Microemulsions of Record Low Amphiphile Concentrations Are

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Microemulsions of Record Low Amphiphile Concentrations Are Affected by the Ambient Gravitational Field Kazuhiro Ishikawa,†,‡ Manja Behrens,† Stefanie Eriksson,† Daniel Topgaard,† Ulf Olsson,† and Håkan Wennerström*,† †

Physical Chemistry, Lund University, Box 124, SE-221 00 Lund, Sweden Kao Cooperation, 2-1-3 Bunka, Sumida-ku, Tokyo 131-8501, Japan

‡

ABSTRACT: It is shown that the ternary system heavy water−heptane−hexadecyl hexaethylene oxide (C16E6) has a stable bicontinuous microemulsion phase down to an exceptionally low concentration at the balanced temperature of 26.8 °C. It is further demonstrated that the ambient gravitational field has an influence on the observed phase equilibria for typical sample sizes (∼1 cm). Direct measurements using a nuclear magnetic resonance imaging technique demonstrate that sample compositions vary with the height in the vials. It is furthermore found that some samples show four phases at equilibrium in apparent violation of Gibbs’ phase rule. It is pointed out that Gibbs’ phase rule strictly applies only when effects of gravity are negligible. A further consequence of the ambient gravitational field is that, for the system studied, the microemulsion one-phase samples are not observed, when using standard size vials, that is, sample heights on the order of a centimeter. Quantitative determinations of concentration profiles can be used to determine parameters of the free-energy density for the system.

1. INTRODUCTION In a microemulsion, a film of amphiphilic molecules separates domains of two immiscible solvents, typically water and oil. The microemulsion is a thermodynamically stable isotropic liquid, and the organization of the domains can be either oil droplets in water (O/W) or water droplets in oil (W/O) or the system can form a bicontinuous structure where both oil and water domains are infinite and continuous in three dimensions.1−4 A particularly important case is represented by so-called balanced conditions, where the amphiphile film, separating the two domains, has its lowest (free) energy when the film is planar. Because the film is at an asymmetric interface such a preference for a planar state can only occur under special conditions. The choice of amphiphile as well as oil provides a coarse tuning of conditions, and one can in addition use temperature or cosolvents or cosurfactants to fine-tune into the balanced state. It is a generic property of microemulsions that under balanced conditions a one-phase sample with the lowest amphiphile conditions occurs when there are equal volumes of water and oil. Further dilution leads to a three-phase equilibrium microemulsion−water−oil.5−8 When studying microemulsions using a thermodynamic perspective, it is a great practical advantage to work with a minimum number of components (pure) water−oil−amphiphile. The clearly most studied class of amphiphiles meeting this requirement is the alkyl oligo ethylene oxides (CnEm). For these surfactants, the molecular film responds to temperature © XXXX American Chemical Society

changes, making it possible to reach the balanced state at convenient temperatures. Such systems have over the years been extensively studied by Shinoda, Kunieda, and coworkers,8,9 by Kahlweit, Strey, and coworkers,6,10 and by our group.11,12 Figure 1 shows a generic ternary phase diagram of such a system at the balanced temperature. Specific features are the minimum surfactant concentration ϕs* of the microemulsion at the tip of the microemulsiom−water−oil threephase triangle. Under balanced conditions there is also a maximum concentration ϕs** at the equilibrium microemulsion−lamellar phase at equal volumes of water and oil. A further feature is that the microemulsion one-phase area has a quasi-triangular shape where the upper cusps are corners of three-phase triangles microemulsion−lamellar phase−water or oil, respectively. One can note that in contrast with the bicontinuous microemulsion, the compositions of the lamellar phase can be very asymmetric in the oil/water ratio. Even though the basic features of these microemulsion systems are largely understood there are still a number of unresolved issues. We focus on a system designed to give a bicontinuous microemulsion at record low surfactant concenSpecial Issue: William M. Gelbart Festschrift Received: February 27, 2016 Revised: March 30, 2016

