Evidence for a Critical Micelle Concentration of Surfactants in

Feb 15, 2013 - Evidence for a Critical Micelle Concentration of Surfactants in. Hydrocarbon Solvents. Gregory N. Smith,. †. Paul Brown,. †,§. Sar...
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Evidence for a Critical Micelle Concentration of Surfactants in Hydrocarbon Solvents Gregory N. Smith,† Paul Brown,†,§ Sarah E. Rogers,‡ and Julian Eastoe*,† †

School of Chemistry, University of Bristol, Cantock’s Close, Bristol, BS8 1TS, United Kingdom ISIS-STFC, Rutherford Appleton Laboratory, Chilton, Oxon, OX11 0QX, United Kingdom

‡

ABSTRACT: The concentration-dependent aggregation of two surfactants, anionic sodium dioctylsulfosuccinate (Aerosol OT or AOT) and nonionic pentaethylene glycol monododecyl ether (C12E5), has been studied in cyclohexane-D12 using small-angle neutron scattering (SANS). A clear monomer-toaggregate transition has been observed for both surfactants, spherical inverse micelles for AOT and hank-like micelles for C12E5. This suggests that a critical micelle concentration exists for surfactants of these kinds in nonpolar solvents. The nature of the transition is different for the two surfactants. AOT aggregates are the same size and shape with decreasing concentration until a sharp critical micelle concentration, after which they cannot be detected. However, C12E5 aggregates gradually decrease in size. These differences demonstrate that the strength of the solvophobic effect can influence the formation of surfactant aggregates in nonaqueous solvents.

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INTRODUCTION Aggregates of amphiphiles in nonpolar solvents, generally called reverse or inverse micelles, find application in many areas of modern science and technology. They can be employed as reaction media for the synthesis of nanoparticles1 and as charge control additives,2,3 for example. The ability of surfactant inverse micelles to stabilize charge in nonpolar solvents is a well-known effect that finds use in industry, such as in petrochemicals as aids to disperse components4,5 and to prevent explosions.6 In recent years, the use of surfactants as charge control additives has enabled the development of electrophoretic displays, now commonly used as electronic paper.7,8 The advance in the technological applications of inverse micelles has coincided with advances in neutron scattering instruments that are now able to detect scattering at lower intensities and a wider range of momentum transfers than previously possible. These developments provide an opportunity to reconsider the nature of aggregation in lowconcentration surfactant solutions and consequently low scattering intensities. Despite the importance of inverse micelles in many applications, the fundamental physical−chemical understanding of their properties and formation is not well understood. This is in contrast to the case in water, where the details of the aggregation of amphiphiles is well developed.9 The thermodynamic origin of aggregation is typically explained using the hydrophobic effect concept originating from the chemical dissimilarity between water and the hydrophobic groups.10 For inverse micelles, the polar headgroups aggregate into the micelle centers rather than the hydrocarbon tails.11 Intermo© 2013 American Chemical Society

lecular interactions in nonpolar solvents are not as strong as hydrogen bonds in water, as can be seen from the significant difference in the Hildebrand solubility parameter (δ, the cohesive density), which has a value of 47.8 MPa1/2 for water and 16.8 MPa1/2 for a typical nonpolar solvent, cyclohexane.12 Hence it might be expected that the free energy reward of micellization is less in a nonpolar solvent than in water. Therefore, the analogous solvophobic effect driving force for inverse micelle formation in a nonpolar solvent is not expected to be as strong as the hydrophobic effect in water. These differences between water and nonpolar solvents as media for aggregation also suggest that an intrinsic property of amphiphiles in water, the critical micelle concentration (CMC), may not exist in both environments. Aggregation is known to occur in nonpolar solvents, but it has been suggested that there may be no distinct CMC.13 The weak solvophobic effect means that the presence of trace amounts of water may be a significant driving force for the formation of inverse micelles. Previous reports have demonstrated that the observed CMC of sodium dioctylsulfosuccinate (Aerosol OT or AOT) in organic solvents depends on the amount of water present.14 By considering the thermodynamics of cluster formation, it has been suggested that, in the absence of water, AOT would form such large aggregates that it should effectively be insoluble.15 Despite the ongoing debates on the existence of a CMC in nonpolar solvents, methods commonly used for studying Received: January 10, 2013 Revised: February 13, 2013 Published: February 15, 2013 3252

