Effects of Ionic Strength on the Critical Micelle Concentration and the Surface Excess ofDodecyldimethylamine Oxide

Hiroshi Maeda,* Shuichi Muroi, and Rie KakehashiDepartment 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 concentrationCs for both nonionic and cationic species by the surface tensionmeasurements. The critical micelle concentration of the cationic species, cmc+, was lower than that of thenonionic species, cmc0, in the range ofCs higher than about 0.2 M, which strongly suggested an attractiveinteraction between the headgroups of two cationic species in micelles, most probably the hydrogen bond.Log(cmc0) decreased linearly withCs, while log(cmc+) gave a nonlinear dependence on the logarithm of thecounterion concentrationCg. The nonlinear Corrin-Harkins relation was discussed in terms of the salting-out 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 onCs up to 3 M NaCl. The surface tensions at surfactant concentrations above cmc,γcmc, decreased linearlyeither withCs for the nonionic species or with logCs 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 thoseexpected from the double-layer theory. The size of the nonionic micelles remained essentially constant overthe entire range ofCs examined, while that of the cationics increased withCs in the rangeCs > 0.5 M. At1 M NaCl, growth of the micelle with the surfactant concentration was observed for the cationics but not forthe nonionics.

Introduction

Dodecyldimethylamine oxide (DDAO) exists as either anonionic or a cationic (protonated form) species depending onthe pH of the aqueous solution, and the solution properties varywith pH.1-21 We have found that the aggregation number ofDDAO exhibits a maximum around the half-ionized state whenthe degree of ionization of micelleRM is varied.19 The inter-actions giving rise to this characteristic dependence are expectedto influence the stability of the micelle. Recent studies ofRathman and Christian15 and us20 have revealed a characteristicpH dependence of the critical micelle concentrations (cmc)which is consistent with that of the aggregation number. Gen-eral correlation of this kind has been extensively discussed byHoffmann.22 In the present study, effects of ionic strength onthe cmc are examined mainly with the surface tension measure-ments. A phenomenological approach in terms of the salting-out effect will be presented to account for the observed nonlinearCorrin-Harkins relation. Dynamic light scattering measure-ments were also carried out to monitor the micelle growth onboth ionic strength and surfactant concentration. Surface ex-cesses of surfactants and small ions at the air-solution interfaceare also evaluated from the concentration dependence of thesurface tension in the surfactant concentration range above cmc.

Experimental Section

Dodecyldimethylamine oxide was prepared as reportedpreviously.19 Surface tension was measured at 25( 0.05 °Cwith the drop volume method using a capillary (radius 0.124cm). The drop was kept for about 10 min to attain theadsorption equilibrium. Corrections to the drop volume weremade according to Harkins and Brown.23 Dynamic lightscattering (DLS) was carried out with Malvern System 4000.

Sampling times were in the range 5-10 µs. Solutions ofdifferent concentrations at constant pH, either 2 or 9 ((0.02)and constant NaCl concentrations (Cs) were prepared both forthe surface tension and DLS measurements. At lowCs, thecounterion concentrationCg was significantly higher thanCs

due to the addition of HCl to ensure the complete protonation.For the rangeCs > 0.2 M, the difference betweenCg andCs

was negligible.

Results

Critical Micelle Concentrations. Critical micelle concentra-tion (cmc) was determined from the break point of theconcentration dependence of the surface tension. Values of cmcare shown with open and filled circles against NaCl concentra-tion Cs in Figures1 and 2, for the cationic (cmc+) and thenonionic (cmc0) species, respectively. In Figures 1 and 2 valuesof cmc0 are smaller than cmc+ at Cs lower than about 0.2 M,as expected from the electric repulsion among cationic head-groups. It is remarkable, however, that in the range ofCs greaterthan 0.2 M, cmc+ is smaller than cmc0. For the nonionics, logcmc decreases linearly withCs, as shown in Figure 1:

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 relation25,26also holdsin the present case.

The parameterKs is closely related to the salting-out effect.Values ofKs for other surfactants carrying a dodecyl chain are0.43 for hexa(ethylene glycol) dodecyl ether (C12E6)27 and 0.29for dodecylbetaine.28 The value of 0.32 for nonionic DDAO is

* Corresponding author.X Abstract published inAdVance ACS Abstracts,September 1, 1997.

log(cmc0/mM) ) -(0.32( 0.01)(Cs/M) + (0.22( 0.01)

log[cmc0/cmc0(Cs ) 0)] ) -Ks(Cs/M) (1)

7378 J. Phys. Chem. B1997,101,7378-7382

S1089-5647(96)03381-0 CCC: $14.00 © 1997 American Chemical Society

between them and closer to that of betaine than to C12E6. Thisis consistent with the polar nature of the headgroup of thenonionic DDAO.The cmc values of many ionic surfactants have been known

to obey the following Corrin-Harkins relation,25,26,29in termsof the counterion concentrationCg.

