Ionic cohesive energy

Fujiwara et al. used the CMC values of sodium and calcium salts to calculate the energetic parameters of the micellization [61]. The cohesive energy change in micelle formation of the a-sulfonated fatty acid methyl esters, calculated from the dependency of the CMC on the numbers of C atoms, is equivalent to that of typical ionic surfactants (Na ester sulfonates, 1.1 kT Ca ester sulfonates, 0.93 kT Na dodecyl sulfate, 1.1 kT). The degree of dissociation for the counterions bound to the micelle can be calculated from the dependency of the CMC on the concentration of the counterions. The values of the ester sulfonates are also in the same range as for other typical ionic surfactants (Na ester sulfonates, 0.61 Ca ester sulfonates, 0.70 Na dodecyl sulfate, 0.66). 

The simple theory of electronegativity fails in this discussion because it is based merely on electron transfer energies and determines only the approximate number of electrons transferred, and it does not consider the interactions which take place after transfer. Several calculations in the alkali halides of the cohesive energy (24), the elastic constants (24), the equilibrium spacing (24), and the NMR chemical shift 17, 18, 22) and its pressure dependence (15) have assumed complete ionicity. Because these calculations based on complete ionicity agree remarkably well with the experimental data, we are not surprised that the electronegativity concept of covalency fails completely for the alkali iodide isomer shifts. 

It is quite remarkable that electrostatic calculations based on a simple model of integral point charges at the nuclear positions of ionic crystals have produced good agreement with values of the cohesive energy as determined experimentally with use of the Born-Haber cycle. The point-charge model is a purely electrostatic model, which expresses the energy of a crystal relative to the assembly of isolated ions in terms of the Coulombic interactions between the ions. 

Seiler and Dunitz point out that the main reason for the widespread acceptance of the simple ionic model in chemistry and solid-state physics is its ease of application and its remarkable success in calculating cohesive energies of many types of crystals (see chapter 9). They conclude that the fact that it is easier to calculate many properties of solids with integral charges than with atomic charge distributions makes the ionic model more convenient, but it does not necessarily make it correct. 

Overlap between p orbitals leads to cohesive energies of typically less than 0.4 eV molec The much stronger ionic and covalent bonding have binding energies of 10 and 3 eV atom respectively. Finally, physisorption is the weakest form of absorption to a solid surface characterized by a lack of a true chemical bond (chemisorption) between substrate and adsorbate and will be discussed in Chapter 4 (see e.g., Zangwill, 1988). 

AFMs have also been used to eshmate the cohesive energy of ionic materials with face-centred-cubic structure (Fraxedas et al., 2002a). In these experiments an ultrasharp AFM hp (hp radius / < 10 nm) indents a hat surface of a single crystal and the dynamical mechanical response of the surface during indentahon is transformed into a force plot (applied force vs. penetrahon). It turns out that the... 

Lee, S.H. and Lee, S.B., The Hildebrand solubility parameters, cohesive energy densities and internal energies of l-alkyl-3-methylimidazolium-based room temperature ionic liquids, Chem. Commun., 3469, 2005. 

The cohesive energy of ionic crystals is mainly due to electrostatic interaction and can be calculated on the basis of a point-charge model. Following Born, the cohesive energy (U) of a crystal containing oppositely charged ions with charges Zj and Zj is written as the sum of two terms, one due to attraction and the other due to repulsion ... 

Equation (1.4) is an expression for the lattice energy of an ionic solid like NaCl, first derived by Born and Mayer. The equation can be used directly for the calculation of cohesive energy of ionic solids provided we know A and p. 

The parameter is obtained by relating the static dielectric constant to Eg and taking in such crystals to be proportional to a - where a is the lattice constant. Phillips parameters for a few crystals are listed in Table 1.4. Phillips has shown that all crystals with a/ below the critical value of0.785 possess the tetrahedral diamond (or wurtzite) structure when f > 0.785, six-fold coordination (rocksalt structure) is favoured. Pauling s ionicity scale also makes such structural predictions, but Phillips scale is more universal. Accordingly, MgS (f = 0.786) shows a borderline behaviour. Cohesive energies of tetrahedrally coordinated semiconductors have been calculated making use... 