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surfactant aggregates at low concentrations, indicating differences between the modes of aggregation of ionic and nonionic surfactants in nonpolar media.

aqueous systems have been extended to nonpolar solvents. These approaches have drawbacks in nonpolar solvents, which present difficulties in identifying a clear and precise value for the CMC. As can be seen in Table 1, a wide range of values

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Table 1. CMC of AOT in Cyclohexanea Measured by Various Methods cyclohexane

a

CMC/(mmol L−1)

method

1 0.2 0.225 6.2 1.80

light scattering17 dye particle18 SANS19 water solubilization20 dye particle21

EXPERIMENTAL METHODS

Sample Preparation. Sodium dioctylsulfosuccinate (AOT, 98%, Aldrich) and pentaethylene glycol monododecyl ether (C12E5, ≥98.0% GC, Sigma) were used to prepare solutions. AOT was purified by dissolution in dry diethyl ether and centrifugation to remove undissolved salts. C12E5 was used as supplied. Cyclohexane-D12 (>99.50 atom % D, Apollo Scientific) was used as supplied. Solutions were prepared by dilution from a stock solution 48 h before SANS analysis. The water content of surfactant solutions was measured using Karl Fischer titration (Metrohm KF Coulometer) in cyclohexane-H12 prepared at the same concentrations. The concentration of water in cyclohexane-H12 was 31.8 ± 0.4 ppm. The number of water molecules per AOT molecule was 0.80 ± 0.02, and that per C12E5 was 0.0661 ± 0.0004. Small-Angle Neutron Scattering (SANS). SANS was carried out on the Sans2d small-angle diffractometer at the ISIS Pulsed Neutron Source (STFC Rutherford Appleton Laboratory, Didcot, U.K.).25,26 A simultaneous Q range of 0.004−0.80 Å−1 was achieved by utilizing an incident wavelength range of 1.75−16.5 Å and employing an instrument setup of L1 = L2 = 4 m, with the 1 m2 detector offset vertically 150 mm and sideways 269 mm. Q is defined as

Relative permittivity (εr) = 2.024.16

have been reported in cyclohexane. Measuring CMCs using dyes or water solubilization necessitates the addition of a third species to the solution and may, therefore, lead to micelles formed from nucleation or induced by the presence of dyes rather than aggregation. Light-scattering signals may be weak because of a low refractive index contrast; electrical conductivity measurements in nonpolar solvents are difficult because of small numbers of charge carriers at the typically low surfactant concentrations. Surface tensiometry, although commonly used in aqueous systems, is not viable because the surfactant monolayers and nonpolar solvents have similar surface energies. Interfacial tensiometry between nonpolar solvents and water might seem promising, but the kinetics of surfactant partitioning makes these dynamic measurements difficult to analyze. In summary, these techniques primarily measure the consequence of inverse micelle formation and not the actual presence or absence of micelles. Small-angle neutron scattering (SANS) presents a promising approach for detecting the presence of inverse micelles and elucidating structures. Importantly, SANS is a direct technique that does not rely on proxy probes or secondary parameters. Also, by selective deuteration, high contrasts can be obtained. As such, SANS has been used to attempt measurements of the CMC of anionic AOT in cyclohexane-D1219 and benzene-D622 and of the nonionic glycol monododecyl ethers (CiEj) in a range of deuterated solvents.23 Because these measurements were performed nearly 30 years ago, the low-intensity resolution prevents distinguishing the scattered signal from the solvent background, and the narrow Q range limits the certainty with which the aggregates can be modeled. Modern SANS instruments overcome these shortcomings by providing a higher flux, better signal-to-noise ratio, and wider range of accessible Q values. These improvements mean that there will be a better chance of unambiguously observing aggregates at low concentration. Therefore, it is now appropriate to reopen the case to verify the concept of a nonaqueous CMC with higher-resolution SANS experiments than were previously available. Here, scattering profiles have been obtained for the anionic surfactant AOT and the nonionic surfactant C12E5 as a function of concentration in cyclohexane-D12. Previous research into the aggregation of AOT and C12E5 in cyclohexane-D12 suggests a possible CMC for C12E5 of 2.5−5 wt % and a maximum possible value for the CMC of AOT of 0.50 wt %.24 Surfactant concentrations were chosen in logarithmically spaced steps to provide results above and below the expected CMC. The results presented provide deeper insight into the nature of

