nonionic surfactant adsorption on alumina

nonionic surfactant adsorption on alumina

Journal of Colloid and Interface Science 342 (2010) 415–426 Contents lists available at ScienceDirect Journal of Colloid and Interface Science www.e...

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Journal of Colloid and Interface Science 342 (2010) 415–426

Contents lists available at ScienceDirect

Journal of Colloid and Interface Science www.elsevier.com/locate/jcis

Thermodynamics of mixed anionic/nonionic surfactant adsorption on alumina Jeffrey J. Lopata, Kendall M. Werts, John F. Scamehorn, Jeffrey H. Harwell, Brian P. Grady * Institute for Applied Surfactant Research and School of Chemical, Biological and Materials Engineering, University of Oklahoma, Sarkey’s Energy Center Room T-335, Norman, OK 73019, USA

a r t i c l e

i n f o

Article history: Received 29 September 2009 Accepted 28 October 2009 Available online 31 October 2009 Keywords: Surfactant adsorption Regular solution theory Mixed micelle Surfactant Surfactant mixtures

a b s t r a c t The adsorption of sodium dodecyl sulfate and a polyethoxylated nonylphenol, and well defined mixtures thereof, was measured on c-alumina. A pseudo-phase separation model to describe mixed anionic/nonionic admicelle (adsorbed surfactant aggregate) formation was developed, analogous to the pseudophase separation model frequently used to describe mixed micelle formation. In this model, regular solution theory was used to describe the anionic/nonionic surfactant interactions in the mixed admicelle and a patch-wise adsorption model was used to describe surfactant adsorption on a heterogeneous solid surface. The formation of mixed anionic/nonionic admicelles in the absence of micelles was accurately described by regular solution theory; mixed admicelle formation exhibited stronger negative deviations from ideality than mixed micelle formation. An adequate description of mixed anionic/nonionic admicelle formation in the presence of mixed micelles was obtained through a simultaneous solution of the pseudo-phase separation models for mixed admicelle and mixed micelle formation, and the appropriate mass balance equations. Anionic/nonionic mixed adsorption in the presence of mixed micelles was shown to correspond to an admicelle composition of approximately a 1:1 anionic/nonionic mole ratio throughout Regions II and III of the adsorption isotherm. Published by Elsevier Inc.

1. Introduction Mixed surfactant adsorption on metal oxide surfaces has importance in detergency, flotation, and enhanced oil recovery, and surfactant mixtures are almost always used in these applications at least partly due to the synergistic behaviors often exhibited by these systems [1]. Because of this frequent use, better thermodynamic models and a better understanding of the mechanisms of mixed surfactant adsorption are needed in order to understand and formulate surfactant mixtures that exploit any synergistic behaviors. In this study, the adsorption of binary anionic/nonionic surfactant mixtures of sodium dodecyl sulfate and polyethoxylated nonylphenol on c-aluminum oxide was investigated. The adsorption of anionic/nonionic surfactant mixtures on hydrophilic metal oxides or minerals has been previously studied [2–12]. It has been shown that anionic/nonionic mixed surfactant layers are formed preferentially to those of anionic/anionic mixed surfactant layers [3]. Thermodynamically, this is indicated by strong negative deviations from ideality [4–6]. Non-idealities in mixed anionic/nonionic surfactant adsorption have been attributed to the nonionic surfactant head groups inserting themselves between the adsorbed anionic surfactant head groups, thereby reducing electrostatic * Corresponding author. E-mail addresses: [email protected] (J.J. Lopata), [email protected] (B.P. Grady). 0021-9797/$ - see front matter Published by Elsevier Inc. doi:10.1016/j.jcis.2009.10.072

repulsion between the adsorbed anionic surfactant head groups. It has also been shown that the adsorbed ionic surfactant aides in the adsorption of the nonionic surfactant [2,11,13–16]. Huang et al. demonstrated that the adsorbed ionic surfactant ‘‘pulls” the nonionic surfactant onto a surface on which it would not normally adsorb [13]. Some studies have dealt with the thermodynamics of surfactant adsorption systems [11,17,18] without producing models for adsorption, while other studies have presented thermodynamic models to describe adsorption. Since regular solution theory has been shown to successfully describe anionic/nonionic mixed micelle formation [1,19–21], regular solution theory has also been used to describe the formation of adsorbed anionic/nonionic surfactant aggregates [4,5]. It has been reported that regular solution theory failed to describe the adsorption of anionic/nonionic surfactant mixtures [4,5]. However, in Harwell et al. [5], mixed anionic/ nonionic adsorption data points that were at total equilibrium concentrations above the mixture critical micelle concentration (CMCm) were mistakenly used in a thermodynamic model developed to describe mixed anionic/nonionic surfactant adsorption in the absence of micelles. Hence, the conclusions concerning the applicability of regular solution theory to describe the formation of mixed admicelles in Harwell et al. [5] are not necessarily valid. A mixed surfactant model for nonionic surfactants was also developed by Kibbey and Hayes [22]. In addition to these, a model for nonionic and anionic surfactant adsorption on latex particles was introduced by Hulden and Kronberg [23].

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Nomenclature CA CAC

CAC* CACm

CACSST;A

CACSST;N

CA,mon Ceq,tot CMC CMCA CMCm

CMCN CN CN,mon DI HMC

total anionic surfactant equilibrium concentration, in monomer and micelle form (total lmoles SDS/L) critical admicelle concentration, or the surfactant concentration at which the first admicelle forms (i.e., the onset of Region II adsorption) (lmoles/L) critical admicelle concentration for a specific local surface patch * (lmoles/L) mixture critical admicelle concentration for the local surface patch *; i.e., the total equilibrium monomer concentration at the set total adsorption level (total lmoles surfactant/L) pure anionic surfactant critical admicelle concentration (or SDS admicelle standard state) for the local surface patch *; i.e., the pure SDS equilibrium monomer concentration at the set total adsorption level (lmoles SDS/L) infinitely dilute nonionic surfactant admicelle standard state for the local surface patch *; where * is defined at the set total adsorption level (lmoles NP(EO)10/L) anionic surfactant equilibrium monomer concentration (lmoles SDS/L) total surfactant equilibrium concentration in monomer and micelle form (total lmoles surfactant/L) critical micelle concentration (lmoles/L) pure anionic surfactant critical micelle concentration (lmoles SDS/L) mixture critical micelle concentration; i.e., the total equilibrium monomer concentration at the mixture CMC (total lmoles surfactant/L) pure nonionic surfactant critical micelle concentration (lmoles NP(EO)10/L) total nonionic surfactant equilibrium concentration, in monomer and micelle form (total lmoles NP(EO)10/L) nonionic surfactant equilibrium monomer concentration (lmoles NP(EO)10/L) distilled and deionized (water) hemimicelle concentration

In this paper, a thermodynamic model to describe mixed anionic/nonionic surfactant adsorption is presented. A complication for this model is that the total surfactant adsorption did not remain constant above the mixture CMC; hence the mixed surfactant adsorption model was combined with the pseudo-phase separation model for mixed micelle formation and the appropriate mass balance equations in order to describe mixed surfactant adsorption in the presence of mixed micelles. Furthermore, for the mixed surfactant systems that do show a plateau in the total adsorption at equilibrium concentrations above the mixture CMC, the composition of the adsorbed surfactant may significantly vary throughout the plateau adsorption. The model presented in this paper accounts for this situation as well. 2. Background on surfactant adsorption 2.1. Region I adsorption Fig. 1 illustrates the four distinct adsorption regions that typically exist when a monoisomeric anionic surfactant adsorbs on a positively charged mineral oxide surface. Region I adsorption occurs at low equilibrium surfactant concentrations and low levels of adsorption, and is frequently called the Henry’s Law adsorption region. Surfactant adsorption occurs in this region primarily due to the electrostatic attraction between the surfactant head groups and the oppositely charged surface, and to a lesser extent, the

