On the Segregative Tendency of Ethoxylated Surfactants in Nonionic

ARTICLE pubs.acs.org/Langmuir

On the Segregative Tendency of Ethoxylated Surfactants in Nonionic Mixed Micelles Gerardino D’Errico* Dipartimento di Chimica, Universit
a di Napoli “Federico II”, Complesso di Montesantangelo, via Cinthia, 80126 Napoli, Italy, and CSGI (Consorzio per lo Sviluppo dei Sistemi a Grande Interfase), Firenze, Italy

bS Supporting Information ABSTRACT: The aqueous mixtures of two nonionic surfactants, pentaethyleneglycol monohexyl ether (C6E5) and hexyl dimethyl phosphine oxide (C6DMPO), were investigated by the pulsed-gradient stimulated-echo NMR technique. Quite unexpectedly, the results show that the mixture behavior significantly deviates from ideality. Particularly, analysis of the data indicates that, in the mixed aggregates, C6E5 molecules prefer to be surrounded by other C6E5 molecules, forming domains of hydrated ethoxilic chains on the micellar surface. Molecular reasons for the segregative tendency of ethoxylated surfactants and its applicative implications in formulation technology are discussed.

’ INTRODUCTION In the last two to three decades, the technological exploitation of surfactant mixtures for both industrial and domestic applications has grown dramatically and continues to increase steadily. In fact, in practical fields, mixed surfactants work better than a single surfactant because the composition and concentration of the mixture can be optimized for each specific application. Particularly, mixtures containing ethoxylated surfactants are appealing to the formulation technologist, for both technological and ecological reasons.1,2 Ethoxylated surfactants present the feature that both the hydrophilic and the hydrophobic chain can be varied, thus allowing a fine-tuning of the aggregation behavior.3 The development of the applications of surfactant mixtures has promoted a wide scientific interest in the subject, from both experimental and theoretical viewpoints. The main results of these studies have been recently summarized in an excellent monograph.4 In general, the aggregation behavior of surfactant mixtures is substantially different from that of the single components. These differences arise from specific interactions (synergistic or antagonistic) between the surfactants in the mixture.5-8 In most of the studies present in the literature, mixtures of surfactants with long hydrophobic tails (in which the number of carbon atoms is equal to or greater than 12) are considered. Much less attention has been paid to mixtures of surfactants with short hydrophobic tails. Because these surfactants micellize at relatively high concentrations, an experimental investigation of premicellar solutions is possible, thus allowing an analysis of the interactions among the surfactant monomers as well as between them and the solvent.9 Consequently, it is possible to relate the properties of the aqueous surfactant mixture to specific interactions among the components. Furthermore, for surfactants with r 2011 American Chemical Society

short hydrophobic tails, the hydrophobic interaction driving the micellization process is reduced, and consequently, other kinds of interactions among the surfactants can be better detected and analyzed. In the past, we have investigated the mixtures of a shortchained (hexyl or octyl) nonionic ethoxylated surfactant with either an anionic sulfonate or a cationic trimethylammonium bromide surfactant.10-13 Our results showed that, in these systems, mixed micellization is strongly favored because the ethoxylated surfactants reduce the electrostatic repulsions among the ionic headgroups. The effects of other kinds of interactions (steric, charge-dipole, dipole-dipole, van der Waals, etc.) as well as the intrinsic behavior of ethoxylated surfactants were not detectable, most likely because they are covered by electrostatic effects. For this reason, we decided to investigate mixtures of two nonionic surfactants, and the results of this study are presented in the present work. Particularly, mixtures of an ethoxylated (pentaethyleneglycol monohexyl ether, C6E5) and a phosphineoxide surfactant (hexyl dimethyl phosphine oxide, C6DMPO) have been considered. Among the various experimental techniques that have been used to characterize surfactant mixtures, the pulsed-gradient spin-echo (PGSE)-NMR technique and its improved versions are some of the most informative. This technique, which was first applied to this kind of system by Carlfors and Stilbs,14 allows the independent determination of the intradiffusion coefficients of all the components present in the system (i.e., water and surfactants) in various aggregation states (i.e., monomers or micelles).15,16 Consequently, a complete description of the system can be obtained, which constitutes a reliable basis to test Received: September 30, 2010 Revised: December 28, 2010 Published: March 03, 2011 3317

