- Email: [email protected]

186, 215–224 (1997)

CS964643

Volumetric Mixing in Anionic/Nonionic, Cationic/Nonionic, and Anionic/Cationic Mixed Micelles JEFFREY J. LOPATA, SI THIEU,

AND

JOHN F. SCAMEHORN 1

Institute for Applied Surfactant Research and School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, Oklahoma 73019 Received February 16, 1993; accepted October 14, 1996

The volumetric mixing in anionic/nonionic, cationic/nonionic, and anionic/cationic mixed micelles was determined by examining the total surfactant apparent molar volumes ( fV,tot ) at total surfactant concentrations (CT ) much greater than the mixture critical micelle concentration (CMCm ). The mixed surfactant systems investigated were sodium dodecyl sulfate and a polyethoxylated nonylphenol, at 0.15 M NaCl and with no added NaCl; cetyl pyridinium chloride and polyethoxylated nonylphenol, at 0.03 M NaCl; and sodium dodecyl sulfate and dodecyl pyridinium chloride, at 0.15 M NaCl. For all of the mixed surfactant systems investigated, the volumetric mixing in the mixed micelles at CT @ CMCm was ideal, even though the free energies of mixing at the onset of mixed micelle formation (as indicated by the mixture critical micelle concentrations at CT Å CMCm ) exhibited strong negative deviations from ideality. Furthermore, added electrolyte was shown to have virtually no effect on the fV,tot data (nor, consequently, the volumetric mixing) for the anionic/nonionic mixed surfactant system. The results of this study suggest that at CT @ CMCm , the electrostatic interactions do not significantly affect the molar volume of the mixed micelle. Therefore, the micelle hydrophobic core dominates the volumetric mixing in mixed micelles at CT @ CMCm . q 1997 Academic Press

INTRODUCTION

The volumetric properties of surfactants in aqueous solution have been widely studied, to investigate surfactant/solvent interactions and the thermodynamics of micelle formation. Very few studies, however, have investigated the volumetric properties of surfactants in mixed surfactant systems (1–4), even though such studies may yield valuable information about the thermodynamics of mixed micelle formation. Thermodynamic functions of transfer (of a surfactant from one surfactant solution to another) have been used to investigate the volumetric properties of surfactants in anionic/anionic (1) and cationic/nonionic (2) mixed micelles, but the volumetric mixing for these mixed surfactant systems 1

To whom correspondence should be addressed.

was not reported (since these studies examined only one mixed surfactant composition). Total surfactant apparent molar volumes have been successfully used to determine the volumetric mixing in nonionic/nonionic (3), cationic/ cationic (4), and cationic/nonionic (4) mixed micelles. Surprisingly, all of these mixed surfactant systems were shown to have a zero excess volume of mixing in the mixed micelles (3, 4); therefore, the volumetric mixing in these nonionic/ nonionic, cationic/cationic, and cationic/nonionic mixed micelles was ideal. The main objective of this study was to further investigate the effects of the electrostatic interactions on the volumetric mixing in mixed micelles and then to compare these results with the pseudo-phase separation modeling of the mixture critical micelle concentrations (when available), to obtain a more complete picture of the thermodynamics of mixed micelle formation. Several binary mixed surfactant systems were investigated, including anionic/nonionic surfactant mixtures with and without the presence of added electrolyte, cationic/nonionic surfactant mixtures, and anionic/cationic surfactant mixtures. To the best of our knowledge, the volumetric mixing in anionic/nonionic and anionic/cationic mixed micelles has not been previously reported, nor has the effect of added electrolyte on the volumetric mixing in a mixed surfactant system. EXPERIMENTAL

Materials Sodium dodecyl sulfate (SDS) was the anionic surfactant used in this study. The SDS was purchased from Baxter Scientific Products and was manufactured by Mallinckrodt with a manufacturer-reported purity of at least 99.97%. The SDS was purified by recrystallizing once in deionized water and once in reagent-grade alcohol and then drying the crystals for 72 h under a vacuum. Further details of the SDS purification procedure may be found elsewhere (5). Nonylphenol polyethoxylate with an average of 10 ethyl-

215

AID

JCIS 4643

/

6g1c$$$161

01-09-97 03:06:21

0021-9797/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.