HPLC high performance liquid chromatography NP(EO)10 alkylphenol polyoxyethylene nonionic surfactant, trade name IGEPAL CO-660 SDS sodium dodecyl sulfate (anionic surfactant) UV ultraviolet (detector) dimensionless regular solution theory interaction badm parameter for mixed admicelle formation dimensionless regular solution theory interaction bmic parameter for mixed micelle formation anionic surfactant-only based micelle mole fraction XA nonionic surfactant-only based micelle mole fraction XN anionic surfactant-only based equilibrium monomer YA mole fraction nonionic surfactant-only based equilibrium monomer YN mole fraction anionic surfactant-only based admicelle mole fraction ZA nonionic surfactant-only based admicelle mole fraction ZN cadm anionic surfactant activity coefficient in the admicelle A pseudo-phase cmon anionic surfactant activity coefficient in the monomer A pseudo-phase cadm nonionic surfactant activity coefficient in the admicelle N pseudo-phase cmon nonionic surfactant activity coefficient in the monomer N pseudo-phase partial fugacity of the anionic surfactant in the admifAadm celle pseudo-phase (lmoles SDS/L) partial fugacity of the anionic surfactant in the monofAmon mer pseudo-phase (lmoles SDS/L) partial fugacity of the nonionic surfactant in the admifNadm celle pseudo-phase (lmoles NP(EO)10/L) partial fugacity of the nonionic surfactant in the monofNmon mer pseudo-phase (lmoles NP(EO)10/L) * designates a specific local patch on the solid surface where admicelle formation is occurring

interaction of the surfactant tail groups with the surface. There is little interaction between the tail groups of the adsorbed surfactant molecules in this adsorption region [24]. 2.2. Region II adsorption At a critical surfactant equilibrium monomer concentration (designated as CAC in Fig. 1), the slope of the adsorption isotherm increases sharply with increasing equilibrium monomer concentration. The equilibrium surfactant concentration at which this first occurs is called the critical admicelle concentration (CAC) [5,25– 27], and marks the onset of Region II adsorption. The majority of surfactant adsorbed throughout Region II forms ‘‘micelle-like” aggregates on the solid surface [5], due to the interactions between the tail groups of the adsorbed surfactant molecules. It is believed that on hydrophilic surfaces, these adsorbed surfactant aggregates are bilayer structures [24,27] which can be assumed to be a pseudo-phase (as was done in this study) [27]. 2.3. Patch-wise adsorption model In a pseudo-phase adsorption model, the adsorption isotherm should theoretically show a step-change at the CAC i.e., a vertical slope on a plot of log(adsorption) versus log(surfactant concentration). This behavior would be the corollary to monomer concentration found at the CMC without adsorption, i.e. the concentration of

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charge on the solid surface [31,32], due to the adsorption of the anionic surfactant head groups; (2) by a Langmuir – like filling of available adsorption sites as admicelles fill the available surface patches; or (3) by a change in the patch-wise free energy distribution of surface sites. Even when the net surface charge is negative, surfactant adsorption is still possible due to the fact that some of the local surface patches are still positively charged and because hydrocarbon tails are able to interact with one another in the adsorbed layer. Surfactant adsorption on like-charged surfaces is commonly observed. Regardless of the exact cause of the transition in adsorption, the model assumes that surfactant adsorption in Region III still corresponds to filling of the most energetically favorable surface patches with admicelles. Therefore, Region III adsorption was not treated any differently than Region II adsorption in the model. 2.5. Region IV adsorption

Fig. 1. Typical anionic surfactant adsorption isotherm on a positively charged mineral oxide surface.

surfactant not in micelles is essentially constant above this concentration. Although vertical Region II adsorption isotherms have been reported in the literature [28], in general the slope is not infinite, but is still >1 above the CAC. The exact value of the slope in Region II is a complex function of many variables; including surfactant purity, surfactant structure, surface chemistry, surface roughness and solid porosity. These effects can be taken into account by using a ‘‘patch-wise” adsorption model. The patch-wise adsorption model assumes that adsorption occurs at distinct free energies corresponding to different levels of adsorption in Regions II and III. With only a few distinct free energies, vertical jumps in adsorption are present. As the number of distinct free energies increases, jumps become indistinguishable and this positive but non-vertical isotherm slope is seen. In the ‘‘patch-wise” adsorption model, the first admicelle forms on the patch that causes the largest negative change in free energy at an equilibrium monomer concentration called the critical admicelle concentration, which is designated as the CAC on Fig. 1. As an infinitesimal amount of surfactant is added at the onset of the first admicelle formation, the equilibrium monomer concentration remains constant at CAC until the admicelle formation on the highest energy level patch is complete. At increasing equilibrium concentrations throughout Region II, admicelle formation occurs on successively less energetic local patches at critical admicelle concentrations designated as CAC* [5,27–29], where the asterisk refers to a concentration that corresponds to the free energy of a specific local patch. Higher monomer chemical potentials (i.e., higher monomer concentrations) are required to form admicelles on these lower energetic patches. As can be seen in Fig. 1, for each CAC* in Region II or III, there exists only one corresponding equilibrium monomer concentration and only one corresponding surfactant adsorption level. 2.4. Region III adsorption As seen in Fig. 1, Region III adsorption is indicated by a decrease in the slope of the log of the surfactant adsorption versus the log of the equilibrium concentration. This decrease in slope in Region III may be caused by: (1) a change in sign of the net

In Region IV of the adsorption isotherm, adsorption remains nearly constant. Hence, Region IV is often called the plateau adsorption region [24]. For pure component (monomeric) surfactant adsorption, the onset of Region IV is associated with the formation of the first micelle in the equilibrium bulk solution. If the equilibrium monomer concentration reaches the critical micelle concentration (or CMC) before surfactant adsorption is complete, almost all of any additional added surfactant ends up in the formation of micelles. Therefore, our model assumes that micelles act as a chemical potential sink—a thermodynamic pseudo-phase—for any additional surfactant added to the solution, thereby keeping the monomer concentration nearly constant and the surfactant adsorption nearly constant above the CMC (since surfactant adsorption is directly dependent upon the monomer concentration). Ellipsometry studies, which presumably have surfaces with the most uniform surface energies and smallest roughnesses, confirm that the CMC and the Region III to Region IV transition occur at the same surfactant concentration [29]. In the presence of mixed micelles, however, solution concentrations of monomer in equilibrium with the micelles can shift, thereby causing a change in monomer chemical potential and a corresponding change in surfactant adsorption: hence, adsorption is not necessarily constant above the CMC for surfactant mixtures [28]. 3. Experimental 3.1. Materials Sodium dodecyl sulfate (SDS) was purchased from Baxter Scientific Products and was manufactured by Mallinckrodt with a manufacturer reported purity of at least 99.97%. SDS is an anionic surfactant, with a negatively charged sulfate head group and an alkyl chain length of twelve carbon units. The SDS was purified by recrystallizing once in distilled and deionized water and once in reagent grade alcohol, followed by drying the crystals for 72 h under a vacuum. Further details of the SDS purification procedure may be found elsewhere [30]. The NP(EO)10 (trade name IGEPAL CO-660) was furnished by GAF Corporation and was used as received. The NP(EO)10 surfactant molecule contains a benzene ring, an alkyl chain length of nine carbon units, and an average of 10 ethylene oxide groups per molecule. The alkylphenol polyoxyethylene nonionic surfactant is a polydisperse surfactant, with a Poisson distribution of ethylene oxide groups. The ethoxylated alkyl phenol was chosen for ease of analysis via high performance liquid chromatography (HPLC). The c-Aluminum oxide used in the adsorption experiments was purchased from Degussa and had a manufacturer reported BET