Q=

4π sin

θ 2

(1)

λ

where θ is the scattering angle and λ is the incident neutron wavelength. Samples were prepared in deuterated solvents, providing the necessary contrast, and were contained in 5 mm path length Hellma quartz cells. The beam diameter was 12 mm. Each raw scattering data set was corrected for the detector efficiencies, sample transmission, and background scattering and converted to scattering cross-section data (∂Σ/∂Ω vs Q) using the instrument-specific software.27 These data were placed on an absolute scale (cm−1) using the scattering from a standard sample (a solid blend of hydrogenous and perdeuterated polystyrene) in accordance with established procedures.28 Data have been fitted to either a sphere or a cylinder model using the FISH iterative fitting program.29 The scale factor and background were varied until there was an acceptable fit to experimental data, and then the geometric parameters were varied until the best fit was achieved. The fit values for radii and lengths are considered to have a certainty of ±1 Å (high Q resolution of Sans2d). The form factor (P(Q)) is linked to the geometry of the aggregates. No structure factor (S(Q)) was required to fit the data, indicating that the aggregates do not significantly interact in this low-dielectric solvent. The form factor for spheres is given in eq 2, where r is the radius. The polydispersity of spheres is determined from a Schultz distribution.30

3[sin(Qr ) − Qr cos(Qr )] (Qr )3

P(Q )sphere =

(2)

The form factor for n randomly oriented rods is given in eqs 3 and 4, integrated over angle γ between the Q vector and the axis of the rod. J1(x) is the first-order Bessel function, r is the radius, l is the length, and V is the volume (πr2l).31 P(Q )rod = n

∫0

π /2

F 2(Q ) sin(γ ) dγ

(3)

( 12 Ql cos γ) 2J1(Qr sin γ)

sin F(Q ) = ΔρV

1 Ql 2

cos γ

Qr sin γ

(4)

The form factor is scaled to the experimentally measured intensity (I(Q)) by the scattering intensity at Q = 0, which is equal to N(Δρ)2V2, where N (cm−3) is the number concentration of particles, 3253

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Figure 1. SANS profiles of AOT in cyclohexane-D12 with varying concentration. All concentrations (shown in the legend) are in mmol kg−1. At these four concentrations, scattering was observed above the weak solvent background. Solid lines show model fits to a noninteracting, polydisperse spherical form factor. Δρ (cm−2) is the scattering length density difference, and V (cm3) is the particle volume. For convenience, the effective scale factor, A, is given in terms of the volume fraction, ϕ, and Δρ.

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A = 10−24ϕ(Δρ)2

the most concentrated sample determined by extrapolation to low Q. This parameter is defined as [I(Q)]/[I(Q = 0)]0. It is, by definition, approximately equal to 1 for low Q values of the most concentrated solutions, and the scattering from lowerconcentration samples should equal the inverse of the logarithmic step (l) raised to the power of the number of times diluted (n).

(5)

RESULTS The concentrations are presented in molal units (mmol kg−1) rather than molar units (mmol L−1) because this requires fewer assumptions about the ideality of mixing and is the quantity directly measured when preparing solutions. The concentrations in molal units are approximately equal to the molar units scaled by the density of cyclohexane-D12 (0.893 g mL−1). The most concentrated solution of AOT at 13.4 mmol kg−1 compares to 11.7 mmol L−1, and the most concentrated solution of C12E5 at 221 mmol kg−1 compares to 197 mmol L−1. Sodium Dioctylsulfosuccinate (AOT). Figure 1 shows SANS data for the most concentrated AOT solutions. The scattering profiles are all similar, and the only change as a function of concentration is a decrease in the magnitude of I(Q), as expected. The data have been fit to a noninteracting, polydisperse sphere model with no S(Q), which has been previously shown to provide good agreement with experimental data.24 The fit parameters are shown in Table 2. The sizes of