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Chart 1. Bond Structure of the Chemical Substances used in the Present Work

theoretical treatments representative of the mixed aggregation process. Here, the pulsed-gradient stimulated-echo (PGSTE)-NMR technique is used to investigate the heavy water-C6E5-C6DMPO ternary mixtures. The intradiffusion data, analyzed in the framework of the pseudo-phase separation model for mixed micellization,17 have allowed the determination of the critical micellar concentration (cmc) and the partitioning of both surfactants between the aqueous and the micellar pseudophases. The results of the experimental investigation are presented and discussed in the first part of the paper. Details of the data analysis, which has been conducted through well-established methods, are available in the Supporting Information (SI). In the second part of the paper, the experimental results are compared with the predictions of different theoretical models of mixed micellization, in an attempt to understand the molecular reasons for the system behavior. Finally, possible implications of our findings in practical applications of ethoxylated species in surfactant mixtures are discussed.

’ EXPERIMENTAL SECTION Materials. Pentaethyleneglycol monohexyl ether (C6E5) was received from Bachem with a declared purity of >99%. Hexyl dimethyl phosphine oxide (C6DMPO) was an Organometallics product with a declared purity of >99%. Surfactants were reagent grade and were used without further purification. As for solvents, D2O was obtained from Sigma (>99.96% isotopic purity) and used for intradiffusion measurements, whereas doubly distilled water was used for viscosity and density measurements. All solutions were prepared by weight. As discussed later, in the micellar composition range, solubilized tetramethylsilane (TMS, Sigma product, purity >99.9%) was used to measure the micelle intradiffusion coefficients. The molecular formulas of the chemical substances are shown in Chart 1. Intradiffusion Measurements. The intradiffusion coefficients characterize the translational Brownian motion of each constituent of a multicomponent mixture in the absence of macroscopic concentration gradients.18,19 The expression “self-diffusion coefficients”, which is more widely used for indicating the same quantities, should be correctly used only for one-component, i.e., pure systems. In the present work, experiments for the determination of the intradiffusion coefficients were performed on a Bruker 600 DRX spectrometer. Concerning the ternary heavy water-C6E5-C6DMPO system, different sets of measurements were performed. In each of them, the total surfactant molality was progressively increased while the mole fraction of the surfactant mixture, xC6E5, was kept constant. xC6E5 is defined as xC6 E5 ¼

mC6 E5 mC6 E5 þ mC6 DMPO

ð1Þ

where mC6E5 and mC6DMPO are the C6E5 and C6DMPO stoichiometric molalities in the system, respectively. Various xC6E5 values were considered (xC6E5 = 0, 0.1, 0.25, 0.5, 0.75, 1). xC6E5 = 0 and xC6E5 = 1

correspond to the binary heavy water-C6DMPO and heavy waterC6E5 systems, respectively. For each ternary mixture, PGSTE-NMR measurements allowed the separate determination of the intradiffusion coefficients for both surfactants, DC6E5 and DC6DMPO, respectively. For the binary heavy water-C6DMPO system, the solvent intradiffusion coefficient, DW, was also determined. 1 H NMR experiments for diffusion measurements were performed at 25 °C using a stimulated echo sequence. The sample temperature was controlled within 0.1 °C during measurements by the passage of controlled-temperature air through the sample holder. For a system of monodisperse diffusing particles, the PGSTE-NMR echo signal, I, is given by20,21 "
# I0 2τ TM IðkÞ ¼ exp þ þ kD 2 T2 T1

