5050
J. Phys. Chem. B 1998, 102, 5050-5054
Rate Effects of AOT-Stabilized Microemulsions on Reactions of Ligand Substitution in Cationic Palladium(II) Complexes F. Paolo Cavasino,* Carmelo Sbriziolo,* and M. Liria Turco Liveri Dipartimento di Chimica Fisica, UniVersita` di Palermo, 90123 Palermo, Italy ReceiVed: February 20, 1998; In Final Form: April 13, 1998
Rate data for the substitution reactions of the coordinated ligand X ()2,2′-bipyridine or 4,4′-dimethyl-2,2′bipyridine) of the palladium(II) complex [Pd(en)X]2+, where en ) ethylenediamine, by en or N,Ndimethylethylenediamine in heptane-AOT-water microemulsions have been obtained at 25.0 °C as a function of the AOT concentration at the constant R ()[H2O]/[AOT]) values of 3, 8, and 20 or 30. The overall second-order rate constants are higher in microemulsions than in bulk water and decrease significantly as both the AOT concentration (at constant R) and the molar ratio R (at a given [AOT]) increase. The quantitative analysis of the kinetic data, made by applying the pseudophase model, leads to the suggestion that a given palladium complex bound to the negatively charged AOT/water interface reacts simultaneously with the nucleophile partitioned between the aqueous and the interfacial phases. Evidence is obtained that the same rate effects of the incoming and leaving ligands are operative in both bulk water and the AOT interface and that the substitution reactions proceed by the same rates and mechanism in the two different media. The estimated “effective” AOT pseudophase volume (per mole of surfactant) in which reaction occurs has been found to increase as the interfacial AOT layer curvature becomes larger.
Introduction
methylethylenediamine (dmen).
In recent years much of our interest in chemical reactivity has been addressed to the study of the effects of compartmentalization on the kinetics of inorganic reactions in organized surfactant assemblies (micelles,1,2 vesicles,3 water-in-oil microemulsions4-6). These studies have been performed with the main purpose of obtaining information on the reaction mechanism and the role of the electrostatic and hydrophobic interactions between reagents and micellar aggregates in altering the reaction rate in the self-assembling systems. As to the kinetic studies in the presence of microemulsions, we have recently examined the effect of AOT-stabilized waterin-oil (w/o) microemulsions on the rates of some electrontransfer5 and substitution reactions4,6 involving inorganic substrates. These w/o microemulsions are described4-7 as consisting of spherical water droplets separated from a continuous oil (organic solvent) phase by a monolayer of the anionic surfactant sodium bis(2-ethylhexyl)sulfosuccinate (AOT). The sizes of the droplets depend on the molar water/surfactant ratio R ()[H2O]/[AOT]) and increase as the parameter R increases. The microemulsions are good solvents for both hydrophopbic and hydrophilic substances and are suitable as reaction media4-6,8-11 capable of altering, like the aqueous micelles or vesicles, chemical equilibria and reactions rates as compared with those in conventional solvents. As a continuation of our previous investigations, we have now studied, at 25.0 °C, the kinetics of the substitution reaction 1 at square-planar palladium(II) complexes in heptane-AOTwater microemulsions as a function of the AOT concentration at the constant R values of 3, 8, and 20 or 30. In reaction 1 en ) ethylenediamine and X ) 2,2′-bipyridine (bipy) or 4,4′dimethyl-2,2′-bipyridine (dmbipy), and Y ) en or N,N-di* To whom correspondence should be addessed. E-mail: cavasino@ mbox.unipa.it.