[I(Q = 0)]n = l −n[I(Q = 0)]0

Figure 2 shows SANS profiles for the three lowest concentrations. The scattering observed for the 0.21 mmol kg−1 solution is representative of the scattering that would be expected if spherical aggregates were present. The values of I(Q) for all of these solutions are very low, and it therefore is difficult to assign the absence of micelles with certainty. However, long collection times of up to 4 h were used to improve the signal-to-noise ratio so that measurements are reliable. Additionally, the scattering intensity for the 0.050 mmol L−1 and 0.012 mmol kg−1 solutions scale with concentration, and the baseline at high Q is greater than can be seen for spherical aggregates. Altogether, this suggests that inverse micelles are not present. Pentaethylene Glycol Monododecyl Ether (C12E5). Measurements were also made with the nonionic surfactant C12E5, being suitable because the anticipated CMC is at a higher concentration than for AOT and because monomeric scattering can be observed that makes studying the sub-CMC region possible. In cyclohexane, the surfactant is known to form hank-like (small cylindrical) micelles with the hydrophilic ethylene oxide groups in the center and the hydrophobic tails extended into the solvent.23,24 Figure 3 shows the SANS profiles for solutions of C12E5 in cyclohexane-D12. In this case, the data have been fit to a noninteracting cylinder model with no S(Q), which has been previously shown to provide good agreement with experimental data.24 Table 3 shows the fit parameters used for all solutions. The scattering profiles are similar, and the small differences between shapes are due to the effect of having two variable parameters. As with AOT, the intensity decreases as the concentration of surfactant decreases. Although the scattering profiles appear to be qualitatively similar, the cylinder dimensions change on dilution as the aggregation numbers

Table 2. SANS Data Fitting Parameters for AOT Solutions [AOT]/ (mmol kg−1)

[I(Q = 0)]n/ [I(Q = 0)]0

A/ (10−5 cm−4)

radius/Å

polydispersity

13 3.4 0.74 0.21

1 0.26 0.058 0.019

1.24 0.325 0.0697 0.0207

15.5 15.2 15.4 15.4

0.03 0.08 0.04 0.02

(6)

the inverse micelles at all concentrations are found to be essentially the same, with radii of 15 Å and polydispersities of between 0.02 and 0.08, consistent with previous reports.19,24 Aggregates have been observed at a low concentration (0.21 mmol kg−1 or 0.18 mmol L−1), as in previous SANS reports. The scattering intensity in Figure 1 is presented as both the absolute intensity measured from the instrument (I(Q) in cm−1) and the intensity normalized by the Q = 0 intensity of 3254

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Figure 2. SANS profiles of AOT in cyclohexane-D12 with varying concentration. All concentrations (shown in the legend) are in mmol kg−1. The lowest two concentrations do not show any scattering above the baseline. Straight lines are shown for the two scattering profiles at the numerical average of all data points. The scattering arising from a 0.21 mmol kg−1 solution is shown to indicate the profile expected from spherical inverse micelles.

Figure 3. SANS profiles of C12E5 in cyclohexane-D12 with varying concentration. All concentrations (shown in the legend) are in mmol kg−1. Scattering is observed at all concentrations, fitting the expectation of monomeric scattering. Solid lines show model fits to a noninteracting cylindrical form factor.

molecular weight, gives the aggregation number (nagg), as shown in eq 7.

