Microstructures in Aqueous Solutions of a Polyoxyethylene Trisiloxane

Aug 27, 2008 - Physics Department, Institute for Energy Technology, P.O.B. 40, N-2027 Kjeller, Norway. ReceiVed January 31, 2008. ReVised Manuscript ...
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Langmuir 2008, 24, 10637-10645

10637

Articles Microstructures in Aqueous Solutions of a Polyoxyethylene Trisiloxane Surfactant and a Cosurfactant Studied by SANS and NMR Self-Diffusion Harald Walderhaug* Department of Chemistry, UniVersity of Oslo, P.O.B. 1033 Blindern, N-0315 Oslo, Norway

Kenneth D. Knudsen Physics Department, Institute for Energy Technology, P.O.B. 40, N-2027 Kjeller, Norway ReceiVed January 31, 2008. ReVised Manuscript ReceiVed July 16, 2008 Microemulsion samples of a polyoxyethylene trisiloxane surfactant, water, and 1-decanol are investigated using pulsed field gradient NMR and small-angle neutron scattering (SANS) to determine the solution structure. The surfactant/ decanol weight ratio has been kept constant at values of 10:1, 8:1, and 6:1 under variation of water content. The temperature was 32 °C for the measurement series at the weight ratio of 10:1 to avoid phase separation at high water content. Also, aqueous surfactant solution samples have been investigated as a function of composition and temperature. Water-rich samples consist of micelles that are close to spherical at very low surfactant concentration and grow into anisometric, that is, oblate formed aggregates, at higher surfactant (or surfactant and decanol) concentration. The aggregates grow with increasing temperature, most probably due to dehydration of the hydrophilic groups. In a concentration range around 50 wt % water, the systems form bicontinuous structures. SANS data are used to estimate surfactant film properties using a model developed for interpretation of neutron scattering data from related systems.

Introduction Silicone surfactants form a group of polymeric surface active molecules made of silicone and polyethers.1-3 One class of these compounds consists of a hydrophobic permethylated siloxane group coupled to a polyoxyethylene chain. These surfactants find applications in cosmetics, in the manufacture of plastic foams, and as spreading and wetting agents. Systems of this kind have recently attracted attention also from academia. By comparing the phase behavior of these systems with that of corresponding hydrocarbon based surfactants with the same or similar hydrophilic groups, more can be learned concerning self-assembly processes. A number of studies of phase behavior and microstructures formed when surfactants of this kind are mixed with water and various cosurfactants or oil have been published in the near past.3-10 Three of these works cover phase behavior and studies of microstructure in aqueous silicone surfactant systems * To whom correspondence should be addressed. Telephone: + 47 22 85 55 88. Fax: + 47 22 85 54 41. E-mail: [email protected]. (1) Hill, R. M. In Chemistry and Technology of Surfactants; Farn, R. D., Ed.; Blackwell: Oxford, 2006; pp 186-203. (2) Hill, R. M. Curr. Opin. Colloid Interface Sci. 2002, 7, 255. (3) Hill, R. M. In Siloxane Surfactants; Hill, R. M., Ed.; Surfactant Science Series 86; Marcel Dekker: New York, 1999, pp 1 -47. (4) Soni, S. S.; Sastry, N. V.; Aswal, V. K.; Goyal, P. S. J. Phys. Chem. B 2002, 106, 2606. (5) Soni, S. S.; Sastry, N. V.; Joshi, J. V.; Seth, E.; Goyal, P. S. Langmuir 2003, 19, 6668. (6) Lin, Y.; Alexandridis, P. Langmuir 2002, 18, 4220. (7) He, M.; Hill, R. M.; Lin, Z.; Scriven, L. E.; Davis, H. T. J. Phys. Chem. 1993, 97, 8820. (8) Li, X.; Washenberger, R. M.; Scriven, L. E.; Davis, H. T.; Hill, R. M. Langmuir 1999, 15, 2267. (9) Garti, N.; Aserin, A.; Wachtel, E.; Gans, O.; Shaul, Y. J. Colloid Interface Sci. 2001, 233, 286. (10) Walderhaug, H. J. Phys. Chem. B 2007, 111, 9821.

that in addition also contain a third polar component that influences the solvent’s properties.4-6 Four studies address the phase behavior and microstructure in aqueous systems of polyoxyethylene trisiloxane surfactants of the type investigated in the present study.7-10 One of these studies covers the phase behavior of aqueous solutions of a number of trisiloxane poly(ethylene oxide) chains that vary in ethylene oxide segment number, n, from 5 to 18.7 The study of Li et al. investigates the influence of silicon oil additives on the trisiloxane poly(ethylene oxide) surfactant with n equal to 12 ethylene oxide (EO) units in the hydrophilic part of the surfactant.8 Rather few works seem to have addressed the phase behavior and structural aspects of aqueous systems of these types of surfactants when mixed with typical cosurfactants.9,10 There, some conclusions regarding the structures formed in the microemulsions as a function of composition were drawn, and one of this type of surfactant with the trade name Silwet L7607 (see below) was used to investigate the structures formed when mixed with water, forming solutions over the whole composition range. In addition, 1-decanol or 1-dodecanol was used to form microemulsion samples at various compositions covering a large area of the microemulsion stability region of the corresponding phase diagram, using pulsed field gradient NMR.10 Pulsed field gradient Fourier-transform NMR (PGSE-FT NMR)11-16 and small-angle neutron scattering (SANS)16-18 are very powerful tools to investigate structures formed in organized (11) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (12) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1. (13) So¨derman, O.; Stilbs, P. Prog. NMR Spectrosc. 1994, 26, 445. (14) Guering, P.; Lindman, B. Langmuir 1985, 1, 464. (15) Fukuda, K.; So¨derman, O.; Lindman, B.; Shinoda, K. Langmuir 1993, 9, 2921.

