Mixed micelles of polyoxyethylene-type nonionic and anionic surfactants in aqueous solutions

Mixed micelles of polyoxyethylene-type nonionic and anionic surfactants in aqueous solutions

Mixed Micelles of Polyoxyethylene-Type Nonionic and Anionic Surfactants in Aqueous Solutions NAGAMUNE NISHIKIDO Department of Chemistry, Faculty of Sc...

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Mixed Micelles of Polyoxyethylene-Type Nonionic and Anionic Surfactants in Aqueous Solutions NAGAMUNE NISHIKIDO Department of Chemistry, Faculty of Science, Kyushu University, Fukuoka 812, Japan

Received June I1, 1976; accepted September 7, 1976 Critical micelle concentrations (CMC) and the solubilization toward dyestuff yellow OB in aqueous solutions of mixed polyoxyethylene-type nonionic and anionic surfactants at 30°C were measured. As for the CMC, the stabilization of the mixed micelles relating to polyoxyethylene chains was suggested by application of the pseudo-phase-separation model. Concerning solubilization, the same measurements were also performed for various other surfactant mixed systems, and we defined the solubilizing power of the mixed surfactant solution and the ratio of this quantity to that in the additivity law. Solubilization in the system of mixed polyoxyethylene-type nonionic and anionic surfactants showed a specific behavior as compared with the other systems. From the CMC and solubilization studies, we proposed the model concerning the mixed micelles of polyoxyethylenetype nonionic and anionic surfactants. In the model, polyoxyethylene chains in the mixed micelle have an attracting interaction with anionic head groups, and the interaction is enhanced by the formation of a hydrocarbon core. This status is different from that in free polyethylene glycol and surfactant systems. INTRODUCTION

agreed well with the theory. However, it is difficult to predict theoretically the C M C of mixtures of nonionic and ionic surfactants in aqueous solution (8), because of specific interactions between components and also because of the difference in status of the hydrophobic and hydrophilic parts of components in the mixed micelles and those in the single micelles. Anionic surfactants bind with the watersoluble polymer, polyethylene glycol, and form the aggregates termed "complex" in aqueous solution (9-13). As for cationic surfactants, the extent of binding is much weaker than that of anionic surfactants (10, 14-16). The nonionic surfactants used in the present study have polyoxyethylene chains as the hydrophilic moiety, and so specific interactions between polyoxyethylene chains and anionic surfactants are expected to contribute to mixed micelle formation.

The properties of aqueous solutions of surfactants can be modified by the addition of other surfactants to the solutions. The properties of surfactant solutions depend on the structure of the mixed micelle, i.e., the size, form, and arrangement of components in the micelle. In the case of mixed micelles whose components have the same ionic nature, i.e., ionic-ionlc or nonionic-nonionic, the structure of the mixed micelles is expected to be similar to that of each single micelle. T h a t is to say, the mixed micelles are formed in the same manner as the single micelles, in which specific interactions between different surfactant molecules have been excluded. Therefore, the critical micelle concentrations (CMC) of mixtures of ionic-ionic or nonionic-nonionic surfactants in aqueous solution, and also the Krafft point, have been predicted theoretically (1-7). In fact, the experimental data have 242

Journal of Colloid and Interface Science, Vol. 60, No. 2, June 15, 1977 ISSN 0021-9797

Copyright ~} 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.

243

MIXED MICELLES OF SURFACTANTS In the present study, we determined the CMC of polyoxyethylene-type nonionic and anionic surfactant mixtures in aqueous solutions. In addition, we measured the saturated amounts of an oil-soluble dye, yellow OB, in aqueous solutions of various surfactant mixtures. From these results, we tried to visualize the features of mixed micelles formed in aqueous solutions of polyoxyethylene-type nonionic and anionic surfactant mixtures.