Table 3. SANS Data Fitting Parameters for C12E5 Solutions [C12E5]/ (mmol kg−1)

[I(Q = 0)]n/ [I(Q = 0)]0

A/ (10−4 cm−4)

radius/Å

length/Å

220 88 33 13 7.6 2.1

1 0.31 0.098 0.035 0.011 0.0056

1.71 1.03 0.704 0.324 0.105 0.0521

5.8 4.4 3.2 3.0 3.1 2.8

33.2 28.6 24.0 21.0 20.0 20.2

nagg

⎧ 4πr 3 ⎪ for spheres ⎪ 3vm =⎨ ⎪ πr 2l for cylinders ⎪ ⎩ vm

(7)

nagg, plotted as a function of concentration, is shown in Figure 4. The aggregation number varies as a function of concentration differently for the two surfactants. For AOT, it is constant at 23 until no micelles are present at 0.21 mmol kg−1. For C12E5, it decreases from 5 at 220 mmol kg−1 to 1 at 33 mmol kg−1. These trends continue at higher concentrations.24 The CMC is determined to be the concentration where nagg increases from 0 (in the case of AOT) or 1 (in the case of C12E5) and is defined by the midpoint between the final monomeric solution and the first micellar one. Table 4 shows the value of the CMC measured in cyclohexane compared to literature values in water.

decrease to approach the limit of single-molecule scattering. Both the radius and length decrease with decreasing concentration for the most concentrated solutions but reach a plateau of approximately 3 Å in radius and 20 Å in length at 13 mmol kg−1. These dimensions agree with previous results.24 Aggregation Number. It is possible to estimate the micellar volume by treating the micelles as monodisperse geometric objects, using either the radius of a sphere (r) or the radius (r) and length (l) of a cylinder. Dividing by the molecular volume (vm), as calculated using the density and 3255

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Figure 4. Aggregation numbers of AOT and C12E5 as a function of concentration. The lines drawn through both sets of data are guides for the eye. The line through the AOT data is a constant value drawn at the numerical average of the four measurements, and the line through the C12E5 data is fit to an exponential function.

and C12E5 would then serve to reduce the driving force for aggregation, and the surfactant aggregates appear more gradually over a broad concentration range. It is not possible to determine whether this tendency to aggregate arises from spontaneous self-assembly or from hydrated water nucleation, but the outcome is the same. In water, the hydrophobic effect can be only slightly tuned while retaining the amphiphilicity. Hydrocarbon and fluorocarbon surfactants may show different aggregation properties in water,35,36 but this provides a limited set of hydrophobic moieties. There are more ways to achieve polarity in surfactant headgroups; nonionic, anionic, cationic, and zwitterionic groups can all be incorporated into typical surfactants. In cyclohexane, AOT has a “strongly” solvophobic headgroup whereas, in contrast, C12E5 has a “weakly” solvophobic one. The difference in the onset of aggregation between the two surfactants suggests an interesting feature of the solvophobic effect that could be generalized for all solutes and solvents. By considering the driving force for aggregate formation as the difference between solvent and amphiphile polarities, it may be possible to tune the “criticality” of aggregate formation by using more- or less-polar solutes or solvents. A dead zone of solvent quality has been observed where surfactant and solvent polarities are similar and no aggregation is found to occur,24 and it would be expected that near this point the onset of aggregation would be gradual and that away from this point the onset of aggregation would be sharp.

Table 4. CMC Measured for AOT and C12E5 solvent a

water cyclohexane-D12b a b

[AOT]/(mmol kg−1)

[C12E5]/(mmol kg−1)

2.56 0.13 ± 0.08

0.065 61 ± 28

Literature values using surface tension: AOT32 and C12E5.33 Measured in this study.

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DISCUSSION From these results on micellar solutions in a typical hydrocarbon solvent, it appears that there is a critical concentration where micelles begin to form, as in aqueous solutions. However, for these two surfactants, the nature of the monomer-to-micelle transition is very different. The ionic surfactant, AOT, sharply changes from a monomeric surfactant solution to an inverse micellar dispersion. However, the nonionic surfactant C12E5 changes more gradually from a free monomeric surfactant solution to hank-like micelles. It is worthwhile to consider how the CMC should be defined given the evolution of the aggregation number with the total surfactant concentration. Previous studies of low-concentration aggregates of AOT in nonpolar solvents,19,22 including this one, are consistent with a sharp transition from micelles to aggregates, suggesting a CMC transition analogous to that seen in aqueous systems.32 For studies of CiEj surfactants at low concentrations,23 surfactants that exhibit a transition from monomers to micelles also show a plateau in nagg at higher concentration. The nature of the headgroups and chains of AOT and C12E5 is obviously different, which offers an explanation of this behavior. Although both surfactants are polar, the calculated dipole moments of the two differ (18 D for AOT and 5.7 D for C12E5).34 This marked difference in polarity is considered to be the origin of the contrasting monomer-to-aggregate transition. The large dissimilarity in polarity between cyclohexane and AOT means that there is a strong propensity for aggregation, to minimize contact between the polar group and nonpolar solvent. The lower dissimilarity in polarity between cyclohexane