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DOI: 10.1021/acs.jpcb.6b02041 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

direction, which is in the direction of the inserted NMR tube. A phase-encoding gradient with duration 0.2 ms and ramp time of 0.1 ms was incremented from −0.384 to +0.378 T m−1 in 128 steps, giving a resolution of 153 μm. The applied gradients defined a 19.6 mm field-of-view, which was effectively limited to 12 mm by the height of the RF coil. To avoid relaxation affecting the relative peak intensities, we minimized effects from longitudinal and transverse relaxation, T1 and T2, by keeping the repetition time long (TR = 10 s) and the echo time as short as possible (TE = 0.6 ms). The experimental temperature was controlled by a Bruker variable temperature unit with thermostatic air flow (±0.1 °C). The peaks in the NMR spectra were identified as water at 4.7 ppm, the EO group of the surfactant at 2 ppm, and oil at 1.3 and 0.9 ppm. The chemical shifts of the peaks change slightly with the position in the tube. This is because of inhomogeneity in the magnetic field caused by different magnetic susceptibilities of the different phases. The peak intensities were calculated by integration, and in the case of overlapping peaks, a deconvolution was made in MATLAB by fitting a sum of Lorentzian functions to the spectrum to estimate the area of each individual peak.16 The contribution from the surfactant CH2 and CH3 groups was assumed to have no influence of the intensities of the oil peaks. The volume of the different components at each position was calculated by dividing the peak intensities with the number of protons for each molecule/molecular site and multiplying with the molecular volume.

Figure 1. Schematic ternary surfactant (S)−water (W)−oil (O) phase diagram under balanced conditions, corresponding to the phase inversion temperature, T0, in the case of a nonionic surfactant. M denotes the microemulsion phase and Lα is the lamellar phase. W and O are essentially pure phases of water and oil, respectively. The microemulsion phase has a finite swelling with the solvent and separate into three phases, W + M + O, at lower surfactant concentrations.

trations. This is achieved within the framework of the CnEm surfactant systems by increasing n and m and by choosing a short-chain normal alkane as the oil. Thus, we have investigated the properties of the system D2O−C16E6−heptane. We know from previous work13,14 that the excess free energy per molecule is on the order 10−6 to 10−7 kBT for highly dilute microemulsions. It follows that these soft matter systems have the potential to respond to even weak perturbations that are normally neglected. Specifically we will demonstrate that the dilute systems are affected by the ambient gravitational field of the earth.

3. RESULTS AND DISCUSSION Phase Equilibia. The phase equilibria in the system D2O− C16E6−heptane were studied by preparing vials in a range compositions. The phase equilibria were then monitored in two different ways. For the subset of samples with equal volumes of water and heptane but with varying surfactant concentration the temperature was varied stepwise. The number and character of the phases were then determined after a limited equilibration time. The vials were investigated by visual observation using crossed polarizers to detect anisotropic (lamellar) phases. The choice of D2O rather than ordinary water had the dual effect of facilitating NMR investigations and to enhance gravity effects. Figure 2 shows a so-called fish plot10 of the observed temperature dependence of the phase equilibria at equal volumes of water and oil. This plot reveals an apparent generic behavior, and the balanced temperature is found to be T0 = 26.8 °C. At this temperature, a finite microemulsion swelling, corresponding to a concentration ϕs* = 0.016 of surfactant, is observed. A microemulsion with such a high dilution has to our knowledge not been observed previously. Shinoda realized that obtaining such dilute microemulsions required a “strong” long chained amphiphile, like lecithin.20 The observation of a balanced microemulsions with only 2.3 wt % lecithin was reported at the addition of substantial amounts of the cosurfactant/cosolvent propanol. Highly dilute microemulsions (ϕs ≤ 0.05) can also be accomplished by using a boosting effect of an amphiphilic block copolymer.21 This is a method of significant practical importance, but also in this case one loses the simplicity of a three-component system. To characterize the system in more detail, we investigated the ternary system at the balanced temperature to see if the system shows the generic behavior illustrated in Figure 1. In this case samples were equilibrated for long times on the order of a week. It is apparent from Figure 3 that the observed phase