M(DS) 2

i00

50

EXPERIMENTAL Materials. As anionic surfactants having CMC values close to those of nonionic surfactants we chose bivalent metal dodecyl sulfates (abbreviated as M(DS)2; M: bivalent metals Zn, Mn, Cu, Mg). The M(DS)2 were prepared by the substitution of bivalent metal cations for sodium cations of highly purified sodium dodecyl sulfate (SDS) in aqueous solution. The SDS was synthesized from the reaction of fractionally distilled dodecanol with chlorosulfonic acid and the neutralization with sodium hydroxide. A small amount of nonreacted dodecanol was eliminated by solvent extraction of petroleum ether and heating at constant temperature of ll0°C under reduced pressure for more than 10 hr. Purification of M(DS)2 was performed by repeated recrystallization from water. The nonionic surfactants, polyoxyethylene alkyl ethers (C,,E,,; m: the number of methylene groups, n: the number of ethylene oxide groups), were the same materials as those used in a previous paper (6). The cationic surfactant, dodecylammonium chloride (DAC), which was prepared by the neutralization of dodecylamine with hydrochloric acid and recrystallized five times from ethanol-ether, was supplied by Dr. S. Miyagishi at the Kanazawa University. The dyestuff yellow OB (1-o-tolyl-azo-2naphthylamine) as a solubilizate was supplied by the Wako Pure Chemical Company and was recrystallized four times from ethanolwater (volume ratio: 4//1). I t was then dried under reduced pressure before use.

I

0,5 ~LE FRACTIONOF M(DS)2 IN THE MIXTUREIN BULK

FIG. 1. The plots of CMC against the mole fraction of M(DS)2 in mixtures in the bulk solution at 30°C. O, Zn(DS)~; O, Mn(DS)2; V], Cu(DS)2; A, Mg(DS)2. CMC measurements. The values of the CMC of mixtures of M(DS)2 and C12E, (n = 6, 29, 49) in aqueous solutions at 30°C were determined as the concentrations at sharp breaks in the plots of the surface tension vs the logarithm of the concentration. Surface tensions were measured with the Du Notiy tensiometer. The CMC determined in the above way coincided with the concentrations deviating from the straight lines in the specific conductance vs concentration plots. The examples are shown in Fig. 2. The specific conductances were measured with Conductivity Outfit Model MY-7 manufactured by Yanagimoto Seisakusho. Solubilization measurements. The weighing bottle containing 10-15 ml of mixed surfactant solution and an appropriate amount of yellow OB was stirred for 48 hr at 30°C. After the unsolubilized yellow OB had attained the equilibrium of solubilization, it was filtered off. The filtered solution was diluted with ethanol, and the final volume ratio of ethanol to water was 4//1. The amount of the solubilized yellow OB was determined from the optical density at 445 nm with a Hitachi 124 Spectrophotom-

Journal of Colloid and Interface Science, Vo]. 60, No. 2, June 15, 1977

244

NAGAMUNE NISHIKIDO TABLE I

C M C of Nonionic and Anionic Surfactants Used in the C M C Study in the Aqueous Solution at 30°C Surfactant

CMC (10 5 mole/liter)

Cl2E6 Cl.oE!0 C1~E~9 M (DS) ~

7.5 21.5 43.7 120

eter or a Beckman-Toshiba DSB-70 Spectrophotometer. RESULTS AND DISCUSSION

i. CMC of Mixed Anionic and Nonionic Surf actants The CMC values of the mixtures of C12E, (n = 6, 29, 49) and M(DS)2 in aqueous solutions at 30°C are plotted in Fig. 1 against the mole fraction of M(DS)2 in the mixture in the bulk solution. Those of the pure components are listed in Table I. In the plots in Fig. 1, differences among the various bivalent metals in M(DS)2 are not observed. If specific interactions among the polyoxyethylene chains of nonionic and anionic surfactants contribute to mixed micelle formation, differences in stability of the mixed micelles among the three mixed systems involving various ethylene oxide chain lengths can be expected. In order to compare the stability of the mixed micelles among the three mixed systems, we apply the pseudo-phase-separation model and determine the excess free energy in the micelle phase as follows. The condition for equilibrium of the associating dodecyl sulfate ion D S - between the bulk and micelle phases is ~.s ~ = ~Ds

TM,

[1]

where # is an electrochemical potential and superscripts b and m refer to the bulk and micelle phases, respectively. In the anionic surfactant single system, the CMC is fairly low, and so we can write #DS b = #DS bO +

Fel b a n d Fel TM represent the electrical work necessary for transferring a mole of D S from the position with the zero of the electrical potential to the bulk and micelle near the CMC, respectively; and XI is the CMC in mole fraction units. In the anionic-nonionic surfactant mixed system, near the CMC the electrochemical potentials in Eq. [-1] are expressed by where