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CONCLUSIONS By using SANS, aggregation has been unambiguously observed for two surfactants of extremely different polarities, anionic AOT and nonionic C12E5, in a nonpolar solvent, cyclohexaneD12. Long measurements with high neutron flux have made it possible to identify the presence of surfactant aggregates at very low concentrations and to collect data for scattering at high Q values. This has enabled confident identification of the presence of micelles and modeling of their structure. Previous attempts to measure CMCs for AOT inverse micelle formation, for 3256

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Langmuir example, have shown a low degree of precision with values varying by more than an order of magnitude.17,18,20,21 (See Table 1.) The only technique that reliably gives a consistent, and importantly low, value is neutron scattering.19,22,23 Therefore, unlike in water for which a range of techniques have been developed to measure CMCs based on proxies of micelle formation, in nonpolar solvents, scattering techniques that directly measure the presence or absence of aggregates are required to identify the CMC with any degree of certainty. By considering both ionic and nonionic surfactants, it is clear that the monomer-to-aggregate transition is different for amphiphiles of different polarity. AOT demonstrates a sharp critical inverse micelle concentration, and C12E5, a more gradual transition. This indicates that the nature of the solvophobic effect driving force for aggregate formation in nonpolar solvents can be tuned by varying the nature of the solvophobic group. Neutron scattering can confirm the existence of a CMC for inverse micelle formation in nonpolar solvents. As mentioned in the Introduction, the presence of water is recognized to be an important consideration in the formation of inverse micelles,14 and future neutron scattering experiments will explore the effects of water. The preparation of strictly anhydrous systems, however, is extremely difficult, or practically impossible, to achieve. Obtaining surfactants without hydrated water is either challenging or not possible: nonionic surfactants are known to be hygroscopic,37 anionic surfactants require water during synthesis,32,38 and cationic surfactants can potentially be synthesized under anhydrous conditions39 but as dry powders are only sparingly soluble in aliphatic solvents.40 Even if completely anhydrous surfactants could be produced, organic solvents still solubilize trace amounts of water.41 Given these experimental challenges, the use of simulation will be important in further understanding the formation of inverse micelles. Molecular dynamics simulations have proven useful in probing the structure of microemulsions, including relatively dry ones with w > 1.42−45 It may therefore be more possible to study systems devoid of water by simulation rather than experiment, and collaboration between both approaches should be sought. These results present insight into the physical−chemical nature of the monomer-to-micelle transition in nonpolar solvents, indicating the similarities and differences between aqueous and nonaqueous solvents. For AOT, the transition is a sharp, critical one as in water. By varying the surfactant headgroup polarity, it is possible to tune the nature of the aggregation from sharp to broad in a way not possible in water. It is not only insight into the driving force of micelle formation that is gained. Aggregates in nonpolar solvents are important as charge control additives and as nanoreactors, and by understanding the low-concentration structure of these surfactants, it will be possible to better tune the structures formed and enable efficient use of these additives.

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ACKNOWLEDGMENTS

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REFERENCES

Article

G.N.S. acknowledges Merck Chemicals Ltd. U.K., an affiliate of Merck KGaA, Darmstadt, Germany, and the U.K. Engineering and Physical Sciences Research Council (EPSRC) for the provision of a CASE Ph.D. studentship. The U.K. Science and Technology Facilities Council (STFC) is thanked for allocation of beamtime at ISIS and grants towards consumables and travel.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

§ Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.

Notes

The authors declare no competing financial interest. 3257

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dx.doi.org/10.1021/la400117s | Langmuir 2013, 29, 3252−3258