7378
J. Phys. Chem. B 1997, 101, 7378-7382
Effects of Ionic Strength on the Critical Micelle Concentration and the Surface Excess of Dodecyldimethylamine Oxide Hiroshi Maeda,* Shuichi Muroi, and Rie Kakehashi Department of Chemistry, Faculty of Science, Kyushu UniVersity, Fukuoka 812-81, Japan ReceiVed: October 30, 1996; In Final Form: February 23, 1997X
Critical micelle concentrations (cmc) of dodecyldimethylamine oxide (DDAO) were determined at 25 ( 0.05 °C as a function of NaCl concentration Cs for both nonionic and cationic species by the surface tension measurements. The critical micelle concentration of the cationic species, cmc+, was lower than that of the nonionic species, cmc0, in the range of Cs higher than about 0.2 M, which strongly suggested an attractive interaction between the headgroups of two cationic species in micelles, most probably the hydrogen bond. Log(cmc0) decreased linearly with Cs, while log(cmc+) gave a nonlinear dependence on the logarithm of the counterion concentration Cg. The nonlinear Corrin-Harkins relation was discussed in terms of the saltingout contribution and/or micelle growth in addition to the contribution of the electric free energy of micelles. Surface excesses of both nonionic and cationic species were very similar and did not depend significantly on Cs up to 3 M NaCl. The surface tensions at surfactant concentrations above cmc, γcmc, decreased linearly either with Cs for the nonionic species or with log Cs for the cationic species. On the basis of these data, surface excesses of Na+ and Cl- were evaluated by the Gibbs adsorption isotherm and compared with those expected from the double-layer theory. The size of the nonionic micelles remained essentially constant over the entire range of Cs examined, while that of the cationics increased with Cs in the range Cs > 0.5 M. At 1 M NaCl, growth of the micelle with the surfactant concentration was observed for the cationics but not for the nonionics.
Introduction Dodecyldimethylamine oxide (DDAO) exists as either a nonionic or a cationic (protonated form) species depending on the pH of the aqueous solution, and the solution properties vary with pH.1-21 We have found that the aggregation number of DDAO exhibits a maximum around the half-ionized state when the degree of ionization of micelle RM is varied.19 The interactions giving rise to this characteristic dependence are expected to influence the stability of the micelle. Recent studies of Rathman and Christian15 and us20 have revealed a characteristic pH dependence of the critical micelle concentrations (cmc) which is consistent with that of the aggregation number. General correlation of this kind has been extensively discussed by Hoffmann.22 In the present study, effects of ionic strength on the cmc are examined mainly with the surface tension measurements. A phenomenological approach in terms of the saltingout effect will be presented to account for the observed nonlinear Corrin-Harkins relation. Dynamic light scattering measurements were also carried out to monitor the micelle growth on both ionic strength and surfactant concentration. Surface excesses of surfactants and small ions at the air-solution interface are also evaluated from the concentration dependence of the surface tension in the surfactant concentration range above cmc. Experimental Section Dodecyldimethylamine oxide was prepared as reported previously.19 Surface tension was measured at 25 ( 0.05 °C with the drop volume method using a capillary (radius 0.124 cm). The drop was kept for about 10 min to attain the adsorption equilibrium. Corrections to the drop volume were made according to Harkins and Brown.23 Dynamic light scattering (DLS) was carried out with Malvern System 4000. * Corresponding author. X Abstract published in AdVance ACS Abstracts, September 1, 1997.
