JOURNAL OF COLLOID AND INTERFACE SCIENCE 202, 359–368 (1998)ARTICLE NO. CS985484

Micellar and Thermodynamic Properties of Sodium Dodecyl Sulfatein Binary Aqueous Solutions of Di-, Tri-, and Tetraethylene Glycols

Dale Turner, 1 Kim Gracie,2 Trudy Taylor, and R. Palepu3

Department of Chemistry, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5

Received August 20, 1997; accepted February 19, 1998

London-dispersion interactions as the driving force for theThermodynamic and micellar properties of sodium dodecyl sul- micellization process (3, 4) . The satisfactory way to investi-

fate in aqueous solutions of di-, tri-, and tetraethylene glycols were gate the effect of hydrophobic interaction on ionic micelledetermined employing conductivity, potentiometric, and fluores- formation would be to study the micellar properties of ioniccence spectroscopic techniques. Intermicellar properties such as

surfactants in altered water structure by adding alcohols ofeffective degree of dissociation, monomer and counter ion concen-varying chain length. All substances containing hydrophobictrations, and activity coefficients were obtained from the massmoities decrease the hydrophobic effect, that is, it wouldaction model. From the evaluated intermicellar parameters, thedecrease the standard chemical potential of the monomer forhydrophobic and electrostatic contributions to Gibbs free energythe micelle-forming amphiphile without any effect on theof micellization were evaluated. The difference in Gibbs energies

of micellization of SDS between water and mixed solvent systems standard chemical potential of the micelle and would there-and the results were also interpreted in terms of hydrophobic and fore increase the cmc. If alcohols are dissolved in water,electrostatic contributions to the micellization process. Surfactant the solvent hydrophobicity will increase. This results in anaggregation numbers (Nagg ) obtained from the fluorescence increase of the critical micellar concentration because thequenching method decrease with increasing glycol content in the micellization energy gained by the system decreases. Thissolvent composition. The micropolarity of the micellar interior was is the case when adding short chain alcohols. Following thedetermined from the pyrene I1 /I3 ratios. q 1998 Academic Press

alcohol addition, the micellar aggregation number decreasesKey Words: thermodynamics; micellization; aggregation num-and when the alcohol concentration exceeds a certain thresh-bers; intermicellar properties; mass action model.old value, the micelles are known to breakdown ultimately(5) . Many studies have been dedicated to the study of alco-hol/micelle system in recent years (6–13). Lengthening ofINTRODUCTIONthe alkyl chains in alcohols leads to a decrease of the lowercritical solution temperature (LCST). This causes a misci-As part of a comprehensive study of the micellar processbility gap in aqueous solutions, thereby limiting the alcoholin mixed solvent systems containing water plus polar organicconcentration in the mixed solvent system. It has been showncompounds with hydrogen bonding ability, we report in thisthat the inclusion of one or more oxyethylene groups into apaper the micellar and thermodynamic properties of sodiumglycol molecule increases the LCST and consequently thedodecyl sulfate (SDS) in binary aqueous mixtures con-aqueous miscibility (14, 15).taining di-, tri-, and tetraethylene glycols (DG, TEG, and

We have reported recently the micellization process ofTTEG).alkyl trimethyl and pyridinium bromides in pure ethyleneThe aggregation phenomena of ionic surfactant moleculesglycol employing the membrane selective electrodes (16)is a balance between the repulsive forces primarily fromand extended the study in aqueous binary mixtures of ethyl-electrostatic repulsion between polar head groups (1) andene glycol with water in the entire composition range (17,the attractive forces mainly due to hydrophobic interactions18). In this investigation we present micellar properties such(2). Recently, considerable emphasis has been placed onas cmc, effective degree of dissociation (a) , equivalent con-ductance at infinite dilution, and aggregation numbers of

1 Present address: Department of Chemistry, University of Calgary, 2500 sodium dodecyl sulfate in binary mixtures of water con-University Drive N.W., Calgary, Alberta, Canada T2N 1N4. taining different amounts of di-, tri-, and tetraethylene gly-2 Present address: Department of Chemistry, McMaster University, ABB-

cols. Techniques employed are conductance, potentiometry,203, 1280 Main St. W., Hamilton, Ontario, Canada L8S 4MI.and fluorescence spectroscopy. Also by employing a mass3 To whom correspondence should be addressed. E-mail: rpalepu@juliet.

stfx.ca. action model, a complete analysis of thermodynamic proper-

359 0021-9797/98 $25.00Copyright q 1998 by Academic Press

All rights of reproduction in any form reserved.