[Pd(en)X]2+ + Y f [Pd(en)Y]2+ + X
(1)
The conditions used in this work are such that, at a given R value, the amount of water in the microemulsion varies in proportion to the AOT concentration, but the water droplets do not change their size. The kinetic results are quantitatively analyzed by a rate expression derived by applying the pseudophase model,1-6,8-15 which is widely used for reactions in the presence of normal micelles and assumes competition between possible reactions in different microphases. Moreover, the reactions investigated allow us to ascertain the kinetic effects of steric hindrance and hydrophobicity brought about by the alkyl substituents of both the entering and leaving ligands. To our knowledge, apart from our two previous4,6 investigations, no other kinetic study of the effects of microemulsion systems upon the substitution reactions at square-planar palladium(II) complexes exists despite the numerous rate data available in water and other solvents. Experimental Section Heptane and the ligands en and dmen were obtained from Fluka and used without further purification. AOT (Sigma) was dried for several days under vacuum to remove water. The palladium(II) complexes were prepared4 by the standard procedure and characterized spectrophotometrically. Water was doubly distilled from alkaline permanganate solution. The kinetic measurements began by mixing two microemulsions containing separately the two reactants at a given R and AOT concentration value and prepared before use as described elsewhere.4-6 Depending on the reaction rate to be measured, a HI-TECH SF-61 stopped-flow or a Beckman DU-7 HS spectrophotometer was used, both apparatus being equipped with thermostated compartments and interfaced to a computer for
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Ligand Substitution in Pd(II) Complexes
J. Phys. Chem. B, Vol. 102, No. 26, 1998 5051
all data collection and analysis. In all runs pseudo-first-order conditions were used with a large excess of the nucleophilic reagent ([nucleophile] ) 2.50 × 10-3 mol dm-3), the initial overall concentration of the palladium(II) complex always being equal to 2.50 × 10-5 mol dm-3. The rates of disappearance of the palladium(II) complexes were followed at the wavelength of 307-309 nm. The observed pseudo-first-order rate constants, kobs, were reproducible to within (3%. Other experimental details have been given previously.4 The temperature of the experiments was 25.0 ( 0.1 °C. All the concentration values reported in this work are referred to the whole volume of microemulsion, unless otherwise indicated. Results and Discussion According to previous4 findings, the substitution reactions (1) follow a second-order rate law, first-order with respect to each reactant, the plots of kobs as a function of [Y] yielding straight lines with zero intercepts. As a consequence, the overall second-order rate constants k are calculated simply by the ratios kobs/[Y]. The suggested4 reaction mechanism is of associative type involving the direct attack of nucleophile at the palladium. Table 1 assembles all the second-order rate constants obtained in this work over a wide range of AOT concentration at the constant R values of 3, 8, and 20 (for reactions involving the nucleophile dmen) or 3, 8, and 30 (for reactions involving the ligand en). The second-order rate constants, kaq, estimated previously4 for the four substitution reactions in homogeneous aqueous solution are also given in Table 1. The data of Table 1 show that, for each reaction examined in microemulsion at a particular R value, the rate constants k are always notably higher than the rate constant kaq obtained for the corresponding reaction in the conventional aqueous solution. Moreover, in all cases the k values decrease significantly as both the AOT concentration (at constant R) and