10.1021/la800344h CCC: $40.75  2008 American Chemical Society Published on Web 08/27/2008

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liquids such as microemulsions and other surfactant or polymer systems. In the present work, the Silwet L7607 surfactant is used to make aqueous solutions and, together with 1-decanol, microemulsion samples. SANS measurements are used to investigate the structures formed in this system as a function of its composition. Comparison will be made with results from pulsed field gradient NMR measurements of self-diffusion coefficients of the various components.

Experimental Section Materials. The surfactant was supplied by GE Bayer Silicones and was used as received. This type of surfactant is commonly denoted M(D′En)M, where, in our case, n ) 16 for the Silwet L7607 surfactant, and corresponds to a molecular weight of ∼1000 g/mol. See also ref 8 for more details. In that work, a molecular structure for this type of compound is also given. 1-Decanol (99%) was from Aldrich. Light water (H2O) was of “Type 1” (Millipore) quality with conductivity < 5.6 µS · m-1. Heavy water (D2O) (>99.5%, type “CIL-4”) was provided by the Institute for Energy Technology, Norway. The samples were prepared by weighing the various components, followed by thorough mixing in closed glass ampules. Only samples with a clear appearance and with no tendency to cloud at experimental temperatures (see below) over a time span of several days were investigated. The samples were subsequently transferred to 5 mm NMR tubes for the NMR experiments and to 1 mm quartz cuvettes for the SANS measurements. Methods. The PGSE-FT NMR experiments were performed on a Bruker DMX-200 spectrometer. For details of the experimental procedure, see ref 10 and references therein. The intensities I of the signals of the various components are fitted to the following equation:

I ⁄ I0 ) exp(-(γgδ)2(∆ - δ ⁄ 3)D)

Figure 1. SANS data for the two-component water-surfactant system as a function of surfactant concentration up to 14 wt %. The lines through the data sets represent fits to eq 2. See text. Inset: Guinier plot of one of the low-concentration samples (1.75 wt %), showing the linearity of the fit. This plot gives a radius of gyration (Rg) equal to 21.2 ( 0.5 Å. The q-range used was 0.02-0.07 Å-1.

(1)

I0 is the corresponding signal intensity without magnetic field gradient g, and γ is the magnetogyric ratio of the proton. δ denotes the duration of the magnetic field gradients (typically 2 ms), and ∆ is the diffusion observation time, typically 100 ms. D is the self-diffusion coefficient of the component. The temperature was (32 ( 1) °C. The SANS experiments were carried out on the SANS installation at the IFE reactor at Kjeller, Norway. The investigated scattering vector q-range was defined by the neutron wavelength λ between 5.1 and 10.2 Å, and the sample-to-detector distance was from 1.0 to 3.4 m, covering the experimental q-range 8 × 10-3 e q e 0.22 Å-1. In all the SANS measurements, D2O was used as solvent instead of H2O to obtain good contrast and low incoherent background. The measuring cells were placed on a copper base for good thermal contact and mounted in the sample chamber that was maintained at the desired temperature. Standard reductions of the scattering data, including transmission corrections, were conducted by incorporating data collected from an empty cell, the beam without a cell, and the blocked-beam background. The data were transformed to an absolute scale (coherent differential cross section (dσ/dΩ)) by calculating the normalized scattered intensity from direct beam measurements.19 For the cases where subsequently a whole pattern fit was performed, the incoherent background was included in the model as a q-independent but sample adjustable background value, I(q) ) Imodel(q) + Ibackground.

Results 1. The Surfactant-Water System. 1.1. Solution Structure Dependence on Surfactant Concentration. Binary composition(16) Olsson,U. In Handbook of Applied Surface and Colloid Chemistry; Holmberg, K., Ed.; John Wiley & Sons Ltd.: Chichester, UK, 2002; Vol. 2, pp 333-356. (17) Pedersen, J. S. AdV. Colloid Interface Sci. 1997, 70, 171. (18) Bagger-Jo¨rgensen, H.; Olsson, U.; Mortensen, K. Langmuir 1997, 13, 1413. (19) Wignall, G. D.; Bates, F. S. J. Appl. Crystallogr. 1987, 20, 28.

temperature phase diagrams for aqueous solutions of the surfactants with similar structure as the Silwet L7607 surfactant, but with number of oxyethylene units, n, equal to 12 and 18, have been published.7 There is a lower consolute temperature of ∼41 °C for the n ) 12 surfactant at low surfactant concentration. At temperatures below ∼10 °C, a hexagonal liquid crystalline phase exists at concentrations around 50 wt %. For the n ) 18 surfactant, the hexagonal phase exists up to a temperature of ∼55 °C at concentrations around 60 wt % surfactant. At higher surfactant concentrations, an inverse micellar phase exists for both surfactants. The Silwet L7607 surfactant PGSE-FT NMR measurements that were performed at 20 °C are reported separately.10 The self-diffusion coefficients of the water and surfactant components clearly showed that the structure was of water-in-oil (w/o) type at high surfactant concentrations, that is, above 60% by weight (wt %), and of oil-in-water (o/w) type (i.e., micelles) at surfactant concentrations below ∼40 wt %. In between these concentration regimes, the structure is judged to be bicontinuous. In the present study, SANS measurements were conducted at various temperatures in the mutual miscibility region. The SANS patterns from measurements at 20 °C for various concentrations in the range ∼0.4-60 wt % are shown in Figures 1 and 2. At low surfactant concentrations, below ∼2 wt %, the patterns show single particle behavior with no sign of mutual interaction between the micelles. In general, particle-particle interactions must be taken into account, and for monodisperse spheres the scattered intensity I(q) may be written as I(q) ) N P(q) S(q), where N denotes the number density of particles (micelles), N ) φm/Vm, where φm and Vm are the volume fraction of particles and volume per particle, respectively.16 P(q) is the form factor. A general expression for P(q), including that for spheres and prolate and oblate ellipsoids