ð2Þ

where k = γ2g2δ2(Δ - δ/3). γ is the magnetogyric ratio of the proton, g is the strength of the magnetic field gradient pulses, δ is the pulse duration, and Δ is the distance between the leading edges of the gradient pulses. In this work, echo delays were kept constant so that the relaxation effect would not be considered; Δ was set to 100 ms and the pulsed gradients, with a duration of 2-8 ms depending on the sample, were increased from 3 to 99 G cm-1 in 32 equally spaced steps. I0 is the equilibrium magnetization, which is a constant for a given set of experimental conditions, and τ and TM are the separation of the rfpulses of the stimulated spin-echo sequence. T2 and T1 are the transverse and the longitudinal relaxation time, respectively. Equation 2 can be linearized by reporting ln(I/I0) as a function of k. The obtained intradiffusion coefficients were calibrated to heavy water with trace amounts of light water (DHDO = 1.872  10-9 m2 s-1, ref 22). Concerning C6E5, the intensity of the NMR signal of the protons of the ethoxylic group was followed (chemical shift = 3.6 ppm). DC6DMPO was determined by following the NMR signal of the methyl groups in the surfactant headgroup (a doublet at 1.5 ppm). The solvent intradiffusion coefficient, DW, was determined by following the signal at 4.8 ppm, due to the HDO impurity of the deuterated solvent. As discussed later, in the micellar composition range, solubilized TMS was used to measure the micelle intradiffusion coefficients, DM. Intradiffusion data are available in the SI. The experimental errors of the intradiffusion coefficients were generally less than 2%. Viscosity and Density Measurements. For the binary waterC6DMPO system, the viscosity was determined in the same concentration range explored by intradiffusion measurements. Analysis of viscosity data allowed the estimation of the hydration of micellized surfactant, as detailed in the SI. Concerning the ternary water-C6E5-C6DMPO system, for each considered surfactant mole fraction, the viscosity at the cmc, ηcmc, was measured to evaluate the hydrodynamic radius of the micellar aggregates from their intradiffusion coefficient through the Stokes-Einstein relation. The viscosity measurements were carried out with an Ubbelhode viscometer with a relatively long water flow time (203 s) to minimize the kinetic energy correction. All measurements were carried out in a water bath (mgw Lauda CS) at 25.00 ( 0.01 °C. At least 3 runs were performed on each solution, with times differing no more than 0.05 s among them. The estimated error of the relative viscosity data is less than 8  10-4. The densities of the solutions at the cmc, dcmc, necessary to compute the dynamic viscosity from the kinematic viscosity, were measured through an Antoon Paar DMA 60 vibrating tube densimeter operating at 25.00 ( 0.01 °C, using distilled water and air (at measured pressure and humidity) for calibration. To correct the viscosity data obtained in light solutions back to those in deuterated water, it is necessary to multiply them by the factor 1.23,23 which is the ratio of viscosity for heavy to light water. 3318

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Figure 1. Intradiffusion coefficient of C6DMPO (b), TMS (9), and solvent (O) vs C6DMPO molality in the binary heavy water-C6DMPO system at 25 °C.

Table 1. Micellization Parameters for the Binary Systems Heavy Water-C6DMPO and Heavy Water-C6E5 at 25 °C C6DMPO -1

a

Figure 2. Intradiffusion coefficient of C6DMPO (b), C6E5 (2), and TMS (9) vs total surfactant molality in the ternary heavy water-C6E5C6DMPO system (xC6E5 = 0.5).

Table 2. Equilibrium and Transport Parameters for the Heavy Water-C6E5-C6DMPO System at 25 °C cmc

C6E5a

cmc/mol kg

0.5

0.1

Rapp/Å

12 ( 1

18 ( 1

hm

98 ( 11

146 ( 15

hM

10 ( 2

20 ( 2

N

11 ( 1

23 ( 3

xC6E5 mol kg-1

Data from refs 24-26.

dcmc  10-3 a ηcmc  103 a DM,cmc  109 kg m-3

kg m-1 s-1

m2 s-1

Rapp Å

N

0.00

0.50

0.994417

1.29

0.118 ( 0.004 12 ( 2 11

0.10

0.28

0.996876

1.12

0.145 ( 0.006 11 ( 2

7

0.25

0.24

0.997118

1.10

0.168 ( 0.005

5

0.50 0.75

0.25 0.15

0.997324 0.998637

1.10 1.07

0.114 ( 0.005 13 ( 2 12 0.104 ( 0.005 15 ( 2 16

1.00

0.10

0.999203

1.05

0.092 ( 0.003 18 ( 1 23

9( 1

’ RESULTS AND DISCUSSION

Density and viscosity data refer to C6E5-C6DMPO mixtures in light water.