S1089-5647(96)03381-0 CCC: $14.00
Sampling times were in the range 5-10 µs. Solutions of different concentrations at constant pH, either 2 or 9 ((0.02) and constant NaCl concentrations (Cs) were prepared both for the surface tension and DLS measurements. At low Cs, the counterion concentration Cg was significantly higher than Cs due to the addition of HCl to ensure the complete protonation. For the range Cs > 0.2 M, the difference between Cg and Cs was negligible. Results Critical Micelle Concentrations. Critical micelle concentration (cmc) was determined from the break point of the concentration dependence of the surface tension. Values of cmc are shown with open and filled circles against NaCl concentration Cs in Figures1 and 2, for the cationic (cmc+) and the nonionic (cmc0) species, respectively. In Figures 1 and 2 values of cmc0 are smaller than cmc+ at Cs lower than about 0.2 M, as expected from the electric repulsion among cationic headgroups. It is remarkable, however, that in the range of Cs greater than 0.2 M, cmc+ is smaller than cmc0. For the nonionics, log cmc decreases linearly with Cs, as shown in Figure 1:
log(cmc0/mM) ) -(0.32 ( 0.01)(Cs/M) + (0.22 ( 0.01) Under no added salt conditions, the cmc is about 1.6 ( 0.1mM,24 and hence the constant term corresponds to log cmc0(Cs)0). The following generally found relation25,26 also holds in the present case.
log[cmc0/cmc0(Cs ) 0)] ) -Ks(Cs/M)
(1)
The parameter Ks is closely related to the salting-out effect. Values of Ks for other surfactants carrying a dodecyl chain are 0.43 for hexa(ethylene glycol) dodecyl ether (C12E6)27 and 0.29 for dodecylbetaine.28 The value of 0.32 for nonionic DDAO is © 1997 American Chemical Society
Salt Concentration Dependence of the cmc
J. Phys. Chem. B, Vol. 101, No. 38, 1997 7379 mole fractions, xm and x1.
µm* - mµ1* ) kT(m ln x1 - ln xm)
(5)
µm* 1 - µ1* ) kT ln x1 - ln xm ≈ kT ln x1 m m
(6)
(
)
A value of cmc in mole fraction x1 is related to the standard chemical potential difference between m-mer µm* and monomer µ1*. For the differences ∆ of the chemical potentials from those of no added salt,
log[x1/x1(Cs)0)] ) (0.434/kT)[∆(µm*/m) - ∆µ1*] Figure 1. Dependence of the logarithm of the critical micelle concentration on NaCl concentration Cs. Cationic species (O); nonionic species (b).
) log[cmc/cmc(Cs)0)] ) -KsCs
(7)
The last equality comes from the experimental results. Now we assume that the effect of salt on the nonionic surfactant micelle can be neglected.
∆(µm*/m) ) 0
(8)
∆µ1* {)µ1* - µ1*(Cs)0)} ) 2.303kTKsCs
(9)
Then we have
Figure 2. Dependence of the logarithm of the critical micelle concentration on the logarithm of the counterion concentration Cg. Cationic species (O); nonionic species (b). A solid line is drawn according to eq 4.
between them and closer to that of betaine than to C12E6. This is consistent with the polar nature of the headgroup of the nonionic DDAO. The cmc values of many ionic surfactants have been known to obey the following Corrin-Harkins relation,25,26,29 in terms of the counterion concentration Cg.
log cmc ) -kCH log Cg + constant
(2)
In the present study, log cmc+ shows a linear dependence on log Cg in the range Cg < 0.5 M as shown in Figure 2,
log(cmc+/mM) ) -(0.64 ( 0.01) log(Cg/M) (0.32 ( 0.01) (Cg < 0.5 M) (3) However, a deviation occurs in the rest of the region, as shown in Figure 2. The slope of the plot exceeds unity in the absolute value (1.43 ( 0.08) in the range of Cg > 1 M. As shown in the next section, the dependence of cmc on Cg should include the contribution from the salting-out effect on the hydrocarbon tail in addition to the salt effect on the electrostatic interaction. We fitted the observed dependence with the following empirical equation.
log(cmc+/mM) ) -kCH′ log(Cg/M) - ks(Cg/M) + constant (4) The results were kCH′ ) 0.55, ks ) 0.24, and constant ) -0.20 and are shown with a solid line in Figure 2. The Dependence of the cmc on Cs. For nonionics, the equilibrium condition between the most probable m-mer and the monomer leads to the following relations in terms of their
The standard chemical potential of the nonionic monomer linearly increases with Cs. An extensive study on the salt effect of nonionic micelles has been worked out by Blankschtein et al.30 The equilibrium condition for the cationics can be written in analogy with eq 5 with additional terms of the electric part of the chemical potentials.