In the general theory of ionic crystals (such as table salt, NaCl), a key physical quantity is the cohesive energy Zsxtal of forming the solid crystal from its constituent ions. For sodium chloride, for example, this is the energy lowering in the reaction... 

Although surprisingly circuitous, this expression for the cohesive energy of an ionic crystal carries the full authority of the first law. 

A Theoretical Investigation into Some Properties of Ionic Crystals. A Quantum Mechanical Treatment of the Cohesive energy, the Interionic Distance, the Elastic Constants, and the Compression at High Pressures with Numerical Ap-... 

P.-O. Lowdin, Ark. Mat. Astr. Fysik A35, 1 (1947). A Quantum Mechanical Calculation of the Cohesive Energy, the Interionic Distance, and the Elastic Constants of Some Ionic Crystals. 

The theorem has the important implication that intramolecular interactions can be calculated by the methods of classical electrostatics if the electronic wave function (or charge distribution) is correctly known. The one instance where it can be applied immediately is in the calculation of cohesive energies in ionic crystals. Taking NaCl as an example, the assumed complete ionization that defines a (Na+Cl-) crystal, also defines the charge distribution and the correct cohesive energy is calculated directly by the Madelung procedure. 

Table 5.3 Structural details and cohesive energies of the metals with Al, A2 and AS structures. Energies (in kJmot1) are listed as ionic and covalent contributions and total energies as calculated and observed [74] cohesive energies.

The cohesive energy of the solvent also is related to the boiling point, so there is a correlation of boiling point ot solvent viscosity as well. A further relationship of the equivalent conductance at infinte dilution is that it is composed of the individual ionic conductances at infinite dilution ... 

The London forces are predominant in the adsorption of gases on solid substances such as carbon. In the adsorption on ionic lattices such as salt layers (CaF2 in electric lamps), silicic acid and aluminium oxide the adsorption of the first layer however depends mainly on polarization by electrostatic forces, in which isolated ions, corners and edges will give a larger heat of adsorption than a perfect crystal surface. In adsorption in multimolecular layers the Van der Waals-London energy is, however, predominant as in the cohesion energy. 

In general, the total interatomic potential between any pair of atoms is the sum of the pair-wise interaction and the interactions between three atoms (triplets), four atoms (quartets), etc. The problem is pair potentials are by far the easiest to compute, however, their exclusive use gives results that are only semiquantitative (even with ionic solids), accounting for only up to 90 percent of the total cohesive energy in a solid. The three-body term simply cannot be neglected, although the higher-order terms often can be. 

To this point, we have considered the interaction of nonionic surfactants within the framework of the mathanatical model. The activity and character of anionics in emulsification is complicated by the ionization steps which an anionic surfactant may take when exposed to salt solutions. For instance, in a dialkyl metallic salt, there are three compounds which may exist in various concentrations, depending ipon the ionic strength of the salt solution which, in turn, would exhibit, at least, three different HLB nuiiibers. To address the problem of generating Cohesive Energy Density parameters for the anionic hydrophiles, certain standardized assunptions... 

Figure 2.10 Dependence of the cohesion of salts of weakly polarizable cations and anions, assessed by Tg value, on the ambient temperature molar volume hence on interionic spacing [(r -i- r) V ]. A broad minimum in the ionic liquid cohesive energy is seen at a molar volume of 250 crrPnmr, which corresponds to an interionic separation of about 0.6nm, assuming face-centered cubic pacidng of anions about cations. The lowest Tg in the plot should probably be excluded from consideration because of the non-ideal Walden behavior for this IL (MOMNMgE BF ) [15]). The line through the points is a guide to the eye. The data for open triangles are from Sun, Forsyth, and MacFatlane [42].

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