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Figure 2. SANS data at 28, 50, and 69 wt % for the two-component surfactant-water system showing fits to the Teubner-Strey model, eq 3.

of revolution, may be written in the following way:20

(∫

P(q) ) (∆F)2Vm2

π⁄2

0

2

)

F1[q, r(R, ε, R)](sin R)dR

(2)

where ∆F is the constant scattering length density (∆F ) F(micelle) - F(solvent)), r(R,ε,R) ) R(sin2 R + ε2 cos2 R)1/2, ε denotes the eccentricity, and Vm ) 4πεR3/3 is the volume of the particle. F1 is the standard expression for the form factor for a uniform sphere. With ε ) 1, the expression is valid for spheres. Prolate ellipsoids are described by ε > 1, and oblate ellipsoids are described by ε in the range 0 < ε < 1, in eq 2. The structure factor S(q), that contains information on intermicellar interactions, approaches a constant value at zero or very low interaction. For the case of monodisperse spheres interacting with a hard-sphere potential, a classical expression known as the Percus-Yevick expression exists.21,22 At concentrations below ∼2 wt %, that is, at volume fractions φ e 0.02, the interparticle interaction is expected to be negligible for this system. A Guinier plot may then be employed to obtain information about the radius of gyration Rg for the micelles, as illustrated in the inset in Figure 1. A nearly constant value, with an average Rg equal to 21.6 ( 0.5 Å, was found for these concentrations. If, as a first assumption, we regard the particles as spherical, this value of Rg would correspond to a radius of approximately 28 Å. The hydrated ethylene oxide (EO) chains contribute insignificantly to the neutron scattering contrast (see below). If we therefore add 20-22 Å corresponding to the expected length of the hydrated EO chains (see below), an overall radius for the micelles may be estimated to ∼50 Å. From PGSEFT NMR on the same system, a hydrodynamic radius RH of micelles that were assumed to be of spherical shape was estimated to be 35 ( 1 Å.10 The difference between the two estimates of the micellar radius may be traced to the fact that the micelles are not completely spherical even at low concentrations. The SANS measurements seem to be more sensitive to deviation from spherical shape of the aggregates than the NMR selfdiffusion measurements. (20) Truffier-Boutry, D.; De Geyer, A.; Guetaz, L.; Diat, O.; Gebel, G. Macromolecules 2007, 40, 8259. (21) Percus, J. K.; Yevick, G. J. Phys. ReV. 1958, 110, 1. (22) Ashcroft, N. W.; Lekner, J. Phys. ReV. 1966, 145, 83.

At concentrations between ∼2 and 30 wt %, both SANS and NMR self-diffusion data strongly indicate that anisometric aggregates are formed around 20 °C. The SANS intensity data may be fitted using a form factor P(q) describing oblate formed micelles with an axial ratio of ∼2:1 and a major semiaxis of ∼36 Å for the samples measured within this concentration region. For the concentrations of 3.5, 7, and 14 wt %, a structure factor was necessary to include together with the form factor in order to obtain adequate fits. We employed a hard-sphere interaction (Percus-Yevick) in this case. It turns out that a slight asymmetry is found when employing the ellipsoidal model also for the SANS data at concentrations below 2 wt %. For the 0.44, 0.87, and 1.75 wt % systems, an axial ratio of ∼1.6:1 was found, demonstrating that the micelles actually show a small deviation from the spherical shape, as discussed above in connection with the Guinier plots. All these different fits are shown together with the data in Figure 1. It may sometimes be difficult to discriminate between the two forms of ellipsoids (oblate and prolate) at small axial ratios. It would actually be possible with the present system to obtain nearly the same visual quality of the fits by using a prolate instead of an oblate model. However, in order for the prolate model to be fitted to the data, very unphysical values for the axis ratios would have to be employed. In addition, obstruction factors (see below) for the water solvent measured by PGSE-FT NMR indicate oblate formed micelles in this concentration range with steadily increasing axial ratio, that is, ∼5:1 at 14 wt %, and in the range 1-5:1 for concentrations between 5 and 14 wt %.10 Thus, a growth into anisometric aggregates is demonstrated, even though the quantitative figures do not completely agree. Taken into account the experimental uncertainty in the NMR results, the agreement seems acceptable. At concentrations around 50 wt %, self-diffusion coefficients of surfactant and water have shown that the system is bicontinuous. SANS intensity data at these concentrations form a characteristic peak, as shown in Figure 2. The 50 wt % data may be fitted to the periodic random two-phase or Teubner-Strey model developed for the interpretation of scattering data from bicontinuous microemulsions with the same amount of oil and water.23,24 The model is therefore not a priori applicable to aqueous two-component surfactant systems or to the other systems in the present study. We will, however, use it here as a parametric model and obtain an interpretation of the parameters. The intensity I(q) of the scattered radiation may for this model be written in the following way (non-normalized units):

{[

I(q) ) 8πφ(1 - φ)(∆F)2 ξ-2 +

]

4π2 2 + d2

[

2 ξ-2 -

] }

4π2 2 q + q4 2 d

-1

(3)

The factor 8πφ(1 - φ)(∆F)2 may be regarded as a constant for each material. ξ is a correlation length describing loss of long-range order, and d is a parameter describing local periodicity. The local periodicity reflects the ordering of water and oil into separate microdomains. For two-component systems with only water and surfactant, we will consider “oil” as the hydrophobic part of the surfactant. The loss of long-range order is characteristic for such systems and is manifested in an optically isotropic appearance on a macroscopic level. For the scattered intensity at 50 wt % (see Figure 2), we find that the data may be fitted to eq 3 with a correlation length ξ of (23) Carnahan, N. F.; Starling, K. E. J. Chem. Phys. 1969, 51, 635. (24) Teubner, M.; Strey, R. J. Chem. Phys. 1987, 87, 3195.