µm* + µmel - mµ1* - mµ1el ≈ mkT ln x1
[
]
[
(10)
]
el 0.434 µm* 0.434 µm - µ1* + - µ1el ≈ log x1 (11) kT m kT m
The first term on the lhs of eq 11 can be written as [-(Ks)ionCs + constant] after the reasoning leading to eq 7 for the nonionic micelle in terms of the “salting-out” constant (Ks)ion for the hypothetical discharged surfactant otherwise identical with the cationic species. We can write the Cs dependence of log cmc as follows in terms of a constant:
(
)
el 0.434 µm -(Ks)ionCs + const + - µ1el ) log cmc kT m
(12)
The electric part can be explicitly written as follows in terms of the surface electric potential Ψ0.31
µmel ) e0
∫0mΨ0(m,Cs) dm
(13)
In the case of the planar double layer of the surface charge density σ,31 which is equivalent to the phase separation model,
( )( )
µmel kT σ ) -2 ln Cs + const (flat double layer) m e0 m
(14)
We assume the term (0.434/kT)(µmel/m) can be written as (-kCH log Cg + constant) for the micelles in the present study. The term µ1el is given as follows in terms of the Debye-Hueckel type acitivity coefficient yDHel.
µ1el ) kT ln yDHel ) -kT(lBκ/2)/(1 + κa)
(15)
Here lB and a denote the Bjerrum length and the distance of
7380 J. Phys. Chem. B, Vol. 101, No. 38, 1997
Maeda et al.
the closest approach between the headgroup and Cl- ion taken to be 0.32 nm. In terms of lB, κ2 ) 8πNΑ × 10-3CslB, where NA denotes the Avogadro number and Cs (in M) rather than Cg is used. Finally, eq 12 reduces to eq 16.
log(cmc+/mM) ) -kCH log(Cg/M) - (Ks)ion(Cs/M) 0.434(lBκ/2)/(1 + κa) + b1 (16) The best fit to the obtained data shown in Figure 2 gave kCH ) 0.69, (Ks)ion ) 0.24, and b1 ) - 0.45. The kCH value (0.69) is close to that of eq 3 (0.64) found in the range of Cg < 0.5 M. Therefore, the deviation from the linearity in the present study can be interpreted in terms of the salting-out effect without recourse to a size/shape change of micelles induced at high Cs. However, these two kCH values (0.69 and 0.64) differ from kCH′ (0.55) in eq 4, and the difference originates from the introduction of the term µ1el. It is to be noted that the value of (Ks)ion (0.24) is identical with ks (0.24) of eq 4. In other words, the “salting-out” constant for the hypothetical cationic species (Ks)ion remains unaffected whether the term µ1el is included or not. This coincidence indicates the consistent nature of the present analysis. The (Ks)ion value of 0.24 is smaller than that of zwitterionic betaine (0.29). We now have the following relation concerning Ks for surfactants carrying a dodecyl tail, which is expected to represent the extent of interference between the polar head hydration and the hydrophobic hydration.
Figure 3. Surface excesses Γ of the surfactants as functions of Cs. Cationic species (O); nonionic species (b).
0.24 (ionic) < 0.29 (zwitterionic) < 0.32 (dipolar) < 0.44 (nonpolar ethylene glycol) (17) It is to be stated here that the estimation procedure of (Ks)ion depends on the validity of eq 16 at high ionic strengths. It should be clarified on the basis of a refined electrostatic theory in the future whether the µel term of micelle can be a linear function of log Cg even at high ionic strengths. Surface Excesses of Surfactants. The change of the surface tension γ with the surfactant concentration C at a constant Cs is generally described with the Gibbs adsorption isotherm under constant temperature and pressure. In terms of the surface excesses Γi and the chemical potentials µi of species i, it is given as follows.