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surface area of 100 ± 15 m2/g, an average primary particle size of 20 nm, a point of zero charge at pH 9.0, and consisted of >97% Al2O3 and less than 0.1% TiO2, 0.1% SiO2, and 0.2% Fe2O3. Other materials used in this study were ACS grade sodium chloride (Mallinckrodt), 0.01 N hydrochloric acid (Fisher Scientific), and HPLC grade methanol and acetonitrile (J.T. Baker, Inc.). 3.2. Methods Surfactant solutions for each adsorption isotherm were prepared at 0.15 M NaCl, a pH of 4.00, a constant SDS/NP(EO)10 feed mole ratio, and at the desired total surfactant concentration, using DI water. The final pH after equilibrium under these conditions was found to be 6.94. For this system a concentration of 0.15 M NaCl corresponds to a ‘‘swamping electrolyte” concentration, at which the chemical potential of the surfactant ions can be treated as independent of counter-ion concentration. Fifteen milliliters of each surfactant solution were pipetted into test tubes containing 0.5 grams of aluminum oxide. Samples were then equilibrated for eight days in a water bath that was kept at a constant temperature of 30 °C and gently shaken once a day to insure equilibrium. After eight days, the supernatants of the adsorption samples were removed for analysis and the equilibrium pH’s were measured. SDS and NP(EO)10 equilibrium concentrations were measured using HPLC. The SDS concentrations were determined using a conductivity detector and the NP(EO)10 concentrations were determined using a UV detector at a light wavelength of 225 nm [30]. 4. Theory 4.1. Mixed micelle formation The formation of anionic/nonionic mixed micelles has been successfully described using regular solution theory [4,5], even though regular solution theory does not explicitly account for the reduction in the electrostatic repulsion between the anionic surfactant head groups in the mixed micelles and assumes a random arrangement of molecules in the separate phase (ideal entropy of mixing). Regular solution theory (Eqs. (1)–(4)) successfully predicts the lowest total surfactant monomer concentration (CMCm) at which the first mixed surfactant micelle will form in the bulk solution, for any particular equilibrium monomer mole fraction (YA and YN). Throughout this work, the subscript ‘‘A” refers to the anionic surfactant, the subscript ‘‘N” refers to the nonionic surfactant, and the subscript ‘‘m” refers to the surfactant mixture.

C A;mon ¼ Y A  CMCm ¼ XA  CMCA  EXPðX 2N  bmic Þ

ð1Þ

C N;mon ¼ Y N  CMCm ¼ X N  CMCN  EXPðX 2A  bmic Þ Y A þ Y N ¼ 1:0

ð2Þ ð3Þ

X A þ X N ¼ 1:0

ð4Þ

where CA,mon, CN,mon surfactant equilibrium monomer concentrations (lmoles/L) surfactant-only based equilibrium monomer mole fracYA, YN tions surfactant-only based micelle mole fractions XA, XN mixture critical micelle concentration; i.e., the total monoCMCm mer concentration at the mixture CMC (lmoles/L) CMCA, CMCN pure surfactant critical micelle concentrations (lmoles/L) dimensionless regular solution theory interaction paramebmic ter for mixed micelle formation

Before Eqs. (1)–(4) could be used to predict the mixture critical micelle concentration (CMCm), the dimensionless regular solution theory interaction parameter (bmic) first had to be determined from the experimental data. The ‘‘best fit” regular solution theory interaction parameter was determined using the pure surfactant critical micelle concentrations (CMCA and CMCN – measured at the same temperature, pressure, and salt concentration as the CMCm data) and performing a least squares fit on the measured CMCm data at various corresponding monomer compositions (YA and YN), allowing the mixed micelle compositions (XA and XN) to vary. When solving for bmic it was assumed that at the CMCm, an infinitesimal amount of surfactant was present in the form of mixed micelles; therefore, the surfactant monomer composition (YA and YN) was equal to that in the feed and the total surfactant monomer concentration was equal to the total surfactant feed concentration. Once the interaction parameter for the anionic/nonionic mixed micelle formation (bmic) was determined, CMCm values at any equilibrium monomer composition (YA and YN) could be predicted using Eqs. (1)–(4). 4.2. Mixed admicelle formation: adsorption in the absence of micelles One of the primary objectives of this study was to model the anionic/nonionic mixture adsorption isotherms in Regions II and III, at total equilibrium concentrations below CMCm. Since micelles and admicelles are known to exhibit similar properties and regular solution theory has been shown to accurately describe anionic/ nonionic mixed micelle formation, the ability of regular solution theory to describe the non-idealities of mixed anionic/nonionic admicelle formation was tested. The adsorption of binary surfactant mixtures is directly dependent upon the surfactant monomer concentration and composition [1,28]. The concentrations of surfactant components in the monomer pseudo-phase are dilute: therefore, it can be safely assumed that there are no significant interactions between surfactant monomers [1]. However, the adsorbed surfactant present in the admicelle pseudo-phase is comparatively dense and interactions between adsorbed anionic/nonionic surfactant molecules have been shown to be very significant [5,6]. Therefore, monomer/admicelle equilibrium is analogous to monomer/micelle equilibrium and a pseudo-phase separation model for mixed admicelle formation was developed in a fashion analogous to the pseudo-phase separation model frequently used to describe mixed micelle formation. The pseudo-phase separation approach to model mixed admicelle formation has been shown to be valid for anionic/anionic surfactant mixtures, and it was used to accurately describe ideal mixed admicelle formation [25]. Partial fugacity equations were written for both the anionic surfactant (Eqs. (5) and (6)) and the nonionic surfactant (Eqs. (7) and (8)) in the monomer and admicelle pseudo-phases.

fAmon ¼ Y A  cmon  CACm A adm  CACSST;A A mon  CACm N adm  CACSST;N N

ð5Þ

fAadm fNmon

¼ ZA  c

ð6Þ

¼ YN  c

ð7Þ

fNadm

¼ ZN  c

ð8Þ

where fAmon , fNmon partial fugacities of the surfactants in the monomer pseudo-phase (lmoles/L) fAadm , fNadm partial fugacities of the surfactants in the admicelle pseudo-phase (lmoles/L) surfactant-only based monomer mole fractions YA, YN surfactant-only based admicelle mole fractions ZA, ZN mon cmon , c surfactant activity coefficients in the monomer pseudoN A phase

J.J. Lopata et al. / Journal of Colloid and Interface Science 342 (2010) 415–426 adm cadm surfactant activity coefficients in the admicelle pseudoA , cN

CACm

CACSST;A

CACSST;N

phase mixture critical admicelle concentration for the local surface patch *; i.e., the total equilibrium monomer concentration at the given total adsorption level (total lmoles surfactant/L) pure anionic surfactant critical admicelle concentration (or SDS admicelle standard state) for the local surface patch *; i.e., the pure SDS monomer concentration at the given total adsorption level (lmoles SDS/L) pure nonionic surfactant critical admicelle concentration (or NP(EO)10 admicelle standard state) for the local surface patch *; i.e. the pure NP(EO)10 monomer concentration at the given total adsorption level (lmoles NP(EO)10/L)

It is important to note that the terms CACm and CACSST;A in Eqs. (5)–(7) are equilibrium monomer concentrations. SDS admicelle standard states in Regions II and III were determined from the pure component SDS adsorption isotherm, measured at the same experimental conditions as the mixture adsorption data (i.e., 0.15 M NaCl, a temperature of 30 °C, a solution/solid ratio of 0.03 l/g, and at an equilibrium pH of 6.94). CACSST;A is defined at each total surfactant adsorption level as the corresponding SDS equilibrium monomer concentration at the total adsorption level. An infinitely dilute nonionic surfactant admicelle standard state CACSST;N was used in Eq. (8), since the pure NP(EO)10 did not exhibit Region II or III adsorption without the presence of a co-surfactant. The infinitely dilute nonionic surfactant admicelle standard state at a constant total surfactant adsorption level is defined as the limiting slope of the NP(EO)10 equilibrium monomer concentration versus the NP(EO)10 admicelle mole fraction ZN, as ZN approaches zero. Infinitely dilute surfactant standard states have been previously used to describe anionic/nonionic mixed coacervate [31], mixed microemulsion [32], and mixed admicelle [5] formation. Since the total surfactant monomer concentrations were dilute up to CMCm and swamping electrolyte was always present in the adsorption experiments (0.15 M NaCl), the activity coefficients of the anionic and nonionic surfactants in the monomer pseudophase were assumed to be constant; i.e., the monomer activity can be described by Henry’s Law:

cmon ¼ cmon ¼ 1:0 A N

ð9Þ

Eqs. (10) and (11) are the regular solution theory activity coefficient equations for the admicelle pseudo-phase, and Eq. (12) is a mass balance equation for the surfactant-only admicelle mole fraction. The nonionic surfactant admicelle activity coefficient equation (Eq. (11)) was based on an infinite dilution nonionic admicelle standard state [5]. The admicelle regular solution theory activity coefficient equations (Eqs. (10) and (11)) satisfy the boundary conditions and the Gibbs–Duhem equation.

cadm ¼ EXPðZ 2N  badm Þ A adm cN ¼ EXP½ðZ 2A  1:0Þ  badm 

ð11Þ

Z A þ Z N ¼ 1:0

ð12Þ

ð10Þ

where badm is the dimensionless regular solution theory interaction parameter for mixed admicelle formation. At equilibrium, the partial fugacities for each surfactant component in the monomer and admicelle pseudo-phases are equal. Therefore, Eqs. (5)–(11) can be reduced to Eqs. (13) and (14), which are valid only at a constant total surfactant adsorption level.