coidas

216

LOPATA, THIEU, AND SCAMEHORN

ene oxide groups per molecule [NP(EO)10 , trade name IGEPAL CO-660] was the polydisperse nonionic surfactant used in this study. NP(EO)10 was furnished by GAF Corporation and was used as received. Cetyl pyridinium chloride (CPC) and dodecyl pyridinium chloride (DPC) were the cationic surfactants used in this study. CPC was purchased from HEXCEL Specialty Chemicals and was used as received. DPC was purchased from Pfaltz and Bauer, at an unspecified purity. DPC was purified by recrystallizing four times in a mixture of reagent-grade petroleum ether and reagent-grade alcohol and then drying the crystals for 48 h under a vacuum. Further details of the DPC purification procedure may be found elsewhere (5). Other materials used in this study were deionized (DI) water (ion-exchanged twice and then treated with activated carbon), ACS-grade sodium chloride (Mallinckrodt), 0.01 N hydrochloric acid and 0.01 N sodium hydroxide solutions (Fisher Scientific), and disposable 3-ml plastic hypodermic syringes (Becton Dickinson). Methods For each mixed surfactant system investigated, a solvent was prepared at the desired electrolyte concentration (either 0.15 M NaCl, 0.03 M NaCl, or no added NaCl) using DI water and then the pH of the solvent was adjusted. All of the surfactant solutions were then prepared gravimetrically, or on a molality basis, using the pH adjusted solvent. Note that even though the surfactant solutions were accurately prepared on a molality basis, the apparent molar volumes were reported as a function of the total surfactant molarity (calculated using the measured solution densities), to directly compare the results of this study with the mixture critical micelle concentration data in the literature (which were reported in molarity concentration units). The densities of the surfactant solutions were measured at 30.00 ( {0.05) 7C using an Anton Paar digital density meter (Model DMA 60 processing unit, Model DMA 602 external measuring cell) and a NESLAB EXACAL EX-220 water bath with a NESLAB Model FTC-350A flow-through air cooler. The density meter was calibrated at 30.007C using air and DI water (6), and then the solvent and surfactant solution densities were measured. Paar reports an accuracy of {1.5 1 10 06 g/cm3 in the measured densities (6); however, the actual error was approximately {1.5 1 10 05 g/cm3 (5), due to the fluctuations of the water bath temperature. The total surfactant apparent molar volumes were calculated using the equation (3) fV,tot Å

(1000)( r0 0 r ) (Q1 M1 / Q2 M2 ) / , r mT ( r0 )( r )

[1]

where fV,tot Å total surfactant apparent molar volume (cm3 /

AID

JCIS 4643

/

6g1c$$$162

01-09-97 03:06:21

mol); r, r0 Å measured densities of the mixed surfactant solution and solvent, respectively (g/cm3 ); mT Å total surfactant molality of the solution (total surfactant mol/kg solvent); Q1 , Q2 Å surfactant-only based mole fractions in the mixed surfactant system, for surfactants 1 and 2, respectively; M1 , M2 Å molecular weights of surfactants 1 and 2, respectively (g surfactant/mol surfactant). THEORY

Onset of Mixed Micelle Formation (at CMCm ) The formation of anionic/nonionic, cationic/nonionic, or anionic/cationic mixed micelles can be described using regular solution theory (7). The regular solution theory pseudophase separation model for mixed micelle formation, Eqs. [2] – [5], predicts the lowest total surfactant concentration at which the first mixed surfactant micelle forms in the bulk solution (CMCm ), as a function of the mixed surfactant composition (note that at the onset of mixed micelle formation, Y1 Å Q1 and Y2 Å Q2 ): Y1CMCm Å X1CMC1 exp(X 22Wmic /RT ),

[2]

Y2CMCm Å X2CMC2 exp(X 21Wmic /RT ),

[3]

Y1 / Y2 Å 1.0,

[4]

X1 / X2 Å 1.0,

[5]

where Y1 , Y2 Å surfactant-only based monomer mole fractions for surfactants 1 and 2, respectively; CMCm Å mixture critical micelle concentration, i.e., the lowest total surfactant concentration at which the first mixed micelle forms (total mmol surfactant/liter); X1 , X2 Å surfactant-only based mixed micelle mole fractions for surfactants 1 and 2, respectively; CMC1 , CMC2 Å pure surfactant critical micelle concentrations, i.e., the lowest surfactant concentration at which the first micelle forms for surfactants 1 and 2, respectively ( mmol surfactant 1 or surfactant 2/liter); Wmic /RT Å dimensionless regular solution theory interaction parameter for mixed micelle formation. It should be noted that the regular solution theory pseudo-phase separation model for mixed micelle formation (Eqs. [2] – [5]) describes the thermodynamics (i.e., the free energy of mixing) only at the onset of mixed micelle formation and that Eqs. [2] and [3] are not necessarily valid at total surfactant concentrations greater than the CMCm . Before Eqs. [2] – [5] could be used to predict mixture critical micelle concentrations (CMCm ), the dimensionless regular solution theory interaction parameter (Wmic /RT ) must first be determined from the experimental data. The ‘‘best-fit’’ regular solution theory interaction parameter was determined using the pure surfactant critical micelle concentrations (CMC1 and CMC2 , measured under the same experi-

coidas

217

VOLUMETRIC MIXING IN MIXED MICELLES

mental conditions as the CMCm data) and performing a leastsquares fit on the measured CMCm data. Once the interaction parameter for mixed micelle formation (Wmic /RT ) was determined, CMCm values at any mixed surfactant composition (Y1 Å Q1 and Y2 Å Q2 , at the onset of mixed micelle formation) could be predicted using Eqs. [2] – [5]. Total Surfactant Apparent Molar Volumes in the Mixed Micelle Pseudophase ( fV,tot,mic ) Even though it is currently impossible to designate which part of the total volume of a surfactant solution should be attributed to the surfactant solute, the volume of the solution occupied by the solvent can be arbitrarily defined as being equal to the volume occupied by the pure solvent (8). At a specific total surfactant concentration, the total surfactant apparent molar volume ( fV,tot ) is therefore defined in the following equation as the total volume of the surfactant solution minus the volume of the pure solvent, per unit mole of surfactant solute:

fV,tot

total solution volume 0 volume of pure solvent Å . total moles surfactant solute

[6]