-dγ ) ΓD dµD + ΓDH dµDH + ΓCl dµCl + ΓNa dµNa + ΓH dµH (18) D and DH denote the nonionic and the cationic species of DDAO. We assume that activity coefficients of Na and Cl ions are kept constant owing to the high ionic strengths employed. Then, dµNa ) 0. Since the surfactant concentration was changed at a constant pH and hence at constant degrees of ionization of monomer R1 and micelle RM, we can approximate that dµH ) 0 and dµD ) dµDH ) RT d ln C. Under these assumptions, eq 18 reduces to
-dγ ) (ΓD + ΓDH)RT d ln C + ΓCl dµCl
(19)
To a good approximation, dµCl ) RTR1 dC/Cs. Since values of R1 dC/Cs were small under relatively high Cs values, we can approximate that dµCl ) 0. Finally, we obtain eq 20:
ΓD + ΓDH ) - (0.434/RT) (∂γ/∂ log C)pH,Cs,T
(20)
Since only the cationic or the nonionic species was studied in the present study, obtained values of the maximum surface excesses, written as Γmax, refer to either ΓDH or ΓD. Values of
Figure 4. Dependence of the surface tension at cmc, γcmc, on Cs: (a) nonionic species, (b) cationic species.
ΓDH were obtained in the range Cs > 0.05 M to ensure the condition of excess salt. It is to be noted in Figure 3 that the surface excesses are greater for the cationics than for the nonionics in the range Cs < 0.5 M. From the effects of Cs on the surface tension shown in Figure 4a,b, it is also seen that the cationic species are more surface active than the nonionic one. In the range Cs > 0.5 M, ΓDH and ΓD are almost identical and scarcely depend on Cs up to 3 M. Surface Excesses of Small Ions at Surfactant Concentrations above cmc. Surface excesses of small ions at surfactant concentrations above cmc were evaluated from the variation of the surface tension γcmc with Cs, as shown in Figure 4. For the nonionic species at constant pH and under the condition of the surface neutrality ΓCl ) ΓNa ) ΓS, eq 18 reduces to eq 21 in terms of the mean activity of the salt a(.
-dγcmc ) ΓD dµD + ΓS dµS ) ΓD dµD + 2ΓSRT d ln a( (21) For the nonionic species, the activity coefficient of NaCl was found to be well approximated with that of the pure salt solution.
Salt Concentration Dependence of the cmc
J. Phys. Chem. B, Vol. 101, No. 38, 1997 7381
Figure 5. Surface excesses of small ions at the air-solution interface covered with a monolayer of the cationic surfactant as functions of Cs. Dashed lines were calculated according to the Poisson-Boltzmann equation. Surface excess of small ions (ΓNa + ΓCl): (b) and curve a. Surface excess of Cl- (ΓCl): (4) and curve b. Surface excess of Na+ (ΓNa): (3) and curve c. Surface excess of the cationic surfactant ΓDH is also shown (O).
As shown by eq 8, the chemical potential of the nonionic micelle is assumed to be independent of Cs, and then dµD ) 0 due to the equilibrium between the micelle and the monomer in solution.
ΓCl ) ΓNa ) ΓS ) (-dγcmc/d ln a()/(2RT)
(22)
As shown in Figure 4a, values of γcmc decrease linearly with Cs. The slope (-dγcmc/dCs) was -0.36 ( 0.02 mN m-1 M-1. When plotted against a(, a linear relation was also found in the range a( > 0.25m (m ) molal): (-dγcmc/da() ) -0.43 ( 0.02 mN m-1 m-1. Hence, ΓS/10-8 mol m-2 ) 8.6 ( 0.4 (a(/ m). It is thus shown that NaCl is weakly adsorbed at the airwater interface when the nonionic surfactant is present at the surface. The adsorption linearly increases with Cs or a( in the concentration range examined. For the cationic species at constant pH and also at the salt concentrations (Cs > 0.1 M), where the contributions to the counterion concentration from both excess amount of HCl and the surfactant can be neglected, we can further assume that dµCl ) dµNa ) RT d ln a( under the conditions. Then eq 18 reduces to eq 23.