2. MATERIALS AND METHODS Materials. Hexaethylene glycol hexadecyl ether (C16E6) was purchased from Nikko Chemicals, Japan, and heptane from Sigma-Aldrich, Sweden. Heavy water, D2O, (99.8 atom %) was purchased from ARMAR Chemicals, Switzerland. For NMR experiments the water used was a 50/50 w/w mixture of H2O and D2O. The H2O used here was filtered in-house using a Millipore Milli-Q Gradient A 10, Millipore, France. Sample Preparation. Samples were prepared by weighing the components into 5 mm NMR tubes that then were flamesealed to avoid evaporation. Sample compositions were converted to volume fractions using the following densities, ρD2O = 1.11 g/cm3, ρheptane = 0.68 g/cm3, ρC16E6 = 1.0 g/cm3, and ρH2O = 1.0 g/cm3. Phase Equilibria. Samples were mixed and left to equilibrate in a temperature-controlled (±0.1 °C) water bath. Mixing and equilibration were repeated several times to confirm reproducibility. 1 H NMR Chemical Shift Imaging. Spatially resolved 1H NMR spectra were acquired with a chemical shift imaging pulse sequence.15 The technique is described in detail in Salvati et al.16 and has been used to study several different systems.16−19 The experiment was performed on a Bruker Avance II 200 spectrometer operating at a 1H resonance frequency of 200 MHz and equipped with a Bruker DIF-25 gradient probe, capable of generating gradients of strength 9.6 T m−1 in the z B


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Figure 2. Observed phase behavior at short times for samples of equal volumes of water and oil (“fish plot”) for the system C16E6−water− heptane. Temperature was varied in discrete steps of 0.1 °C, and the samples were stirred during temperature variation. At temperature equilibrium, stirring was turned off and the phase identification was recorded shortly after. In this “short time fish plot” we observe the balance temperature T0 = 26.8 °C and the maximum microemulsion swelling ϕs* = 0.016.

Figure 4. Photograph of two samples in the W+M+Lα+O region at T = T0 = 26.8 °C. Left: ϕs = 0.015, ϕw = 0.58, and ϕo = 0.40. Right: ϕs = 0.015, ϕw = 0.47, and ϕo = 0.51. The sample tube diameter is 5 mm.

The gravitational potential of the earth is clearly weaker than that of the centrifuge and, furthermore, it varies linearly with height rather than with the square; however, we can use the formalism developed in ref 22 to describe the thermodynamic consequences of a linearly varying gravitational field. Following refs 7 and 23, we write the free-energy per unit volume of a microemulsion at zero gravity as G /V = (a0 + a 2(ϕ − 1/2)2 )ϕs3/ls3 + bϕs5/ls3

(1)

Here ϕs is the volume fraction surfactant and ϕ = ϕo + βϕs is the volume fraction of apolar regions, with β ≈ 0.5 being the hydrophobic alkyl chain fraction of the surfactant volume, vs.24 The effective film thickness ls = vs/as, where as is the average area occupied by each amphiphile at the water−oil interface, defines the length scale of the system. The coefficients a0 < 0, a2 > 0, and b > 0 are system-specific and are determined by the elastic properties of the film.7,23 In the sample there is also a gravitational contribution to the energy

Figure 3. Steady-state phase behavior of the C16E6−water−heptane system at balance temperature T = T0 = 26.8 °C observed after a long equilibration time.