R T in (2XI) +

gDS m = gDS n'O = #DS rnO -{- Fel TM,

F d b,

~DS b = ~ D S b e

+ R T In (2XlXmlx)+Fel b',

/TDSm=#DSm°+RT In xDSmTDsm+FcY,

['3]

where xi is the mole fraction of the anionic surfactant M(DS)~ in the surfactant mixture in bulk; Xmix is the CMC in mole fraction units ; XDSTM and 7DSm are the mole fraction and activity coefficients of D S - in micelle; and F , Y and Fd m' are the quantities having the same meanings as F~l b and F~ITM. #DSTM in Eq. ['3-] is expressed for the ideal reference system as (2, 6)

RT in

PDS m'id ~---gDS m0 +

XDS TM "3[- Fcl m,id,

[-4]

where Fo~m,~d satisfies the relation that Fel m,id - - F e l b' = Fel ra - - Eel b.

Introducing Eqs. ['2] and [-3] into Eq. [.1], we obtain /.tDSm0--#DS b e ~---RT

in (2XI) --For

= R T In (2xiXmlx) - - R T In x D S m T D S m - - F e l ',

[-5]

Fd = F~I m - - Fol b and F~I' = Fd ~' --F,, b', which represent the electrical work necessary for transferring a mole of D S - from bulk to micelle near the CMC in the anionic and anionic-nonionic surfactant systems, respectively. Then, from Eq. [--53, we obtain where

7DSTM exp(AFo{RT) =

(xICmix/CI).

(1/XDSm),

[6]

where &Fd = F~I'--Fox; and Cmi, and CI are the CMC's in molar units. For the nonionic surfactant component, owing to the lack of the electrical term in chemical potential, we more easily obtain

[2]

Journal of Colloid and Interface Science, Vol. 60, No. 2, June 15, 1977

~,~. . . .

(~Cm,dCN).

(i/~,,,),

[7]

MIXED MICELLES O1," SURFACTANTS

245

where k~ and ki)s are the ionic equivalent conductances of the bivalent metal cation M s+ 1 and DS- in bulk solution, respectively; c,, is 200 the molarity of the anionic surfactant monomers in equilibrium with micelles at the total anionic surfactant molarity c; Lmi¢ and a are the ionic equivalent conductance of a micelle per anionic monomer concentration and the i00 degree of dissociation of counter ion per micelle, respectively. In order to determine the micelle composition I I by means of Eq. [-9], it is necessary that the 1 2 values of c,,, be determined at a particular MOLALITY ( C ) OF M~(DS)2 (IO-3MOLE/L) concentration c. As the terms of (2XM + 2XDS) FIG. 2. The variation of the specific conductance K and (2aX.~i + 2L,nie) depend on the monomer with molarity of Mn(DS)2 in the single and mixed concentration and micelle composition, respecsurfactant systems. (1) Mn(DS)2 alone,-the mole tively, the following preliminary procedures fraction of Mn(DS)2 in the mixture in bulk is (2) 0.8, (3) 0.3 in the C12E6-Mn(DS)~ system, (4) 0.8, (5) 0.3 are necessary. (1) Beforehand, the relationship in the Ca2E4rMn(DS)2 system. between the values of (2X.~ + 2XDS) and where the subscript N refers to the nonionic the monomer concentration is to be established surfactant. Finally, with the use of Eqs. (4), from K vs c plots below the CMC for the [6], and [7], the excess free energy gEm in anionic surfactant alone; (2) the monomer concentration should be assumed constant the micelle phase is derived as follows. above a certain total anionic surfactant gE"/RT = XDS"I(in TDSm-[-/k Fel) -[-XN m In "}INm concentration, and the composition of the = XDSm In (xi/CiXDsTM) micelles approaches that of the surfactant +XN m In ( x N / C N x N I n ) ' + l n Cmix. [-8] mixture in bulk (19-21). We assume tentaIn Eq. [-8], the excess free energy gem can be tively that the slopes of the linear parts at estimated by determining the values of XDS'" higher concentrations in the ~ vs c plots, e.g., and XNm near the CMC. In what follows, we in Fig. 2, are equivalent to (2aXM + 2L,,lic) at describe the semiempirical successive-approx- the same composition of micelles as that imation method to determine the values of of the mixtures in bulk. We can then tentaXDSm and XN'n, i.e., the composition of the tively assume the relationship between (2ahra + 2Ln, i~) and the micelle composition. After mixed micelles. In general, the composition of mixed performing the above two preliminary promicelles changes with the total surfactant cedures, by referring to the relationship concentration, in contrast to the case of the between the micelle composition and the single micelle. That is to say, the concentration total surfactant concentration reported preof monomers in equilibrium with micelles viously, we predict the micelle composition changes to a greater extent with the total and the monomer concentration at a particular surfactant concentration even above the CMC total anionic surfactant concentration c. And (19-21). And so the specific conductance K of in Eq. [9-], we use this concentration c, the the present mixed anionic-nonionic surfactant experimental ~, and the values of (2X~i + 2XDS) solution can be expressed by the equation and (2aX~ --}-2L,ni~) in the prediction of the (22, 23) monomer concentration and micelle composiK = (1/1000)[-c,.(2XM + 2XDS) tion. By the above procedure, the value of cm at q- (c -- c,,,)(2aXM + 2L,,H~)], [9-] concentration c is derived in one trial. Next,