Thus, the total surfactant apparent molar volumes can be viewed as the volume of the surfactant solution attributed to the presence of the surfactant solute, per unit mole surfactant solute. In most cases, the apparent molar volume of a solute in solution is completely defined by an equation similar to Eq. [6]; however, surfactant molecules in solution are capable of existing in both monomer (unaggregated) and micelle (aggregated) forms, depending on the total surfactant concentration. The environment of the surfactant molecules present in the micelle pseudophase is very different from the environment of the surfactant molecules present in the monomer pseudophase. Therefore, for mixed surfactant solutions at total surfactant concentrations equal to, or infinitesimally greater than, the onset of mixed micelle formation (CT à CMCm ), the total surfactant apparent molar volume ( fV,tot ) defined in Eq. [6] can be partitioned into contributions from the monomer and micelle pseudophases, resulting in fV,tot Å

(CT 0 CMCm ) fV,tot,mic / (CMCm ) fV,tot,mon , CT

[7]

where CT Å total surfactant concentration (total mmol surfactant/liter); fV,tot,mic Å total surfactant apparent molar volume in the mixed micelle pseudophase (cm3 /mol); fV,tot,mon Å total surfactant apparent molar volume in the mixed monomer pseudophase (cm3 /mol). Kale and Zana (9) performed

AID

JCIS 4643

/

6g1c$$$163

a similar partitioning of fV for a pure component surfactant solution. It should be noted that Eq. [7] is valid at total surfactant concentrations equal to, or infinitesimally greater than, the onset of mixed micelle formation (CT à CMCm ) and that it is valid at total surfactant concentrations greater than the onset of mixed micelle formation (CT ú CMCm ) only if the thermodynamic model used to describe mixed micelle formation adequately predicts the total surfactant monomer concentration (represented by CMCm in Eq. [7]) at CT ú CMCm . In this study, we were solely interested in determining the total surfactant apparent molar volumes in the mixed micelle pseudophase ( fV,tot,mic ), to determine the volumetric mixing in the mixed micelles. Theoretically, the fV,tot,mic values could be directly determined using Eq. [7], the fV,tot and CT experimental values, and a mixed micelle formation model that accurately describes the total surfactant monomer concentration (CMCm in Eq. [7]) at CT à CMCm or CT ú CMCm . The fV,tot,mic values in this study, however, could not be accurately determined at the onset of mixed micelle formation (CT à CMCm ) using Eq. [7], due to the fact that the total surfactant apparent molar volumes ( fV,tot ) could not be accurately measured around the CMCm (5). Furthermore, the fV,tot,mic values could not be accurately determined at CT ú CMCm using Eq. [7], due to the experimental inaccuracies described above and the unknown accuracy of the pseudo-phase separation model for mixed micelle formation (Eqs. [2] – [5]) in predicting the total surfactant monomer concentration (CMCm in Eq. [7]) at CT ú CMCm . In light of the above discussion, the fV,tot,mic values in this study were determined by examining the total surfactant apparent molar volumes ( fV,tot ) at total surfactant concentrations much greater than the mixture critical micelle concentration (CT @ CMCm ). At CT @ CMCm , it could be safely assumed that practically all of the surfactant in the system was present in micellar form and that the volumetric contributions from the monomer pseudophase ( fV,tot,mon ) in Eq. [7] were negligible. Therefore, at CT @ CMCm , the measured total surfactant apparent molar volumes ( fV,tot ) were approximately equal to the total surfactant apparent molar volumes in the mixed micelle pseudophase ( fV,tot,mic ) and the mixed micelle surfactant-only based mole fractions (X1 and X2 ) were approximately equal to the surfactant-only based mole fractions in the mixed surfactant system (Q1 and Q2 , respectively), resulting in

01-09-97 03:06:21

fV,tot É fV,tot,mic ,

X 1 É Q1

and

X2 É Q2 .