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Figure 3. SANS pattern of a two-component aqueous solution at a concentration of 0.87 wt % surfactant as a function of temperature in the interval 5-50 °C. The lines through the data represent fits to eq 2. See text. Table 1. Characteristic Dimensions in Units of Å Obtained for the 0.87 wt % Sample As the Temperature Is Varied between 5 and 50 °Ca T (°C)

Rg (Å)

a (Å)

b (Å)

5 20 30 40 50

19.5 21.8 24.7 28.8 34.1

18.5 18.9 18.6 17.7 17.6

29.1 32.2 35.7 44.4 58.4

a The radius of gyration Rg is obtained from Guinier plots in the q-range 0.02-0.07Å-1, and the minor (a) and major (b) axis listed are obtained from a fit to a model corresponding to an ellipsoid of revolution. The standard deviations of the numbers listed are 0.1 Å.

44 Å and a periodicity d of 55 Å. We will return to a discussion on the structure in this 50 wt % solution after a further interpretation of the parameters from the Teubner-Strey analysis below. In Figure 2 is also shown data for two other concentrations, that is, 28 and 69 wt %. For the highest concentration investigated with SANS, that is, 69 wt %, it was still possible to fit the intensity data to eq 3, even though the standard deviation is larger in this case. At this concentration, the system most probably forms inverse micelles.7 1.2. Aggregate Structure As a Function of Temperature. In Figure 3, the SANS pattern at a concentration of 0.87 wt % surfactant in aqueous solution is shown as a function of temperature in the interval 5-50 °C. The radius of gyration obtained via Guinier plots is found to increase steadily from 19.5 to 34.1 Å as the temperature is changed, as shown in Table 1. In this table, we have also included the results from an independent measurement at 20 °C for this sample (presented already in Figure 1). In the same way as mentioned earlier in connection with the 20 °C data, also the data in Figure 3 can be best fitted to the form factor P(q) for an oblate ellipsoid of revolution with a rather small axial ratio. The results shown were obtained without any restrictions on value of the semiaxes, and in all cases the model converges rapidly to an oblate ellipsoid. The minor axis is found to be remarkably stable for all temperatures. It stays in the range 18.3 ( 0.7 Å, whereas the major axis increases gradually from

29 to 58 Å in the temperature range from 5 to 50 °C. For the n ) 12 analogue to the Silwet L7607 surfactant, we note that a phase separation takes place at a temperature close to 50 °C at this concentration.7 The axial ratio changes from approximately 1.6:1 to 3.3:1 in the temperature range studied. It is thus clear that the aggregates grow into a gradually more anisometric form at elevated temperatures. Moreover, as the minor axis is more or less constant, this means that the volume of the micelles increases with temperature. At this low surfactant concentration, the EO groups of the surfactant are fully hydrated, and bind three water molecules each, at 25 °C.9 A well-known property of polyoxyethylene chains in aqueous solution is their decreasing ability to bind water with increasing temperature.25 At a certain temperature, the so-called “cloud point”, the chains start to interact attractively, and eventually a phase separation takes place. For nonionic surfactants such as the oligo EO alkyl ethers CmEn, where m denotes the length of the hydrophobic hydrocarbon chain and n denotes the number of EO groups, the same phenomenon is observed.26 The EO chains repel each other at low temperature when they are fully hydrated, but the interaction becomes steadily more attractive as the temperature is increased, inducing a decrease in the curvature of the aggregates and a tendency for aggregate growth.26,27 The Silwet L7607 surfactant belongs to the group of nonionic surfactants consisting of a hydrophobic group and a hydrophilic EO chain (see above). One may therefore expect an aggregate growth with temperature, as demonstrated by the present SANS measurements. Also, in ref 7, a comparison is made between the phase behavior of aqueous solutions of CmEn surfactants and aqueous solutions of polyoxyethylene trisiloxane surfactants. 2. Water-Surfactant-Cosurfactant Microemulsions at Various Constant Surfactant/Cosurfactant Weight Ratios. 2.1. Surfactant/Cosurfactant Weight Ratio of 10:1. This surfactant/cosurfactant weight ratio corresponds to a mole ratio surfactant/cosurfactant of ∼1.6:1. The polar headgroup of the cosurfactant molecules interferes with the polar region of the surfactant and influences the phase behavior of the mixed system compared to that for the two-component surfactant-water system.28,29 By keeping the temperature at 32 °C, it has been possible to study these microemulsions over a large concentration range extending into the water-rich part of the system. At lower temperatures, a phase separation occurs upon dilution with water. In Figure 4 are displayed the PGSE-FT NMR self-diffusion data for the three components over the whole concentration range in terms of relative diffusion coefficients D/D0, where D0 denotes the self-diffusion coefficient for the pure component at the same temperature. At concentrations below 50 wt %, the relative diffusion coefficients of water are larger than those of decanol. The self-diffusion coefficients D of the decanol component approach those of the surfactant at high water content. The structure of these microemulsion samples is therefore of the o/w type with closed surfactant-cosurfactant aggregates (i.e., micelles).16 At concentrations around 50 wt % surfactant and cosurfactant, the D/D0 values for water and decanol are roughly the same. As judged from the NMR results, in this concentration range, the system may therefore be regarded as a bicontinuous (25) Kjellander, R.; Florin, E. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2053. (26) Nilsson, P. G.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1377. (27) Jo¨nsson, B.; Nilsson, P. G.; Lindman, B.; Guldbrand, L.; Wennerstro¨m, H. In Surfactants in Solution; Mittal, K., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 1, pp 3-21. (28) So¨derman, O.; Stilbs, P. Prog. NMR Spectrosc. 1994, 26, 445. (29) Paruchuri, V. K.; Nalaskowski, J.; Shah, D. O.; Miller, J. D. Colloids Surf., A 2006, 272, 157.