Binary Heavy Water-C6DMPO System. A comparative analysis of the self-aggregation behavior of each single surfactant in aqueous solution is a solid basis for the characterization of their mixtures. The C6E5 micellization has been widely studied in the past.24,25 In the present work, we report the results of a preliminary study on the diffusion properties of the binary heavy water-C6DMPO system. Figure 1 shows both the C6DMPO intradiffusion coefficient, DC6DMPO, and the solvent intradiffusion coefficient, DW, plotted as a function of the surfactant molality, mC6DMPO. In the same figure, the micellar intradiffusion coefficient, measured directly by following the NMR signal of TMS added in traces26 to the system, DCM6DMPO, is also shown. Analysis of these data has been conducted by following well-established methods, whose details can be found in the SI. Briefly, both the DC6DMPO and DW trends allow evaluating the C6DMPO critical micellar concentration, cmcC6DMPO; from the DCM6DMPO values, by using the Stokes-Einstein equation, the hydrodynamic size of the aggregates, Rapp, can be estimated. Analysis of the DW data, according to a two-site model, leads to the number of water molecules hydrating each surfactant in both monomeric and micellized form, hm and hM, respectively.27 Finally, the obtained Rapp and hM values allow estimating the aggregation number of C6DMPO micelles, N. The values of all these parameters are reported in Table 1, in which they are also compared with those reported in the literature for the heavy water-C6E5 system. Inspection of the table reveals that C6E5 presents a higher tendency to selfaggregate, as highlighted by its lower cmc in comparison with that observed for C6DMPO. This means that despite the fact that

alkyl phosphine oxides are less hydrophilic among the surfactants derived from group V oxides (i.e., arsine and ammine oxides),28 they are more hydrophilic than ethoxylated surfactants. The relatively higher aggregation number of C6E5 could be related to the tendency of ethoxylated surfactants to form micellar aggregates surrounded by a quite compact shell, often referred to as palisade, formed by hydrated ethoxylic chains interacting each other.3 Ternary Heavy Water-C6E5-C6DMPO System. Analysis of the surfactants’ intradiffusion coefficients gives a lot of information on the aggregation behavior of the ternary mixtures. As an example, the intradiffusion coefficients relative to the set of measurements with xC6E5 = 0.5 are shown in Figure 2. The complete treatment of these data, conducted by well-established methods, is detailed in the SI. Here, only the main results are presented. Both the C6E5 intradiffusion coefficient, DC6E5, and that of C6DMPO, DC6DMPO, when plotted as a function of the total surfactant molality, m = mC6E5 þ mC6DMPO, show a slope change at the cmc, indicating the comicellization of the two surfactants. The cmc value of the ternary mixtures varies between the cmc values of the two surfactants when reported as a function of xC6E5 (Table 2 and Figure 3). However, the cmc trend shows two marked slope changes: starting from xC6E5 = 0 (pure C6DMPO micelles), the addition of C6E5 causes an initial steep decrease of the cmc (xC6E5 e 0.1), followed by its stabilization at a nearly constant value (0.1 e xC6E5 e 0.5) and a final smooth decrease (xC6E5 g 0.5). In Figure 2, the mixed micelle intradiffusion coefficient, DM, determined by following the signal of TMS added in trace amounts, is also reported. Analysis of these data, as detailed in

a

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Figure 3. Critical micelle concentration vs the mole fraction of the surfactant mixture in the ternary water-C6E5-C6DMPO system. The predictions of the ideal solution mixing model (dotted line), the regular solution mixing model (dashed line) and the molecular-thermodynamic approach (dotted-dashed line) are also reported.

