Electrostatic theories

In principle the use of the entropy of activation as a criterion is straightforward. The electrostatic contribution to this quantity, A5 i, for a reaction between two cations is predicted from simple electrostatic theory to be less than that for a reaction between an ion and a neutral molecule. If the reactions are otherwise similar, the overall entropies of activation can be expected to differ in the same way ... 

Electrostatic Theory. The basis of the electrostatic theory of adhesion is the differences ia the electroaegativities of adheriag materials (1,2). 

Electrostatic theory proposes that two materials are held together by electrical charges. Electrons are transported between the adhesive and the substrate forming... 

The mechanisms of adhesion are explained by four main theories mechanical theory, adsorption theory, diffusion theory, and electrostatic theory. 

It will be recalled that in Chapter 7, in dealing with the anions of weak acids, we found that we were able to obtain good qualitative agreement between theory and experiment, if we replaced Jmv by the electrostatic Jti. As has been pointed out more than once, the use of simple electrostatic theory necessarily implies that there is an increment in the degree of order in the solvent subject to the electrostatic field. In the -coefficients of Table 24, however, we have found that for 6 out of the... 

The last column in the table gives the values of L, calculated from (173). It will be noticed that for AgCl and AgBr the value of L increases with rise of temperature. The sign of dL/dT is thus in agreement with that expected from simple electrostatic theory the work to convey the ions from the solid into solution increases with rise of temperature. For Agl, on the other hand, we see that L is almost independent of temperature. 

The Alkali Chlorides in Methanol-Water Mixtures. Turning to the results for KC1, NaCl, and LiCl, plotted in Fig. 61, we see that in each case the values are nearly linear with 1/t, suggesting that the results may be simply interpreted in terms of electrostatic theory. This apparent simplicity is, however, illusory. In the first place, KC1 gives greater e.m.f. s than NaCl, while LiCl gives smaller e.m.f. s whereas in Sec. 114 we deduced from (199) that the contrary should be the case. In the second place, if a simple electrostatic interpretation is to be given for the variation of AF with the composition of the solvent, a similar simple... 

T AS are obtained from (AF — AH). In the right-hand half of the diagram the magnitude of — T AS is greater than that of AF, in accordance with electrostatic theory compare (24). As pointed out in Sec. 98, although the molecular dipoles in methanol are less numerous than in water, they lose more entropy in fact they lose so much more entropy that the term —T AS is predominant in producing the e.m.f. of the cells (198) placed back to back. 

The corresponding curve for the — T AS of ICCl, instead of lying below the curve for NaCl, as would be expected from simple electrostatic theory for an ion with a largor radius, rises considerably higher, as shown by the broken line at the top of Fig. 64. In Sec. 114 we suggested that this excess is due to the fact that, while the K+ ion produces order when dis-... 

The theoretical potential calculated on the basis of the ceU model shows that PGA is not suitable for testing a purely electrostatic theory since in this case significant specific binding of counterions to the polyion was detected. For an ion like (C Hg) N, this is offset to some extent by the four longer alkyl groups that protect the positive charge of the rigid sphere [15]. 

The models presented above have also been reviewed in Ref 18. Recently, an expression for the adsorption potential at the free water surface based on a combination of the electrostatic theory of dielectrics and classical thermodynamics has also been proposed." ... 

Here, m is the number of electrons involved in the change, Rq the initial bond distance, and N the number of ligand atoms bonded to the metal. Covalent as well as electrostatic theories suggest that n 5. Note that for both A and /, the values appropriate for the initial state of bond length Rq should be employed. 

On the assumption that = 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the above-mentioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene-water and 1,2-dichloroethane-water interfaces. 

As seen in Table 2, the order of the magnitude of rjj for alkali metal ions is the reverse of that of the magnitude of r. This means that a more hydrophilic ion has a larger rji. However, this fact does contradict the expectation from Bornian electrostatic theories. As can be seen in the Born equation [Eq. (2)], it is expected that the larger the radius an ion has, the more positive the value the ion has, that is, the more hydrophobic it... 

The solvent dependence of the reaction rate is also consistent with this mechanistic scheme. Comparison of the rate constants for isomerizations of PCMT in chloroform and in nitrobenzene shows a small (ca. 40%) rate enhancement in the latter solvent. Simple electrostatic theory predicts that nucleophilic substitutions in which neutral reactants are converted to ionic products should be accelerated in polar solvents (23), so that a rate increase in nitrobenzene is to be expected. In fact, this effect is often very small (24). For example, Parker and co-workers (25) report that the S 2 reaction of methyl bromide and dimethyl sulfide is accelerated by only 50% on changing the solvent from 88% (w/w) methanol-water to N,N-dimethylacetamide (DMAc) at low ionic strength this is a far greater change in solvent properties than that investigated in the present work. Thus a small, positive dependence of reaction rate on solvent polarity is implicit in the sulfonium ion mechanism. 

Many approaches have been used to correlate solvent effects. The approach used most often is based on the electrostatic theory, the theoretical development of which has been described in detail by Amis [114]. The reaction rate is correlated with some bulk parameter of the solvent, such as the dielectric constant or its various algebraic functions. The search for empirical parameters of solvent polarity and their applications in multiparameter equations has recently been intensified, and this approach is described in the book by Reich-ardt [115] and more recently in the chapter on medium effects in Connor s text on chemical kinetics [110]. 

On the basis of classical electrostatic theory, a large part of the free energy of a pair of ions depends on the dielectric constant of the medium. In a solvent of high dielectric constant, a charged object creates oriented solvent dipoles by polarization or orients existing... 

When electrical attraction and repulsion operate over distances considerably larger than the hydrated sizes of the ions, we can compute species activities quite well from electrostatic theory, as demonstrated in the 1920s by the celebrated physical chemists Debye and Hiickel. At moderate concentrations, however, the ions pack together rather tightly. In a one molal solution, for example, just a few... 

Classical electrostatic theory gives the energy of interaction of two charges, Ee (sometimes expressed as the work needed to separate them or the Coulomb energy) as... 

---