-dγcmc ) ΓDH dµDH + (ΓCl + ΓNa)RT d ln a(
(23)
In terms of the activity coefficient yDH, dµDH ) RT(d ln cmc+ + d ln yDH),
(ΓCl + ΓNa) ) (d ln Cs/d ln a()[0.434 (-dγcmc/d log Cs)/RT ΓDH {(d log cmc+/d log Cs) + (d log yDH/d log Cs)}] (24) In Figure 4b, values of γcmc decrease linearly with log Cs in the range Cs > 0.1 M and the slope is - 3.1 ( 0.1 mN m-1. Values of ΓDH were known as shown in Figure 3. The term (d log cmc+/d log Cs), which is the slope in the Corrin-Harkins plot, was evaluated using the analytical expression of eq 4. The term yDH is decomposed as yDyDHel. Since we assume dµD/dCs ) 0 throughout the present study (eq 8), (d log yD/d log Cs) ) -(d log cmc0/d log Cs) ) 2.303KsCs. The electric activity coefficient yDHel was calculated according to eq 15. Finally, the values (d ln Cs/d ln a() were approximated with those of pure NaCl solutions in the absence of cationic micelles, and we found them to be constant (1.06) in the present Cs range. The final results are shown in Figure 5. At low Cs, the surface charges are almost compensated by the counterions but slightly negative adsorption of the coions is also significant. With
Figure 6. Radii R of equivalent hydrodynamic spheres of micelles as functions of Cs. Cationic species (O); nonionic species (b). Surfactant concentration: 5 × 10-3 M.
increasing Cs, however, the electroneutrality of the surface region is satisfied by repelling more coions than at low Cs. The results expected from the electrical double layer of the GouyChapman type calculated by the use of the Poisson-Boltzmann (PB) equation are also shown in Figure 5 with dashed curves. In the calculation the surface change density was directly given from ΓDH, shown with open circles in Figure 5. The surface excess of small ions ΓNa + ΓCl is given by eq 25.
ΓNa + ΓCl ) (4 × 103Cs/κ)[{1 + (2πlBΓDHNA/κ)2}1/2 - 1] (25) where ΓNa, ΓCl, and ΓDH are in mol m-2; Cs is in M; κ is in m-1, and lB is in m. Values of ΓNa and ΓCl were evaluated from (ΓNa + ΓCl) coupled with the electroneutrality condition ΓDH + ΓNa ) ΓCl. The PB result indicates nearly complete counterion binding of the macroscopic charged surface; that is the double layer is of the Helmholtz type. At low Cs, the agreement with experimental surface excesses is fair. At high Cs, however, greater accumulation of counterions was suggested from the present PB approach, which is expected to be valid at low ionic strength, since small ions were treated as point charges. Introduction of the distance of the closest approach of counterions to the interface, however, did not change the result appreciably. Any effect caused by the presence of ionic micelles was not taken into account in the calculation. Micelle Size. Several nonlinear Corrin-Harkins plots have been associated with micellar size and/or shape changes.32 To examine this possible correlation in the present case, radii of the equivalent hydrodynamic sphere RH of the present micelles were determined with dynamic light scattering. Dependence of RH on Cs at a given surfactant concentration C of 5 mM is shown in Figure 6. The size of the nonionic micelles remained constant (∼2 nm) over the whole range of Cs examined. This indifferent character of the nonionic micelles toward Cs is consistent with our assumption leading to eq 20 that dµD/dCs ) 0. The size of the cationic micelles, on the contrary, increased with Cs in the range of Cs greater than about 0.4 M. The deviation from the linearity in the Corrin-Harkins plot in the present case is also suggested due to a change in size and/or shape of the micelle. The effect of the surfactant concentration C on RH was examined at Cs ) 1 M. Micelle growth with C was observed for the cationic species, while it was very slight for the nonionic species. Spherical micelles are expected for the latter case.
7382 J. Phys. Chem. B, Vol. 101, No. 38, 1997
Maeda et al.
Discussion Attractive Interaction among Cationic Heads. The finding that cmc+ < cmc0 in the range Cs > 0.2 M strongly suggests the presence of some nonelectric stabilization of the cationic micelles, which has been proposed to be the hydrogen bond. In Figures 1 and 2, the two curves, log cmc0 and log cmc+, are approximately parallel with each other in the range Cs > 1.5 M. Under such a high Cs(>1.5 M), we can approximate that the electric contribution to the chemical potentials can be ignored and the Cs dependence represents mostly the effect of salt on hydrocarbon chains, the salting-out effect. Then, from eqs 6 and 11,
2.303kT log[cmc0/cmc+] ) [∆(µm*/m) - ∆µ1*]D [∆(µm*/m) - ∆µ1*]DH (26) In eq 26, the rhs represents the difference between these two species with respect to the free energy of micellization in a medium of high ionic strength. We can take the rhs as a lower bound for the free energy of the assumed hydrogen bond ∆Ghb. The difference between the two curves in Figure 1 or Figure 2 gives a value of 0.95RT at 25 °C.