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the critical micelle concentration (cmc) probably is very low compared to the actual surfactant concentration used here.4-6,33 Theoretically, the self-diffusion data for the micelles may be fitted to the following equation at low volume fractions φ:31

Ds ) 1 - BΦ D0,s

Figure 4. Relative self-diffusion coefficients (D/D0) as a function of composition for the components in the microemulsion system water (2)-surfactant (9)-decanol (b) at 32 °C. D0 is the self-diffusion coefficient in a system containing one component alone. The values of D0 are as follows: water, 2.4 × 10-9 m2 · s-1; surfactant, 1.8 × 10-11 m2 · s-1; and decanol, 1.1 × 10-10 m2 · s-1.

microemulsion. Extrapolating the trend of the reduced diffusion coefficients for water and decanol into even higher concentrations of surfactant and cosurfactant, it seems that the system gradually is changed to a w/o type with a comparatively slow water selfdiffusion and a fast decanol self-diffusion. It may be noted here that the water self-diffusion is still much faster than that of the surfactant (see Figure 4 and data in the caption to this figure). In a dynamic sense, it is possible to quantify the amount of water bound to the surfactant using the self-diffusion data in the following way:30

Dobs,w ) (1 - p)Dfree,w + pDb

(4)

Dobs,w denotes the observed water self-diffusion coefficient, Dfree,w is the self-diffusion coefficient of free, unrestricted water diffusion, and Db denotes the self-diffusion of the water molecules in a bound state and should in this case be equal to the surfactant self-diffusion coefficient. The parameter p is the fraction of bound water molecules. A state of fast exchange between these two states on the NMR time scale must prevail for eq 4 to be valid. Using the following values for the water and surfactant self-diffusion coefficients measured at 60 wt %, Dobs,w ) 6.80 × 10-10 and Db ) 1.37 × 10-11 m2 · s-1, respectively, yields a value of p of 0.72, disregarding obstruction effects (see below). A value of Dfree,w ) 2.39 ((0.01) × 10-9 m2 · s-1, that is, the measured self-diffusion of pure water at 32 °C, has been used in this calculation of p. Taking obstruction effects into account will reduce this number. Even if we do not take the calculated value of p too literally, qualitatively we may still conclude that some of the water must be in a free state even at these concentrations. In the water-rich part of the present microemulsion system, we have used the surfactant and water self-diffusion data to determine aggregate size and shape. In Figure 5 are shown the self-diffusion coefficients of the surfactant, that is, of the micelles, as a function of the volume fraction of the micelles. The contribution to the observed surfactant self-diffusion coefficients from nonmicellized surfactant is regarded to be negligible, since (30) Jo¨nsson, B.; Wennerstro¨m, H.; Nilsson, P. G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77. (31) So¨derman, O.; Stilbs, P.; Price, W. S. Concepts Magn Reson Part A 2004, 23A, 121.

(5)

Ds denotes the observed micellar self-diffusion coefficient at various volume fractions, D0,s is the self-diffusion coefficient of the micelles at infinite dilution, and B is a factor that takes the theoretical value of 2 for monodisperse hard spheres. A linear least-squares fit of the data in Figure 5 gives the values D0,s ) (4.04 ( 0.09) × 10-11 m2 · s-1 and B ) 4.7 ( 0.3. In a similar analysis of the data from the corresponding surfactant-water two-component system at 20 °C, a value of B ) 4.0 ( 0.4 was found.10 Within error limits, it is hard to say if these two figures for the B parameter are significantly different. The most probable cause of the deviation from the theoretical value of 2 is that the micelles do not behave hydrodynamically as hard spheres. The micelles, as demonstrated below, also deviate from a spherical shape, and a polydispersity size effect may also be conceived of. The value of D0,s is too low to correspond to a hydrodynamic radius RH of 35 Å, determined by the Stokes-Einstein equation D0,s ) kBT/f, where kB is the Boltzmann constant, T is the absolute temperature, and f denotes the frictional coefficient. Therefore, the following equations for f, originally proposed by Perrin to describe diffusion of anisometric, that is, oblate (eq 6a) or prolate (eq 6b) formed ellipsoidal particles, will be used to draw conclusions about size and shape in this case:32,33

b - 1] ( [ a) f) b tan [( ) - 1] a a 6πηb[1 - ( ) ] b f) a 1 + [1 - ( ) ] b ln 6πηa -1

2

1⁄2

2

1⁄2

(6a)

2 1⁄2

{

2 1⁄2

a b

}

(6b)

a and b denote the semiminor and semimajor axis of the ellipsoid, respectively. η is the viscosity of the solvent. Using a value of 35 Å for a (see above), and a value of 0.76 cP for the viscosity η of water at 32 °C,34 the use of eq 6a with the above quoted value for D0,s gives an axial ratio b/a of ∼2.5:1 for oblate shaped micelles and, using eq 6b, an axial ratio b/a of ∼5:1 for prolate shaped micelles. In Figure 6 are shown the obstruction factors for the water self-diffusion over an extended region in the o/w part of the microemulsion system. The obstruction of the solvent self-diffusion results from an excluded volume effect caused by the micelles and therefore increases with the volume fraction of such aggregates. It is also sensitive to the actual shape of the obstructing particles.30 The obstruction factors are defined as Dfree,w/D0,w (see eq 4), where D0,w is the measured self-diffusion coefficient of pure water at 32 °C (see above) and Dfree,w is the self-diffusion coefficient of unbound water molecules, calculated using eq 4, assuming that the surfactant molecules bind 3 water molecules per EO group, that (32) Perrin, F. J. Phys. Radium 1934, 10, 497. (33) Soni, S. S.; Sastry, N. V.; George, J.; Bohidar, H. B. J. Phys. Chem. B 2003, 107, 5382. (34) Handbook of Chemistry and Physics, 84th ed.; CRC Press: Boca Raton, FL, 2003.