C A;mon ¼ Y A  CACm ¼ Z A  CACSST;A  EXPðZ 2N  badm Þ C N;mon ¼ Y N 

CACm

¼ ZN 

CACSST;N



EXP½ðZ 2A

 1:0Þ  badm 

ð13Þ ð14Þ

419

Regular solution theory pseudo-phase separation model for mixed admicelle formation (Eqs. (3), (12), (13) and (14)) is very similar to the regular solution theory pseudo-phase separation model frequently used to describe mixed micelle formation (Eqs. (1)–(4)). Both models describe surfactant equilibrium between an extremely dilute monomer phase and an aggregated admicelle or micelle phase. The two models were not entirely analogous, however, since the pseudo-phase separation model for mixed admicelle formation (Eqs. (13) and (14)) was written in terms of a specific local free energy patch. A ‘‘patch-wise” adsorption model was used to describe the anionic/nonionic mixed surfactant adsorption on the alumina surface. Each local patch is described as having its own characteristic mixture critical admicelle concentration CACm , which is defined as the total equilibrium monomer concentration required to form an admicelle on that local ‘‘homogeneous” free energy patch. CACm in the pseudo-phase separation model for mixed admicelle formation is analogous to CMCm in the pseudophase separation model for mixed micelle formation; both terms describe the total equilibrium monomer concentration required to cause the onset of surfactant aggregate formation, as a function of the anionic/nonionic surfactant monomer mole ratio. In order to correctly test any mixing theory to describe the nonidealities in the mixed admicelle pseudo-phase, CACm at various admicelle compositions and the admicelle standard states (CACSST;A and CACSST;N ) have to be compared on the same specific energy level patch. As can be seen in Fig. 1, each CACm in Region II or III has only one corresponding total surfactant adsorption level. It was therefore assumed that setting the total surfactant adsorption level (in Region II or III) defined a specific local patch which was just energetic enough for mixed admicelle formation to occur, regardless of the composition of the surfactant mixture adsorbing. Furthermore, it was assumed that at the set total surfactant adsorption level the ‘‘defined” patch and all local patches of higher energy were filled with admicelles, while all surface patches at lower adsorption energies contained only Henry’s Law adsorption (these Henry’s Law patches are assumed to contain a negligible amount of surfactant). Using the ‘‘patch-wise” adsorption model to describe the anionic/nonionic mixed surfactant adsorption resulted in the constraint that Eqs. (13) and (14) be solved at a constant total surfactant adsorption level. By examining constant total surfactant adsorption levels, regular solution theory was tested on specific ‘‘homogeneous” patches. 4.3. Mixed admicelle formation: adsorption in the presence of micelles Before the mixed admicelle formation equations (Eqs. (13) and (14)) could be used at total surfactant equilibrium concentrations above CMCm, the equations had to be modified to account for the presence of mixed micelles in the equilibrium bulk solutions. The mixture critical admicelle concentration CACm in Eqs. (13) and (14) is defined as the total surfactant equilibrium monomer concentration. However, for mixed surfactant adsorption at equilibrium concentrations above CMCm, the total equilibrium monomer concentration is the mixture critical micelle concentration CMCm (from the pseudo-phase separation model for mixed micelle formation). Therefore, for mixed surfactant adsorption at equilibrium concentrations above CMCm, CACm in Eqs. (13) and (14) can be replaced by CMCm, resulting in Eqs. (15) and (16), respectively.

C A;mon ¼ Y A  CMCm ¼ Z A  CACSST;A  EXPðZ 2N  badm Þ

ð15Þ

C N;mon ¼ Y N  CMCm ¼ Z N  CACSST;N  EXP½ðZ 2A  1:0Þ  badm 

ð16Þ

The simultaneous solution of both the mixed admicelle formation equations and the mixed micelle formation equations at each total surfactant adsorption level investigated can be visualized by

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examining Figs. 9–11. In Figs. 9–11, if the mixed surfactant adsorption predictions for adsorption below CMCm were extended to a point beyond the monomer/micelle phase boundary (ignoring the fact that mixed micelle formation occurs), the predictions would intersect the monomer/micelle phase boundary at only one CMCm value at each individual total surfactant adsorption level; these CMCm values are the only total surfactant monomer concentrations (and compositions) which satisfy both the admicelle and micelle pseudo-phase separation models at a specific total surfactant adsorption level. Eqs. (12), (15), (16) and Eqs. (1)–(4) were solved simultaneously at each individual total surfactant adsorption level by inputting badm, bmic, CACSST;A , CACSST;N , CMCA and CMCN while solving for YA, YN, ZA, ZN, XA, XN and CMCm; resulting in seven equations and seven unknowns. The interaction parameter for mixed admicelle formation (badm) was pre-determined using a least squares fit approach (similar to that used for mixed micelle formation interaction parameter bmic) from the mixed adsorption data in the absence of micelles, using a procedure as yet to be described. Since there is only one CMCm value at each individual total surfactant adsorption amount or level which satisfies all of the equations for the adsorption of binary anionic/nonionic surfactant mixtures at total equilibrium concentrations above CMCm, the simultaneous solution of the pseudo-phase separation model for mixed admicelle formation and the pseudo-phase separation model for mixed micelle formation predicts that the surfactant compositions in the mixed monomer (YA, YN), micelle (XA, XN) and admicelle (ZA, ZN) pseudo-phases are constant at each total surfactant adsorption level. However, these constant pseudo-phase compositions are dependent upon the total adsorption level, since the anionic and nonionic surfactant admicelle standard states (CACSST;A and CACSST;N ) in Eqs. (15) and (16) are functions of the total adsorption level. In order to predict the mixed surfactant adsorption above CMCm, the information obtained thus far needs to be combined with the appropriate mass balance equations. Eq. (17) is a total mass balance on the surfactant present in the equilibrium bulk solution, Eq. (18) is a mass balance on the anionic surfactant present in the equilibrium bulk solution, and Eq. (19) is a mass balance on the nonionic surfactant present in the equilibrium bulk solution.

