Dielectric constant equilibrium

Both Saegusa63 and Schmidt52 have shown that macrocycles are more likely to be formed when charge cancellation polymerizations are carried out in solvents of low dielectric constant. The equilibrium concentration of cyclic ion pairs will increase at the expense of linear ion pairs and free ions if the dielectric constant of the medium falls. Naturally under these circumstances there is a relative increase in the rate of macrocycle formation. 

Our thinking in terms of acid strength is usually confined to aqueous solutions where we have considerable quantitative data, but in strongly basic or strongly acid nonaqueous solvents differences in acid or basic strength of weak acids or bases will be marked. As a specific example, let us consider the interaction of the methylbenzenes with the solvent anhydrous hydrogen fluoride. As this solvent has a high dielectric constant, the equilibrium constant for the reaction... 

K—conductivity K—dielectric constant K—equilibrium constant K—rate constant of forward reaction... 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

Sn2 reactions with anionic nucleophiles fall into this class, and observations are generally in accord with the qualitative prediction. Unusual effects may be seen in solvents of low dielectric constant where ion pairing is extensive, and we have already commented on the enhanced nucleophilic reactivity of anionic nucleophiles in dipolar aprotic solvents owing to their relative desolvation in these solvents. Another important class of ion-molecule reaction is the hydroxide-catalyzed hydrolysis of neutral esters and amides. Because these reactions are carried out in hydroxy lie solvents, the general medium effect is confounded with the acid-base equilibria of the mixed solvent lyate species. (This same problem occurs with Sn2 reactions in hydroxylic solvents.) This equilibrium is established in alcohol-water mixtures ... 

In addition to the normal homolytic dissociation of N2O4 into 2NO2, the molecule sometimes reacts as if by heterolytic fission thus in media of high dielectric constant the compound often reacts as though dissociated according to the equilibrium N2O4, NO" " + NOj" (see... 

As noted above, there is no physical evidence for this equilibrium in pure N2O4, but the electrical conductivity is considerably enhanced when the liquid is mixed with a solvent of high dielectric constant such as nitromethane (e 37), or with donor solvents (D) such as MeC02Et, Et20, Mc2SO, or Et2NNO (diethylnitrosamdne) ... 

D2O and the tritium analogue T2O (p. 41). The high bp is notable (cf. H2S, etc.) as is the temperature of maximum density and its marked dependence on the isotopic composition of water. The high dielectric constant and measurable ionic dissociation equilibrium are also unusual and important properties. The ionic mobilities of [H30] and [OH] in water are abnormally high (350 X 10 " and 192 x 10 cms per V cm... 

The macroscopic dielectric constant of liquid formic acid at 25° has the value 64, not much lower than that of water. Hence, from the simple electrostatic point of view, we should expect. /c for the proton transfer (211) carried out in formic acid solution, to have a value somewhat greater, but not much greater, than when the same proton transfer is carried out in water as solvent. In Table 12 we found that, in aqueous solution, the value of (./ + Jenv) rises from 0.3197 at 20°C to 0.3425 at 40°C. Measurements in formic acid at 25°C yielded for the equilibrium of (211) the value — kT log K = 4.70. Since for formic acid the number of moles in the b.q.s. is M = we find... 

Becker and Israel (1979) have studied the influence of the solvent in more detail. They determined the constant KD of the equilibrium between free ions and ion pairs (Schemes 10-12 and 10-13) conductometrically in five solvents (H20, MeCN, MeOH, EtOH, and Me2CO). An inverse linear relationship was found between the ratio of products [ArOS]/[ArF] (where ArOS is the product of heterolytic solvolysis) and Kd/e (e = dielectric constant). This result indicates that solvolysis products are formed mainly from free diazonium ions, whereas fluoro-de-diazoniation takes place in the ion pair. Of the solvents used, acetone gives the lowest value of KD, and thus the yield of the fluorinated product is highest in this solvent. 