[8] [9]

It is important to note that even though the fV,tot,mic values in this study could not be directly determined at CT à CMCm or CT ú CMCm using Eq. [7], determining the fV,tot,mic

coidas

218

LOPATA, THIEU, AND SCAMEHORN

values at CT @ CMCm has the distinct advantage that the fV,tot,mic values (and, hence, the volumetric mixing in the mixed micelles) were determined independently of the thermodynamic model used to describe mixed micelle formation. Volumetric Mixing in Mixed Micelles (at CT @ CMCm ) Once the total surfactant apparent molar volumes in the mixed micelle pseudophase ( fV,tot,mic ) are known at various mixed micelle compositions (X1 and X2 ), determining the volumetric mixing in the mixed micelles for each mixed surfactant system is a relatively simple matter. Ideal solution theory was used throughout this study to predict the volumetric mixing in the mixed micelles, to quantify any deviations from ideal mixing by comparison with experimental data. According to ideal solution theory, when micelles of surfactant 1 and micelles of surfactant 2 form ideal mixed micelles (i.e., assuming a zero excess volume of mixing in the mixed micelles), the total surfactant apparent molar volume in the mixed micelle pseudophase ( fV,tot,mic ) can be described by fV,tot,mic Å X1fV,Pure 1 / X2fV,Pure 2

[10]

where fV,tot,mic Å total surfactant apparent molar volume in the mixed micelle pseudophase, i.e., fV,tot at CT @ CMCm (cm3 /mol); fV,Pure 1 , fV,Pure 2 Å pure component surfactant apparent molar volumes in the pure surfactant micelles for surfactants 1 and 2, respectively, i.e., fV at CT @ CMC (cm3 /mol). Equations [5] and [8] – [10] can be combined to obtain fV,tot É fV,tot,mic É ( fV,Pure 1 0 fV,Pure 2 )Q1

[11]

/ fV,Pure 2 ,

which is valid only at CT @ CMCm . In this work, Eq. [11] was used to make a priori ideal solution theory predictions of the measured total surfactant apparent molar volumes ( fV,tot ) at various surfactant-only based mole fractions in the mixed surfactant system (Q1 ), for surfactant mixtures at CT @ CMCm . The fV,tot-versus-Q1 predictions made using Eq. [11] are linear for each mixed surfactant system, since fV,Pure 1 and fV,Pure 2 are constants at surfactant concentrations much greater than the pure component CMCs. By predicting the fV,tot data at CT @ CMCm using Eq. [11], the volumetric mixing in the mixed micelles was predicted assuming a zero excess volume of mixing. Determining the Volumetric Mixing in Mixed Micelles (at CT @ CMCm) f rom the Experimental Data Described below is the procedure used to determine the volumetric mixing in the mixed micelles (at CT @ CMCm ) from the experimental data. All of the total surfactant appar-

AID

JCIS 4643

/

6g1c$$$163

01-09-97 03:06:21

ent molar volumes ( fV,tot ) for each mixed surfactant system were first calculated using Eq. [1], the surfactant molecular weights (M1 and M2 ), and the measured experimental values ( r, r0 , mT , Q1 , and Q2 ). The fV,tot-versus-CT data [at various constant surfactant-only based mole fractions in the mixed surfactant system (Q1 )] were then plotted for each mixed surfactant system, excluding any fV,tot data containing an estimated error greater than {10% (5). These fV,tot-versusCT plots were then visually examined for each mixed surfactant system, to determine the lowest total surfactant concentration at which the fV,tot-versus-CT data reached a plateau (or leveled off) for all of the surfactant-only based mole fractions in the mixed surfactant system (0.0 £ Q1 £ 1.0). It was assumed that these lowest total surfactant concentrations for each mixed surfactant system corresponded to a point at which practically all of the surfactant in the system was present in micellar form and that the volumetric contributions from the monomer pseudophase ( fV,tot,mon in Eq. [7]) were negligible (i.e., CT @ CMCm and Eqs. [8] and [9] were valid). The fV,tot data between the lowest total surfactant concentration at which CT @ CMCm (determined above) and the highest measured total surfactant concentration were then averaged for each constant surfactant-only based mole fraction in the mixed surfactant system (Q1 ). The averaged fV,tot data (at CT @ CMCm ) were then plotted against the various surfactant-only based mole fractions in the mixed surfactant system (0.0 £ Q1 £ 1.0), along with the a priori ideal solution theory predictions of the volumetric mixing in the mixed micelles at CT @ CMCm (made using Eq. [11]). The fV,Pure 1 and fV,Pure 2 terms in Eq. [11] were determined from the averaged fV,tot data points at Q1 Å 1.0 and Q1 Å 0.0, respectively. The averaged fV,tot-versus-Q1 data (at CT @ CMCm ) were then compared with the ideal solution theory predictions (Eq. [11]), to quantify any deviations from ideality. RESULTS

Anionic/Nonionic Mixed Surfactant System: With and Without Added Electrolyte Figure 1 illustrates the CMCm data from Ref. (10) and the regular solution theory CMCm predictions (made using Eqs. [2] – [5]), for the SDS/NP(EO)10 mixed surfactant system at 0.15 M NaCl and 307C. As can be seen in Fig. 1, regular solution theory provides an excellent description of the CMCm data, and strong negative deviations from ideality are observed (Wmic /RT Å 01.86) for the formation of the first anionic/nonionic mixed micelle in the bulk solution (at CT Å CMCm ). The total surfactant apparent molar volumes ( fV,tot ) for the SDS/NP(EO)10 mixed surfactant system at 0.15 M NaCl

coidas

VOLUMETRIC MIXING IN MIXED MICELLES

219

FIG. 1. Regular mixing theory fit of CMCm data for SDS/NP(EO)10 mixtures at 0.15 M NaCl [data from (10)].