the molar ratio R (at a given AOT concentration) increase. Further, the comparison of the kinetic data obtained at a given R and AOT concentration shows that the reaction rates depend to a significant extent on the nature of both the incoming and the leaving ligands. The variety of the kinetic data obtained can be interpreted quantitatively by applying the pseudophase model1-6,8-15 generally used for reactions occurring in the presence of normal micelles. With this approach the microemulsion under study is assumed to be divided into three phases corresponding to the central aqueous core (w), the oil-rich domain (o), and the charged surfactant interfacial region (s), respectively. The volume fractions of these pseudophases can be estimated5,6,10,13 by the expressions 2-4, where 0.018 is the molar volume of water and V may be considered either the molar volume of AOT (V ) 0.390 dm3 mol-1) or an “effective” pseudophase volume (per mole of surfactant) in which reaction occurs.8,13
φw ) 0.018[AOT]R
(2)
φs ) V[AOT]
(3)
φo ) 1 - (φw + φs)
(4)
The kinetic data obtained for each reaction examined have been analyzed by the nonlinear least-squares method by taking into account different possible contributions of pathways to the overall reaction rate and found to be consistent with the reaction Scheme 1, where M2+ represents a given palladium complex. According to this scheme, two reactions contribute significantly to the overall rate of the substitution process 1, i.e., the reactions
TABLE 1: Experimental and Calculateda Second-Order Rate Constants (dm3 mol-1 s-1) for the Substitution Reaction 1 in Heptane-AOT-Water Microemulsions at Varying C (10-2 mol dm-3) and R Values (t ) 25.0 °C) [Pd(bipy)(en)]2+ enb,c C
k
[Pd(dmbipy)(en)]2+
dmenb,d
k(calc)
k
enb,e
k(calc)
k
k(calc)
dmenb,f k
k(calc)
3.5 1.78 1.33 0.85 0.48 0.33 0.200
3.7 1.97 1.38 0.79 0.46 0.33 0.205
0.80
0.73
0.60 0.35 0.261 0.192 0.120 0.090 0.060
0.60 0.36 0.283 0.182 0.119 0.089 0.060
0.44
0.45
0.33
0.33
0.209 0.169
0.209 0.174
0.112 0.091 0.063
0.110 0.090 0.062
0.041
0.042
R)3 6.9 170 8.1 135 12.1 73 15.3 50 22.8 28.0 34.0 16.3 45.0 11.8 66.7 7.4 6.8 6.9 8.0 12.1 15.0 22.3 33.0 43.3 63.0
35 29.4 19.0 12.0 6.8 4.5 3.3 2.30
173 133 71 50 28.4 16.7 11.8 7.4
35 28.5 16.0 12.1 7.3 4.6 3.4 2.23
3.0 3.4 4.0 4.5 6.0 6.7 7.9 11.6 12.1 14.6 21.0 29.2 30.8 37.7 39.6 54.8 55.4
7.9 5.2 3.7 2.43 1.39 1.02 0.70
8.5 5.0 3.7 2.29 1.45 1.06 0.69
2.64
R)8 2.64
80 60 34 23.0
2.23 1.22 1.16 0.77 0.47 0.36 0.247
2.20 1.39 1.10 0.72 0.48 0.36 0.246
1.50
R ) 20 1.80
1.12
1.35
0.74
0.90
0.61 0.46
0.68 0.47
86 65 33 22.1
6.5 4.6 2.60
6.6 4.4 2.65
8.4 6.8 3.9 2.78 1.70 0.90 0.70 0.45
8.7 6.9 3.7 2.72 1.59 0.96 0.69 0.45
0.36 0.37 0.272 0.257 0.183 0.185 0.132 0.143
0.0317 0.0322 0.099 0.098 0.0230 0.0229 R ) 30
5.9 6.7 7.8 12.1 14.5 19.5 20.5 27.7 29.2 35.2 36.9 48.2 50.4
9.1
8.9
5.9 3.3 2.41 1.70
5.9 3.2 2.51 1.72
1.07
1.12
0.85
0.85
0.60
0.59
1.27 1.04 0.64 0.51
1.27 1.05 0.62 0.52
0.35
0.34
0.226
0.233
0.187
0.182
0.130
0.131
a
Calculated by using the data of Table 2 and eq 7. b Entering ligand. kaq ) 0.140 dm3 mol-1 s-1 (ref 4). d kaq ) 0.013 dm3 mol-1 s-1 (ref 4). e kaq ) 0.029 dm3 mol-1 s-1 (ref 4). f kaq ) 0.0030 dm3 mol-1 s-1 (ref 4). c
of the palladium complex bound to the negatively charged AOT/ water interface with the nucleophile Y present in both the water pools and the interfacial region, the corresponding second-order rate constants being ks,w and ks. A reaction path analogous to that associated with ks,w was also taken into account by Berezin et al.12 for bimolecular association reactions occurring in the presence of normal micelles. Moreover, reactions between the two reactants solubilized in two different pseudophases have also been observed previously1-3 to contribute significantly
5052 J. Phys. Chem. B, Vol. 102, No. 26, 1998
Cavasino et al.