C eq;tot ¼ C A þ C N

ð17Þ

C A ¼ Y A  CMCm þ X A  ðC eq;tot  CMCm Þ

ð18Þ

C N ¼ Y N  CMCm þ X N  ðC eq;tot  CMCm Þ

ð19Þ

Mixed anionic/nonionic adsorption predictions at total equilibrium concentrations above CMCm were made at each individual total surfactant adsorption level investigated by inputting various CN values and calculating the corresponding CA values, using Eq. (20). The calculated CA values at various CN values were then plotted on the surfactant phase equilibrium plots (above the monomer/micelle phase boundary) in order to compare the predictions with the experimental data. 5. Results and discussion 5.1. Mixed micelle formation CMC values for the pure and mixture surfactant solutions were determined at the same experimental conditions as the adsorption experiments (0.15 M NaCl and 30 °C) by the surface tension method. A least squares fit of the mixture CMCm data resulted in a dimensionless regular solution theory interaction parameter for mixed micelle formation of bmic = 1.86. As can be seen in Fig. 2, regular solution theory provides an excellent description of the CMCm data. 5.2. Pure anionic and nonionic surfactant adsorption isotherms Pure component SDS and NP(EO)10 adsorption isotherms on the

c-aluminum oxide are shown in Fig. 3. The SDS readily adsorbed on the gamma alumina, and it could be argued that the four characteristic regions of adsorption illustrated in Fig. 1 are displayed. However, the NP(EO)10 barely adsorbed on the gamma alumina. In Fig. 3, pure NP(EO)10 surfactant adsorption remained in the Henry’s Law adsorption region until the equilibrium monomer concentration reached the pure NP(EO)10 critical micelle concentration, CMCN, at 45 lmoles NP(EO)10/L. At equilibrium concentrations above CMCN, the pure NP(EO)10 surfactant adsorption decreased and then began to increase again, until the change in surfactant concentration upon adsorption could no longer be measured, consistent with behavior expected for isomeric mixes of surfactants. In Harwell et al. [5], the same pure nonionic surfactant adsorbing on the same c-alumina also exhibited low NP(EO)10 adsorption and similar trends in the NP(EO)10 adsorption isotherm at equilibrium concentrations above CMCN. The behavior of the pure NP(EO)10 adsorption isotherm at equilibrium concentrations above

where Ceq,tot

total surfactant equilibrium concentration in monomer and micelle form (lmoles/L) total anionic or nonionic surfactant equilibrium concentraCA, CN tions in monomer and micelle form (lmoles/L) YA CMCm concentration of anionic surfactant present in the monomer pseudo-phase (lmoles/L) YN CMCm concentration of nonionic surfactant present in the monomer pseudo-phase (lmoles/L) XA (Ceq,tot  CMCm) concentration of anionic surfactant present in the micelle pseudo-phase (lmoles/L) XN (Ceq,tot  CMCm) concentration of nonionic surfactant present in the micelle pseudo-phase (lmoles/L) Eqs. (17)–(19) can be reduced to Eq. (20). Since XA, XN, YA, YN and CMCm are constant at each individual total surfactant adsorption level for mixed surfactant adsorption above CMCm, Eq. (20) is linear at a constant total adsorption level, as illustrated in Fig. 8.

C A ¼ ðX A =X N ÞC N þ CMCm ½Y A  ðX A =X N ÞY N 

ð20Þ

Fig. 2. Regular solution theory fit of CMCm data for SDS/NP(EO)10 mixtures at 0.15 M NaCl.

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Fig. 3. Pure SDS and pure NP(EO)10 equilibrium adsorption isotherms. A solution/ solid ratio of 0.03 stands for 30 mL of solution per gram of alumina.

CMCN is thought to be due to the fact that the nonionic surfactant was polydisperse. Throughout this work, the nonionic surfactant was treated as a single component, even though it was polydisperse [5].

5.3. Mixed anionic/nonionic surfactant adsorption isotherms Pure component SDS and NP(EO)10 adsorption isotherms and the mixture total adsorption isotherms are shown in Fig. 4, where the total equilibrium surfactant adsorption is plotted versus the total equilibrium surfactant concentration. The mixture adsorption isotherms in Fig. 4 are at constant NP(EO)10/SDS feed mole ratios as indicated on the graph, which were not necessarily equal to

Fig. 4. Total surfactant adsorption versus total equilibrium concentration for various SDS/NP(EO)10 feed mole ratios.

421

the NP(EO)10/SDS equilibrium monomer mole ratios, due to preferential surfactant adsorption. Anionic/nonionic mixture adsorption isotherms in Fig. 4 showed strong negative deviations from ideality in Regions II and III, since the total surfactant adsorption occurred at lower total equilibrium concentrations as the NP(EO)10 surfactant-only feed mole fraction was increased. At increasing NP(EO)10 feed mole fractions (up to an NP(EO)10 feed mole fraction of 0.6 – the highest investigated in this study), the mixture adsorption isotherms in Fig. 4 became more vertical in Regions II and III. When little or no nonionic surfactant was added in the feed, the Region II to Region III transition was clearly visible. However, as the nonionic surfactant feed mole fraction was increased, the Region II to Region III transition virtually disappeared. The mixture adsorption data in Fig. 4 supports the theory that the Region III adsorption of a pure anionic surfactant on a positively charged mineral oxide surface is primarily caused by the electrostatic repulsion of the adsorbed anionic surfactant head groups [33]. As more nonionic surfactant was added to the anionic surfactant feed, it is believed that the adsorbed nonionic surfactant molecules significantly shielded the electrostatic repulsion between the adsorbed anionic surfactant molecules, thereby causing the Region II to Region III transition to disappear. At increasing NP(EO)10 feed mole fractions, the total surfactant plateau adsorption levels in Fig. 4 slightly decreased. The lower plateau total adsorption levels at higher NP(EO)10 feed mole fractions may be due to steric hindrance or less surface area available for adsorption, since the hydrophilic groups of the NP(EO)10 surfactant molecule are significantly larger than that of the SDS surfactant molecule. For the surfactant-only feed mole ratios of 0.4 NP(EO)10/0.6 SDS, 0.5 NP(EO)10/0.5 SDS, and 0.6 NP(EO)10/0.4 SDS, the mixture adsorption isotherms nearly coincide in all of Region II and most of Region III. Individual SDS and NP(EO)10 component adsorption isotherms are shown in Figs. 5 and 6, respectively. In Fig. 5, the SDS component plateau adsorption levels steadily decreased with increasing NP(EO)10 feed mole fractions. In Fig. 6, the NP(EO)10 component plateau adsorption levels increased with increasing NP(EO)10 feed mole fractions, up to the 0.3 NP(EO)10/0.7 SDS feed mole ratio. At

Fig. 5. SDS component equilibrium adsorption versus SDS equilibrium concentration for various SDS/NP(EO)10 feed mole ratios.

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Fig. 6. NP(EO)10 component equilibrium adsorption versus NP(EO)10 equilibrium concentration for various SDS/NP(EO)10 feed mole ratios.

NP(EO)10 feed mole fractions above 0.3, the NP(EO)10 component plateau adsorption levels remained nearly constant. This further supports the theory that the adsorption of NP(EO)10 was sterically hindered. SDS component adsorption isotherms in Fig. 5 displayed the typical Regions II and III adsorption illustrated for a pure component in Fig. 1. However, the NP(EO)10 component adsorption isotherms in Fig. 6 were ‘‘S” shaped, especially at low NP(EO)10 feed mole fractions. At increasing NP(EO)10 feed mole fractions in Fig. 6, the ‘‘S” shape gradually disappeared and the NP(EO)10 adsorption isotherms were nearly vertical in Regions II and III. Previous investigators have also reported ‘‘S” shaped nonionic component adsorption isotherms when studying the adsorption of mixtures of anionic and nonionic surfactants on alumina [4,5]. Pure NP(EO)10 was shown to barely adsorb on the c-alumina under the experimental conditions used in this study (Fig. 3). In the mixed system, however, before the adsorption plateau, almost all of the nonionic surfactant in solution was adsorbed especially at low NP(EO)10 feed mole fractions (Fig. 6). One explanation for these results is that the SDS preferentially adsorbs in the layer closest to the surface, while the tails of the nonionic surfactant molecules interact with the anchored anionic surfactant tail groups to form the second layer of the bilayer, with the nonionic surfactant head groups facing the water interface. An interesting question is whether at the concentration corresponding to where all of the surface charge has been neutralized, which is well before the entire surface is covered with anionic surfactant, the nonionic or anionic surfactant preferentially adsorbs [34]. Fig. 7 is a schematic of the proposed adsorbed anionic/nonionic admicelle and its equilibrium with the monomer phase. A mixed micelle is also depicted in Fig. 7, to illustrate the fact that the adsorption of surfactant mixtures from solution is only dependent upon the monomer phase, even when mixed micelles are present. 5.4. Determining adsorption above CMCm Regular solution theory predictions for monomer/micelle equilibrium (determined using bmic = 1.86 and Eqs. (1)–(4)) were plotted as a function of the total SDS and total NP(EO)10 equilib-

Fig. 7. Schematic of mixed anionic/nonionic surfactant adsorption equilibrium.

