Dielectric properties of binary mixtures. 5. Dilute alcohol/nonpolar solvent systems

A simple model is used for dilute polar/nonpolar systems, based on the additivity of electric susceptibilities of a solute/solvent interaction species and a nonpolar solvent. A spherical cavity is considered. Permittivity values, calculated as a function of concentration, are in good agreement with experimental results when the model is applied to systems containing water or lower alcohols in nine nonpolar solvents.


Introduction
In very dilute solutions of polar solutes in nonpolar solvents, the permittivity is found experimentally to be a linear function of solute concentration. This is an important region because permittivity (e), specific volume (V), and refractive index ( ) are measured therein to calculate the dipole moment (µ) of the solute. However, there is so far no satisfactory model to describe completely the details of this behavior at very low solute concentrations.
The sizable amount of work reported on water and the lower alcohols (R-OH, wherein R = H, Me, Et, n-Pr, n-Bu) as polar solutes in a number of nonpolar solvents (benzene, n-hexane, dioxane, carbon tetrachloride, cyclohexane, carbon disulfide, and toluene) makes these systems good candidates with which to reexamine the problem.
Six known equations based on spherical cavity models were used to evaluate the existing data, but they do not predict satisfactorily the linear behavior of permittivity as a function of concentration. An equation based on a simple model was developed, which proved to be adequate in the case of the chosen systems.

Examination of Data
In very dilute solutions the gradient of the linear concentration response observed experimentally for the permittivity could have any one of several origins: (i) the dielectric properties of the pure components may remain unchanged in mixtures regardless of their proportions, (ii) there may exist some form of ideal behavior, or (iii) there could be solute/solvent interactions of some kind. Known data can be examined considering each of them.
Values calculated through direct use of the pure-component permittivities and a simple additive law of the form «12 = « ^ + e2w2 (I) (subscripts: 1 = solvent, 2 = solute, and 12 = solution; w represents the weight fraction concentration) rule out the first possibility (i) because of the large differences between experimental and calculated values (see third column, Table II). Consequently eq I can be discarded. The second possibility (ii) requires that no interactions exist at all. On this basis, in the particular case of water, Oehme2 calculated a very low permittivity (c = 28.3 at 298 K) using Onsager's equation3 with the dipole moment ( (Table I).
Oehme suggested that the low calculated t values represented "idealized water". On the other hand, low numbers as these are not uncommon. Stem4 claimed < = 20 (at 298 K) measured on water adsorbed on the surface of solids and in fine capillaries. Also Foster and Resing5 estimated values of e = 14 and e = 20 for interstitial water in hydrated zeolites. But since these values are a consequence of the interaction of water molecules with the silicate surface, it is not logical to consider them a result of idealized water. What is actually being studied is a system formed by water adsorbed on the surface of a solid silicate.
Therefore both solute/ solute interactions (i) and ideal behavior (ii) must be discarded. This leaves the third possibility (iii) to be considered, in other words, interactions of solute molecules with the surrounding medium.
These are the solute/solvent interactions or solvation suggested by Muller6 78910**while discussing the influence of solvent effects on dipole moments.

Discussion
Studies on the state of aggregation of water and the lower alcohols in nonpolar solvents have already been made. 1,8"13 In all cases the plots of e = f(w2) (wherein w2   is the solute weight fraction concentration) appear as a succession of straight lines suggesting different forms of interactions as the solute concentration increases. This can be seen in Figure 1 for methanol in benzene, n-hexane, and CC14.9 The first region in these and the other systems mentioned corresponds to the high dilution conditions used for dipole moment calculations. This stems from the generally made assumption that it contains the solute not only in a monomeric state but also free of interactions, either solute/solute (due to the distance between the solute molecules) or solute/solvent (as claimed in the abovementioned references). Consequently these have to be discarded after the preceding discussion.
An alternative possibility would imply evaluating known equations. But their number is very large, starting with the original one by Mossotti and Clausius. So, it was decided to begin with only those models based on a spherical cavity introducing no correction factors. This narrowed the choice to just six equations: Mossotti- Grosse-Greffe (GG), the difference between the first two and the last four being the introduction of molecular parameters in the latter. The initials in parentheses correspond to the respective headings in Table . All of them were discussed in detail and expressed in coherent form recently by Grosse and Greffe.14 Suitable computer programs were prepared for each equation, and previously reported data were evaluated.9"12,15"17 In each case the slope (S) and the extrapolated solution permittivity (c120) were calculated («120 corresponds to the permittivity of the solution in the limit of zero solute concentration). Under the corresponding initials the results are listed in Table II and they show the following: (a) The basic model for the MC and MCD treatments seems to provide values for the change in permittivity (slope) of the binary systems considered, which are within the order of magnitude of the experimental results, (b) Equations due to D, 0, and OGG show no coincidence in the slopes. The equations by GG show very good coincidence for the solution in benzene, but none with the other solvents, (c) Although a cavity model appears promising, the introduction of molecular parameters does not lead to any improvement.
A different approach was attempted on the basis of electrical susceptibilities and the auxiliary use of a cavity as will be discussed in the next section.