SCHEME 1
to the overall rate of other types of reactions in the presence of micelles and vesicles. According to the proposed reaction scheme, under the pseudofirst-order conditions used ([Y] . [M2+]), the overall secondorder rate constant k is given by eq 5, where KM ()[M2+]s/ [M2+]wC) and KY ()[Y]s/[Y]wC) are the binding constants for the given species partitioning between the two pseudophases indicated by the subscripts and C ) [AOT]. As mentioned in the Experimental Section, the concentrations are based on the whole volume of solution. Bearing in mind the reaction paths shown in the Scheme 1 (note that the organic phase is not involved), eq 5 can be easily obtained by appropriate transformation of that reported previously5,6,9 in terms of the dimensionless partition coefficients (PM and PY) of the two reactants and utilizing eqs 2 and 3 and, then, adding a further term for the pathway associated with the rate constant ks,w. The partition coefficient (PX) of a particular species X is related to the corresponding binding constant KX by eq 6, where the ratios [X]s/φs and [X]w/φw represent the local concentrations in each pseudophase. It should be noted that eq 5, apart from the additional term ks,wKMC/φw, is analogous to that derived previously8 by Fletcher and Robinson for complexation reactions in micelles and microemulsions.
k)
kobs [Y]
)
PX )
(ks/V)KMKYC + ks,wKMC/φw (1 + KMC)(1 + KYC) ([X]s/φs)
([X]w/φw)
) KXC (φw/φs)
(5)
(6)
In all the cases studied the experimental kinetic data give good fits when the linear eq 7, obtained from eq 5 with KMC and KYC . 1, is used. In this context we recall that the divalent cationic complex [Pd(Et4dien)(H2O)]2+, where Et4dien ) Et2N(CH2)2NH(CH2)2NEt2, was found previously to be strongly bound to both the AOT interface6 and the anionic micelles14 of the surfactant sodium dodecyl sulfate. In the latter case a binding constant equal to 2.2 × 104 dm3 mol-1 was estimated, electrostatic and hydrophobic interactions being operative. Moreover, the observed significant contribution of the pathway involving Yw (with rate constant ks,w) leads us to deduce that the binding constant KY has to be quite smaller than KM.
kC2 )
()
ks,w ks + C 0.018RKY V
(7)
Typical linear plots of kC2 as a function of the AOT concentration (C ) are shown in Figure 1, where the solid lines represent the least-squares fits. The correlation coefficients of the straight lines obtained for all the reactions examined range from 0.999 to 0.996. It should be noted that the linear eq 7 also holds for microemulsions (usually called reverse micelles) at the lower R values examined where water exhibits peculiar physicochemical properties13,16 which are different from those in bulk. This might be mainly due to the fact that water molecules are not directly involved in the rate-determining step of the substitution reaction 1.
Figure 1. Typical plots of kC2 against C ()[AOT]) for substitution reaction 1 in heptane-AOT-water microemulsions at various values of the parameter R: (b) X ) bipy, Y ) dmen, R ) 3 (m ) 4); (O) X ) dmbipy, Y ) dmen, R ) 3 (m ) 3.5); (2) X ) bipy, Y ) dmen, R ) 8 (m ) 2.5); (4) X ) dmbipy, Y ) en, R ) 8 (m ) 1); (9) X ) bipy, Y ) en, R ) 30 (m ) 0). The parameter m is added to the ordinate-axis to avoid overlapping of lines.
The values of ks/V ()slope) and ks,w/KY ()intercept × 0.018R) estimated in accordance with eq 7 are reported in Table 2, while the experimental rate constants k are compared in Table 1 with those, k(calc), calculated by using eq 7 and the data of Table 2. It can be seen that the agreement between the two sets of data is very good, providing support to the validity of the above reaction scheme and of the least-squares analysis of the experimental data. Examining first the values of ks,w/KY, Table 2 shows that this ratio depends on both the type of reaction investigated and the parameter R. Owing to the composite nature of the ratio ks,w/ KY, it is impossible to establish whether one or both the quantities ks,w and KY cause the observed changes. However, we can obtain some information from these data by considering the relative ks,w/KY values. These relative values are estimated by the reasonable assumption that, at a given R value, the binding constant KY is not (appreciably) affected by the palladium complex bound to the AOT interface, but depends solely on the type of entering nucleophile (en or dmen). Thus the ratio between the quantity ks,w/KY for the reaction of the bound [Pd(bipy)(en)]s2+ with a particular ligand (Yw) and that for the analogous reaction involving the bound [Pd(dmbipy)(en)]s2+ and the same ligand represents the relative reactivity of the complex [Pd(bipy)(en)]s2+ with respect to [Pd(dmbipy)(en)]s2+. When the entering ligand is en, the values of this ratio are 1.7, 3.0, and 11 at R ) 3, 8, and 30, respectively.