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Figure 5. Self-diffusion coefficients of micelles in the microemulsion system where the weight fraction surfactant/decanol is 10:1 as a function of volume fraction of micelles at a temperature of 32 °C. The line represents a fit of the data to eq 5. See text.

Figure 7. SANS data for the microemulsion system where the weight fraction surfactant/decanol is 10:1 as a function of concentration of surfactant and decanol (wt %) at a temperature of 32 °C. Inset: data for the 6.2 wt % sample with fits to the various micelle shapes.

Figure 6. Obstruction factors (see text) for the micelles (9) of the microemulsion system at 32 °C as a function of the volume fraction of the micelles. Also shown are theoretical obstruction factors for micelles of spherical shape, represented by the line and the symbol (/).

is, 48 water molecules per surfactant molecule (see above). In Figure 6 are also shown the theoretical obstruction factors for spherical aggregates.30 The experimental obstruction factors are slightly lower than the theoretical spherical shape factors and are in line with the above findings of possible shapes for the micelles. Prolate shapes produce obstruction factors that are close to those for spherical shape, and the obstruction factors are rather independent of axial ratios. For oblate shape, on the other hand, the obstruction factors are quite dependent on the axial ratio. Our data presented in Figure 6 are therefore, within experimental uncertainty, consistent with either a prolate shape of any axial ratio or an oblate shape with a low axial ratio. In Figure 7 are shown the SANS data for a number of concentrations in the range 1.6-50 wt % surfactant and decanol at a weight ratio surfactant/decanol of 10:1. When the 6.2 and 12.5 wt % data are fitted to a form factor P(q) for an asymmetrically shaped particle (different semiaxes a and b), the model converges rapidly to that of an oblate ellipsoid, using eq 2. The inset in Figure 7 shows the details of the fits for the 6.2

wt % sample. In this figure, it is also shown that a corresponding form factor for prolates gives a qualitatively poorer fit, in particular in the higher q-range, and this possibility for the shape of the aggregates is therefore considered less probable. This conclusion holds as well for the spherical as for cylindrical shapes, and this is shown in the figure. In this analysis we assume a constant value S(q) ) 1 for the structure factor, as the fits are significantly poorer if an interaction corresponding to the volume fraction of particles is included. We believe this is due to the fact that for these anisometric micelles there is also a certain degree of size polydispersity35 that affects the pattern, in particular in the low-q range, and that this may be the reason for the slight deviation between the oblate model and the data at the lowest q-values. From the fits to the data, a value for the minor semiaxis of ∼13 Å appears for both the 6.2 and 12.5 wt % concentrations. This finding can be rationalized by taking into account fully hydrated EO chains of the surfactant molecules, forming a hydrophilic “shell” around the hydrophobic “core”, saturated with water molecules, and with very low scattering contrast with respect to the solvent D2O. The latter has a scattering length density F of ∼6.4 × 1010 cm-2.16 The scattering length density for a waterfree “core” of L-7607 trisiloxane groups may be estimated to be approximately -1.1 × 1010 cm-2, which results in a very large scattering contrast of approximately (6.4 - (-1.1)) × 1010 cm-2 ) 7.5 × 1010 cm-2. Thus, only the “core” part of the micelles will contribute significantly to the measured scattering when using D2O as solvent. From the PGSE-FT NMR self-diffusion measurements (see above), a value of the minor axis was estimated to be ∼35 Å. The difference (35 - 13) Å ) 22 Å may therefore be considered as a measure of the hydrated EO chain length in the aggregates. This value is quite close to the corresponding values in the range 24-26 Å suggested for the fully hydrated EO chains of the (35) Israelachvili, J. N. Intermolecular and Surface Forces. With Applications to Colloidal and Biological Systems; Academic Press: London, 1985.

Microstructures in Aqueous Silwet L7607 Solutions

Langmuir, Vol. 24, No. 19, 2008 10643

Table 2. Values for the Periodicity d and the Correlation Length ξ in Units of Å, Determined Using the Teubner-Strey Model on SANS Data from the Indicated Samplesa system surfactant/decanol weight ratio, and concentration in wt %

d (Å)

ξ (Å)

κ/kBT

6:1, 50 6:1, 25 8:1, 50 8:1, 25 10:1, 50 10:1, 25 two-component surfactant-water system, 50

65.5 117.4 68.5 139.5 47.0 120.3 55.0

36.4 26.8 35.8 24.0 27.5 14.0 44.0

0.47 0.19 0.44 0.15 0.50 0.10 0.68

a Also shown are the corresponding calculated values for the bending rigidity κ in units of kBT (see text). The standard deviations for d and ξ are both 4%. The standard deviation for κ is 6%.

surfactant/cosurfactant weight ratio was observed. At a weight ratio of 8:1, the phase separation takes place close to a concentration of 12 wt % surfactant and decanol, and for the weight ratio of 6:1 there seems to be some traces of phase separation already at 25 wt %. However, a distinct clouding was observed only at compositions well below this concentration. The SANS patterns displayed in Figure 8 for the two weight ratios are qualitatively similar for the two concentrations, although quantitative differences are apparent. At the highest concentration, that is, 50 wt %, a distinct correlation peak is present. A fit of the data to eq 3 for weight ratio 8:1 gives the values of 36 Å for ξ and 69 Å for d. The corresponding results using the data at a weight ratio of 6:1 give ξ ) 36 Å and d ) 66 Å (see also Table 2). At 25 wt %, the data still show some signs of a correlation peak, but it is now very weak. A fit of the data to eq 3 gives the following values for ξ: 24 Å at a weight ratio of 8:1 and 27 Å at a weight ratio of 6:1. For d, the results were, respectively, 140 and 117 Å (Table 2).

