Interactions Between Ions

The SPC/E model approximates many-body effects m liquid water and corresponds to a molecular dipole moment of 2.35 Debye (D) compared to the actual dipole moment of 1.85 D for an isolated water molecule. The model reproduces the diflfiision coefficient and themiodynamics properties at ambient temperatures to within a few per cent, and the critical parameters (see below) are predicted to within 15%. The same model potential has been extended to include the interactions between ions and water by fitting the parameters to the hydration energies of small ion-water clusters. The parameters for the ion-water and water-water interactions in the SPC/E model are given in table A2.3.2. 

The theory of strong electrolytes due to Debye and Htickel derives the exact limiting laws for low valence electrolytes and introduces the idea that the Coulomb interactions between ions are screened at finite ion concentrations. 

The interaction between ions of the same sign is assumed to be a pure hard sphere repulsion for r < a. It follows from simple steric considerations that an exact solution will predict dimerization only if i < a/2, but polymerization may occur for o/2 < L = o. However, an approximate solution may not reveal the fiill extent of polymerization that occurs in a more accurate or exact theory. Cummings and Stell [ ] used the model to study chemical association of uncharged atoms. It is closely related to the model for adliesive hard spheres studied by Baxter [70]. 

Fehsenfeld F C 1975 Associative Detachment Interactions Between Ions and Molecules ed P Ausloos (New York Plenum)... 

The correlation functions of the partly quenched system satisfy a set of replica Ornstein-Zernike equations (21)-(23). Each of them is a 2 x 2 matrix equation for the model in question. As in previous studies of ionic systems (see, e.g.. Refs. 69, 70), we denote the long-range terms of the pair correlation functions in ROZ equations by qij. Here we apply a linearized theory and assume that the long-range terms of the direct correlation functions are equal to the Coulomb potentials which are given by Eqs. (53)-(55). This assumption represents the mean spherical approximation for the model in question. Most importantly, (r) = 0 as mentioned before, the particles from different replicas do not interact. However, q]f r) 7 0 these functions describe screening effects of the ion-ion interactions between ions from different replicas mediated by the presence of charged obstacles, i.e., via the matrix. The functions q j (r) need to be obtained to apply them for proper renormalization of the ROZ equations for systems made of nonpoint ions. 

To describe the simple phenomena mentioned above, we would hke to have only transparent approximations as in the Poisson-Boltzmann theory for ionic systems or in the van der Waals theory for non-coulombic systems [14]. Certainly there are many ways to reach this goal. Here we show that a field-theoretic approach is well suited for that. Its advantage is to focus on some aspects of charged interfaces traditionally paid little attention for instance, the role of symmetry in the effective interaction between ions and the analysis of the profiles in terms of a transformation group, as is done in quantum field theory. 

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. 

High sorption capacities with respect to protein macromolecules are observed when highly permeable macro- and heteroreticular polyelectrolytes (biosorbents) are used. In buffer solutions a typical picture of interaction between ions with opposite charges fixed on CP and counterions in solution is observed. As shown in Fig. 13, in the acid range proteins are not bonded by carboxylic CP because the ionization of their ionogenic groups is suppressed. The amount of bound protein decreases at high pH values of the solution because dipolar ions proteins are transformed into polyanions and electrostatic repulsion is operative. The sorption maximum is either near the isoelectric point of the protein or depends on the ratio of the pi of the protein to the pKa=0 5 of the carboxylic polyelectrolyte [63]. It should be noted that this picture may be profoundly affected by the mechanism of interaction between CP and dipolar ions similar to that describedby Eq. (3.7). 

Our starting point for understanding the interaction between ions in a solid is the expression for the Coulomb potential energy of the interaction of two individual ions (Section A) ... 

Self-Tfst 2.3B The ionic solids KBr and KCl crystallize to form structures of the same type. In which compound are the interactions between ions stronger ... 

Ionic solids typically have high melting points and are brittle. The coulombic interaction between ions in a solid is large when the ions are small and highly charged. 

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). 

The strength of interaction between ions in a solid is measured by the lattice enthalpy, which can be determined by using a Bom-Haber cycle. 