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360 TURNER ET AL.

ties of micellization was carried out. In the present study,glycols were regarded as a cosolvent rather than a cosurfac-tant forming mixed micelles.

EXPERIMENTAL

Materials

Sodium dodecyl sulfate (BDH) was crystallized severaltimes from hot methanol, further purified through Soxhletextraction with diethyl ether for 72–100 h, and dried undervacuum. All glycols are of the stated purityú99% (Aldrich)and were used as received without any further purification.All solutions were prepared with Milli-Q water (Millipore) ,and the specific conductance of water was less than 2 mScm01 . Pyrene (Aldrich ú99.1%) was purified by sublima-tion and crystallized from ethanol. Hexadecylpyridiniumbromide (CPBr) was purified by crystallization from ace-tone.

Measurements

Conductivity measurements were made in a thermostatedjacketed beaker with a dip cell having a cell constant of0.978 cm01 and an automatic conductivity CDM 83 bridgeoperating at 1000 Hz. Conductivity titrations containing atleast 25 different concentrations of surfactant at a fixed sol-vent composition were carried out at four different tempera-tures.

A Fisher sodium ion selective electrode coupled with adouble-junction reference electrode (Fisher 13-620-47) wasused to measure the sodium ion activities. To prevent theprecipitation of potassium dodecyl sulfate at the junction ofthe reference electrode, ammonium nitrate solution was usedinstead of potassium nitrate in the outer chamber.

Fluorescence quenching measurements were carried outFIG. 1. Specific conductance (K) vs concentration of SDS in aqueouson a Shimadzu RF-1501 spectrophotometer. Pyrene is used

mixtures of DEG at 298 K.as a fluorescence probe, and the concentration was heldaround 2 1 1006 M. The concentration of the quencher,hexadecylpyridinium bromide was held low enough to not

micellar region up to a concentration of ten times the cmcinterfere with the assembly of the micelles. The emissionvalue. The input parameters required for these calculationsand excitation slits were 5 nm, and a wavelength of 335are aggregation number, cmc value, and the degree ofnm was selected for excitation. The emission intensity wascounter ion binding of the micelle. These parameters weremeasured from 350 to 600 nm. The intensities (I) at 373obtained from static fluorescence quenching, conductome-nm was used in the plots of ln(Io /I) versus quencher concen-tric, and potentiometric methods.tration.

Ratios of the intensities of the first and third vibronicRESULTS AND DISCUSSIONSpeaks were measured using a Perkin-Elmer MPF 66 fluores-

cence spectrophotometer to determine the micropolarity ofthe micellar interior and the corresponding solvent systems. The cmc is defined as a break point on a plot of specific

conductivity vs surfactant concentration plots (Fig. 1) . TheThe I1 /I3 ratios were measured directly from the spectra.Employing a computer program based on the mass action effective degree of dissociation of micelle (a) was obtained

from the ratio of the slopes of the lines above and belowmodel as outlined by Moroi et al. (19), we obtained themonomer, counter ion, and micelle concentration in the post- the cmc in the plots of specific conductivity versus concen-

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361MICELLIZATION IN MIXED SOLVENT SYSTEMS

observed. The increase in cmc values with glycol concentra-tion is attributed to the decrease in hydrophobic effect dueto the structure-breaking ability of glycols in water. Also,the decrease in the dielectric constant of the aqueous phasewould cause an increase in repulsion between the ionic headgroups, thus opposing the micellization process. The in-crease in cmc values can also be attributed to the formationof small aggregates, like dimers, trimers, etc. Evidence forthe formation of these aggregates was obtained from thedifferential equivalent conductivity plots.