and with no added NaCl are shown in Figs. 2 and 3, respectively, where the fV,tot data are plotted as a function of the total surfactant concentration (CT ), at various constant SDS/ NP(EO)10 mole ratios. The fV,tot data in Figs. 2 and 3 were calculated using Eq. [1] and were known to be inaccurate at very low total surfactant concentrations, due to the nature of Eq. [1] and the effects of the water bath temperature fluctuations on the measured densities (5). Therefore, the fV,tot data at low total surfactant concentrations containing an estimated error of ú10% (5) were excluded from Figs. 2 and 3. As can be seen by comparing Figs. 1 and 2, the fV,tot data (in Fig. 2) could not be accurately determined around the CMCm for any of the SDS/NP(EO)10 mole ratios

FIG. 2. Total surfactant apparent molar volume versus total surfactant concentration for SDS/NP(EO)10 mixtures at 0.15 M NaCl.

AID

JCIS 4643

/

6g1c$$$164

01-09-97 03:06:21

FIG. 3. Total surfactant apparent molar volume versus total surfactant concentration for SDS/NP(EO)10 mixtures with no added NaCl.

in the anionic/nonionic mixed surfactant system (at 0.15 M NaCl). To determine the volumetric mixing in the mixed micelles, the total surfactant apparent molar volumes ( fV,tot ) in Figs. 2 and 3 were investigated at CT @ CMCm (i.e., when most of the surfactant in the system was present in micellar form). The lowest total surfactant concentrations at which the fV,tot data reached a plateau (or leveled off) for all of the SDS/ NP(EO)10 mole ratios in Figs. 2 and 3 were approximately 10,000 and 55,000 mmol/liter, respectively. It was assumed that these concentrations represented the lowest total surfactant concentrations at which CT @ CMCm for the SDS/ NP(EO)10 mixed surfactant system at 0.15 M NaCl and with no added NaCl, respectively. For each constant SDS/ NP(EO)10 mole ratio in Figs. 2 and 3, the fV,tot data were then averaged at total surfactant concentrations between 10,000 and 100,000 mmol/liter and between 55,000 and 100,000 mmol/liter, respectively. These averaged fV,tot data points at CT @ CMCm represent the total surfactant apparent molar volumes in the mixed micelle pseudophase ( fV,tot,mic ) at various mixed micelle mole fractions (Eqs. [8] and [9]). The averaged fV,tot data points (at CT @ CMCm ) at their corresponding NP(EO)10 mole fractions for the SDS/ NP(EO)10 mixed surfactant system at 0.15 M NaCl and with no added NaCl are shown in Fig. 4, along with the a priori ideal solution theory fV,tot predictions at CT @ CMCm (made using Eq. [11]). The a priori ideal solution theory fV,tot predictions at CT @ CMCm for each electrolyte concentration were made by drawing a line between the pure component surfactant apparent molar volumes in Fig. 4 ( fV,tot at

coidas

220

LOPATA, THIEU, AND SCAMEHORN

FIG. 5. Regular mixing theory fit of CMCm data for CPC/NP(EO)10 mixtures at 0.03 M NaCl [data from (11)].

FIG. 4. Total surfactant apparent molar volume versus NP(EO)10 mole fraction for SDS/NP(EO)10 mixtures at 0.15 M NaCl and with no added NaCl (CT @ CMCm ).

QNP ( EO ) 10 Å 0.0 and fV,tot at QNP ( EO ) 10 Å 1.0). As can be seen in Fig. 4, ideal solution theory provides an excellent description of the total surfactant apparent molar volumes in SDS/NP(EO)10 mixed micelles at CT @ CMCm : therefore, a zero excess volume of mixing was determined for the anionic/nonionic mixed surfactant system investigated in this study. In Fig. 4, it can clearly be seen that added electrolyte had virtually no effect on the fV,tot data (nor consequently, the volumetric mixing) for the SDS/NP(EO)10 mixed surfactant system at CT @ CMCm .

mixed surfactant system (described above). As can be seen by comparing Figs. 5 and 6, the fV,tot data (in Fig. 6) could not be accurately determined around the CMCm for any of the CPC/NP(EO)10 mole ratios in the cationic/nonionic mixed surfactant system. For each constant CPC/NP(EO)10 mole ratio in Fig. 6, the fV,tot data were averaged at total surfactant concentrations between 50,000 and 300,000 mmol/liter. The averaged fV,tot data points (at CT @ CMCm ) at their corresponding NP(EO)10 mole fractions are shown in Fig. 7, along with the a priori ideal solution theory fV,tot predictions at CT @ CMCm (made using Eq. [11]). As can be seen in Fig. 7, ideal solution theory provides an excellent description of the total surfactant apparent molar volumes in CPC/ NP(EO)10 mixed micelles at CT @ CMCm : therefore, a zero