In the present study, log cmc+ shows a linear dependenceon logCg in the rangeCg < 0.5 M as shown in Figure 2,

However, a deviation occurs in the rest of the region, asshown in Figure 2. The slope of the plot exceeds unity in theabsolute value (1.43( 0.08) in the range ofCg > 1 M. Asshown in the next section, the dependence of cmc onCg shouldinclude the contribution from the salting-out effect on thehydrocarbon tail in addition to the salt effect on the electrostaticinteraction. We fitted the observed dependence with thefollowing empirical equation.

The results werekCH′ ) 0.55,ks ) 0.24, and constant) -0.20and are shown with a solid line in Figure 2.The Dependence of the cmc onCs. For nonionics, the

equilibrium condition between the most probablem-mer andthe monomer leads to the following relations in terms of their

mole fractions,xm andx1.

A value of cmc in mole fractionx1 is related to the standardchemical potential difference betweenm-merµm* and monomerµ1*. For the differences∆ of the chemical potentials from thoseof no added salt,

The last equality comes from the experimental results. Nowwe assume that the effect of salt on the nonionic surfactantmicelle can be neglected.

Then we have

The standard chemical potential of the nonionic monomer linear-ly increases withCs. An extensive study on the salt effect ofnonionic micelles has been worked out by Blankschtein et al.30

The equilibrium condition for the cationics can be written inanalogy with eq 5 with additional terms of the electric part ofthe chemical potentials.

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 nonionicmicelle in terms of the “salting-out” constant (Ks)ion for thehypothetical discharged surfactant otherwise identical with thecationic species. We can write theCs dependence of log cmcas follows in terms of a constant:

The electric part can be explicitly written as follows in termsof the surface electric potentialΨ0.31

µmel ) e0∫0mΨ0(m,Cs) dm (13)

In the case of the planar double layer of the surface chargedensityσ,31 which is equivalent to the phase separation model,

We assume the term (0.434/kT)(µmel/m) can be written as (-kCHlog Cg + constant) for the micelles in the present study. Theterm µ1el is given as follows in terms of the Debye-Hueckeltype acitivity coefficientyDHel.

Here lB anda denote the Bjerrum length and the distance of

Figure 1. Dependence of the logarithm of the critical micelleconcentration on NaCl concentrationCs. Cationic species (O); nonionicspecies (b).

Figure 2. Dependence of the logarithm of the critical micelleconcentration on the logarithm of the counterion concentrationCg.Cationic species (O); nonionic species (b). A solid line is drawnaccording to eq 4.

log cmc) -kCH logCg + constant (2)

log(cmc+/mM) ) -(0.64( 0.01) log(Cg/M) -(0.32( 0.01) (Cg < 0.5 M) (3)

log(cmc+/mM) ) -kCH′ log(Cg/M) - ks(Cg/M) + constant(4)

µm* - mµ1* ) kT(m ln x1 - ln xm) (5)

µm*

m- µ1* ) kT(ln x1 - 1

mln xm) ≈ kT ln x1 (6)

log[x1/x1(Cs)0)] ) (0.434/kT)[∆(µm*/m) - ∆µ1*]

) log[cmc/cmc(Cs)0)] ) -KsCs (7)

∆(µm*/m) ) 0 (8)

∆µ1* {)µ1* - µ1*(Cs)0)} ) 2.303kTKsCs (9)

µm* + µmel - mµ1* - mµ1

el≈ mkTln x1 (10)

0.434kT [µm*

m- µ1*] + 0.434

kT [µmel

m- µ1

el] ≈ log x1 (11)

-(Ks)ionCs + const+ 0.434kT (µm

el

m- µ1

el) ) log cmc (12)

µmel

m) -2(kTe0)(σ

m) ln Cs + const (flat double layer) (14)

µ1el ) kT ln yDH

el ) -kT(lBκ/2)/(1+ κa) (15)

Salt Concentration Dependence of the cmc J. Phys. Chem. B, Vol. 101, No. 38, 19977379

the closest approach between the headgroup and Cl- ion takento be 0.32 nm. In terms oflB, κ2 ) 8πNΑ × 10-3CslB, whereNA denotes the Avogadro number andCs (in M) rather thanCg

is used. Finally, eq 12 reduces to eq 16.