Molar conductivities (L) for SDS were calculated andfitted to the Onsager equation (22),

L Å Lo 0 (ALo / B)√C , [2]

to determine the limiting molar conductivities at infinite dilu-tion (Lo) in the premicellar region as described in the litera-ture (23, 24). The values of Lo obtained from Eq. [2] areplotted in Fig. 3 as a function of wt % of glycols. Thevalues of Lo decrease with increase in glycol concentration,indicating the association of the surfactant monomer andcounter ions with the glycols. In view of the large size andhydrophobic nature of the DS0 ion, the major contributionof the molar conductivity can be attributed to solvated Na/

ions in solution.The potentiometric determination of degree of dissocia-

tion using a sodium specific ion electrode and a referenceelectrode was detailed in our previous publications (17, 18),and the values obtained by this method are presented inTable 1.FIG. 2. Differential equivalent conductance vs mean concentration.

TABLE 1tration. To differentiate between a cooperative micellizationMicellar Properties of SDS in Various Glycol / Water Mixturesand a more gradual association prior to cmc, the differential

equivalent conductance (DLeq ) , which is given by the fol- aa

lowing equation (20, 21),Wt% cmc/cmc7 Method 1 Method 11 Method 111

0 1.00 0.40 0.38 0.32DLeq Å 1003 K1 0 Ki1

C1 0 Ci1

, [1]

10 DEG 1.01 0.51 0.47 0.4020 DEG 1.09 0.59 0.55 0.50

(where K1 0 Ki1 is the increment in conductivity and C1 0 30 DEG 1.49 0.61 0.61 0.55

40 DEG 2.29 0.69 0.64 0.59Ci1 is the corresponding increment in concentration) is plot-

ted vs mean concentration C Å (C1 / Ci1) /2. 10 TEG 0.93 0.56 0.47 0.40

20 TEG 1.24 0.57 0.53 0.49A cooperative micelle formation is accompanied by a ver-30 TEG 1.74 0.61 0.64 0.57tical decrease over a narrow concentration range compared40 TEG 2.27 0.67 0.69 0.60to a decrease over a wider range of concentration for a non-10 TTEG 0.95 0.55 0.51 0.46cooperative micelle formation (Fig. 2) . The cmc values and20 TTEG 1.27 0.60 0.62 0.53a values obtained from conductivity measurements are pre-30 TTEG 1.66 0.63 0.67 0.58sented in Table 1 along with the values obtained by other40 TTEG 2.15 0.70 0.68 0.60

techniques. In all cases, it is observed that the cmc valuesincrease with increasing glycol concentration and beyond a a Method 1, conductometric; Method 11, potentiometric; Method 111,

model. Estimated error in a is {0.05.certain concentration of glycol, no aggregate formation was

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362 TURNER ET AL.

linearity (Fig. 4) , and the aggregation numbers were deter-mined from the values of the slopes of these plots, and arelisted in Table 2. The aggregation numbers and I1 /I3 ratiosobtained in the present study for SDS in 2 and 6% TTEGsolutions are in agreement with the results of Marangoni etal. (30). The ratios of the intensities of the first and thirdvibronic peaks of the pyrene for the solvent system and inthe presence of micelles are presented in Table 2. The inten-sity ratios of I1 /I3 are sensitive to the microenvironmentaround the probe (28–32). Therefore, this parameter can beused to detect the changes in the microenvironment sensedby the probe in the micelle on addition of glycols. From theexamination of Table 2, it is obvious that the probe in themicelles sensed an increase in the polarity of its microenvi-ronment on addition of glycols. It is known that pyrene issolubilized in the Palisade layer of micelles, near the polarhead groups, where it senses relatively high polar environ-ment (33). When glycol is added to the solution, the surface

FIG. 3. Plot of Ú7 vs of wt % of glycols. area per head group increases, thereby inducing the incorpo-ration of water molecules or glycol molecules intercalatedbetween the head groups. It is also possible that the increase