7

Journal of Colloid and Interface Science, Vol. 60, No. 2, June 15, 1977

246

NAGAMUNE NISHIKIDO

J

~2.0

ELLIZE

==

L

z

1,0

0

F- 1,ol ~0.5

~'~ I/~ o

0

2,0

, Cz2E49

3,0

//

4,0

_

/ , CMC

C12E49' MONOMER

1.0 2,0 3.0 TOTAL SURFACTANT CONCENTRATION (IO-3MOLE/L)

4,0

FIG. 3. The variation of the concentration of micellized and monomer of DS- and C12E49 with the total surfactant concentration for the ½Mn(DS)2-CnE49 system, where the mole fraction of ½Mn(DS)2 is 0.667 in the mixture in bulk. on the curves of C M C (C,~i~) vs the mole fraction of the anionic surfactant (xx) of the mixture in bulk (Fig. 1), we find the point at which the relation XICmi.-= C~ holds. The value of XNCrnixat this point is the concentration of nonionic component monomers in equilibrium with micelle at the total nonionic surfactant concentration (C/XI)'XN. Then, the concentrations of micellized anionic, i.e., D S - ,

and the nonionic components are derived b y 2(c - Cm) and (C/XI)'XN -- (the concentration of nonionic monomers), respectively, which easily lead to the micetle composition. T h e micelle composition thus determined usually differs from t h a t first predicted and also from the case with the monomer concentration.

w

~

m XDS

2.0

led v

0.5

o >-

,,q N 1.0 ._J

y

o

- 0 , 5

o~

0

1.0

2.0

SURFACTANT CONCENT~TION (IO-2~LE/L) -1,0

FIG. 4. The excess free energy gem against the mole fraction of DS- in the micelle for the systems of the ½Mn(DS)~- (1) CnEn, (2) C1~E29, (3) CnEo.

FIG. 5. The plots of the amount of solubilized yellow OB against the surfactant concentration in the single surfactant systems. O, CnE6; ~D, C12E49; Q, ½Mn(DS)~.

Journal of Colloid and Interface Science, Vol, 60, No. 2, June 15, 1977

MIXED MICELLES OF SURFACTANTS That is, the values of (2~,M~-2~DS) and (2aXM + 2Llnie) must be used at c,,, and the micelle composition determined above. However, in one trial the correlation among these values is poor, which indicates that we have not chosen suitable values. Therefore, we repeat the calculation until we obtain a good correlation among these values. In Fig. 3, a well-defined example of the variation of the concentrations of micellized anionic and nonionic components and monomers with the total surfactant concentration is shown, in which the mole fraction of anionic surfactant ½Mn(DS)2 is 0.667 in the mixture in bulk. From the values of XDSm and Xn TM near the CMC determined by the above method, the excess free energy gem is estimated in Eq. [83. Figure 4 shows the gEm/RT vs XDSTM plots for the present three mixed systems. From Fig. 4, it is found that the mixed micelles in the system involving the nonionic surfactant with the longer polyoxyethylene chain are more stable. Of the factors determining the stability of the mixed micelles, the degree of counter±on binding to micelles is significant because this factor affects the electrical work Fel' in Eq. [53 through the shielding toward DS-. I t is seen from Fig. 2 that the mixed micelle in the system involving the longer polyoxyethylene chain has counterion binding to a lesser degree at the same micelle composition. That is, the greater the value of a in Eq. [93, the higher the specific conductance in the C12E4a-M(DS)2 system as compared with that in the C12E6 M(DS)2 system at a higher concentration in the K vs c plots at the same composition of the surfactant mixture in bulk (17). Then, only from the viewpoint of counter±on binding, the mixed micelle in the system involving the longer polyoxyethylene chain is predicted to be relatively unstable. Nevertheless, Fig. 4 shows distinctly the relative stabilization of the mixed micelle in the system involving the longer polyoxyethylene chain. Therefore, it is reasonably concluded that the mixed micelle of polyoxyethylene-type nonionic and anionic