Ligand Substitution in Pd(II) Complexes
J. Phys. Chem. B, Vol. 102, No. 26, 1998 5053
TABLE 2: Kinetic Parameters Obtained for the Substitution Reaction 1 in Heptane-AOT-Water Microemulsions at Various R Values (t ) 25.0 °C) R 3
8
20
+ en (ks,w/KY)a/10-3 s-1 29 ( 1 11 ( 1 (ks/V)b/10-2 s-1 410 ( 5 128 ( 5 V c/10-2 dm3 mol-1 3.41 ( 0.04 10.9 ( 0.4 [Pd(bipy)(en)]2+
30 8.6 ( 0.5 25.3 ( 0.5 55 ( 1
[Pd(bipy)(en)]2+ + dmen (ks,w/KY)a/10-3 s-1 1.1 ( 0.2 0.3 ( 0.1 d (ks/V)b/10-2 s-1 43 ( 1 15.2 ( 0.3 5.4 ( 0.1 V c/10-2 dm3 mol-1 3.02 ( 0.07 8.6 ( 0.2 24.1 ( 0.4 [Pd(dmbipy)(en)]2+ + en (ks,w/KY)a/10-3 s-1 17 ( 1 3.6 ( 0.3 (ks/V)b/10-2 s-1 129 ( 5 24.2 ( 0.7 V c/10-2 dm3 mol-1 2.25 ( 0.09 12.0 ( 0.3
0.8 ( 0.2 6.3 ( 0.1 46 ( 1
[Pd(dmbipy)(en)]2+ + dmen (ks,w/KY)a/10-3 s-1 0.8 ( 0.1 0.13 ( 0.03 0.04 ( 0.01 (ks/V)b/10-2 s-1 11.4 ( 0.4 3.65 ( 0.06 1.25 ( 0.01 V c/10-2 dm3 mol-1 2.63 ( 0.09 8.2 ( 0.1 24.0 ( 0.2 a Intercept × 0.018R (eq 7). bSlope (eq 7). cCalculated by taking k s equal to kaq (see text). d Intercept of the linear plot (eq 7) is too small for an accurate value of ks,w/KY to be estimated.
With the entering nucleophile dmen, the ratios are equal to 1.4 and 2.3 at R ) 3 and 8, respectively (no value can be calculated at R ) 20). These values first indicate that, for each entering ligand, the complex [Pd(dmbipy)(en)]s2+ is less reactive than the complex [Pd(bipy)(en)]s2+ and that the difference in their reactivity increases with increasing the parameter R. These findings might be attributed either to a simple steric effect of the reactant [Pd(dmbipy)(en)]s2+ hindering the nucleophile attack at the metal or to the fact that this complex is located and/or orientated in the AOT interfacial region in a manner that is unfavorable for reaction. For the presence of the two hydrophobic methyl groups in the coordinated ligand, the complex might penetrate more deeply between the AOT’s hydrocarbon chains as compared to [Pd(bipy)(en)]s2+, the penetration being facilitated by an increase in the interfacial layer curvature as the droplet size (i.e., parameter R) increases. Of course, both effects might also be operative. The above ratios also show that there is some rate effect due to the different nature of the entering nucleophile.