Micellar Aggregation Numbers and Sizes of surface area per head group and the small micellar sizeforce the probe to be located slightly outward in the micelle,

Micellar aggregation numbers were determined by the thereby sensing higher polarity.static quenching method developed by Turro and Yetka The volume of the individual chain in the micelle (£) ,(25). This method has been successfully applied to the deter- and the critical chain length lc were obtained using Tanford’smination of aggregation numbers of SDS micelles in water equation (34):and in the presence of additives (25–27). Pyrene–hexade-cylpyridinium ion pair is found to be suitable for the determi-

£ Å 27.4 / 26.9n (AL 3) , [6]nation of the aggregation numbers of ionic surfactants in

lc Å 1.5 / 1.265n (AL ) , [7]micellar solutions (28, 29). When the steady-state fluores-cence quenching method is applicable, the ratio of lumines-

where n is the number of carbon atoms in the chain. Assum-cence ratio (Io /I) without and with quencher Q is related toing spherical shape for the micelles, the surface area perthe micelle concentration [M] by the equationhead group (ao) , micellar size, and the critical packing pa-rameter (£ /aolc ) , which is a parameter controlling the micel-lar shape, were calculated (35). The micellar parameters arelnS Io

I D Å [Q][M]

. [3]also presented in Table 2. The surface area per head groupincreases linearly with glycol content (Fig. 5) , and this may

The micelle concentration [M] is given by be attributed to the replacement of water molecules in thesolvation layer of the micelle head group by glycol mole-cules. The decrease in the critical packing parameter indi-

[M] Å S 0 cmcNagg

, [4] cates that the addition of glycols favors the formation ofsmaller spherical micelles (36).

where S is the total surfactant concentration and Nagg is the Thermodynamic Propertiesmicelle aggregation number. Substitution of [M] in Eq. [3]

Free energy of micellization can be treated as a sum ofresulted in the following equation:DsG

o and DHPGo (37). The value of DHPG

o represents thehydrophobic free energy of transfer of the surfactant hydro-carbon chain from the medium to the interior of the micelle.

lnS Io

I D Å Nagg

S 0 cmc[Q]. [5]

The energy associated with the surface contributions con-sisting of electrostatic interactions between the head groupsand counter ions along with all other contributions due toPlots of ln(Io /I) vs [Q] for all the systems depicted good

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363MICELLIZATION IN MIXED SOLVENT SYSTEMS

FIG. 4. Plot of ln(Io /I) vs quencher concentration in binary mixtures of glycols containing 50 mM SDS.

specific interactions is represented in the value of DsGo . By stant can be written in terms of the standard free energy of

micelle formation per monomer (DMG o) as follows:employing the equilibrium model proposed by Ueno et al.(37), we determined the value of DHPG

o as described below:The equilibrium between monomers, counter ions, and

DMG o Å RTF0S1n D ln XMp0

monodispersed micelles can be written as follows (38):

ns0 / (n 0 p)c/ T Mp0 , [8] / ln Xs0 / S1 0 p

nD ln Xc/G . [9]

where s0 , c/ and Mp0 stand for monomer, counterion, andmicelle concentrations, respectively. The equilibrium con- A generally accepted procedure in the literature (10–18)

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364 TURNER ET AL.

TABLE 2Aggregation Numbers, Micellar Parameters, and I1/I3 Ratios

I1/I3

0.05 M SDSSystem % Glycol Nagg ({3) Ra (A) ao

b (A2) v/a01cc Glycol in glycol

DEG 0 62 17.3 60.7 0.34 1.83 1.262 58 16.9 62.1 0.34 1.79 1.246 51 16.2 64.8 0.32 1.80 1.24

10 43 15.3 68.6 0.31 1.77 1.2320 35 14.3 73.5 0.29 1.75 1.2530 27 13.1 80.1 0.26 1.71 1.2840 20 11.9 88.5 0.24 1.71 1.34