247 TABLE II

Solubilizing Powers of Various Surfactants Used in This Study in Aqueous Solutions at 30°C Surfactant

S,lubilizing power (10 -2 mole/mole of surfactant)

CsE6 C10E6 Cl2E6 C1~E15 CI~E29 Cl2E49 ½Mn(DS)2 DAC

6.2 ± 0.4 10.0 ± 0.4 14.5 ± 0.5 14.5 4- 0.5 14.5 ± 0.5 13.6 ± 0.5 1.8 ± 0.1 3.1 4- 0.3

surfactants has a stabilizing factor relating to the polyoxyethylene chain. In the next section, we examine this conclusion from the viewpoint of the solubilizing behavior of mixed surfactant solutions.

2. Solubilization in Mixed Surfactant Solutions The solubilization of yellow OB in micelles has been considered to occur in the hydrocarbon core (H) and polyoxyethylene shell (P) near the hydrocarbon core (24). As yellow OB dissolves only slightly in water, the amount of solubilization is assumed to be proportional to the size and number (K) of the micelles in the same way as hydrocarbon (25). The size of the micelles is proportional to the aggregation number (A) of the micelles if the shape of the micelles is kept invariant over the concentration range studied. Then, the amount of solubilization S at concentration C in single surfactant solution is expressed by SN(C) = (aH,N + apf)ANKN or

[103 SI (C) = ota,iAiKi,

where subscripts N and I refer to nonionic and ionic surfactants, respectively; f is the degree of compactness of the polyoxyethylene shell (24) ; and a is a proportional constant. Assuming that the concentration of monomers is constant above the CMC and that the shape of the micelles is kept invariant, we can write

K = [C-

(cmc)]/A.

[11]

Journal of Colloid and Interface Science, Vol. 60, No. 2, June 15, 1977

248

NAGAMUNE NISHIKIDO 3.C

/"

/

2,0

/ O,667

f

$7 i >

J

A /

/

/

o 1,0

i

0,5

4

/ /

t

l,fO

'

2'.0

'

310

TOTAL SURFACTANTCONCENTRATION(IO-2MOLE/L)

FIG. 6. The amount of solubilized yellow OB and the mole fraction of DS- in the micelle as a function of the total surfactant concentration in the C12E4r½Mn(DS)2 system, where the mole fraction of ½Mn(DS)2 is 0.667 in the mixture in bulk.

Then, Eqs. [-107 are rewritten as

s~(c)

= ~[c

-

(~m~)],

or

[121 SI(C)

= ai[C -- (cmc)l.

The linear relations of S vs C are shown in Fig. 5 for the representative examples. The proportionality constants in Eqs. [121 or the slopes of the stralight lines are characteristic constants expressing the amount of solubilization per monomer concentration unit of micelles, and are referred to as the solubilizing powers (24). The solubilizing powers of various surfactants used in this study are tabulated in Table II. In this table, approximately constant solubilizing powers of C12E~ (n = 6, 15, 29, 49) are considered to be caused by the main contribution of six ethylene oxide groups near the hydrocarbon core to solubilization. This coincides with our model of the polyoxyethylene-type nonionic rnicelles whose six or fewer ethylene oxide groups pack together (6). The nonionic surfactant with the shorter hydrocarbon chain solubilizes less. This is considered to be due to a decrease in the degree of compactness f in Eq. [101, which is brought about through a decrease in the diameter of the

hydrocarbon core in the micelles since more is solubilized in the polyoxyethylene shell than in the hydrocarbon. In addition, the cationic surfactant, DAC, solubilizes more than the anionic surfactant, ½Mn(DS)2. This has been considered to be due to the attraction between the cationic head groups of the DAC and ~r electrons in the aromatic rings of the dye (16). Figure 6 shows an example of the amount of solubilization vs total surfactant concentration in the mixed surfactant system, where the mole fraction of ½Mn(DS)2 is 0.667 in the mixture in bulk. Above a particular concentration the linear relation holds, and at a lower concentration a deviation from the linear is observed. This relation is attributable to the variation of the micelle composition with the total surfactant concentration. Figure 6 shows the mole fraction of D S - in the mixed micelles calculated on the basis of Fig. 3. Over the concentration range where the composition of the micelles is nearly constant, a linear relation is observed. Therefore, the solubilizing power a~t of mixed surfactant system is equivalent to the slope of the linear part, where the composition of the micelles has been deter-