Ugrav = A vial

∫0

h

dz gazρ(z)

(2)

where ρ is the density, h denotes the vertical height (size) of the sample in the vial and Avial is its cross section area, z is the coordinate in the vertical direction, and ga = 9.81 m/s2 is the gravitational acceleration. For an incompressible fluid one can assume that the local density is determined by the local composition so that

equilibria deviate qualitatively from the one of Figure 1. We fail to observe a single-phase microemulsion, and for some samples there are clearly four phases in the vial, as illustrated in Figure 4. This amounts to a violation of Gibbs’ phase rule, as it is normally stated, and the observations call for an explanation. The samples are highly dilute in surfactant so that the freeenergy difference between different phases is minute. Thus, the observations of four phases could be due to a nonequilibrium effect or an artifact due to impurities or small temperature gradients; however, the observations were fully reproducible, and the equilibration process is distinct even if it is slow. This leads to the conclusion that the observations are due to true equilibrium properties and that we observe a genuine violation of Gibbs’ phase rule in its standard form. It is our conclusion that the most probable cause of such a violation is the presence of the ambient gravitational field of the earth. Microemulsion Systems in a Gravitational Field. It is a standard technique to use the gravitational field of a centrifuge for separation purposes. We have previously shown that the centrifugal field can also be used to induce phase separation and to measure interbilayer forces in a amphiphile lamellar phase.22

ρ(z) = ρw ϕw + ρo ϕo + ρϕ ≈ ρw − Δρϕ(z) s s

(3)

where subscripts w, o, and s refer to water, oil, and surfactant, respectively. The second equality, with Δρ = ρw − ρo (∼430 kg/m3 for heavy water), is based on the assumption that the surfactant has a density close to the average density of water and oil. Furthermore, the surfactant concentration is so low that its influence on the density of a given phase nevertheless is small. Using this approximation, eq 2 for the gravitational energy simplifies to Ugrav = constant − A vial gaΔρ

∫0

h

dz zϕ(z)

(4)

Now consider a bicontinuous microemulsion with equal volumes of water and oil under balanced conditions. There is C


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enlarged version of the generic phase diagram of Figure 1. Consider a symmetric sample with ϕ = 1/2 as indicated by the cross in the microemulsion phase of the schematic phase diagram of Figure 5a. For small h there is a concentration gradient in the one phase microemulsion, along a horizontal line at constant ϕs. The difference in the oil volume fraction, Δϕ, between the top, z = h, and bottom, z = 0, of the sample increases with increasing h. At a value h = h′, the line spans the whole microemulsion phase, M, and touches the phase boundaries toward excess water and oil, respectively. As h further increases above h′, the sample separates into three phases and the microemulsion now coexists with excess pure water and oil phases. In a routine investigation, one would at this point conclude that the sample composition corresponds to a composition in a three phase triangle, while, in fact, the zero gravity sample gives a single phase. The excess water and oil volumes increase as h increases and as a consequence, ϕs increases in the microemulsion phase. At a certain value h = h″, ϕs has increased to a value corresponding to the microemulsion corners of the three phase triangles W + Lα + M and M + Lα + O. For h > h″, the microemulsion phase then also coexists with a water-rich (Lα′) and an oil-rich lamellar phase (Lα″), respectively, resulting in a total of five coexisting phases, W + Lα′ + M + Lα″ + O. The precise values of h′ and h″ depends on the initial average composition. Above, we have described the scenario for an ideal symmetric model system. In the more realistic case that the average composition deviates from ϕ = 1/ 2 or the system is “off-balance”, that is, the spontaneous curvature H0 ≠ 0, then the additional coexisting phases appear one by one as h increases. For example as M → M + W → W + M + O → W + Lα′ + M + O → W + Lα′ + M + Lα″ + O. In the experimental system, there is a non-negligible solubility of the C16E6 surfactant in the oil, ϕs,o ≈ 0.005, resulting in a slight loss of the symmetry so that the microemulsion corners of the W + Lα′ + M and the M + Lα″ + O three phase triangles may not occur at the same values of ϕs or absolute deviation from ϕ = 1/2. In the experimental diagram of Figure 3 there is no microemulsion single phase area, indicating that the sample height, on the order of 2 cm, is larger than h′ in the illustrative example. This suggests that the absence of this pure phase is an effect of gravity. Additionally the observation of four phases at equilibrium indicates that for some average compositions the height exceeds the value h″. One way to verify this conclusion is