TEG 2 53 16.4 64.0 0.33 1.80 1.256 50 16.1 65.2 0.32 1.78 1.26

10 44 15.4 68.0 0.31 1.76 1.2720 36 14.4 72.8 0.29 1.73 1.2830 29 13.4 78.2 0.27 1.71 1.3040 18 11.5 91.7 0.23 1.69 1.36

TTEG 2 52 16.3 64.4 0.33 1.80 1.256 43 15.3 68.6 0.31 1.78 1.27

10 41 15.1 69.7 0.30 1.80 1.2920 30 13.6 77.3 0.27 1.79 1.2930 22 12.3 85.7 0.24 1.77 1.3340 16 11.0 95.4 0.22 1.76 1.43

a Micellar radius calculated assuming spherical micelles.b Surface area per head group.c Critical packing parameter.

and experimental values at higher concentrations can be at-is to neglect the term 0 (1 /n ) ln XMp0 and to substitute lntributed to micelle–micelle interactions.Xcmc for the concentrations of the surfactant monomers and

Various thermodynamic and equilibrium properties of mi-counter ions. This modification results in the followingcellization of SDS such as mean activity coefficient (g{) ,equation:effective degree of dissociation (a) , and free energy of mi-cellization in mixed solvent systems were evaluated. TheDMG o Å (2 0 a)RT ln Xcmc . [10]mean activity coefficient (g{) values were obtained usingthe modified Debye–Huckel equation (22):In the present study, a computer program was developed to

calculate the concentrations of monomers, counter ions andmicelles in the post micellar region for SDS in the concentration

log g{ Å0

√I

1 /√

I, [12]ranging from 0.02 to 0.10 M, as outlined by Moroi (19).

It can also be shown that

where the ionic strength I is given byDsG

o Å 0bRT ln Xc/ , [11]

where b is the counterion binding. Therefore, by evaluating I Å 12

[Cs0 / Cc/ / CMp0] . [13]DMG o and DsG

o values, one can obtain DHPGo values.

The monomer concentrations obtained by the model inthe postmicellar region were compared to the experimentally The values of mean activity coefficients obtained were

compared with the experimentally determined (39) valuesobtained values from specific ion membrane electrode mea-surements (39) for the tetradecylpyridinium bromide plus and presented in Fig. 7 for tetradecylpyridinium bromide

in water. The agreement between the calculated and experi-water system. The calculated and experimental values arerepresented in the Fig. 6. There was excellent agreement mental values illustrates that the concentrations obtained

from theory are reliable and can be used to calculate otherbetween these values. Any deviation between the calculated

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365MICELLIZATION IN MIXED SOLVENT SYSTEMS

FIG. 5. Surface area per head group (a0) of SDS micelles vs glycol composition.

parameters with confidence. The slight differences between measurements. In the latter procedures, it is assumed thatthe concentration of the monomer in the postmicellar regionthe values obtained by these two methods can be attributed

to the fact that micelle concentrations were not included remain constant and equal to the cmc value.To calculate the DHPG 7 values, initially the values ofin the calculations of ionic strength in the experimental

DMG 7 and DsG 7 were evaluated. The procedure employedprocedure.was as follows:The monomer concentrations for 2% and 10% of DEG

system are presented in Fig. 8. The monomer concentration By equating DMG 7(1) Å RT[01/n ln XMp0 / ln Xs0] and

decreases and depends on the glycol concentration. For a DMG 7(11) Å RT(1 0 (p /n)) ln Xc , the values of DMG 7(1) andgiven glycol it can be seen from Fig. 9 that the relative DMG 7(11) were evaluated in the range 0.02–0.10 M SDS.decrease in monomer concentration depends on the number The values were then extrapolated to cmc value by numericalof EO groups present in the glycol. methods. The sum of these quantities yielded DMG 7. The

The effective degree of dissociation was calculated from value of DsG 7 is obtained by changing the sign ofthe slopes of a plot of log m1g{ vs log m2g{ where m1 and DMG 7(11) . These values along with DMG 7 obtained by Eq.m2 represent the monomer and counter ion concentrations. [10] are listed in Table 3. The differences in DMG 7 valuesThe values of a calculated are presented in Table 1. A typical between the two methods reflects in the assumption madeplot for 10% DEG is presented in Fig. 10. The values of a in Eq. [10].are slightly lower than the values obtained from the slope Now the effect of an additive on the free energy of micelli-

zation (40, 41) can be calculated as follows:ratios of conductivity plots or from the counter ion electrode

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366 TURNER ET AL.