A hypothetical solution that obeys Raoult s law exactly at all concentrations is called an ideal solution. In an ideal solution, the interactions between solute and solvent molecules are the same as the interactions between solvent molecules in the pure state and between solute molecules in the pure state. Consequently, the solute molecules mingle freely with the solvent molecules. That is, in an ideal solution, the enthalpy of solution is zero. Solutes that form nearly ideal solutions are often similar in composition and structure to the solvent molecules. For instance, methylbenzene (toluene), C6H5CH, forms nearly ideal solutions with benzene, C6H6. Real solutions do not obey Raoult s law at all concentrations but the lower the solute concentration, the more closely they resemble ideal solutions. Raoult s law is another example of a limiting law (Section 4.4), which in this case becomes increasingly valid as the concentration of the solute approaches zero. A solution that does not obey Raoult s law at a particular solute concentration is called a nonideal solution. Real solutions are approximately ideal at solute concentrations below about 0.1 M for nonelectrolyte solutions and 0.01 M for electrolyte solutions. The greater departure from ideality in electrolyte solutions arises from the interactions between ions, which occur over a long distance and hence have a pronounced effect. Unless stated otherwise, we shall assume that all the solutions that we meet are ideal. 

A note on good practice Keep in mind the approximations required for the use of the Henderson-Hasselbalch equation (that the concentrations of both the weak acid and its conjugate base are much greater than the hydronium ion concentration). Because the equation uses molar concentration instead of activities, it also ignores the interactions between ions. 

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. 

Therefore, the activity coefficients in solutions are determined primarily by the energy of electrostatic interaction w j between the ions. It is only in concentrated solutions when solvation conditions may change, that changes in (but not the existence of) solvation energy must be included, and that nonelectrostatic interactions between ions must be accounted for. 

An appreciable advance in the theory of electrostatic interaction between ions in solution was made in 1923 by Peter Debye and Erich Hiickel, who introduced the concept of ionic atmosphere to characterize the averaged distribution of the ions. In its initial form the theory was applied to fully dissociated electrolytes hence, it was named the theory of strong electrolytes. 

The first ideas concerning a role of pairwise electrostatic interaction between ions were advanced in 1924 by Vladimir K. Semenchenko. A quantitative theory of the formation of ion pairs was formulated in 1926 by Niels Bjerrum. 

Ion-pair formation (or the formation of triplets, etc.) is a very simple kind of interaction between ions of opposite charge. As the electrolyte concentration increases and the mean distance between ions decreases, electrostatic forces are no longer the only interaction forces. Aggregates within which the ions are held together by chemical forces have certain special features (i.e., shorter interatomic distances and a higher degree of desolvation than found in ion pairs) and can form a common solvation sheath instead of the individual sheaths. These aggregates are seen distinctly in spectra, and in a number of cases their concentrations can be measured spectroscopically. 

Proteins that are polyampholytes, upon addition of electrolyte, first undergo some salting in up to a certain ionic strength, since electrostatic interactions between ions are shielded by the additional simple ions of both sign. Adding more salt will then cause salting out as the added ions compete for water that would otherwise solvate the protein. 

Changes in activity coefficients (and hence the relationship between concentration and chemical activity) due to the increased electrostatic interaction between ions in solution can be nicely modeled with well-known theoretical approaches such as the Debye-Huckel equation ... 

Braga D, Maini L, Polito M, Grepioni F (2004) Hydrogen Bonding Interactions Between Ions A Powerful Tool in Molecular Crystal Engineering 111 1-32 Brechin EK, see Aromf G (2006) 122 1-67... 

The simplest theory of interactions between ions and the solvent, proposed by M. Born, assumed that the ions are spheres with a radius of rt... 

Bjerrum s theory includes approximations that are not fully justified the ions are considered to be spheres, the dielectric constant in the vicinity of the ion is considered to be equal to that in the pure solvent, the possibility of interactions between ions other than pair formation (e.g. the formation of hydrogen bonds) is neglected and the effect of ion solvation during formation of ion pairs is not considered (the effect of the solvation on ion-pair structure is illustrated in Fig. 1.7). 

The approach introduced by E. A. Guggenheim and employed by H. S. Harned, G. Akerlof, and other authors, especially for a mixture of two electrolytes, is based on the Br0nsted assumption of specific ion interactions in a dilute solution of two electrolytes with constant overall concentration, the interaction between ions with charges of the same sign is non-specific for the type of ion, while interaction between ions with opposite charges is specific. 

The Gibbs energy of an ion changes on transfer from one solvent to another primarily because the electrostatic interaction between ions and the medium changes as a result of the varying dielecric constant of the solvent. This can be expressed roughly by the Born equation (see Eq. 1.2.7),... 

For simple monovalent metals, the pseudopotential interaction between ion cores and electrons is weak, leading to a uniform density for the conduction electrons in the interior, as would obtain if there were no point ions, but rather a uniform positive background. The arrangement of ions is determined by the ion-electron and interionic forces, but the former have no effect if the electrons are uniformly distributed. As the interionic forces are mainly coulombic, it is not surprising that the alkali metals crystallize in a body-centered cubic lattice, which is the lattice with the smallest Madelung energy for a given density.46 Diffraction measurements... 

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