The best fit to the obtained data shown in Figure 2 gavekCH) 0.69, (Ks)ion ) 0.24, andb1 ) - 0.45. ThekCH value (0.69)is close to that of eq 3 (0.64) found in the range ofCg < 0.5 M.Therefore, the deviation from the linearity in the present studycan be interpreted in terms of the salting-out effect withoutrecourse to a size/shape change of micelles induced at highCs.However, these twokCH values (0.69 and 0.64) differ fromkCH′(0.55) in eq 4, and the difference originates from the introductionof the termµ1el.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” constantfor the hypothetical cationic species (Ks)ion remains unaffectedwhether the termµ1el is included or not. This coincidenceindicates 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 concerningKs forsurfactants carrying a dodecyl tail, which is expected to representthe extent of interference between the polar head hydration andthe hydrophobic hydration.

It is to be stated here that the estimation procedure of (Ks)iondepends on the validity of eq 16 at high ionic strengths. Itshould be clarified on the basis of a refined electrostatic theoryin the future whether theµel term of micelle can be a linearfunction of logCg even at high ionic strengths.Surface Excesses of Surfactants.The change of the surface

tensionγ with the surfactant concentrationC at a constantCs

is generally described with the Gibbs adsorption isotherm underconstant temperature and pressure. In terms of the surfaceexcessesΓi and the chemical potentialsµi of speciesi, it is givenas follows.

D and DH denote the nonionic and the cationic species ofDDAO. We assume that activity coefficients of Na and Cl ionsare kept constant owing to the high ionic strengths employed.Then, dµNa) 0. Since the surfactant concentration was changedat a constant pH and hence at constant degrees of ionization ofmonomerR1 and micelleRM, we can approximate that dµH )0 and dµD ) dµDH ) RTd ln C. Under these assumptions, eq18 reduces to

To a good approximation, dµCl ) RTR1 dC/Cs. Since valuesof R1 dC/Cs were small under relatively highCs values, we canapproximate that dµCl ) 0. Finally, we obtain eq 20:

Since only the cationic or the nonionic species was studiedin the present study, obtained values of the maximum surfaceexcesses, written asΓmax, refer to eitherΓDH or ΓD. Values of

ΓDH were obtained in the rangeCs > 0.05 M to ensure thecondition of excess salt. It is to be noted in Figure 3 that thesurface excesses are greater for the cationics than for thenonionics in the rangeCs < 0.5 M. From the effects ofCs onthe surface tension shown in Figure 4a,b, it is also seen thatthe cationic species are more surface active than the nonionicone. In the rangeCs > 0.5 M,ΓDH andΓD are almost identicaland scarcely depend onCs up to 3 M.Surface Excesses of Small Ions at Surfactant Concentra-

tions above cmc. Surface excesses of small ions at surfactantconcentrations above cmc were evaluated from the variation ofthe surface tensionγcmc with Cs, as shown in Figure 4. For thenonionic species at constant pH and under the condition of thesurface neutralityΓCl ) ΓNa ) ΓS, eq 18 reduces to eq 21 interms of the mean activity of the salta(.

For the nonionic species, the activity coefficient of NaCl wasfound to be well approximated with that of the pure salt solution.

log(cmc+/mM) ) -kCH log(Cg/M) - (Ks)ion(Cs/M) -0.434(lBκ/2)/(1+ κa) + b1 (16)

0.24 (ionic)< 0.29 (zwitterionic)< 0.32 (dipolar)<0.44 (nonpolar ethylene glycol) (17)

-dγ ) ΓD dµD + ΓDH dµDH + ΓCl dµCl +ΓNa dµNa + ΓH dµH (18)

-dγ ) (ΓD + ΓDH)RTd lnC+ ΓCl dµCl (19)

ΓD + ΓDH ) - (0.434/RT) (∂γ/∂ logC)pH,Cs,T (20)

Figure 3. Surface excessesΓ of the surfactants as functions ofCs.Cationic species (O); nonionic species (b).

Figure 4. Dependence of the surface tension at cmc,γcmc, onCs: (a)nonionic species, (b) cationic species.