a gravitational contribution to the chemical potentials of the water and the oil, which within a one-phase sample cause a concentration gradient in the z direction (the direction of the gravitational field). At the given level of approximation, the surfactant concentration is constant, implying that from bottom to top in the vial one samples a composition line in the ternary phase diagram that is parallel to the baseline in Figure 1. The length of this line depends on the height, h, of the sample. It is normally implicitly assumed that this length is negligible for realistic sample sizes; however, it is our conclusion that this is not the case for dilute microemulsion systems. Because of the marked difference in density between water and oil, the gravitational term contribution in eq 4 is large relative to most other liquid systems. Additionally, the free-energy differences between different phases are unusually small. Using the formalism presented in the appendix of ref 22, one can obtain the concentration profile in a sample based on an Euler− Lagrange equation. Because the gravitational potential varies linearly with height, z, there is a linear relation 2a 2(ϕ − 1/2)ϕs3/ls3 − gaΔρz − λ = 0

(5)

between concentration and position, assuming a constant value of ϕs. The Lagrangian multiplier, λ, can be determined from a given (average) ϕ. If the gravitational effects are sizable, what are the expected consequences? In Figure 5 we illustrate the scenario using an

Figure 5. (left) Schematic ternary phase diagram at T = T0 and zero gravity. The cross in the microemulsion phase denotes the average sample composition. (right) Schematic illustration of how the relative volumes of coexisting phases vary with the sample height for a sample with the average composition of a balanced microemulsion corresponding to the cross in the left panel.

Figure 6. (left) Concentration profiles of water (blue squares), oil (red triangles), and surfactant (black circles). (right) Surfactant concentration profile on an expanded scale. Also marked are the positions of the four different phases, water (W), lamellar phase (Lα), microemulsion (M), and oil (O). D


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diagram. Gibbs phase rule does not apply, and tie-lines have lost their original meaning. Is it possible to use the data to reconstruct the “true” phase diagram at zero gravity, where the conventional thermodynamic rules apply? The qualitative effects of gravity emerge easily. Compositions that at zero gravity give one phase can show multiphase character in the presence of gravity, while the reverse is never the case. Thus, the extent of one-phase areas is always underestimated when working with samples of finite height. For the specific case previously discussed the microemulsion area was completely suppressed for samples with a height of 2 cm. Using samples of finite height it is possible to reconstruct the phase diagram by carefully measuring the height profile of the concentration, as in the example of Figure 6. It follows, for example, that the microemulsion composition in the water-rich three-phase triangle is ϕ = 0.35; ϕs ≈ 0.03. For the composition of the water-rich lamellar phase in the three-phase triangle we find ϕ ≈ 0.18, and it is also possible to estimate the composition of the water-rich lamellar phase in the three-phase triangle and we find ϕ ≈ 0.18 and ϕs ≈ 0.025. Similarly, for the oil-rich three-phase triangle one has a solvent content ϕ ≥ 0.60. This is the maximum value found for the microemulsion on the two-phase boundary with excess oil. On the basis of the symmetry properties, the cusp in the one-phase area should occur for ϕ ≈ 0.65. The two-phase equilibrium between lamellar phase and microemulsion at equal volumes of oil and water is not primarily affected by gravity effects because the coexisting phases have similar densities. From Figure 2 we conclude that this occurs at ϕs ≈ 0.035. It requires substantial additional measurements of concentration profiles to establish the full zero gravitation phase diagram; however, we can use the estimated values for the coefficients in the thermodynamic model to estimate the swelling limit ϕs*. Equation 7 provided us with a relation between the coefficients a0 and b. For the finite swelling of the balanced microemulsion, we have23