Discussion

Figure 8. SANS data at concentrations of 25 and 50 wt % for the microemulsion systems where the weight fractions surfactant/decanol are, respectively, 6:1 and 8:1. A ) 8:1 L7607/decanol and B ) 6:1 L7607/decanol. The lines through the data sets represent fits to eq 3. See text.

present surfactant elsewhere.9 See, however, more discussion on the length of this EO chain below, where a value close to 20 Å is suggested. The values for the major axis of the oblate core are determined from our SANS data to be 95 Å at 6.2 wt % and 70 Å at 12.5 wt %. Adding the value of 22 Å for the EO chain, these numbers indicate major axes for the aggregates of 117 and 92 Å, respectively. The corresponding axial ratios amount to 3.3:1 and 2.6:1, respectively. These values for the axial ratios are close to the corresponding value of 2.5:1 for oblate shaped micelles as determined by NMR self-diffusion data (see above). At 50 wt %, the SANS data may be fitted to a Teubner-Strey model, similarly to what was done for the surfactant-water system, and the analysis gives a value of 28 Å for the correlation length ξ and a value of 47 Å for the periodicity d. At 25 wt %, the SANS data may in fact also be fitted to this model, even though the PGSE-FT NMR data (see above) indicate that the solution structure is o/w at this concentration. The analysis here gives a value of 14 Å for the correlation length ξ and a value of 120 Å for the periodicity d. See also Table 2. We return to a discussion on further interpretation of the parameters below. 2.2. SANS Measurements at Other Surfactant/Cosurfactant Weight Ratios. In Figure 8 are shown SANS data at 25 and 50 wt % surfactant and decanol at surfactant/decanol weight ratios of 8:1 and 6:1. The temperature was 23 °C during these measurements. At this temperature, an increasing tendency for a phase separation at high water content with decreasing

In microemulsion systems consisting of nonionic surfactants of the CmEn type, oil, and water, it has been demonstrated that the phase behavior and solution structure may be rationalized in terms of the Gibbs energy of the surfactant film.36,37 According to Helfrich, this Gibbs energy is a rather simple function of a mean curvature H and a Gaussian curvature K, with corresponding moduli κ, also called the bending modulus, and κj, also called the saddle splay modulus.38 The curvature parameters H and K are dependent on sample composition, and the moduli are temperature dependent.14,37-39 In the work of Byelov et al., SANS measurements were used to determine κ using d and ξ parameters from a Teubner-Strey analysis of the measured scattering cross section of various aqueous bicontinuous microemulsion samples made by the surfactant C10E4 and n-decane. The influence of various polymers on the phase equilibria in this system was investigated.36 In a recent work by Frank et al., an analogous analysis of SANS measurements of aqueous three-component bicontinuous microemulsion systems, made using, for example, the surfactant C10E5 and decane, was performed to obtain information on, for example, surfactant film thickness and κ.37 From values of d and ξ, using the Teubner-Strey model (eq 3), it is possible to determine κ from the following simple relation:

κ ξ ) 0.85 kBT d

(7)

Table 2 summarizes the values of κ determined using the parameters from the Teubner-Strey analysis of the SANS measurements in the present work. The largest value, that is, 0.68 kBT, is found for the two-component aqueous surfactant system at 50 wt %. For the corresponding three-component (microemulsion) samples, κ/kBT is found to be rather constant and equal to 0.47 ( 0.03. These values are quite close to corresponding values for κ determined for aqueous microemulsion samples of various nonionic surfactants of the C10E5 type at a concentration of 26% by volume.37 In that work, the thickness δ of the surfactant films were calculated using the following equation: (36) Byelov, D.; Frielinghaus, H.; Holderer, O.; Allgaier, J.; Richter, D. Langmuir 2004, 20, 10433. (37) Frank, C.; Frielinghaus, H.; Allgaier, J.; Prast, H. Langmuir 2007, 23, 6526. (38) Helfrich, W. Z. Naturforsch., A: Phys. Sci. 1978, 33A, 305. (39) Brown, W.; Stilbs, P.; Johnsen, R. M. J. Polym. Sci., Part B: Polym. Phys. 1983, 21, 1029.

10644 Langmuir, Vol. 24, No. 19, 2008

d)

[

Walderhaug and Knudsen

( ( ) )]

κ 2δ 1 kBT 1+ ln c Ψ 4π κ kBT

1⁄2

d 2A

(8)