Fig. 8. Surfactant phase equilibrium plot.

rium concentrations (CA and CN, respectively) in Fig. 8, in order to produce a phase diagram for mixed surfactant adsorption. By plotting the mixture adsorption data on a phase diagram, the presence of mixed micelles in the equilibrium bulk solutions could easily be detected. At low SDS and NP(EO)10 equilibrium concentrations in Fig. 8, only the monomer and admicelle pseudo-phases were present in the adsorption experiments. At SDS and NP(EO)10 equilibrium concentrations above the monomer/micelle phase boundary in Fig. 8, the surfactant was present in the mixed monomer, admicelle, and micelle pseudo-phases in the adsorption experiments. In Fig. 4, horizontal cuts can be made at sixteen constant total surfactant adsorption levels throughout Regions II and III. The

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constant total surfactant adsorption levels investigated were at 1, 2, 4, 6, 8, 10, 15, 20, 30, 40, 60, 80, 100, 150, 200 and 300 lmoles/g. SDS and NP(EO)10 equilibrium concentrations for the mixture adsorption isotherms were plotted on a phase diagram for each constant total adsorption level. Surfactant phase diagrams at total surfactant adsorption levels of 4.0, 20.0, and 200.0 lmoles/ g are illustrated in Figs. 9–11, respectively. For the adsorption data at equilibrium concentrations above the monomer/micelle phase boundary in Figs. 9–11, mixed micelles were present in the equilibrium bulk solution. As can be seen in Figs. 9–11, the 0.6 NP(EO)10/ 0.4 SDS feed mole ratio mixture adsorption isotherm in Fig. 4 contained mixed micelles in the equilibrium bulk solution at all of the adsorption levels investigated (from 1 to 300 lmoles/g). The 0.5 NP(EO)10/0.5 SDS feed mole ratio mixture adsorption isotherm in Fig. 4 contained mixed micelles in the equilibrium bulk solution at total adsorption levels above 4 lmoles/g. The only other mixture adsorption data point investigated in Fig. 4 that contained mixed micelles in the equilibrium bulk solution was at a feed mole ratio of 0.4 NP(EO)10/0.6 SDS and at a total adsorption level of 300 lmoles/g. It is interesting to note that the 0.5 NP(EO)10/0.5 SDS and 0.6 NP(EO)10/0.4 SDS feed mole ratio mixture adsorption isotherms in Fig. 4 remained in what appeared to be adsorption Regions II and III, even though mixed micelles were present. The onset of mixed micelle formation in the equilibrium bulk solutions did not cause a plateau in the mixed surfactant adsorption (or the onset of Region IV). The shapes of the mixture adsorption isotherms in Regions II and III at equilibrium concentrations above CMCm appear nearly unaffected by the presence of mixed micelles, except for the fact that the adsorption isotherms almost coincide. Therefore, for this adsorption system, the onset of Region IV adsorption was caused by the saturation of the available adsorption sites on the solid surface. These results support the theory that local surfactant bilayer coverage on a solid surface is possible without attaining complete bilayer, or even complete monolayer, coverage on the entire surface. Somasundaran [4] also reported that at high nonionic surfactant feed mole fractions, the adsorption of anionic/nonionic surfactant mixtures on alumina in Regions II and III occurred in the presence of mixed micelles. Even though the 0.5 NP(EO)10/0.5 SDS and 0.6 NP(EO)10/0.4 SDS mixture adsorption isotherms in Fig. 4 occurred in the presence of mixed micelles throughout most of Regions II and III, and the mixed micelles did not cause a plateau in the total surfactant adsorption, the pseudo-phase separation model for mixed micelle formation was not necessarily violated. Since the mixed surfactant adsorption experiments in this study were conducted at constant surfactant-only feed mole ratios, the anionic and nonionic surfac-

423

Fig. 10. Surfactant phase equilibrium plot – total surfactant adsorption 20.0 lmoles/g.

Fig. 11. Surfactant phase equilibrium plot – total surfactant adsorption 200.0 lmoles/g.

tant monomer concentrations (or chemical potentials) will vary with the total surfactant concentration above the mixture CMC [28]. If the mixture critical micelle concentration (CMCm) is reached before local bilayer adsorption is complete on all of the available surface patches (as was the case for the 0.5 NP(EO)10/ 0.5 SDS and 0.6 NP(EO)10/0.4 SDS feed mole ratio mixture adsorption isotherms in Fig. 4), surfactant adsorption still occurs and any additional added surfactant is distributed between the mixed admicelles and mixed micelles that form. Therefore, the total adsorption of surfactant mixtures may increase at total equilibrium concentrations above CMCm without violating the pseudophase separation assumption for mixed micelle formation [28].

5.5. Mixed anionic/nonionic surfactant adsorption in the absence of micelles

Fig. 9. Surfactant phase equilibrium plot – total surfactant adsorption 4.0 lmoles/g.

Regular solution theory pseudo-phase separation model for mixed admicelle formation can now be used to describe the mixed anionic/nonionic surfactant adsorption in Regions II and III that occurred at total equilibrium concentrations below CMCm. The mixed admicelle formation equations were solved in a fashion analogous to the mixed micelle formation equations, except that the mixed admicelle formation equations had to be solved at constant total surfactant adsorption levels to account for patch-wise adsorption

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on a heterogeneous solid surface. For each constant total surfactant adsorption level investigated, the dimensionless admicelle interaction parameter (badm) was first determined using the measured mixture critical admicelle concentrations (CACm ) at various equilibrium monomer mole fractions and the anionic surfactant admicelle standard state CACSST;A at the total surfactant adsorption level. As stated previously, CACSST;N could not be determined in the same manner as CACSST;A . Instead, the infinitely dilute NP(EO)10 admicelle standard states CACSST;N at each total surfactant adsorption level can theoretically be determined from the mixture adsorption data by plotting the NP(EO)10 equilibrium monomer concentrations versus the NP(EO)10 admicelle mole fractions (ZN). Fig. 12 illustrates how the infinitely dilute NP(EO)10 admicelle standard state should be determined from the mixture adsorption data at a total surfactant adsorption level of 20.0 lmoles/g. As can be seen in Fig. 12, the mixture adsorption data had not yet reached a limiting slope at the lowest NP(EO)10 admicelle mole fraction measured (as was the case for all of the total surfactant adsorption levels investigated). Mixture adsorption data points at lower NP(EO)10 equilibrium concentrations and lower NP(EO)10 admicelle mole fractions were too small to be measured. Therefore, the CACSST;N values at the various total adsorption levels could not be accurately determined experimentally. Instead, the best values of CACSST;N that could be determined using the measured mixture adsorption data was the slope of a straight line drawn from the origin to the data point at the lowest NP(EO)10 equilibrium monomer concentration and lowest NP(EO)10 admicelle mole fraction (illustrated as ‘‘2” on Fig. 12). The experimental CACSST;N values were believed to be much higher than the actual CACSST;N values for all of the total surfactant adsorption levels investigated in this study, since a limiting Henry’s Law slope was never obtained. The only way to further model the anionic/nonionic mixed surfactant adsorption data was to treat the CACSST;N values as unknown constants at each total surfactant adsorption level. The CACSST;N values were therefore adjustable parameters at each total adsorption level, which were constrained by a lower bound of zero and an upper bound determined from the mixture adsorption data. The procedure used to solve the mixed admicelle formation equations was not entirely analogous to the procedure used to solve the mixed micelle formation equations, since the mixed sur-

(CACSST;N )

Fig. 12. Determining the NP(EO)10 admicelle standard state mixture adsorption data – total surfactant adsorption 20.0 lmoles/g.