to measure the height variation of the composition in the vials. Figure 6 shows the concentration profiles of water and oil (left) and surfactant (right) for a four-phase sample, determined using the same NMR imaging method as in ref 23. The average sample composition is ϕ = 0.40 and ϕs = 0.009. To have similar concentrations of water and oil protons, the water in this experiment consisted of a mixture of H2O and D2O at equal weight. Because of the replacement of part of the D2O with H2O, the temperature was adjusted to 28.0 °C. The measurement reveals clear step changes in the concentrations at the phase boundaries. At the bottom of the vial there is pure water. This is followed by ca. 4 mm of a lamellar phase with ϕ ≈ 0.15 and ϕσ ≈ 0.027, which varies only slightly with height. Then follows a microemulsion phase of ca. 4.5 mm, where ϕ varies from 0.35 to 0.60 while ϕσ ≈ 0.032 is constant. Finally, at the top, there is an oil phase. The detailed study of this sample demonstrates that the composition is indeed dependent on height, that the composition of the lamellar phase is strongly asymmetric in oil/water ratio, as expected from the generic phase diagram, and that the sequence of phases is consistent with the theoretical expectation. These combined observations convincingly demonstrate that the gravitational field from the earth has a significant influence on the phase equilibria in the system. Determining Free Energies Using the Gravitational Interaction. We have shown that for dilute microemulsion systems the gravitational field of the earth gives rise to concentration gradients in the sample. The chemical potential of all components is constant in the samples, and one has an accurate knowledge of the (varying) gravitational component. It is thus possible to estimate coefficients in the intrinsic (zero gravity) free-energy density of eq 1 from the measured concentration profile. The principle can be illustrated using the data shown in Figure 6. Within experimental accuracy the solvent composition varies linearly with z in the microemulsion phase, as predicted from eq 5. From the slope g Δρls3 ∂ϕ = a 3 ∂z 2a 2ϕs

(6)

ϕs* =

we find that a2 ≈ 3.3kBT using Δρ = 375 kg/m (50% H2O, 50% D2O), ls = 2.0 nm and the measured values ϕs = 0.030, corrected for the surfactant solubility in the oil, and ∂ϕ/∂z = 42 m−1. The value of a2 is slightly smaller the value a2 = 20kBT estimated in ref 13 for the H2O−C12E5−decane system. On the basis of the expression for G/V in eq 1, it follows that at the coexistence microemulsion−lamellar phase−pure water one has the relation7 3

ϕ = 1/2 − 2(2bϕs2 + a0)/a 2

⎛ −a0 ⎞1/2 ⎜ ⎟ ⎝ 2b ⎠

(9)

which we estimate to ϕs* = 0.014 from the short time phase behavior (Figure 1) including correction for the surfactant solubility in the oil, Combining these two equations allows us to calculate both a0 and b, and we obtain a0 = −0.071kBT and b = 180kBT. These values can be compared with a0 = −0.34kBT and b = 130kBT obtained in the related C12E5−water−octane system14 from a combined analysis of phase behavior, osmotic compressibility, and interfacial tension data. A smaller value of a0 in the C16E6 system is expected as we expect this surfactant to give a somewhat stiffer film compared with C12E5. The b value is more difficult to understand. With the C12E5 surfactant, this value was found to depend significantly on the chain length of the oil.14 A complication with nonionic CmEn surfactants is the fact that there is a non-negligible solubility (here ϕs(oil) ≈ 0.005) of the surfactant in the oil phase and thus also in the oil regions of the microemulsion.26 We attribute the deviation from a perfect symmetry in the exchange to 1 − ϕ in Figure 3 as mainly caused by the asymmetry in solubility of surfactant in the two solvents.