Table 3. Aqueous and Micellar Pseudo-Phases Composition at the cmc for the Ternary Heavy Water-C6E5-C6DMPO System at 25 °C XC6E5

YC6E5

0.00

0.00

0.10

0.18

0.25

0.43

0.50

0.65

0.75

0.86

1.00

1.00

the SI, allows for the computation of the apparent hydrodynamic radii of the mixed micelles through the Stokes-Einstein equation. The Rapp values, collected in Table 2, pass through a shallow minimum at xC6E5 = 0.25; upon further increasing xC6E5, Rapp steeply increases. In the micellar concentration range the experimental intradiffusion data are the mean values of the free and micellized molecules. Consequently, their analysis allows the estimation of the molality of free and micellized surfactant i in the mixture, F M indicated as mFi and mM i , respectively. In turn, the mi and mi data allow for the computation of the “surfactant mole fractions” in the two pseudophases (i.e., aqueous medium and micelles) coexisting above the cmc mFC6 E5 ð3Þ X C6 E 5 ¼ F mC6 E5 þ mFC6 DMPO YC6 E5 ¼

mM C6 E 5

mM C6 E 5 þ mM C6 DMPO

3 4 3 πRapp NA  M YC6 E5 ðV C6 E5 þ hC6 E5 VH2 O Þ þ YC6 DMPO ðV C6 DMPO

* is molar solvent volume; VhC6E5 and VhC6DMPO are the where VH2O partial molar volumes of the micellized C6E5 and C6DMPO,  10-6 m3 mol-1, ref 25; V respectively (V hC6DMPO = hC E = 309.75 -6 6 35 -1 172.9  10 m mol , ref 28). The partial molar volumes and the hydration numbers of both surfactants were considered to be independent of the micelle composition, so that the values measured for the correspondent binary system water-surfactant were used. Although unavoidable, this is a quite rough approximation, and consequently, the aggregation numbers computed through eq 5 give only qualitative indications (estimated uncertainty ∼20-30%). Inspection of Table 2 shows that N passes through a minimum with increasing xC6E5. Comparison of the Experimental Results with Theoretical Models of Mixed Micellization. Application of theoretical models of mixed micellization to our experimental findings could help in identifying the molecular reasons of the observed behavior. In the pseudophase separation model, the cmc of the mixture of two surfactants, such as C6E5 and C6DMPO, is related to those of the pure components by 1 x C6 E 5 1 - x C6 E5 ¼ þ cmc γC6 E5 cmcC6 E5 γC6 DMPO cmcC6 DMPO



þ hM C6 DMPO VH2 O Þ

ð5Þ

ð6Þ

where γi is the activity coefficient of component i in the micelles, whereas the monomeric phase is assumed to be ideal; cmci is the critical micellar concentration of surfactant i in the binary system water-surfactant. Furthermore, the compositions of the micellar pseudophase, Yi, as well as that of the monomeric pseudophase, Xi, are related to the cmc of the surfactant mixture as follows:

ð4Þ

The XC6E5 and YC6E5 values extrapolated at the cmc, i.e., at infinite dilution of micelles, are collected in Table 3 and plotted in Figure 4. In the entire composition range, the micelles contain a larger fraction of the ethoxylated surfactant than the bulk solution; thus, YC6E5 is higher than XC6E5. It is possible to combine the YC6E5 and Rapp data to estimate the aggregation number of micelles, N, according to the relation N ¼

Figure 4. Micellar pseudophase composition, YC6E5, vs. aqueous pseudophase composition, XC6E5, for the ternary heavy water-C6E5C6DMPO system at the cmc. The predictions of the ideal solution mixing model (dotted line), the regular solution mixing model (dashed line), the molecular-thermodynamic approach (dotted-dashed line), and the Georgiev approach (dashed-double dotted line) are also reported.