Cationic/Nonionic Mixed Surfactant System Figure 5 illustrates the CMCm data from Ref. (11) and the regular solution theory CMCm predictions (made using Eqs. [2] – [5]), for the CPC/NP(EO)10 mixed surfactant system at 0.03 M NaCl and 307C. As can be seen in Fig. 5, regular solution theory provides an excellent description of the CMCm data, and strong negative deviations from ideality are observed (Wmic /RT Å 01.28) for the formation of the first cationic/nonionic mixed micelle in the bulk solution (at CT Å CMCm ). The total surfactant apparent molar volumes ( fV,tot ) for the CPC/NP(EO)10 mixed surfactant system at 0.03 M NaCl and 307C (i.e., the same experimental conditions as the CMCm data in Fig. 5) are shown in Fig. 6, where the fV,tot data are plotted as a function of the total surfactant concentration (CT ) at various constant CPC/NP(EO)10 mole ratios. The discussion of the fV,tot data and volumetric mixing results for the cationic/nonionic mixed surfactant system is analogous to that of the results for the anionic/nonionic

AID

JCIS 4643

/

6g1c$$$164

01-09-97 03:06:21

FIG. 6. Total surfactant apparent molar volume versus total surfactant concentration for CPC/NP(EO)10 mixtures at 0.03 M NaCl.

coidas

VOLUMETRIC MIXING IN MIXED MICELLES

FIG. 7. Total surfactant apparent molar volume versus NP(EO)10 mole fraction for CPC/NP(EO)10 mixtures at 0.03 M NaCl (CT @ CMCm ).

excess volume of mixing was determined for the cationic/ nonionic mixed surfactant system investigated in this study. Anionic/Cationic Mixed Surfactant System The volumetric mixing in SDS/DPC mixed micelles was investigated at 0.15 M NaCl, pH 8.4, and 307C. Since anionic/cationic surfactant mixtures readily precipitate from solution, the fV,tot experiments for the SDS/DPC mixed surfactant system were carefully designed to avoid the formation of precipitate. The SDS/DPC precipitation phase boundary at 0.15 M NaCl, pH 8.4, and 307C is illustrated in Fig. 8 (12). As can be seen in Fig. 8, surfactant precipitation occurs at most SDS and DPC concentrations. The SDS and DPC concentrations at which the fV,tot data were measured are illustrated by dashed lines in Fig. 8, where each dashed line is at a constant SDS/DPC mole ratio. In Fig. 8, the fV,tot data measured at a 0.85 SDS/0.15 DPC mole ratio lie just inside of the precipitation phase boundary reported by Stellner et al. (12); however, the precipitation phase boundary predictions along the ‘‘SDS-rich branch’’ (illustrated in Fig. 8) were inaccurate at high SDS and high DPC concentrations, due to the formation of coacervate (12). All of the SDS/DPC mixture fV,tot data reported in this study were visually clear of both coacervate and precipitate. Even though the SDS/DPC mixture critical micelle concentrations could not be measured (due to surfactant precipitation), a dimensionless regular solution theory interaction parameter for SDS/DPC mixed micelle formation (Wmic / RT Å 08.62) was determined from the precipitation phase boundary modeling presented in Stellner et al. (12). Figure 9 illustrates the measured pure SDS and DPC critical micelle

AID

JCIS 4643

/

6g1c$$$164

01-09-97 03:06:21

221

FIG. 8. SDS/DPC precipitation phase boundary, and SDS and DPC concentrations at which fV,tot experiments conducted [phase boundary from (12)].

concentrations and the regular solution theory CMCm predictions (made using Wmic /RT Å 08.62 and Eqs. [2] – [5]), for the SDS/DPC mixed surfactant system at 0.15 M NaCl, pH 8.4, and 307C. As can be seen in Fig. 9, the hypothetical SDS/DPC mixture critical micelle concentrations exhibit very strong negative deviations from ideality (Wmic /RT Å 08.62), as expected. The total surfactant apparent molar volumes ( fV,tot ) for the SDS/DPC mixed surfactant system at 0.15 M NaCl, pH 8.4, and 307C (i.e., the same experimental conditions as the SDS/DPC precipitation phase boundary in Fig. 8 and the SDS/DPC CMCm data in Fig. 9) are shown in Fig. 10, where the fV,tot data are plotted as a function of the total surfactant concentration (CT ), at various constant SDS/DPC mole ratios. Once again, the discussion of the fV,tot data and volu-

FIG. 9. Regular mixing theory predictions of CMCm for SDS/DPC mixtures at 0.15 M NaCl [data from (12)].

coidas

222

LOPATA, THIEU, AND SCAMEHORN

FIG. 10. Total surfactant apparent molar volume versus total surfactant concentration for SDS/DPC mixtures at 0.15 M NaCl.