Journal of Collcid and Interface Science, Vol. 60, No. 2, June 15, 1977

249

MIXED MICELLES OF SURFACTANTS 1,5

1,5

g:l.O ©

0,5

O

0,4

015 MOLEFRACTIONOF Cz2E6 IN MICELLE

FIo. 7. The ratio a~/aM ~a as a function of the composition of the mixed miceUe in the CsE6 (@)-, and C10E6 ( O ) - C 1 2 E 6 systems at 30°C. mined. Next, we introduce the quantity Or'Mad : OtMaa ----- a l X l m "~- Ot2X2m,

[13]

where at and a~ denote the solubilizing powers of pure components 1 and 2, respectively. The quantity aM~a denotes the solubilizing power in the ideal state if each component forming mixed miceUes contributes separately to total solubilization. Therefore, the ratio aM/aM ad is regarded as a measure of the multiplicative effect in solubilization. Figures 7-10 show the ratios a ~ / a ~ ~d as a function of the micelle compositions for the various surfactant mixed

~1,5[

i

0,5 MOLEFRACTIONOF DA+ IN MICELLE

1

FIG. 9. The ratio a a / a a ~ as a function of the composition of the mixed micelle in the systems of DAC-CI2Ee (O) and-C1sE49 (@) at 30°C. systems. The mixed micelles formed b y two surfactants involved in the system in Figs. 7 and 8 have been the ideal mixtures from the viewpoint of the pseudo-phase-separation model (2, 3, 6). Accordingly, it is expected that additivity, i.e., Eq. [13], holds for these systems. However, except for the Ct0E6-Ct2Ee system, negative deviations from additivity are observed. The difference in hydrocarbon chain lengths in mixed surfactants is so large that the mixed micelle is the non-ideal mixture 2.0

1,5

1,0

0.5

0 0,5 ~LE F~CTIONOF C12E29ORCIzE49 IN MICELLE

0,.~

01S MOLEFRACTIONOF DS- IN MICELLE

Fio. 10. The ratio .a/aM ~d as a function of the Fro. 8. The ratio aa/a~s "a as a function of the composition of the mixed micelle in the systems of composition of the mixed micelle in the Cl~Ezg-C12E~9 ~Mn(DS)s-CI~Ee (O),-CI~E16 (@),-C12E~. (0), and -C12E4. (~)) at 30°C. (C)) and C12ErCI2Es.,4. (@) systems at 30°C. Journal of Colloid and Interface Science, Vol. 60, No. 2, June 15. 1977

250

NAGAMUNE NISHIKIDO

and leads to instability as compared with the ideal mixture (2). Also, in the mixed systems in which one component has five or fewer ethylene oxide groups, the mixed micelle is unstable (6). From these facts, in the CsEsC12E6, C12Ee-Cl~E29.49, and C12E29-C12E49systems, it is considered that two surfactants barely form the ideally mixing micelles, in which the polyoxyethylene chains of each component retain a status similar to that in the case of each single micelle. However, by the penetration of a rather large molecule such as yellow OB into these ideally mixing micelles, the status of the polyoxyethylene shell is disturbed. As a result, the amount of solubilization is less than that of the ideally mixing micelles. In the case of the system of mixed cationic (DAC)-nonionic (C12E6, C12E49) surfactants shown in Fig. 9, deviations from additivity are negative in both systems. And the extent of the deviation in the DAC-C12E49 system is small, but that in the DAC-CI~E6 system is large. In the anionic (~Mn(DS)~)-nonionic (C12E,) system shown in Fig. 10, as the polyoxyethylene chain length in the nonionic component becomes larger, the deviation becomes positive. In general, a negative deviation is expected in ionic-nonionic surfactant systems, since compactness f in Eq. [-10] in the mixed micelle decreases as compared with that in the nonionic single micelle by the introduction of ionic charge heads into the shell. A positive deviation from additivity is characteristic only of the mixed systems of anionic and polyoxyethylene-type nonionic surfactants. Therefore, it is concluded that some interaction between polyoxyethylene chains and anionic surfactants contribute favorably to solubilization, which ratifies the conclusion obtained in the preceding CMC data. From the discussion above, we propose a model depicting mixed micelles between polyoxyethylene-type nonionic and anionic surfactants in aqueous solutions. The mixed micelles stabilize primarily through the contact of hydrocarbon chains of both nonionic and anionic surfactants, which is termed hydro-