∆Ghb(cationic-cationic) < -0.95RT
(27)
We have estimated the free energy of the hydrogen bond between nonionic-cationic to be -1.4RT or more negative at 25 °C.21 The hydrogen bond in aqueous media has been known to be weak because of the hydration of polar groups. It was claimed that the carboxyl/carboxylate hydrogen bond of fatty acids is completely disrupted in aqueous media,33 while in polymeric systems the hydrogen bonds have been proposed.34-37 The R-helix random coil transition of polypeptides has been known to be highly cooperative, partly because the hydrogen bond stabilization per mole peptide group is below RT, on the order of 100 cal/mol.38 It is interesting, therefore, to examine further the supposed hydrogen bond mechanism of DDAO, since the stabilities estimated above are much more stable than carboxyl or peptide groups. A detailed discussion in favor of the hydrogen bonds has been given21 and hence is not repeated here. Nonlinear Corrin-Harkins Plots. In the present study, we have proposed a phenomenological approach to account for the observed nonlinear Corrin-Harkins plot in terms of the saltingout effect operating on the hydrocarbon chain. At the same time, we have found a shape/size change of the cationic micelle in the present study in the range of Cs where the deviation from linearity was significant. It is pertinent to discuss the linearity and/or nonlinearity of the plot. Several reported CorrinHarkins plots can be classified into three groups: (a) linear relations29,39 up to 4 M NaCl,40 (b) downward deviations,41 and (c) upward deviations.32,42 The salting-out constant for a dodecyl chain with an ionic head is shown to be greater than 0.2 (inequality 17). If a value of 0.2 is tentatively taken for Ks, then we expect ∆ log cmc ) -0.6 for ∆Cs from 1 to 3 M, and this change cannot be negligible. The salting-out effect always causes downward deviations and hence it cannot explain groups a and c. On the other hand, changes of micellar size have been found in the salt concentration range where deviation from the linear Corrin-Harkins plot is significant. The two factors salting-out and shape change can be correlated somehow. A naive hypothesis that the saltingout effect induces the shape change does not work, however, since the salting-out effect does not induce any significant size/ shape change of the nonionic micelles, as shown in Figure 6.
It has been found that log cmc is proportional to the surface electric potential ψ0.43 The linear ψ0-log cmc relation leads to linear Corrin-Harkins plots only when ψ0 linearly varies with log Cg. When the data of Healy et al.43 were examined with respect to the relation ψ0-log Cg, linear and upward deviations were observed for DTAC/NaCl and DTAB/NaBr, respectively. A unified picture seems lacking to compromise the two findings at high ionic strengths: the salting-out effect and the linear ψ0-log cmc relation. Acknowledgment. The authors thank Mr. Tsuyoshi Fukuda and Ms. Yukiko Imaishi for their measurements of dynamic light scattering. This work was partly supported by the Nippon Oil & Fats Co. Ltd. References