(7)

for the composition of the microemulsion. Using the measured values ϕ = 0.35 and ϕs = 0.030 (oil solubility corrected) and the value of a2 ≈ 3.3kBT determined from eq 6, it follows that b ≈ 560(0.25 − a0)kBT. We conclude this section by pointing out that the gravity effects can be utilized to measure weak interlamellar forces in the undulation regime in a way similar to what was accomplished in ref 22. This could be used to settle the uncertainty concerning the value of the prefactor25 in the expression for the undulation force; however, we have, so far, not been able to complete such a study. Phase Equilibria at Zero Gravity. The observed phase behavior of Figure 3 does not correspond to a proper phase E


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(11) Olsson, U.; Wennerström, H. Globular and Bicontinuous Phases of Nonionic Surfactant Films. Adv. Colloid Interface Sci. 1994, 49, 113− 146. (12) Wennerström, H.; Olsson, U. Microemulsions as Model Systems. C. R. Chim. 2009, 12, 4−17. (13) Kabalnov, A.; Olsson, U.; Wennerström, H. Polymer Effects on the Phase Equilibrium of a Balanced Microemulsion. Langmuir 1994, 10, 2159−2169. (14) Balogh, J.; Kaper, H.; Olsson, U.; Wennerström, H. Effects of Oil on the Curvature Elastic Properties of Nonionic Surfactant Films: Thermodynamics of Balanced Microemulsions. Phys. Rev. E 2006, 73, 041506. (15) Brown, T. R.; Kincaid, B. M.; Ugurbil, K. NMR Chemical Shift Imaging in Three Dimensions. Proc. Natl. Acad. Sci. U. S. A. 1982, 79, 3523−3526. (16) Salvati, A.; Lynch, I.; Malmborg, C.; Topgaard, D. Chemical Shift Imaging of Molecular Transport in Colloidal Systems: Visualization and Quantification of Diffusion Processes. J. Colloid Interface Sci. 2007, 308, 542−550. (17) Hedin, J.; Ö stlund, Å.; Nydén, M. UV Induced Cross-Linking of Starch Modified with Glycidyl Methacrylate. Carbohydr. Polym. 2010, 79, 606−613. (18) Ö stlund, Å.; Bernin, D.; Nordstierna, L.; Nydén, M. Chemical Shift Imaging NMR to Track Gel Formation. J. Colloid Interface Sci. 2010, 344, 238−240. (19) Knöös, P.; Topgaard, D.; Wahlgren, M.; Ulvenlund, S.; Piculell, L. Using NMR Chemical Shift Imaging To Monitor Swelling and Molecular Transport in Drug-Loaded Tablets of Hydrophobically Modified Poly(acrylic acid): Methodology and Effects of Polymer (In)solubility. Langmuir 2013, 29, 13898−13908. (20) Shinoda, K.; Araki, M.; Sadaghiani, A.; Khan, A.; Lindman, B. Lecithin-Based Microemulsions: Phase Behavior and Microstructure. J. Phys. Chem. 1991, 95, 989−993. (21) Jakobs, B.; Sottmann, T.; Strey, R.; Allgaier, J.; Richter, D. Amphiphilic Block Copolymers as Efficiency Boosters for Microemulsions. Langmuir 1999, 15, 6707−6711. (22) Bulut, S.; Åslund, I.; Topgaard, D.; Wennerström, H.; Olsson, U. Lamellar Phase Separation in a Centrifugal Field. a Method for Measuring Interbilayer Forces. Soft Matter 2010, 6, 4520−4527. (23) Wennerström, H.; Olsson, U. On the Flexible Surface Model of Sponge Phases and Microemulsions. Langmuir 1993, 9, 365−368. (24) Olsson, U.; Schurtenberger, P. Structure, Interactions, and Diffusion in a Ternary Nonionic Microemulsion Near Emulsification Failure. Langmuir 1993, 9, 3389−3394. (25) Wennerströ m, H.; Olsson, U. The Undulation Force; Theoretical Results Versus Experimental Demonstrations. Adv. Colloid Interface Sci. 2014, 208, 10−13. (26) Burauer, S.; Sachert, T.; Sottmann, T.; Strey, R. On Microemulsion Phase Behavior and the Monomeric Solubility of Surfactant. Phys. Chem. Chem. Phys. 1999, 1, 4299−4306.