YC6 E5 γC6 E5 cmcC6 E5 ¼ XC6 E5 cmc

ð7Þ

YC6 DMPO γC6 DMPO cmcC6 DMPO ¼ XC6 DMPO cmc

ð8Þ

At the cmc, i.e., at infinite dilution of micelles, Xi = xi. As a first approximation, one could assume an ideal behavior also for the micellar pseudophase (γi = 1). This approach, proposed by Clint,29 furnishes good results for mixed micelles formed by very similar surfactants, such as mixtures of different ethoxylated surfactants30 or mixtures of different bile salts.31 The ideal model, in our case, predicts the micellar composition at the cmc drawn in Figure 4 (dotted line). It is found that the ideal model overestimates YC6E5 in the whole composition range. The cmc trend can be also predicted (dotted line in Figure 3). Inspection of the 3320

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figure reveals that the cmc is overestimated for xC6E5 < 0.25 and underestimated at higher xC6E5 values. The strong deviation from the ideal behavior observed for a mixture of nonionic surfactants such as that considered here is quite unexpected. The comparison between our experimental results and the prediction of the ideal model gives some indications on the synergistic or antagonistic behavior of the surfactants in the micellization process. Indeed, trying to explain what these results indicate, one could say that the addition of C6E5 to an aqueous mixture of C6DMPO strongly favors micellization. In other words, C6E5 induces C6DMPO micellization. In contrast, the addition of C6DMPO to an aqueous mixture of C6E5 does not favor micellization. Holland and Rubingh32 utilized the regular solution approximation for the micellar pseudophase, assuming ideal entropy variation for surfactants mixing in the aggregates. In this case, the activity coefficient γi can be expressed as the function of the micelle composition by introducing a single interaction parameter β γC6 E5 ¼ exp½βð1 - YC6 E5 Þ2 

ð9Þ

γC6 DMPO ¼ expðβYC6 E5 2 Þ

ð10Þ

β corresponds to the energy interaction difference between equal (i.e., HC6E5-C6E5 and HC6DMPO-C6DMPO) and nonequal (HC6E5C6DMPO) surfactant molecules. Application of the regular solution model to our experimental micellar composition data, keeping β as an optimization parameter, furnishes the estimation of the micellar composition showed in Figure 4 (dashed line, β = -1.4 ( 0.2). This β value corresponds to the cmc prediction showed in Figure 3. Inspection of both figures shows that also the regular solution model is not suitable to describe the behavior of the system under consideration. In this respect, it is interesting to note that the same model was found to satisfactorily describe the mixed micellization process in the aqueous mixtures of C6E5 and the anionic surfactant C6SO3Na.11 In that system, the prevalent effect was found to be the reduction of the electrostatic interactions between the anionic headgroups due to the interposition of the ethoxylic chains. In such a situation, the regular solution approach, which assumes ideal entropy of mixing and ascribes the nonideality of the system only to enthalpic effects, is a reasonable approximation. Coming back to the mixtures considered in the present work, which were formed by two nonionic surfactants, other reasons for deviation from ideality have to be sought. Various attempts have been made to go beyond the regular solution theory.33-36 Among others, particularly valuable is the “molecular-thermodynamic approach”, proposed by Blankschtein and co-workers, in which a macroscopic thermodynamic theory of micellar solutions and a microscopic molecular description of mixed aggregate formation are blended.37-40 In some details C6 E 5 C6 DMPO þ YC6 DMPO gmic gmic ¼ YC6 E5 gmic C E , C DMPO þ YC6 E5 YC6 DMPO gmic6 5 6 þ kB T½YC6 E5 ln YC6 E5 þ YC6 DMPO ln YC6 DMPO  ð11Þ 6 E5 6 DMPO and gCmic are the free energy of micellization of where gCmic the two pure surfactants. These terms, which represents the free energy change when a surfactant molecule is transferred from the aqueous medium to a micellar aggregate, are computed as the sum of the contributions of the different molecular events into

which the process can be conceptually divided i i i ¼ gw=hc þ ghc=mic þ gσi þ gsti gmic