-dγcmc) ΓD dµD + ΓS dµS ) ΓD dµD + 2ΓSRTd ln a(

(21)

7380 J. Phys. Chem. B, Vol. 101, No. 38, 1997 Maeda et al.

As shown by eq 8, the chemical potential of the nonionic micelleis assumed to be independent ofCs, and then dµD ) 0 due tothe equilibrium between the micelle and the monomer insolution.

ΓCl ) ΓNa ) ΓS ) (-dγcmc/d ln a()/(2RT) (22)

As shown in Figure 4a, values ofγcmc decrease linearly withCs. The slope (-dγcmc/dCs) was-0.36( 0.02 mN m-1 M-1.When plotted againsta(, a linear relation was also found inthe rangea( > 0.25m (m) molal): (-dγcmc/da() ) -0.43(0.02 mN m-1m-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 air-water interface when the nonionic surfactant is present at thesurface. The adsorption linearly increases withCs or a( in theconcentration range examined.For the cationic species at constant pH and also at the salt

concentrations (Cs > 0.1 M), where the contributions to thecounterion concentration from both excess amount of HCl andthe surfactant can be neglected, we can further assume that dµCl) dµNa ) RTd ln a( under the conditions. Then eq 18 reducesto eq 23.

In terms of the activity coefficientyDH, dµDH ) RT(d ln cmc++ d ln yDH),

In Figure 4b, values ofγcmc decrease linearly with logCs inthe rangeCs > 0.1 M and the slope is- 3.1( 0.1 mN m-1.Values ofΓDH were known as shown in Figure 3. The term (dlog cmc+/d logCs), which is the slope in the Corrin-Harkinsplot, was evaluated using the analytical expression of eq 4. ThetermyDH is decomposed asyDyDHel. Since we assume dµD/dCs

) 0 throughout the present study (eq 8), (d logyD/d logCs) )-(d log cmc0/d log Cs) ) 2.303KsCs. The electric activitycoefficient yDHel was calculated according to eq 15. Finally,the values (d lnCs/d ln a() were approximated with those ofpure NaCl solutions in the absence of cationic micelles, andwe found them to be constant (1.06) in the presentCs range.The final results are shown in Figure 5. At lowCs, the surfacecharges are almost compensated by the counterions but slightlynegative adsorption of the coions is also significant. With

increasingCs, however, the electroneutrality of the surfaceregion is satisfied by repelling more coions than at lowCs. Theresults expected from the electrical double layer of the Gouy-Chapman 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 givenfrom ΓDH, shown with open circles in Figure 5. The surfaceexcess of small ionsΓNa + ΓCl is given by eq 25.

ΓNa + ΓCl ) (4× 103Cs/κ)[{1+ (2πlBΓDHNA/κ)2}1/2 - 1]

(25)whereΓNa, ΓCl, andΓDH are in mol m-2; Cs is in M; κ is inm-1, and lB is in m. Values ofΓNa andΓCl were evaluatedfrom (ΓNa + ΓCl) coupled with the electroneutrality conditionΓDH + ΓNa ) ΓCl.The PB result indicates nearly complete counterion binding

of the macroscopic charged surface; that is the double layer isof the Helmholtz type.At low Cs, the agreement with experimental surface excesses

is fair. At highCs, however, greater accumulation of counter-ions was suggested from the present PB approach, which isexpected to be valid at low ionic strength, since small ions weretreated as point charges. Introduction of the distance of theclosest approach of counterions to the interface, however, didnot change the result appreciably. Any effect caused by thepresence of ionic micelles was not taken into account in thecalculation.Micelle Size. Several nonlinear Corrin-Harkins plots have

been associated with micellar size and/or shape changes.32 Toexamine this possible correlation in the present case, radii ofthe equivalent hydrodynamic sphereRH of the present micelleswere determined with dynamic light scattering. Dependenceof RH on Cs at a given surfactant concentrationC of 5 mM isshown in Figure 6. The size of the nonionic micelles remainedconstant (∼2 nm) over the whole range ofCs examined. Thisindifferent character of the nonionic micelles towardCs isconsistent with our assumption leading to eq 20 that dµD/dCs

) 0. The size of the cationic micelles, on the contrary, increasedwith Cs in the range ofCs greater than about 0.4 M. Thedeviation from the linearity in the Corrin-Harkins plot in thepresent case is also suggested due to a change in size and/orshape of the micelle. The effect of the surfactant concentrationC on RH was examined atCs ) 1 M. Micelle growth withCwas observed for the cationic species, while it was very slightfor the nonionic species. Spherical micelles are expected forthe latter case.