As to the quantity ks/V, we can see from Table 2 that this ratio, like the ratio ks,w/KY examined above, varies significantly when both the parameter R and the two reactants bound to the AOT surface change. Since the molar volume V would be expected to depend primarily on the physicochemical properties of the AOT interfacial region, for a particular R value it should not be (appreciably) influenced by the type of species solubilized in this region. Therefore we can eliminate the effect of the parameter V by calculating the ratio between the quantities ks/V for two given reactions at each R value examined. Table 3 assembles the values of these ratios estimated for all the reactions investigated together with the ratios between the rate constants kaq for the corresponding reactions in homogeneous aqueous solution. Bearing in mind that the ratio between two variable quantities is sensitive to the changes in their values and taking into account that the variations in the reactivities are quite large, we can reasonably consider the calculated kaq ratios (Table 3) to be very close to the corresponding ks ()ks/V) ratios obtained at varying R values. These observations strongly suggest that the same rate effects of the incoming and leaving ligands are operative in both bulk water and the AOT interface and that the reactions proceed by the same mechanism in the two different media. Moreover, since it seems very unlikely that all the rate constants ks may change in a manner that yields the estimated ks ratios for a fortuitous compensation, we have to deduce that ks is substantially equal to kaq at the various R values examined, so allowing the parameter V to be easily obtained from the quantity ks/V ()kaq/V). Assumptions that ks ) kaq were made previously2,8,11a,15 for some organic and inorganic reactions occurring in both aqueous micelles and interfacial microemulsion region. For all the reactions studied the estimated V values (Table 2) are found to depend on the parameter R (i.e., the droplet size), but at fixed R the volume V is substantially independent of the type of reaction examined, taking the mean values of 0.028 ((0.006), 0.10 ((0.02), 0.240 ((0.001), and 0.50 ((0.05) dm3 mol-1 at R ) 3, 8, 20, and 30, respectively. The parameter V is a linear function of R up to R ) 20, with substancially zero intercept, while at R ) 30 the value of V is higher than that calculated from the linear dependence of V on R.
TABLE 3: Comparison of the Ratios between the Quantities (ks/V) for Two Given Reactions at Various R Values with the Ratios between the Rate Constants kaq for the Corresponding Reactions in Bulk Water (t ) 25.0 °C) R
(ks/V){[Pd(bipy)(en)]s2+ + ens} (ks/V){[Pd(bipy)(en)]s2+ + dmens} (ks/V){[Pd(bipy)(en)]s2+ + ens} (ks/V){[Pd(dmbipy)(en)]s2+ + ens} (ks/V){[Pd(bipy)(en)]s2+ + ens} (ks/V){[Pd(dmbipy)(en)]s2+ + dmens} (ks/V){[Pd(bipy)(en)]s2+ + dmens} (ks/V){[Pd(dmbipy)(en)]s2+ + ens} (ks/V){[Pd(bipy)(en)]s2+ + dmens} (ks/V){[Pd(dmbipy)(en)]s2+ + dmens} (ks/V){[Pd(dmbipy)(en)]s2+ + ens} (ks/V){[Pd(dmbipy)(en)]s2+ + dmens}
3
8
9.5
8.4
3.2
5.3
36
0.63
3.8
4.2
6.6
30
kaq ratio 11
4.0
35
0.33
11
20
4.8
47
0.45
4.3
4.3
9.7
5054 J. Phys. Chem. B, Vol. 102, No. 26, 1998 With the assumption that ks ) kaq, values of V of 0.28 and 0.15 dm3 mol-1 (at R ) 10) were calculated previously8 for two Ni2+ complexation reactions in heptane-AOT-water microemulsions. These values are in fair agreement with that of 0.13 dm3 mol-1 evaluated at R ) 10 by interpolating the V values obtained in this work. Moreover, it can be calculated that the parameter V takes the value of the molar volume of AOT (V ) 0.390 dm3 mol-1) at R approximately equal to 26. The present findings lead thus to the conclusion that the “effective” pseudophase volume (per mole of AOT) in which reaction occurs is not a constant parameter for AOT-stabilized microemulsions when the molar ratio R is changed and increases as the interfacial AOT layer curvature becomes larger. This result is of particular interest in kinetic studies of chemical reactions performed in these microheterogeneous media. Acknowledgment. This work was supported by CNR (Roma) and by Cofin MURST 97 CFSIB. References and Notes (1) Calvaruso, G.; Cavasino, F. P.; Sbriziolo, C.; Turco Liveri, M. L. J. Chem. Soc., Faraday Trans. 