ð12Þ

giw/hc

where represents the free energy gain in transferring the hydrophobic tail of surfactant i from water to the micellar core; gihc/mic is the free energy loss associated with the anchoring of one tail end to the core surface; giσ is the free energy per monomer associated with creating an interface between the micellar core and the bulk solution; gist represents the steric interactions between the surfactant headgroups at the interface. Structural details on the surfactant molecules (e.g., alkyl chain length and volume, area occupied by the headgroup on the micellar surface, etc.), which can be generally desumed from the analysis of their molecular structure, are required to compute the values of 6E5,C6DMPO = the different contributions. Finally, the term gCmic C6E5,C6DMPO C6 E5,C6DMPO þ gelec should reflect contributions due ghc to surfactants mixing within the aggregate. gChc6E5,C6DMPO, accounting for the mixing of the hydrophobic tails in the micellar core, is null because the two surfactants in consideration have the 6 E5,C6DMPO is null because same tail length. At the same time, gCelec 6E5,C6DMPO is both surfactants are nonionic. Consequently, gCmic predicted to be null for the mixture under consideration.37 The knowledge of gmic allows the estimation of both the cmc and micelle composition. The resulting model has been demonstrated to reasonably describe the properties of aqueous solutions of surfactant mixtures (e.g., cmc value, micellar composition, and aggregation number) using solely information on the nature of the surfactant molecules and on the state of the system (e.g., temperature, pressure, and ionic strength).41 However, the predicted micelle composition and cmc values reported in Figures 4 and 3, respectively, show that this sophisticated method also fails to furnish reliable results for our system. Particularly, it overestimates the effectiveness of C6E5 and C6DMPO in reducing the mixture cmc, i.e., in favoring micellization. This finding indicates that the behavior of C6E5-C6DMPO mixtures cannot be desumed from the molecular features of the single surfactants, even when considered in great detail. Thus, the nonideality of the system has to be ascribed to some specific interaction between the aggregated molecules. An alternative approach has been proposed by Georgiev.42 Differently from the models discussed above, this one has not been developed in the framework of the pseudophase separation description of mixed micellization; consequently, it does not allow prediction of cmc values. The Georgiev model relies on the extension of the Markov chain model to mixed surfactant systems: mixed micellization is described by four equilibrium reactions that, for our system, can be expressed as follows: ∼ C6 E5 þ C6 E5 ¼ ∼ C6 E5 C6 E5

ð13Þ

∼ C6 E5 þ C6 DMPO ¼ ∼ C6 E5 C6 DMPO

ð14Þ

∼ C6 DMPO þ C6 E5 ¼ ∼ C6 DMPO C6 E5

ð15Þ

∼ C6 DMPO þ C6 DMPO ¼ ∼ C6 DMPO C6 DMPO ð16Þ where ∼C6E5 and ∼C6DMPO are the “aggregate active centers”; ∼C6E5 C6E5, ∼C6E5 C6DMPO, ∼C6DMPO C6E5, and ∼C6DMPO C6DMPO are the “dyad aggregate active centers”. According to this model, the aggregate active center and the dyad aggregate active center are the last and the pair of the last and next to last surfactants addited to the aggregates. Two interaction parameters 3321

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Figure 5. Application of the model proposed by Georgiev (ref 42) to the ternary heavy water-C6E5-C6DMPO system.

are defined (gC6E5 and gC6DMPO), which reflect the tendency of a given surfactant to be situated, in the mixed aggregate, closer to other molecules of the same kind with respect to those of the other surfactant. Thus, the value of gC6E5 indicates the preference of C6E5 for other C6E5 molecules rather than for C6DMPO ones. The Georgiev model requires the determination of XC6E5 and YC6E5 to be applied. Indeed, gC6E5 and gC6DMPO can be obtained from the experimental XC6E5 and YC6E5, by defining v = YC6E5/ YC6DMPO and w = XC6E5/XC6DMPO. Then, the following relation holds: ðv - 1Þ v ¼ gC6 E5 - 2 gC6 DMPO ð17Þ w w Figure 5 shows that the (v - 1)/w linearly depends on v/w2; i.e., gC6E5 and gC6DMPO remain constant in the whole composition range (gC6E5 = 2.1 ( 0.3; gC6DMPO = 0.50 ( 0.03). This evidence indicates that this model well describes the system behavior, as also confirmed by Figure 4, in which the model prediction of the YC6E5 vs XC6E5 trend is shown. Being gC6E5 > 1 and gC6DMPO < 1, one can conclude that, in the mixed aggregate, C6E5 molecules prefer to be surrounded by molecules of the same kind. This holds true even in C6DMPO-rich micelles. In contrast, C6DMPO molecules prefer to be surrounded by C6E5 ones. This phenomenon explains the cmc experimental trend shown in Figure 3: starting from pure C6DMPO aggregates, the insertion of C6E5 molecules favors micellization, lowering the cmc value more than expected on the basis of the ideal solution model. In contrast, starting from pure C6E5 aggregates, the insertion of C6DMPO molecules does not favor micellization, leading to the cmc values higher than those expected on the basis of the ideal solution model. The C6E5 tendency to “segregate” from C6DMPO could be ascribed to attractive interactions among the ethoxylic chains.43 These interactions have been described in the literature as related to the wide network of H-bonds that hydrated ethoxilic chains can form, in a sort of cooperative process.44,45 In the case of ethoxylated surfactants with long headgroups, the attraction among them can be balanced and overcome by the steric repulsion; however, our evidence indicates that this repulsion can be neglected for ethoxylated surfactants with relatively short headgroups. The C6DMPO tendency to mix with C6E5 in mixed micelles can be related to the charge polarization on the DMPO group, which can induce some electrostatic repulsion among C6DMPO headgroups, thus favoring the intercalation of the C6E5 ethoxilic heads.