However, the equilibrium of the indicator adsorbed at an interface may also be affected by a lower dielectric constant as compared to bulk water. Therefore, it is better to use instead pH, the interfacial and bulk pK values in Eq. (50). The concept of the use at pH indicators for the evaluation of Ajy is also basis of other methods, like spin-labeled EPR, optical and electrochemical probes [19,70]. The results of the determination of the Aj by means of these methods may be loaded with an error of up to 50mV [19]. For some the potentials determined by these methods, Ajy values are in a good agreement with the electrokinetic (zeta) potentials found using microelectrophoresis [73]. It is proof that, for small systems, there is lack of methods for finding the complete value of A>. 

The successive equilibria are characterized by K12 and K23, respectively, and when Kl2 (often denoted K0) cannot be directly determined, it may be estimated from the Fuoss equation (3), where R is the distance of closest approach of M2+ and 1/ (considered as spherical species) in M OH2 Um x) +, e is the solvent dielectric constant, and zM and zL are the charges of Mm+ and Lx, respectively (20). Frequently, it is only possible to characterize kinetically the second equilibrium of Eq. (2), and the overall equilibrium is then expressed as in Eq. (4) (which is a general expression irrespective of mechanism). Here, the pseudo first-order rate constant for the approach to equilibrium, koba, is given by Eq. (5), in which the first and second terms equate to k( and kh, respectively, when [Lx ] is in great excess over [Mm+]. When K0[LX ] <11, koba - k,K0[Lx ] + k.it and when K0[LX ] > 1, fc0bs + k l. Analogous expressions apply when [Mm+] is in excess. 

Section 3.3.4 pointed out that cosolvents alter aqueous ionization constants as the dielectric constant of the mixture decreases, acids appear to have higher pKa values and bases appear (to a lesser extent than acids) to have lower values. A lower dielectric constant implies that the force between charged species increases, according to Coulomb s law. The equilibrium reaction in Eq. (3.1) is shifted to the left in a decreased dielectric medium, which is the same as saying that pKa increases. Numerous studies indicate that the dielectric constant in the region of the polar head groups of phospholipids is 32, the same as the value of methanol. [381,446-453] Table 5.2 summarizes many of the results. 

If the dielectric constant of an amphiprotic solvent is small, protolytic reactions are complicated by the formation of ion pairs. Acetic acid is often given as an example (denoted here as AcOH, with a relative dielectric constant of 6.2). In this solvent, a dissolved strong acid, perchloric acid, is completely dissociated but the ions produced partly form ion pairs, so that the concentration of solvated protons AcOH2+ and perchlorate anions is smaller than would correspond to a strong acid (their concentrations correspond to an acid with a pK A of about 4.85). A weak acid in acetic acid medium, for example HC1, is even less dissociated than would correspond to its dissociation constant in the absence of ion-pair formation. The equilibrium... 

Thus, the dissociation equilibrium is affected by the ionic strength, temperature and dielectric constant of the solvent as well as by the parameter h (involved in AGf,). On the other hand, the term dG /dn does not depend on the degree of polymerization (except for very small values of n). The degree of polymerization does not affect, for example, the course of the potentiometric titration of a poly acid. 

In addition to the described above methods, there are computational QM-MM (quantum mechanics-classic mechanics) methods in progress of development. They allow prediction and understanding of solvatochromism and fluorescence characteristics of dyes that are situated in various molecular structures changing electrical properties on nanoscale. Their electronic transitions and according microscopic structures are calculated using QM coupled to the point charges with Coulombic potentials. It is very important that in typical QM-MM simulations, no dielectric constant is involved Orientational dielectric effects come naturally from reorientation and translation of the elements of the system on the pathway of attaining the equilibrium. Dynamics of such complex systems as proteins embedded in natural environment may be revealed with femtosecond time resolution. In more detail, this topic is analyzed in this volume [76]. 

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