from the

factant adsorption occurred on patches. Adsorption on patches resulted in the additional constraint that the mixed admicelle formation equations (Eqs. (3), (12), (13) and (14)) be simultaneously solved at a constant total surfactant adsorption level. By solving the equations at constant total adsorption levels in Regions II and III, the total equilibrium monomer concentrations CACm (at various mixed admicelle compositions) required to form a mixed admicelle on the same homogeneous patch were being compared. The requirement that the pseudo-phase separation model for mixed admicelle formation be solved at a constant total surfactant adsorption level can clearly be seen by the fact that the anionic surfactant admicelle standard state CACSST;A was a function of the total surfactant adsorption level (Fig. 3). Regular solution theory predictions of the mixed anionic/nonionic surfactant adsorption below CMCm were made by first determining the least squares fit admicelle interaction parameters (badm) and infinite dilution nonionic surfactant admicelle standard states ðCACSST;N Þ at each total surfactant adsorption level investigated [30]. The least squares fit badm and CACSST;N values, the interpolated CACSST;A values, and Eqs. (12)–(14) can then be used to predict the mixed anionic/nonionic surfactant adsorption (i.e., CACm as a function of YA or YN) at each total surfactant adsorption level [30]. However, a universal adsorption model for these systems to predict the mixed anionic/nonionic admicelle formation in Regions II and III would use only one value of badm for all of the total adsorption levels to describe the non-ideal anionic/nonionic surfactant interactions in the mixed admicelle, and it would incorporate all of the effects of surfactant adsorption on a heterogeneous solid surface (or the dependence upon the total adsorption level) into the anionic and nonionic surfactant admicelle standard states. Therefore, an average of badm = 5.25 was calculated from the least squares fit badm values at each individual total adsorption level investigated. It is interesting to note that mixed anionic/nonionic admicelle formation (badm = 5.25) exhibited stronger negative deviations from ideality than mixed anionic/nonionic micelle formation (bmic = 1.86). A least squares fit was again performed at each constant total surfactant adsorption level investigated using badm = 5.25, in order to recalculate the ‘‘best fit” CACSST;N values (since badm and CACSST;N in Eqs. (13) and (14) were strong functions of each other [30]). The calculated CACSST;N values are plotted as a function of the total adsorption level in Fig. 13. The calculated CACSST;N value at a total adsorption level of 20.0 lmoles/g is illustrated as ‘‘1” on Fig. 12, in order to compare the calculated CACSST;N value to the ‘‘upper boundary” experimental CACSST;N value (designated by

Fig. 13. Infinite dilution nonionic surfactant admicelle standard states versus total surfactant adsorption. CACSST;N calculated using adsorption data in the absence of micelles and using badm = 5.25 for all total surfactant adsorption levels in Regions II and III.

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‘‘2”). As can be seen in Fig. 12, the calculated CACSST;N value was very reasonable when compared to the ‘‘upper boundary” experimental CACSST;N value (as was the case for all of the total adsorption levels investigated [30]). In Fig. 13, the calculated CACSST;N values were nearly constant throughout the corresponding Region II adsorption in Fig. 4 (between 1 and 10 lmoles/g), slightly decreased throughout Region III up to a total adsorption level of 100 lmoles/g, and then slightly increased at total adsorption levels above 100 lmoles/g. Fig. 13 indicates that using one value of badm to describe the mixed anionic/nonionic admicelle interactions throughout Regions II and III, provides an accurate description of the thermodynamics of mixed anionic/nonionic admicelle formation. Regular solution theory predictions of the anionic/nonionic mixed surfactant adsorption in the absence of micelles, using badm = 5.25 for all of the total adsorption levels investigated in Regions II and III, are shown in Fig. 14 and in Figs. 9–11 (below the monomer/micelle phase boundary). The predictions of the NP(EO)10 equilibrium monomer concentrations versus the NP(EO)10 admicelle mole fraction (using badm = 5.25) at a total adsorption level of 20.0 lmoles/g is shown in Fig. 12. As can be seen in Figs. 14 and 9–11, regular solution theory provides an excellent description of the mixed anionic/nonionic surfactant adsorption in Regions II and III. 5.6. Mixed anionic/nonionic surfactant adsorption in the presence of micelles Fig. 15 illustrates the constant nonionic surfactant-only based mole fractions in the mixed monomer (YN), micelle (XN), and admicelle (ZN) pseudo-phases versus the total adsorption level, for mixed anionic/nonionic surfactant adsorption at total equilibrium concentrations above CMCm. The nonionic surfactant admicelle mole fraction ZN is nearly constant throughout all of the total surfactant adsorption levels investigated and is approximately equal to 0.5. Therefore, for mixed anionic/nonionic surfactant adsorption in the presence of micelles, the mixed admicelle formation oc-

Fig. 14. Regular solution theory predictions of the mixed SDS/NP(EO)10 surfactant adsorption in the absence of micelles. Calculated using badm = 5.25 for all total surfactant adsorption levels in Regions II and III.

425

Fig. 15. Surfactant mole fractions in the mixed micelle, admicelle, and monomer pseudo-phases versus the total surfactant adsorption level for mixed SDS/NP(EO)10 surfactant adsorption in the presence of mixed micelles.

curred at approximately a 1:1 NP(EO)10/SDS mole ratio. This result, along with the fact that pure NP(EO)10 barely adsorbs but NP(EO)10 readily adsorbs in the presence of SDS, suggests that the structure of the mixed admicelle illustrated in Fig. 7, i.e. SDS near the surface and NP(EO)10 near the water, is correct. For mixed anionic/nonionic surfactant adsorption above CMCm, the nonionic surfactant monomer mole fraction (YN) and micelle mole fraction (XN) remained nearly constant at total adsorption levels between 1 and 60 lmoles/g, as shown in Fig. 15. It is interesting to note that from 1 to 60 lmoles/g, YN is approximately equal to 0.5, while XN is approximately equal to 0.81. The NP(EO)10 surfactant molecule therefore prefers the mixed micelle pseudophase over the mixed admicelle pseudo-phase. At total adsorption levels above 60 lmoles/g in Fig. 15, both YN and XN decrease. In Fig. 12, the mixed anionic/nonionic adsorption predictions of the nonionic surfactant equilibrium concentration CN versus the nonionic surfactant admicelle mole fraction ZN at a total surfactant adsorption level of 20.0 lmoles/g is shown along with the mixed adsorption data. Even though all of the mixed adsorption data points in Fig. 12 were at total equilibrium concentrations below CMCm, at increasing NP(EO)10 admicelle mole fractions (ZN), both the adsorption data and the mixed anionic/nonionic surfactant adsorption predictions do, indeed, approach a constant ZN, as predicted by the simultaneous solution of the pseudo-phase separation models for mixed admicelle and micelle formation. The mixed anionic/nonionic surfactant adsorption predictions at total equilibrium concentrations above CMCm and at total surfactant adsorption levels of 4.0, 20.0, and 200.0 lmoles/g, are shown in Figs. 9–11. The mixed adsorption predictions were shown on surfactant phase equilibrium plots for the sake of clarity, since the 0.5 NP(EO)10/0.5 SDS and 0.6 NP(EO)10/0.4 SDS mixture adsorption isotherms in Fig. 4 overlapped. As can be seen in Figs. 9– 11, the mixed anionic/nonionic surfactant adsorption predictions above the monomer/micelle phase boundary do a fairly good job of describing the mixture adsorption data points. The adsorption predictions at a feed mole ratio of 0.5 NP(EO)10/0.5 SDS were slightly better than the predictions at a feed mole ratio of 0.6 NP(EO)10/0.4 SDS. In general, however, the model developed to describe mixed anionic/nonionic surfactant adsorption in the presence of mixed micelles predicted higher total anionic surfactant concentrations (CA) than were experimentally observed, for most of the total surfactant adsorption levels investigated in this study. There are several possible reasons for the error in the predictions above CMCm. Some possible reasons are that only the mixed adsorption data below CMCm was used to determine badm and that the infinitely dilute nonionic admicelle standard states CACSST;N