ψ is the volume fraction of surfactant, A is the square root of the interfacial area per surfactant molecule in the monomolecular surfactant film, and c is a so-called cutoff variable describing the high wavelength number cutoff, and given the numerical value 1.84. The other symbols have their usual meaning (see above). For the surfactants used in that work, a value of A equal to 7.8 Å was determined independently and used in eq 8 to calculate values of δ close to 14 Å. We have not measured the corresponding value of A for the surfactant used in the present work. However, using the values of d determined from the Teubner-Strey analysis and the values of the bending modulus (see Table 2), we have used eq 8 to calculate values for the film thickness δ for reasonable values of A, using the same value for c as in ref 38, anticipating ψ ) 0.5 and 0.25 at 50 and 25 wt %, respectively. For values of A in the range 10-20 Å, the values of δ determined using eq 8 are quite constant in the range 10-16 Å and are rather independent of the sample composition (data not shown). Without independent measurement of A, it is hard to be more specific on the dimension of the film at present, but a value of A in the indicated range for the surfactant containing 16 EO groups is not unrealistic. Brown et al. have shown that for poly(ethylene oxide) polymers dissolved in water the infinite dilution values for the self-diffusion coefficients scale with the molecular weight with an exponent of -0.61 at 25 °C.39 Scaling a chain consisting of 16 EO units using the exponent 0.61 leaves a length of: 7.8 · (16/5)0.61 Å ) 16 Å for this chain. The estimated film thickness points to a situation where most of the EO groups are located at or close to the surface. For the C10E5 surfactants in ref 37, the film thickness in a concentration range ψ ) 0.2-0.3 was also found to be in the range 13-15 Å, depending on the surfactant. There, it was concluded that the surfactant chains in the film are in a tilted configuration. Also, the film is monomolecular, separating water and well-defined oil domains. In our case, a surfactant film only separates water layers, at least for the two-component system. The organization of such a film must be somewhat different and would logically point to a situation of a double layer. But then it is admittedly hard to rationalize the suggested dimensions; they should rather be expected to be of the order of at least the double. The Teubner-Strey model is theoretically based on the assumption of equal volume fractions of oil and water,24 a situation different from that in the present systems. An alternative interpretation of the results could be the following: If the hydrophobic trisiloxane groups of the surfactant molecules together with the hydrocarbon chains of the alcohol, if present, can be viewed as the “oil” and the EO chains thus form the “film”, the dimension with a range 10-16 Å for the thickness δ may be interpreted as the thickness of this “monolayer”. We reiterate that, at 25 wt % surfactant or surfactant and decanol, the NMR self-diffusion measurements show that the solution structure is of o/w type; see Figure 4. However, we conclude that the micelles at this concentration are of oblate form with large axial ratios (see above). We therefore cannot rule out the possibility that the SANS measurements recognize this situation as one with a local lamellar structure. At higher dilution, that is, at concentrations less than ∼25 wt % surfactant or surfactant and decanol, the systems definitely are of o/w type. For the cosurfactant containing system, the micelles seem to be of marked anisometric shape even at infinite dilution, while it has been previously concluded that the surfactant-water system forms micelles of nearly spherical shape at this condition.

The radius of hydration was found to be∼35 Å in this case. The EO chain in spherical C12E8 micelles has been shown to have a length of ∼14 Å.26 If the length scales with the number of EO groups as in a random coil (see above), then an expected length for a chain with 16 EO groups would be∼20 Å. If 20 Å of the radius of 34-35 Å can be ascribed to the EO chain, a radius of the hydrophobic core can be estimated to be of the order of 14-15 Å. The self-diffusion coefficient at infinite dilution for the three-component (microemulsion) system was determined at a higher temperature (i.e., 32 °C) than that for the two-component system (20 °C). It is hard to say if this aggregate growth results from the presence of the decanol component, or is a result of possible dehydration of the EO-chain or a combination of both effects. An aggregate growth is demonstrated also in the twocomponent system with increasing surfactant concentration.10 Previous work on aqueous C12E5 and C12E8 systems has shown that there is aggregate growth with temperature for the former surfactant with temperature, due to dehydration of the EO chain. However, this effect was not observed for the latter surfactant.26 At concentrations above ∼60% surfactant or surfactant and cosurfactant, the systems gradually transform into a w/o structure. At these concentrations, the EO chains are not fully hydrated (see above), and the volume occupied by the EO chain headgroup is reduced. The ability for the surfactants to form inverted structures is therefore larger in this concentration range compared to more dilute samples, based on surfactant packing considerations.7,35

Conclusions The solution structure in aqueous two-component solutions of the nonionic polyoxyethylene trisiloxane surfactant Silwet L7607 and three-component microemulsion samples that in addition also contain decanol have been investigated using PGSE-FT NMR and SANS measurements. It has been possible to make thermodynamically stable solutions over a large water-surfactant composition range for a system with a surfactant/decanol weight ratio of 10:1 at a temperature of 32 °C. At low surfactant concentrations, that is, below ∼25 wt %, this system forms o/w type solutions that consist of normal micelles. For the twocomponent system, the micelles formed at low surfactant concentration are of a nearly spherical shape and grow into anisometric, that is, oblate, shape at higher concentration. For the microemulsion system, the micelles even at low surfactant concentration are of an oblate form of low axial ratio. At a low surfactant concentration of 0.9 wt % in the aqueous two-component solution, it was demonstrated from SANS measurements that the micelles grow with increasing temperature. This behavior may be rationalized by considering a decreasing hydration of the EO chains with increasing temperature, thereby decreasing the spontaneous curvature for the surfactants in the aggregates. This behavior is analogous to that for micelles formed by surfactants of the CmEn type. For concentrations in the range around 50 wt %, both types of systems have a bicontinuous solution structure. The SANS data may be fitted to the Teubner-Strey model, even at concentrations of 25 wt %, and the parameters have been used to estimate surfactant film thickness. The estimated values for this film thickness in the range 10-16 Å seem to be too small by at least a factor of 2 for such films in the present type of systems. However, if one can view the present systems as consisting of an “oil” component formed by the hydrophobic part of the surfactant and, if present, alcohol, and a monomolecular “film” formed by the EO chains of the surfactant, the estimated film thickness is reasonable. At surfactant concentrations above

Microstructures in Aqueous Silwet L7607 Solutions

∼60 wt %, the systems gradually are transformed into a w/o type, as judged from the self-diffusion coefficients of the components. The trend of solution structures as a function of surfactant (or surfactant and decanol) concentration can be rationalized by considering the hydration of the EO groups of the polar headgroup of the surfactant. With increasing surfactant concentration, the hydration of these groups decreases, and the spontaneous curvature of the micellar aggregates decreases. This

Langmuir, Vol. 24, No. 19, 2008 10645

behavior is partly analogous to that for surfactants of the CmEn type systems. Acknowledgment. The surfactant was a gift from Dr. David Degville, GE Bayer Silicones, U.K. This gift is highly acknowledged. LA800344H