1995, 91, 1075 and references therein. (2) Calvaruso, G.; Cavasino, F. P.; Sbriziolo, C. J. Chem. Soc., Faraday Trans. 1996, 92, 2263. (3) Cavasino, F. P.; Di Stefano, S.; Sbriziolo, C. J. Chem. Soc., Faraday Trans. 1997, 93, 1585. (4) Cavasino, F. P.; Sbriziolo, C.; Turco Liveri, M. L.; Turco Liveri, V. J. Chem. Soc., Faraday Trans. 1994, 90, 311. (5) Cavasino, F. P.; Sbriziolo, C.; Turco Liveri, M. L. J. Chem. Soc., Faraday Trans. 1998, 94, 395. (6) Cavasino, F. P.; Sbriziolo, C.; Turco Liveri, M. L. J. Phys. Chem. B 1998, 102, 3143. (7) (a) Fendler, J. H. Membrane Mimetic Chemistry. Characterization and Application of Micelles, Microemulsions, Monolayers, Bilayers,
Cavasino et al. Vesicles, Host-Guest Systems and Polyions; Wiley: New York, 1982. (b) ReVerse Micelles; Luisi, P. L., Straub, B. E., Eds.; Plenum Press: New York, 1984. (c) Robinson, B. H. Chem. Br. 1990, 26, 342 and references therein. (d) Lo˜pez-Quintela, M. A.; Rivas, J. In Structure, Dynamics and Equilibrium Properties of Colloidal Systems; Bloor, D. M., Wyn-Jones, E., Eds.; Kluwer Academic: Dordrecht, 1990. (e) Casado, J.; Izquierdo, C.; Fuentes, S.; Moya´, M. L. J. Chem. Educ. 1994, 71, 446 and references therein. (8) Fletcher, P. D. I.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1984, 80, 2417. (9) Schoma¨cker, R.; Stickdorn, K.; Knoche, W. J. Chem. Soc., Faraday Trans. 1991, 87, 847. (10) Miyake, Y.; Owari, T.; Ishiga, F.; Teramoto, M. J. Chem. Soc., Faraday Trans. 1994, 90, 979. (11) (a) Athanassakis, V.; Bunton, C. A.; McKenzie, D. C. J. Phys. Chem. 1986, 90, 5858 and references therein. (b) Da Rocha Pereira, R.; Zanette, D.; Nome, F. J. Phys. Chem. 1990, 94, 356 and references therein. (c) Lo´pez, P.; Rodrı´guez, A.; Go´mez-Herrera, C.; Sa´nchez, F.; Moya´, M. L. Int. J. Chem. Kinet. 1995, 27, 525 and references therein. (d) Garcı´aRı´o, L.; Leis, J. R.; Mejuto, J. C. J. Phys. Chem. 1996, 100, 10981 and references therein. (e) Blagoeva, I. B.; Gray, P.; Ruasse, M. F. J. Phys. Chem. 1996, 100, 12638 and references therein. (f) Vanag, V. K.; Hanazaki, I. J. Phys. Chem. 1997, 101, 2147 and references therein. (12) Berezin, I. V.; Martinek, K.; Yatsimirsckii, A. K. Russ. Chem. ReV. 1973, 42, 787. (13) Fletcher, P. D. I. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2651. (14) Cusumano, M.; Giannetto, A.; Cavasino, F. P.; Sbriziolo, C. Inorg. Chim. Acta 1992, 201, 49. (15) (a) Fletcher, P. D. I.; Reinsborough, V. C. Can. J. Chem. 1981, 59, 1361. (b) Hicks, J. R.; Reinsborough, V. C. Aust. J. Chem. 1982, 35, 15. (c) Reinsborough, V. C.; Stultz, T. D. M.; Xiang, X. Aust. J. Chem. 1990, 43, 11. (16) (a) Kubik, R.; Eicke, H. F.; Jo¨nsson, B. HelV. Chim. Acta 1982, 65, 170. (b) Bardez, E.; Goguillon, B. T.; Keh, E.; Valeur, B. J. Phys. Chem. 1984, 88, 1909. (c) Boned, C.; Peyrelasse, J.; Moha-Ouchane, M. J. Phys. Chem. 1986, 90, 634. (d) Hauser, H.; Haering, G.; Pande, A.; Luisi, P. L. J. Phys. Chem. 1989, 93, 7869 and references therein. (e) Nishimoto, J.; Iwamoto, E.; Fujiwara, T.; Kumamaru, T. J. Chem. Soc., Faraday Trans. 1993, 89, 535 and references therein. (f) Biasutti, M. A.; Sereno, L.; Silber, J. J. J. Colloid Interface Sci. 1994, 164, 410 and references therein.