4. CONCLUSIONS We have shown that for the system D2O−heptane−C16E6 one obtains microemulsions of record high dilution. The “fish plot” of Figure 2 indicates a surfactant concentration of 1.6% at the limit of the microemulsion system; however, phase studies at the balanced temperature reveal an unexpected absence of a microemulsion one-phase area, and one also observes four phases in equilibrium seemingly in violation of Gibbs’ phase rule. It is demonstrated that for these dilute systems there are sizable effects of the ambient gravitational field. Thus, Gibbs’ phase rule strictly applies only at zero gravity. This restriction is normally neglected in text books. For microemulsion systems, in general, gravity has the effect of diminishing the size of the microemulsion one-phase area. For small domain sizes, that is, large surfactant concentration, the effect is generally negligible; however, as demonstrated here, it becomes significant in balanced microemulsions with a low surfactant content. For the system studied in the present paper, the one-phase area is completely eliminated when using samples of manageable (cm) sizes. On the basis of a measured concentration profile, it is possible to estimate thermodynamic parameters and compare them with measurements on other related systems. We find a maximum dilution of the microemulsion phase of ϕs* ≈ 0.016, which includes a contribution from surfactants dissolved in the oil regions. This is, to our knowledge, a balanced microemulsion of record low surfactant concentration.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work supported by the Swedish Research Council, partly through the Linnaeus Centre Organizing Molecular Matter. REFERENCES

(1) Micelles, Membranes, Microemulsions and Monolayers; Gelbart, W. M., Ben-Shaul, A.; Roux, D., Eds.; Springer-Verlag: New York, 1994. (2) Evans, D. F.; Wennerström, H. The Colloidal Domain: Where Physics, Chemistry, Biology and Technology Meet, 2nd ed.; Wiley-VCH: New York, 1999. (3) Kahlweit, M. Microemulsions. Science 1988, 240, 617−621. (4) Kronberg, B.; Holmberg, K.; Lindman, B. Surface Chemistry of Surfactants and Polymers; John Wiley & Sons: New York, 2014. (5) Winsor, P. A. Solvent Properties of Amphiphilic Compounds; Butterworth, London, 1954. (6) Kahlweit, M.; Strey, R.; Firman, P. Firman Search for Tricritical Points in Ternary Systems: Water-Oil-Nonionic Amphiphile. J. Phys. Chem. 1986, 90, 671−677. (7) Daicic, J.; Olsson, U.; Wennerström, H. Phase Equilibria of Balanced Microemulsions. Langmuir 1995, 11, 2451−2458. (8) Shinoda, K.; Kunieda, H.; Arai, T.; Saijo, H. Principles of Attaining Very Large Solubilization (Microemulsion): Inclusive Understanding of the Solubilization of Oil and Water in Aqueous and Hydrocarbon Media. J. Phys. Chem. 1984, 88, 5126−5129. (9) Kunieda, H.; Shinoda, K. Phase-Behavior in Systems of NonIonic Surfactant − Water − Oil around the Hydrophile-Lipophile Balance Temperature (HLB-Temperature). J. Dispersion Sci. Technol. 1982, 3, 233−244. (10) Kahlweit, M.; Strey, R. Phase Behavior of Ternary Systems of the Type H2O-Oil-Nonionic Amphiphile (Microemulsions). Angew. Chem., Int. Ed. Engl. 1985, 24, 654−668. F


Microemulsions of Record Low Amphiphile Concentrations Are

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