Proposed Equation
As already mentioned, there is enough experimental evidence indicating that water and the lower alcohols interact with nonpolar solvents.1,7"12 But all of the models and equations mentioned do not describe this situation in a satisfactory manner because the calculated values for S and e120 do not agree with the experimental results. To overcome this problem, we propose a different approach.  If solute/solvent interactions are to be considered in order to describe the linear behavior of the permittivities of all of these solutions (e12) with solute concentration, at the lowest concentration, it is convenient to describe properties of the solution through the number of molecular species present per unit volume. To do so, one can consider the existence of Nl molecules of solvent and N2 molecules of solute, related to each other in some form of molecular species. This latter would then be formed by one solute molecule and the solvent molecules that surround it. Therefore, because of the observed linear behavior in these solutions, it is necessary to accept that the external and the dipolar fields become superimposed.
This allows one to consider the electric susceptibility of the solution as being where 12 is the electric susceptibility of the solution, is the electric susceptibility of the solvent, and 3 is the electric susceptibility of the species formed by solute and solvent.
In the case of the linear behavior of mixture permittivities, the following fundamental equations are valid,19 since they are applicable to all material systems: where is the total susceptibility and a is the total molecular polarizability. Therefore, if ax is the total solvent polarizability Xi = #i«i The a3 term in eq II, representing the polarizability of the solute/solvent interaction product, contains the contributions of both solute and solvent. As a consequence, the dipole moment of the species will have to be different from that of the pure solute.
However, in highly dilute systems, these are weak changes, and a model with additive polarizabilities is still valid, so that now a3 contains the contributions of the solute molecule plus the unchanged atom and electron polarizabilities, in its particular state of interaction with the solvent. Therefore, the total polarizability of the interaction species can be written as   where 2 is the refractive index of the solute and µ0 is the dipole moment of the solute under vacuum. But this is a very dilute system, so it is possible to assign to each molecule its own cavity as if it were immersed in solvent. The approximation or model is then applicable, wherein 2 represents the refractive index of the cavity filled with the corresponding solute molecule. Consequently the following Onsager3 relations can be used: Regarding a^, it could be either disregarded or estimated as a certain percentage of a2e. The latter seems far more reasonable because there is sufficient evidence that justifies considering as being between 5% and 15% of a2e. Therefore, to cover all possibilities, it is best to take the upper value so that The same experimental data were evaluated with eq III, and the results are listed in Table II under M. All calculated values are in good agreement with experiment.
In the above discussion, although a cavity is considered and solute and solvent properties are included, the solution is viewed as a system formed by a solute/solvent species in a sea of solvent. This is substantially simpler than many previous treatments, because eq III only contains the permittivity of the pure solvent and the refractive index of the solute, the vapor-phase dipole moment of the solute, and the molecular radius of the solute (calculated from bulk properties).

Conclusions
(1) Spherical cavity models with no correction factors do not describe the behavior of the permittivity as a function of concentration of simple hydroxyl compounds (R-OH; R = H, Me, Et, ro-Pr, and n-Bu) in very dilute solutions of nonpolar solvents. (2) The original Mossotti-Clausius model is an exception regarding only the slope, while the Grosse-Greffe model is useful only to describe those systems having benzene as solvent.
(3) The permittivity of the candidate systems, as a function of concentration, can best be described considering a solute/solvent interaction product or species located in a spherical cavity immersed in a sea of solvent. Under these conditions the electric susceptibilities of both components are additive and their values can be calculated by using the permittivity and the refractive index of the pure solute, the dipole moment of the solute in the vapor state, and the molecular radius of the pure solute calculated from experimental weights and volumes. (4) In the water/dioxane system there is no agreement between the experimental and calculated values, using the proposed equation. Such behavior can be attributed to a solute /solvent interaction, typical of these two components, which differs significantly from what occurs when one of the hydrogen atoms in the water molecule is replaced by a small alkyl group (Cx~C4) This singular situation is by no means unexpected since Jaffer20 already found evidence for particular solute/solvent associations in the water/dioxane system. (5) With the proposed equation, calculated values of e for very dilute solutions as a function of concentration, with one exception, are in good agreement with experiment.

Introduction
The catalytic decomposition of hydrogen peroxide has been extensively studied by using various metal ions and their complexes as a model for the catalysis promoted by catalase. 1 The reaction has often been explained in terms of the Haber-Weiss mechanism,2 including the redox of the central ion. We have reported that the activities of transition-metal ions exchanged onto zeolites vary in a bell-shaped pattern against their redox potentials.3 Such a dependency on their redox potentials suggests that the proper modification of the redox potential of an ion by any means may enhance its catalytic activity. Suitable coordination has been known to increase the catalytic activity.4 Some chelating ligands brought remarkable enhancement5 to give an activity comparable to that of catalase.
A series of metaUotetraphenylporphyrins (M-TPP's) are known to show a sequence of redox potentials, and their catalytic activities have been examined in several systems.6 Some of the oxide carriers are reported to be able to modify the properties of the metals and some complexes supported on them through their electronic interactions. 7 We found that Co-TPP showed a very high catalytic activity for the reduction of nitric oxide after being supported on titanium dioxide. The enhancement can be assumed to be due to an electron transfer from the support to the complex.8 Such a strong interaction of the catalytic material with the support may be a key factor for the development of a novel catalyst.9 In the present study, catalytic activities of some M-TPP's for the decomposition of hydrogen peroxide were investigated to describe the roles of their metal ions and ligands in this catalysis and to reveal the effects of metal oxide supports on their activities since a sequence of the redox potentials and their strong interaction with the support may attract interest. The interaction can be evaluated not only in the catalytic reaction but also in the chemistry of the complex which may play a role as a probe to reflect the interaction. The supports were selected from fairly large varieties to define what properties were essential for the interaction. Although Okura et al. 10 already reported the activities of Cu-TPP and Co-TPP supported on silica gel for the same reaction, their activities were rather limited to decomposing only 4 mol of the peroxide per mole of the catalyst even at 70°C. Sigel et al.11 ex-