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were an approximation. Another possible source of error is in determining the monomer/micelle phase boundary in Fig. 8. Even though the anionic/nonionic surfactant mixed micelle formation equations appear to provide an excellent description of the mixture critical micelle concentration data in Fig. 2, when the same experimental data and regular solution theory predictions are plotted on the surfactant phase equilibrium plot in Fig. 8, the mixture critical micelle concentration data shows more scatter. 6. Conclusions In this study, a pseudo-phase separation model to describe mixed anionic/nonionic admicelle (adsorbed surfactant aggregate) formation was developed, analogous to the pseudo-phase separation model frequently used to describe mixed anionic/nonionic micelle formation. In this model, regular solution theory was used to describe the interactions between the anionic and nonionic surfactant molecules in the mixed admicelle, and a ‘‘patch-wise” adsorption model was used to describe surfactant adsorption on a heterogeneous solid surface. Regular solution theory was tested on specific free energy patches by examining constant total surfactant adsorption levels, and was shown to accurately describe the mixed anionic/nonionic surfactant adsorption in Regions II and III. Furthermore, mixed anionic/nonionic admicelle formation was shown to exhibit stronger negative deviations from ideality than mixed anionic/nonionic micelle formation. One value of the regular mixing parameter for mixed admicelle formation provided an adequate description of the mixed surfactant adsorption throughout Regions II and III. For the anionic/nonionic surfactant mixtures investigated in this study, some of the mixture adsorption isotherms in Regions II and III were shown to occur in the presence of mixed micelles. Therefore, the onset of mixed micelle formation in the equilibrium bulk solutions (determined by surface tension measurements) did not cause a plateau in the total surfactant adsorption; instead, the mixed surfactant adsorption greatly increased throughout Regions II and III in the presence of mixed micelles. For binary surfactant mixtures adsorbing at total equilibrium concentrations above the mixture critical micelle concentration in Regions II and III, a simultaneous solution of the pseudo-phase separation model for mixed admicelle formation and the pseudo-phase separation model for mixed micelle formation predicts that the surfactant compositions in the monomer, micelle, and admicelle pseudo-phases are constant at a constant total adsorption level. This information, along with the appropriate mass balance equations, was shown to provide an adequate description of mixed anionic/nonionic surfactant adsorption in the presence of mixed micelles. One of the major difficulties encountered in this work was that accurately measured nonionic surfactant admicelle standard states could not be determined from the adsorption data. Future work on mixed anionic/nonionic surfactant adsorption should consider selecting anionic and nonionic surfactants that both readily adsorb on the substrate, in order to determine pure anionic and pure nonionic surfactant admicelle standard states. By inputting accurately measured anionic and nonionic surfactant admicelle standard states into the pseudo-phase separation model for mixed admicelle formation, and solving the equations at each individual total surfactant adsorption level in order to determine the ‘‘best fit” dimensionless admicelle interaction parameter, it could be determined whether or not the dimensionless admicelle interaction parameter was actually a function of the total surfactant adsorption level.

Acknowledgments Financial support for this work was provided by the National Science Foundation Grant No. CBT-8814147, Department of Energy Office of Basic Energy Sciences Grant No. DE-FG05-84ER13678, Bureau of Mines Grant No. G1125132-4001, Department of Energy Grant No. DE-FG01-87FE61146, Environmental Protection Agency Grant R-817450-01-0, and the following sponsors of the Institute for Applied Surfactant Research: Akzo Nobel, Church & Dwight, Clorox, Conoco/Phillips, Dow Chemical, Ecolab, Halliburton Services, Huntsman, Oxiteno, Procter & Gamble, Sasol, S.C. Johnson, Shell Chemical and Unilever. References [1] J.F. Scamehorn, ACS Symposium Series 311 (1986) 1–27. [2] S.H. Lu, P. Somasundaran, Langmuir 24 (2008) 3874–3879. [3] K. Esumi, Y. Sakamoto, K. Yoshikawa, K. Meguro, Colloids and Surfaces 36 (1989) 1–11. [4] P. Somasundaran, Colloids and Surfaces 26 (1987) R7. [5] J.H. Harwell, B.L. Roberts, J.F. Scamehorn, Colloids and Surfaces 32 (1988) 1–17. [6] J.F. Scamehorn, R.S. Schechter, W.H. Wade, Journal of Colloid and Interface Science 85 (1982) 494–501. [7] K. Esumi, Y. Sakamoto, K. Meguro, Journal of Colloid and Interface Science 134 (1990) 283–288. [8] K. Esumi, Y. Sakamoto, K. Yoshikawa, K. Meguro, Bulletin of the Chemical Society of Japan 61 (1988) 1475–1478. [9] Y.Y. Gao, C.Y. Yue, S.Y. Lu, W.M. Gu, T.R. Gu, Journal of Colloid and Interface Science 100 (1984) 581–583. [10] M.J. Schwuger, H.G. Smolka, Colloid and Polymer Science 255 (1977) 589–594. [11] E. Fu, P. Somasundaran, Q. Xu, ACS Symposium Series 501 (1992) 366–376. [12] M.L.G. Martin, C.H. Rochester, Journal of the Chemical Society, Faraday Transactions 88 (1992) 873–878. [13] L. Huang, C. Maltesh, P. Somasundaran, Journal of Colloid and Interface Science 177 (1996) 222–228. [14] P. Somasundaran, E. Fu, Q. Xu, Langmuir 8 (1992) 1065–1069. [15] L. Huang, C. Maltesh, P. Somasundaran, Surfactant Adsorption and Surface Solubilization 615 (1995) 241–254. [16] W. Wang, J.C.T. Kwak, Colloids and Surfaces a-Physicochemical and Engineering Aspects 156 (1999) 95–110. [17] D. Goralczyk, K. Hac-Wydro, P. Wydro, Journal of Colloid and Interface Science 277 (2004) 202–205. [18] R. Denoyel, F. Giordano, J. Rouquerol, Colloids and Surfaces a-Physicochemical and Engineering Aspects 76 (1993) 141–148. [19] T. Arai, K. Takasugi, K. Esumi, Journal of Colloid and Interface Science 197 (1998) 94–100. [20] P.C. Griffiths, J.A. Roe, R.L. Jenkins, J. Reeve, A.Y.F. Cheung, D.G. Hall, A.R. Pitt, A.M. Howe, Langmuir 16 (2000) 9983–9990. [21] K. Kameyama, A. Muroya, T. Takagi, Journal of Colloid and Interface Science 196 (1997) 48–52. [22] T.C.G. Kibbey, K.F. Hayes, Journal of Colloid and Interface Science 197 (1998) 198–209. [23] M. Hulden, B. Kronberg, Journal of Coatings Technology 66 (1994) 67–77. [24] J.F. Scamehorn, R.S. Schechter, W.H. Wade, Journal of Colloid and Interface Science 85 (1982) 463–478. [25] J.J. Lopata, J.H. Harwell, J.F. Scamehorn, ACS Symposium Series 373 (1988) 205–219. [26] B.L. Roberts, J.F. Scamehorn, J.H. Harwell, ACS Symposium Series 311 (1986) 200–215. [27] J.H. Harwell, J.C. Hoskins, R.S. Schechter, W.H. Wade, Langmuir 1 (1985) 251– 262. [28] J.F. Scamehorn, R.S. Schechter, W.H. Wade, Journal of Colloid and Interface Science 85 (1982) 479–493. [29] F. Tiberg, Journal of the Chemical Society, Faraday Transactions 92 (1996) 531– 538. [30] J.J. Lopata, Ph. D. Dissertation, Department of Chemical Engineering, University of Oklahoma, (1992). [31] O.E. Yoesting, J.F. Scamehorn, Colloid and Polymer Science 264 (1986) 148– 158. [32] O. Haque, J.F. Scamehorn, Journal of Dispersion Science and Technology 7 (1986) 129–157. [33] D. Bitting, J.H. Harwell, Langmuir 3 (1987) 500–511. [34] R. Atkin, V.S.J. Craig, E.J. Wanless, S. Biggs, Advances in Colloid and Interface Science 103 (2003) 219–304.