Figure 5. Surface excesses of small ions at the air-solution interfacecovered with a monolayer of the cationic surfactant as functions ofCs.Dashed lines were calculated according to the Poisson-Boltzmannequation. 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 surfactantΓDH

is also shown (O).

Figure 6. RadiiRof equivalent hydrodynamic spheres of micelles asfunctions ofCs. Cationic species (O); nonionic species (b). Surfactantconcentration: 5× 10-3 M.

-dγcmc) ΓDH dµDH + (ΓCl + ΓNa)RTd ln a( (23)

(ΓCl + ΓNa) )(d lnCs/d ln a()[0.434 (-dγcmc/d logCs)/RT-

ΓDH {(d log cmc+/d logCs) + (d logyDH/d logCs)}] (24)

Salt Concentration Dependence of the cmc J. Phys. Chem. B, Vol. 101, No. 38, 19977381

Discussion

Attractive Interaction among Cationic Heads. The findingthat cmc+ < cmc0 in the rangeCs > 0.2 M strongly suggeststhe presence of some nonelectric stabilization of the cationicmicelles, which has been proposed to be the hydrogen bond. InFigures 1 and 2, the two curves, log cmc0 and log cmc+, areapproximately parallel with each other in the rangeCs > 1.5M. Under such a highCs(>1.5 M), we can approximate thatthe electric contribution to the chemical potentials can be ignoredand theCs dependence represents mostly the effect of salt onhydrocarbon chains, the salting-out effect. Then, from eqs 6and 11,

In eq 26, the rhs represents the difference between these twospecies with respect to the free energy of micellization in amedium of high ionic strength. We can take the rhs as a lowerbound for the free energy of the assumed hydrogen bond∆Ghb.The difference between the two curves in Figure 1 or Figure 2gives a value of 0.95RT at 25°C.

We have estimated the free energy of the hydrogen bondbetween nonionic-cationic to be-1.4RTor more negative at25 °C.21The hydrogen bond in aqueous media has been known to be

weak because of the hydration of polar groups. It was claimedthat the carboxyl/carboxylate hydrogen bond of fatty acids iscompletely disrupted in aqueous media,33 while in polymericsystems the hydrogen bonds have been proposed.34-37 TheR-helix random coil transition of polypeptides has been knownto be highly cooperative, partly because the hydrogen bondstabilization per mole peptide group is belowRT, on the orderof 100 cal/mol.38 It is interesting, therefore, to examine furtherthe supposed hydrogen bond mechanism of DDAO, since thestabilities estimated above are much more stable than carboxylor peptide groups. A detailed discussion in favor of thehydrogen 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 theobserved nonlinear Corrin-Harkins plot in terms of the salting-out effect operating on the hydrocarbon chain. At the sametime, we have found a shape/size change of the cationic micellein the present study in the range ofCs where the deviation fromlinearity was significant. It is pertinent to discuss the linearityand/or nonlinearity of the plot. Several reported Corrin-Harkins plots can be classified into three groups: (a) linearrelations29,39up 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 ionichead is shown to be greater than 0.2 (inequality 17). If a valueof 0.2 is tentatively taken forKs, then we expect∆ log cmc)-0.6 for ∆Cs from 1 to 3 M, and this change cannot benegligible. The salting-out effect always causes downward devi-ations and hence it cannot explain groups a and c. On the otherhand, changes of micellar size have been found in the salt con-centration range where deviation from the linear Corrin-Harkinsplot is significant. The two factors salting-out and shape changecan be correlated somehow. A naive hypothesis that the salting-out 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 surfaceelectric potentialψ0.43 The linearψ0-log cmc relation leadsto linear Corrin-Harkins plots only whenψ0 linearly varieswith log Cg. When the data of Healy et al.43 were examinedwith respect to the relationψ0-log Cg, linear and upwarddeviations were observed for DTAC/NaCl and DTAB/NaBr,respectively. A unified picture seems lacking to compromisethe two findings at high ionic strengths: the salting-out effectand the linearψ0-log cmc relation.

Acknowledgment. The authors thank Mr. Tsuyoshi Fukudaand Ms. Yukiko Imaishi for their measurements of dynamiclight scattering. This work was partly supported by the NipponOil & Fats Co. Ltd.

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2.303kT log[cmc0/cmc+] ) [∆(µm*/m) - ∆µ1*] D -[∆(µm*/m) - ∆µ1*] DH (26)

∆Ghb(cationic-cationic)< -0.95RT (27)

7382 J. Phys. Chem. B, Vol. 101, No. 38, 1997 Maeda et al.