FIG. 8. Monomer concentration of SDS in the postmicellar region asFIG. 6. Monomer concentration of tetradecylpyridinium bromide vsa function of DEG composition.total concentration.

DHPG 7(11) Å DHPG 7glycol/H2O 0 DHPG 7H2O, [14] The free energy of micellization is negative and becomesless favorable with increasing glycol concentration in the

DsG 7(11) Å DsG 7glycol/H2O 0 DsG 7H2O. [15] solvent system. The overall free energy change when micelleswere transferred from water to mixed solvent system becomes

The values of DHPG7(11) and DsG7(11) are listed in Table 3. less negative. The decrease in hydrophobic effect is reflected

FIG. 9. Comparison of monomer concentration at a fixed compositionFIG. 7. Activity coefficients vs total concentration of tetradecylpyridin-ium bromide micelles in water of SDS. of glycol.

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367MICELLIZATION IN MIXED SOLVENT SYSTEMS

in the degree of dissociation of the micelles. Removal ofcounter ions from the surface enhances the surface potentialby increasing the electrostatic repulsion between the headgroups which consequently destabilizes the micelles.

The free energy of micellization as a function of tempera-ture was calculated from the dependency of cmc and a ontemperature, using Eq. [11]. The enthalpy and entropy ofmicellization were obtained as follows, and the values arelisted in Table 3.

DMS 7 Å 0 d

dT[DMG 7]p , [16]

DMH 7 Å DMG 7 / TDMS 7. [17]

The values of DMH 7 and DMS 7 should be viewed only asapproximate, since the equation used in the evaluation ofDMG 7 strictly applies when the aggregation number is large(42). However, some general conclusions can be drawnfrom the analysis of the present data. The enthalpy of micelli-zation value becomes increasingly negative and dominatesFIG. 10. Plot of log(m1g{) vs log(m2g{) in aqueous 10% DEG solution.in the micellization process at higher glycol content.

in the increase in the values of DHPG 7(11) with glycol. All SUMMARYthese results lead to the conclusion that glycols act as struc-ture breakers, thereby lowering the hydrophobic effect. The The increase in cmc values and a decrease in aggregation

numbers with the addition of glycols can be attributed toincreasing negative values of DsG7(11) reflects in the increase

TABLE 3Thermodynamic Properties of Micellizationa

Wt% DMG7(1) DHPG7 DMG7 DMG7b DsG7 DHPG7(11) DsG7(11) DMH 7 DMS 7

Water 014.4 023.5 037.9 037.8 14.4 0.0 0.0 01.8 111

2 DEG 012.8 021.1 033.9 034.8 12.8 2.4 01.66 DEG 011.6 020.9 032.5 033.4 11.6 2.6 02.810 DEG 011.1 020.7 031.9 032.3 11.1 2.8 03.3 010.5 7320 DEG 08.8 020.3 029.1 030.0 8.8 3.2 05.6 015.1 5930 DEG 08.1 019.0 027.1 028.1 8.1 4.5 06.3 020.3 2640 DEG 06.1 017.0 023.1 024.9 6.1 6.5 08.3 020.4 15

2 TEG 012.7 021.9 034.6 034.9 12.7 1.7 01.76 TEG 011.4 021.4 032.9 033.5 11.4 2.1 03.010 TEG 010.6 021.0 031.7 031.3 10.6 2.5 03.8 014.6 5620 TEG 010.1 020.0 030.1 030.1 10.1 3.5 04.3 017.7 4230 TEG 09.2 018.9 028.1 027.6 9.2 4.6 05.1 019.8 2640 TEG 06.5 017.9 024.4 025.1 6.5 5.6 07.9 020.4 16