metric mixing results for the anionic/cationic mixed surfactant system is analogous to that of the results for the anionic/ nonionic mixed surfactant system. As can be seen by comparing Figs. 9 and 10, the fV,tot data (in Fig. 10) could not be accurately determined around the CMCm for any of the SDS/DPC mole ratios in the anionic/cationic mixed surfactant system. For each constant SDS/DPC mole ratio in Fig. 10, the fV,tot data were averaged at total surfactant concentrations between 55,000 and 100,000 mmol/liter, regardless of the fact that the fV,tot data in Fig. 10 never quite reached a plateau at 55,000 mmol/liter (nor even 100,000 mmol/liter). This phenomenon was attributed to strong electrostatic interactions between the SDS and DPC surfactant molecules in the monomer pseudophase. The averaged fV,tot data points (at CT @ CMCm ) at their corresponding DPC mole fractions are shown in Fig. 11, along with the a priori ideal solution theory fV,tot predictions at CT @ CMCm (made using Eq. [11]). As can be seen in Fig. 11, ideal solution theory provides an excellent description of the total surfactant apparent molar volumes in SDS/DPC mixed micelles at CT @ CMCm ; therefore, a zero excess volume of mixing was determined for the anionic/cationic mixed surfactant system investigated in this study. This result was surprising, especially since anionic/cationic surfactant mixtures usually exhibit very strong negative deviations from ideality.

accurately described by ideal solution theory; therefore, the volumetric mixing in the anionic/nonionic, cationic/nonionic, and anionic/cationic mixed micelles at CT @ CMCm was ideal. By comparing the results of the anionic/nonionic mixed surfactant system at two different electrolyte concentrations, added electrolyte was shown to have virtually no effect on the total surfactant apparent molar volumes at CT @ CMCm and, consequently, no effect on the volumetric mixing in the anionic/nonionic mixed micelles (at CT @ CMCm ). Unfortunately, for all of the mixed surfactant systems investigated in this study, the total surfactant apparent molar volumes (and, hence, the volumetric mixing in the mixed micelles) could not be accurately determined at the onset of mixed micelle formation (CT Å CMCm ), to directly compare the volumetric mixing results with the regular solution theory pseudophase separation modeling of the mixture critical micelle concentration data (at CT Å CMCm ). Determining the volumetric mixing in mixed micelles at CT @ CMCm does, however, have the distinct advantage that the volumetric mixing results were determined independently of the thermodynamic model used to describe mixed micelle formation. The fact that the volumetric mixing in mixed micelles (at CT @ CMCm ) is independent of the charges on the surfactant head groups is surprising, especially since the free energies of mixing at the onset of mixed micelle formation (as indicated by the mixture critical micelle concentrations at CT Å CMCm ) for these mixed surfactant systems exhibited strong negative deviations from ideality, and the enthalpies and entropies of mixing on anionic/nonionic and cationic/nonionic mixed micelle formation have been shown to generally be nonideal (13). Furthermore, added electrolyte usually has

DISCUSSION

For all of the mixed surfactant systems investigated in this study, the total surfactant apparent molar volumes (at CT @ CMCm ) at various mixed micelle compositions were

AID

JCIS 4643

/

6g1c$$$164

01-09-97 03:06:21

FIG. 11. Total surfactant apparent molar volume versus DPC mole fraction for SDS/DPC mixtures at 0.15 M NaCl (CT @ CMCm ).

coidas

VOLUMETRIC MIXING IN MIXED MICELLES

a very strong effect on the free energy changes on mixed micelle formation involving ionic surfactants, yet was shown to have virtually no effect on the volumetric mixing in the anionic/nonionic mixed micelles (at CT @ CMCm ) investigated in this study. The discrepancies between the volumetric mixing results presented in this study (at CT @ CMCm ) and the corresponding thermodynamic data on mixed micelle formation (at CT Å CMCm ) can possibly be explained by the fact that ‘‘a system exhibiting no volume change on mixing need not conform to all the equations for ideal solution behavior’’ (14). The results of this study suggest that the electrostatic interactions in mixed micelles (at CT @ CMCm ) do not significantly affect the molar volume of the mixed micelle, even though the free energy, enthalpy, and entropy of mixing on mixed micelle formation can be strongly affected by surfactant head group interactions and added electrolyte. Therefore, the micelle hydrophobic core dominates the volumetric mixing in mixed micelles at CT @ CMCm .

CT @ CMCm

DI DPC M1 , M2

mT NP(EO)10

Q1 , Q2

APPENDIX: NOMENCLATURE

SDS CMC CMC1 , CMC2

CMCm

CPC CT CT Å CMCm

CT à CMCm

CT ú CMCm

AID

JCIS 4643

critical micelle concentration ( mmol surfactant/liter) pure surfactant critical micelle concentrations, i.e., the lowest surfactant concentration at which the first micelle forms for surfactants 1 and 2, respectively ( mmol surfactant 1 or 2/liter) mixture critical micelle concentration, i.e., the lowest total surfactant concentration at which the first mixed micelle forms (total mmol surfactant/liter) cetyl pyridinium chloride (cationic surfactant) total surfactant concentration (total mmol surfactant/liter) total surfactant concentration equal to the onset of mixed micelle formation; i.e., one (the first) mixed micelle exists and the rest of the surfactant is present in the monomer pseudophase total surfactant concentration equal to, or infinitesimally greater than, the onset of mixed micelle formation; i.e., one or several mixed micelles exist and the rest of the surfactant is present in the monomer pseudophase total surfactant concentration greater than the onset of mixed micelle formation; i.e., the surfactant in the system exists in both the monomer and micelle pseudophases