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’ CONCLUSIONS In this work, an experimental investigation on the heavy water-C6E5-C6DMPO system has been reported and discussed, the focus being on the peculiarities of the mixtures of different nonionic surfactants. The results, quite unexpectedly, have shown that such mixtures can show significant deviation from the ideal behavior. Particularly, the ethoxylated surfactant has been found to segregate from the other one. Because ethoxylated surfactants are the most used nonionic surfactants in practical applications, our results are relevant in designing and formulating new surfactant mixtures. In fact, domains formed on the micelle surface by hydrated ethoxylic chains could act as preferential solubilization site of specific substances (e.g., aromatics, see ref 3). Formation of such domains has to be expected not only in mixtures of non ionic surfactants, but also in formulations including ionic surfactants, whenever the ionic strength is high enough to minimize the electrostatic repulsion on the micellar surface. The possibility to selectively solubilize different substances on the surface of the same micellar aggregate dramatically enlarges the opportunities in practical applications of surfactant formulations. ’ ASSOCIATED CONTENT

bS

Supporting Information. Detailed discussion of intradiffusion and viscosity data. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel: þ39081 674248. Fax: þ39081 674090. E-mail: gerardino. [email protected].

’ ACKNOWLEDGMENT This research was carried out with financial support from the Italian MIUR (PRIN 2008, Grant No. 2006030935). The author thanks Prof. Lucia Costantino for her helpful comments. ’ REFERENCES (1) Tadros, T. F. Applied Surfactants: Principles and Applications; Wiley-VCH: Weinheim, Germany, 2005. (2) Scott, M. J.; Jones, M. N. Biochim. Biophys. Acta 2000, 1508, 235–251. (3) Vitagliano, V.; D’Errico, G.; Ortona, O.; Paduano, L. Physicochemical properties of ethoxylated surfactants in aqueous solutions. In Encyclopaedia of Surface and Colloid Science; Hubbard, A. T., Ed.; Marcel Dekker, New York, 2002; pp 4105-4123. (4) Abe, M.; Scamehorn, J. F. Mixed Surfactant Systems; Marcel Dekker, New York, 2005. (5) Rosen, M. Prog. Colloid Polym. Sci. 1998, 109, 35–41. (6) Nordstierna, L.; Furo, I.; Stilbs, P. J. Am. Chem. Soc. 2006, 128, 6704–6712. (7) Almgren, M.; Garamus, V. M.; Nordstierna, L.; Luc-Blin, J.; Stebe, M. J. Langmuir 2010, 26, 5355–5363. (8) Landry, J. M.; Marangoni, D. G. Colloid Polym. Sci. 2008, 286, 655–662. (9) Vitagliano, V.; D’Errico, G.; Ortona, O.; Paduano, L. Mixed micellar aggregates of nonionic surfactants with short hydrophobic tails. In Mixed Surfactant Systems; Abe, M., Scamehorn, J. F., Ed.; Marcel Dekker: New York, 2005; pp165-204. 3322

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