and Notes (1) Herrmann, K. W. J. Phys. Chem. 1962, 66, 295. (2) Herrmann, K. W. J. Phys. Chem. 1964, 68, 1540. (3) Benjamin, L. J. Phys. Chem. 1964, 68, 3575. (4) Tokiwa, F.; Ohki, K. J. Phys. Chem. 1966, 70, 3437. (5) Goddard, E. D.; Kung, H. C. J. Colloid Interface Sci. 1973, 43, 511. (6) Maeda, H.; Tsunoda, M.; Ikeda, S. J. Phys. Chem. 1974, 78, 1086. (7) Funasaki, N. J. Colloid Interface Sci. 1977, 60, 54. (8) Ikeda, S.; Tsunoda, M.; Maeda, H. J. Colloid Interface Sci. 1978, 67, 336. (9) Ikeda, S.; Tsunoda, M.; Maeda, H. J. Colloid Interface Sci. 1979, 70, 448. (10) Mille, M. J. Colloid Interface Sci. 1981, 81, 169. (11) Chang, D. L.; Rosano, H. L. In Structure/Performance Relationships in Surfactants; Rosen, M. I., Ed.; ACS Symposium Series 253; 1984; p 129. (12) Chang, D. L.; Rosano, H. L.; Woodward, A. E. Langmuir 1985, 1, 669. (13) Warr, G. G.; Grieser, F.; Evans, D. F. J. Chem. Soc., Faraday Trans. 1 1986, 82, 1829. (14) Maeda, H. J. Phys. Chem. 1988, 92, 4490. (15) Rathman, J. F.; Christian, S. D. Langmuir 1990, 6, 391. (16) Weers, J. G.; Rathman, J. F.; Scheuing, P. R. Colloid Polym. Sci. 1990, 268, 832. (17) Zhang, H.; Dubin, P. L.; Kaplan, J. I. Langmuir 1991, 7, 2103. (18) Brackman, J. C.; Engberts, J. B. F. N. Langmuir 1992, 8, 424. (19) Kaimoto, H.; Shoho, K.; Sasaki, S.; Maeda, H. J. Phys. Chem. 1994, 98, 10243. (20) Maeda, H.; Muroi, S.; Ishii, M.; Kaimoto, H.; Kakehashi, R.; Nakahara, T.; Motomoura, K. J. Colloid Interface Sci. 1995, 175, 497. (21) Maeda, H. Colloid Surf. A 1996, 109, 263. (22) Hoffmann, H. Prog. Colloid Polym. Sci. 1990, 83, 16. (23) Harkins, W. D.; Brown, F. E. J. Am. Chem. Soc. 1919, 41, 499. (24) Imaishi, Y.; Kakehashi, R.; Maeda, H. To be published. (25) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; John Wiley & Sons: New York, 1989. (26) Hunter, R. J. Foundations of Colloid Science; Oxford University Press: Oxford, 1991; Vol. 1, Chapter 10. (27) Nishikido, N.; Matuura, R. Bull. Chem. Soc. Jpn. 1977, 50, 1690. (28) Tori, K.; Nakagawa, T. Kolloid-Z. 1963, 189, 50. (29) Corrin, M. L.; Harkins, W. D. J. Am. Chem. Soc. 1947, 69, 683. (30) Carale, T. R.; Pham, Q. T.; Blankschtein, D. Langmuir 1994, 10, 109. (31) Verway, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (32) Ozeki, S.; Ikeda, S. Colloid Polym. Sci. 1984, 262, 409. (33) Friberg, S. E.; Mandel, L.; Ekwall, P. Kolloid Z. Polym. 1969, 223, 955. (34) Schultz, A. W.; Strauss, U. P. J. Phys. Chem. 1972, 76, 1767. (35) Muto, N.; Komatsu, T.; Nakagawa, T. Bull. Chem. Soc. Jpn. 1973, 46, 2711. (36) Kawaguchi, S.; Kitano, T.; Ito, S. Macromolecules 1991, 24, 6030. (37) Kawaguchi, S.; Kitano, T.; Ito, S. Macromolecules 1992, 25, 1294. (38) Nagasawa, M.; Holtzer, A. J. Am. Chem. Soc. 1964, 86, 538. (39) Emerson, M.; Holtzer, A. J. Phys. Chem. 1967, 71, 1898. (40) Ozeki, S.; Ikeda, S. Bull. Chem. Soc. Jpn. 1981, 54, 552. (41) Ikeda, S.; Ozeki, S.; Tsunoda, M. J. Colloid Interface Sci. 1980, 73, 27. (42) Kushner, L. M.; Hubbard, W. D.; Parker, R. A. J. Res. Natl. Bur. Stad. 1957, 59, 113. (43) Healy, T. W.; Prummond, C. J.; Grieser, F.; Murray, B. S. Langmuir 1990, 6, 506.