/

6g1c$$$164

01-09-97 03:06:21

Wmic /RT

X1 , X2

Y1 , Y2

r r0 fV fV,Pure 1 , fV,Pure 2

fV,tot fV,tot,mic

fV,tot,mon

223

total surfactant concentration much greater than the onset of mixed micelle formation; i.e., practically all of the surfactant in the system is present in mixed micelles deionized (water), ion-exchanged twice and then treated with activated carbon dodecyl pyridinium chloride (cationic surfactant) molecular weights of surfactants 1 and 2, respectively (g surfactant/mol surfactant) total surfactant molality of the solution (total surfactant mol/kg solvent) nonylphenol polyethoxylate with an average of 10 ethylene oxide groups per molecule; trade name IGEPAL CO-660 (nonionic surfactant) surfactant-only based mole fractions in the mixed surfactant system, for surfactants 1 and 2, respectively sodium dodecyl sulfate (anionic surfactant) dimensionless regular solution theory interaction parameter for mixed micelle formation surfactant-only based mixed micelle mole fractions for surfactants 1 and 2, respectively surfactant-only based monomer mole fractions for surfactants 1 and 2, respectively density of the surfactant solution (g/cm3 ) density of the solvent (g/cm3 ) pure surfactant apparent molar volume (cm3 /mol) pure component surfactant apparent molar volumes in the pure surfactant micelles for surfactants 1 and 2, respectively, i.e., fV at CT @ CMC (cm3 /mol) total surfactant apparent molar volume (cm3 /mol) total surfactant apparent molar volume in the mixed micelle pseudophase, i.e., fV,tot at CT @ CMCm (cm3 /mol) total surfactant apparent molar volume in the mixed monomer pseudophase (cm3 / mol) ACKNOWLEDGMENTS

Financial support for this work was provided by National Science Foundation Grant CBT 8814147 and an Applied Research Grant from the Okla-

coidas

224

LOPATA, THIEU, AND SCAMEHORN

homa Center for the Advancement of Science and Technology. In addition, support was received from the industrial sponsors of the Institute for Applied Surfactant Research including Akzo Nobel, Amway, Amoco, Colgate–Palmolive, Dow, Dowelanco, DuPont, Henkel, ICI, Kerr–McGee Lever, Reckitt and Colman, Lubrizol, Nikko, Phillips Petroleum, Pilot Chemical, Shell, Sun, and Witco. Dr. Scamehorn holds the Asahi Glass Chair in chemical engineering at the University of Oklahoma.

REFERENCES 1. Perron, G., Lisi, R. D., Davidson, I., Genereux, S., and Desnoyers, J. E., J. Colloid Interface Sci. 79, 432 (1981). 2. Hetu, D., and Desnoyers, J. E., Can. J. Chem. 66, 767 (1988). 3. Funasaki, N., and Hada, S., J. Phys. Chem. 86, 2504 (1982). 4. Nishikido, N., Imura, Y., Kobayashi, H., and Tanaka, M., J. Colloid Interface Sci. 91, 125 (1983). 5. Lopata, J. J., Ph.D. dissertation, University of Oklahoma, 1992.

AID

JCIS 4643

/

6g1c$$$164

01-09-97 03:06:21

6. ‘‘Parr Digital Density Meter Manual, Anton Paar, K. G., A-8054, Graz, Austria.’’ 7. Scamehorn, J. F., in ‘‘Phenomena in Mixed Surfactant Systems’’ (J. F. Scamehorn, Ed.), ACS Symposium Series, Vol. 311, p. 1. Am. Chem. Soc., Washington, DC, 1986. 8. Klotz, I. M., and Rosenberg, R. M., ‘‘Chemical Thermodynamics,’’ 4th ed., Chapter 18. Benjamin-Cummings, Redwood City, CA, 1986. 9. Kale, K. M., and Zana, R., J. Colloid Interface Sci. 61, 312 (1977). 10. Harwell, J. H., Roberts, B. L., and Scamehorn, J. F., Colloids Surf. 32, 1 (1988). 11. Nguyen, C. M., Rathman, J. F., and Scamehorn, J. F., J. Colloid Interface Sci. 112, 438 (1986). 12. Stellner, K. L., Amante, J. C., Scamehorn, J. F., and Harwell, J. H., J. Colloid Interface Sci. 123, 186 (1988). 13. Rathman, J. F., and Scamehorn, J. F., Langmuir 4, 474 (1988). 14. Balzhiser, R. E., Samuels, M. R., and Eliassen, J. D., ‘‘Chemical Engineering Thermodynamics: The Study of Energy, Entropy, and Equilibrium,’’ Ch. 9, p. 380. Prentice–Hall, Englewood Cliffs, NJ, 1972.

coidas