phobic bonding. In single micelles of the nonionic surfactant alone, polyoxyethylene groups beyond the sixth extend to the aqueous medium (6). In mixed micelles, the slightly positively charged ether oxygen atoms (26-32), i.e., oxonium ions, in polyoxygethylene groups beyond the sixth are attracted by anionic head groups in anionic surfactants at several points on the micelle surface. As a result of this interaction, the compactness of polyoxyethylene chains increases as compared with that in single micelles, and the extent of the increase in compactness is greater for the longer polyoxyethylene chain which has the more attracting positions of oxonium ions. Therefore, the stronger solubilization is realized for the system involving the longer polyoxyethylene chain, which leads to the positive deviation in the solubilizing power. At this time, the greater the extent of the shielding of the longer polyoxyethylene chains, the greater the lowering of the electrical work Fe~' in Eq. [-5], and so the mixed micelles are considered to be relatively stable in the system involving the longer polyoxyethylene chains. This involves the model concerning the "complex" formed between free polyethylene glycol and anionic surfactants, which was recently suggested by Smith and Muller (12). In the systems of mixed cationic-nonionic surfactants, it is reported that the fraction of unshielding of cationic head groups in mixed micelles by counterions is greater in the system involving the longer polyoxyethylene chain at the same micelle composition (18). Then, the number of the dyes attracted by cationic head groups is greater in the system involving the longer polyoxyethylene chain. This effect is considered to appear in the difference in the chain length of polyoxyethylene involved in the systems shown in Fig. 9. At any rate, the coulombic interaction between polyoxyethylene chains and anionic head groups is enhanced by the formation of the hydrocarbon core. It is considered that the interaction, which is not found distinctly in the free polyethylene glycol with low molecular

Journal of Callold and Interface Science. Vol. 60. No. 2, June 15, 1977

MIXED MICELLES OF SURFACTANTS weight a n d s u r f a c t a n t systems (12), a p p e a r s in mixed s u r f a c t a n t systems. ACKNOWLEDGMENTS The author expresses hearty thanks to the Ka6 Soap Co., Ltd., and to Dr. N. Moriyama for the supplement of nonionic surfactants used in this study, and to Professor R. Matuura for discussions. REFERENCES 1. LANGE, H., Kolloid Zh. 131, 96 (1953). 2. SHINODA,K., NAKAGAWA,T., TAMAMUSHI,B., AND ISEMURA, T., "Colloidal Surfactants," p. 63. Academic Press, New York, 1963. 3. LANGE,H., AND BECK, K. I{., Kolloid-Z. Z. Polym. 251, 424 (1973). 4. MOROI, Y., MOTOMURA, K., AND MATUURA, R., J. Colloid Interface Sci. 46, I l l (1974). 5. MOROI, Y., ~N~ISHIKIDO,N., AND MATUURA, R., J. Colloid Interface Sci. 50, 344 (1975). 6. NISHIKIDO, N., MOROI, Y., AND MATUURA, R., Bull. Chem. Soc. Japan 48, 1387 (1975). 7. HATO, M., Nippon Kagaku Zasshi 92, 496 (1971). 8. MOROI, Y., NISHIKIDO, N., AND MATUURA, R., J. Colloid Interface Sci. 52, 356 (1975). 9. JONES, M. N., J. Colloid Interface Sci. 23, 36 (1967). 10. SCHWUGER,M. J., J. Colloid Interface Sci. 43, 491 (1973). 11. SmRArlAMA,K., Colloid Polym. Sci. 252, 978 (1974). 12. SMITH,K. L., AND MULLER, N., J. Colloid Interface Sci. 52, 507 (1975).

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.louvnal of Colloid and Interface Science, Vol. 60, No. 2, June 15, 1977