2 TTEG 012.1 020.8 032.9 033.8 12.1 2.8 02.36 TTEG 010.3 020.5 030.8 031.3 10.3 3.0 04.110 TTEG 09.9 020.2 030.2 030.8 9.9 3.3 04.5 011.8 6420 TTEG 07.9 019.4 027.3 028.4 7.9 4.2 06.5 012.9 5230 TTEG 07.6 018.3 025.9 025.9 7.6 5.2 06.8 013.8 4140 TTEG 05.3 016.7 022.1 023.7 5.3 6.8 09.1 014.6 30

a Units for DG and DH are kJ/mol with an error of {0.5 kJ. Units for DS are J/K mol with an error of {5 J.b Calculated using Eq. [10].

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368 TURNER ET AL.

14. Mitchell, D. J., Tiddy, G. J. T., Waring, L., Bostock, T., and MacDon-the decrease in the solvophobic effect due to the structureald, M. P., J. Chem. Soc., Faraday Trans. 79, 975 (1983).breaking abilities of the glycols. The increase in the effective

15. Degiorgio, V., in ‘‘Physics of Amphiphiles, Micelles, Vescicles anddegree of dissociation with glycol content is due to the de- Microemulsions’’ (V. Degiorgio and M. Conti, Eds.) , Vol. 303. Northcrease in the charge density at the micellar surface caused Holland, Amsterdam, 1985.

16. Gharibi, H., Palepu, R., Bloor, D. M., Hall, D. G., and Wyn-Jones, E.,by the increase in the surface area per head group and aLangmuir 8, 782 (1992).decrease in aggregation number. Employing the mass action

17. Callaghan, A., Doyle, R., Alexander, E., and Palepu, R., Langmuir 9,model, the intermicellar properties such as effective degree3422 (1993).

of dissociation, monomer, counter ion concentrations, and 18. Gracie, K., Turner, D., and Palepu, R., Can. J. Chem. 74, 1616 (1996).activity coefficients were evaluated. The hydrophobic and 19. Moroi, Y., J. Colloid Interface Sci. 122, 308 (1988).

20. Backlund, S., Bergenstahl, B., Molander, O., and Warnheim, T. J., J.electrostatic contributions toward Gibbs free energy of mi-Colloid Interface Sci. 131, 393 (1989).cellization were calculated from the intermicellar properties

21. Guveli, D., Colloids Surf. 39, 349 (1989).given by the model. Intermicellar properties are required22. Mortimer, R. G., ‘‘Physical Chemistry.’’ Benjamin/Cummings, New

in the interpretation of kinetic data on monomer/micelle York, 1993.equilibria and solubilization processes. 23. Miyata, I., Takada, A., Yonese, M., and Kishimoto, H., Bull. Chem.

Soc. Jpn. 63, 3502 (1990).24. Sesta, B., D’Aprano, A., Prinli, S., Fillippi, C., and Iammarino, M., J.ACKNOWLEDGMENTS

Phys. Chem. 96, 9545 (1992).25. Turro, N. J., and Yekta, A., J. Am. Chem. Soc. 100, 5951 (1978).This work was supported by Natural Sciences and Engineering Research26. Almgren, M., Swarup, S., J. Colloid Interface Sci. 91, 256 (1983).Council of Canada (NSERC). D.T. acknowledges the grant of NSERC27. Lissi, E. A., Aubin, E., J. Colloid Interface Sci. 105, 1 (1985).Undergraduate Summer Research Award (1994). We acknowledge Dr. G.28. Zana, R., in ‘‘Surfactant Solutions: New Methods of Investigation’’Marangoni of St. Francis Xavier University for his interest in the work.

(R. Zana, Ed.) Marcel Dekker, New York, 1987.29. Almgren, M., and Lofroth, J. E., J. Colloid Interface Sci. 81, 486

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