dielectric constant was taken as unity. (It may be noted that these calculations, and subsequent ones83 which couple this model for the metal with a model for the interface, take the position of the outer layer of metal ion cores to be on the jellium edge, which is at variance with the usual interpretation in terms of Wigner-Seitz... 

Equation (2.33) now defines the double layer in the final model of the structure of the electrolyte near the electrode specifically adsorbed ions and solvent in the IHP, solvated ions forming a plane parallel to the electrode in the OHP and a dilfuse layer of ions having an excess of ions charged opposite to that on the electrode. The excess charge density in the latter region decays exponentially with distance away from the OHP. In addition, the Stern model allows some prediction of the relative importance of the diffuse vs. Helmholtz layers as a function of concentration. Table 2.1 shows... 

Absolute values of the rate constants ks (s ) and kp (s ). In most cases these rate constants were determined from the values of kaz/ks (M 1) or kaz/kp (M-1) for partitioning of the carbocation between reaction with azide ion and solvent, by using the diffusion-limited reaction of azide ion, kaz = 5 x 109m 1s, as a clock for the slower reactions of solvent.7 8 13 32 82... 

Fig. 14. A few diagrams involving solvent-ion and solvent-solvent interactions.

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