pubs.acs.org/Langmuir © 2009 American Chemical Society
Structure and Rheology of a Self-Standing Nanoemulsion Hiromitsu Kawada,† Takuji Kume,† Takuro Matsunaga,‡ Hidetaka Iwai,† Tomohiko Sano,† and Mitsuhiro Shibayama*,‡ †
Beauty Care Research Laboratories, Kao Corporation, Ltd., 2-1-3 Bunka, Sumida-ku, Tokyo, 131-8501 Japan, and ‡Institute for Solid State Physics, The University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Received August 5, 2009. Revised Manuscript Received September 5, 2009 A stable nanoemulsion consisting of nanometer-sized oil droplets in water having a self-standing capability was prepared by high-pressure emulsification. The nanoemulsion does not flow and has a yield stress. This nonfluidity is ascribed to the crystal-like lattice structure of nanodroplets. The lattice structure was observed by transmission electron microscopy of a freeze-fractured surface of the specimen. Small-angle neutron scattering (SANS) revealed the presence of an ordered structure in addition to spherical domains with a radius of 17 nm. This long-range order is, in principle, due to electrostatic repulsive interaction between charged nanodroplets. Dynamic light scattering (DLS) showed two relaxation modes, one for the collective motion of the lattice and the other for the translational diffusion of the nanodroplets. Dilution of the nanoemulsion resulted in a transition from a crystal-like structure to a typical colloidal solution.
1. Introduction Colloids are dynamic-equilibrium systems in which various interactions and forces are in delicate balance, such as electrostatic and van der Waals interactions, gravity, and Brownian motion.1 To increase the surface to volume ratio and the stability of colloids, numerous efforts have been made to decrease the size of colloidal particles. High-pressure emulsification is one of the practical methods for the preparation of nanometer-order emulsion (NE). High-pressure emulsification has been widely used in the food, pharmaceutical, cosmetic, and paint industries to prepare infusion liquids containing sugars, amino acids, electrolytes, fat emulsions and vitamins, medicines, lipids, and pigments.2,3 We recently succeeded in preparing a stable NE by highpressure emulsification that does not flow and sustains itself against gravity as shown in Figure 1. This is an oil-in-water emulsion in which the particle (oil þ surfactant) concentration is about 25 vol % (φ ≈ 0.25). Because the concentration was relatively low, the viscosity of the continuous phase is low enough (4.26 mPa s), and the continuous phase is a Newtonian fluid, such an emulsion was expected to flow. However, as shown in the Figure, the emulsion was pastelike and did not flow against its own gravity. In this respect, this NE is a kind of gel emulsion.4-6 Gel emulsions are usually pastelike and self-standing (i.e., they have high viscosity and high yield stress). However, as shown in Figure 2, our NE is completely different from these gel emulsions because the internal-phase ratio (IPR) is around 25%, which is much less than those in gel emulsions (J74%). Here, Figure 2 was *To whom correspondence should be addressed. E-mail: sibayama@issp. u-tokyo.ac.jp. (1) Kleman, M.; Lavrentovich, O. D. Soft Matter Physics; Springer-Verlag: New York, 2003. (2) Panagiotou, T.; Fisher, R. J. Chem. Eng. Prog. 2008, 104, 33–39. (3) Panagiotou, T.; Mesite, S.; Fisher, R.; Gruverman, I. In Production of Stable Drug Nanospensions Using Microfluidics Reaction Technology; 2007 NSTI Nanotechnology Conference and Trade Show - NSTI Nanotech 2007, Technical Proceedings, Santa Clara, CA, 2007; pp 246-249. (4) Lissant, K. J. J. Colloid Interface Sci. 1966, 22, 462–468. (5) Solans, C.; Pons, R.; Zhu, S.; Davis, H. T.; Evans, D. F.; Nakamura, K.; Kunieda, H. Langmuir 1993, 9, 1479–1482. (6) Kunieda, K.; Fukui, Y.; Uchiyama, H.; Solans, C. Langmuir 1996, 12, 2136– 2140.
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constructed in order to clarify the flow behavior as a function of the droplet size, and the internal-phase ratio (i.e., the volume fraction of the droplet phase; we constructed a phase diagram based on the literature of gel emulsions4-6 and colloidal crystals7-11). The sizes of droplets in NE are on the order of tens of nanometers, which is a few orders of magnitude smaller than in gel emulsions. Therefore, the self-standing mechanism in NE is completely different from those in gel emulsions. Because the size of the NE studied in this work is on the order of nanometers, where the electrostatic repulsive force is effective in stabilizing ordered structures, the mechanism is rather similar to that of colloidal crystals. Colloidal crystals usually have a lower concentration than do gel emulsions, as shown in Figure 2. In spite of low IPRs, however, the colloidal crystals are stabilized by a long-range-electrostatic repulsion and sometimes exhibit self-standing behavior.7-11 However, its stability is strongly dependent on the ionic strength of the solvent. In the case of typical colloid crystals, the particle size is on the order of micrometers or submicrometers. Hence, a high degree of deionization is necessary for the colloid crystal to acquire an electrostatic potential strong enough to keep the crystal structure on the order of micrometers because the electrostatic potential is a decreasing function of distance and is also screened by counterions. The NE systems studied in this work, however, are formed only with 17 nm oil droplets and are capable of colloidal crystal formation even in ordinary aqueous solutions. On the basis of the above literature review on gel emulsions and colloidal crystals, the NE systems have the following unique properties,: (1) high viscosity, (2) relatively low concentration, and (3) the presence of ordered structures. Therefore, this is a rather unique nanoemulsion capable of self-standing stabilized by electrostatic repulsion even at low concentration. In general, solid colloid particles are used in colloidal crystals to apply them to (7) Okubo, T. Prog. Polym. Sci. 1993, 18, 481–517. (8) Megens, M.; van Kats, C. M.; Bsecke, P.; Vos, W. L. Langmuir 1997, 13, 6120–6129. (9) Vos, W. L.; Megens, M.; an Kats, C. M.; Bsecke, P. Langmuir 1997, 13, 6004– 6008. (10) Clarke, S. M.; Ottewill, A. R. R. H. Langmuir 1997, 13, 1964–1969. (11) Goodwin, J. W.; Ottewill, R. H.; Parentich, A. J. Phys. Chem. 1980, 84, 1580–1586.
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Figure 1. Appearance of nanoemulsion NE1. It self-stands against gravity, and no flow occurs over months.
photonic crystals and so on. However, liquid-state dispersoids are capable of size reduction by high-pressure emulsification. In addition, those are more favorable than solid-state dispersoids for pharmaceutical and/or cosmetic applications because of percutaneous and/or oral absorption, moisture retention, and so forth. The objective of this article is to elucidate the nonfluidity of the NE within the scope of medical and cosmetic applications.
Figure 2. Ordering-jamming phase diagram showing the relationship between droplet size and the internal-phase ratio (IPR).
where φ is the volume fraction of the particles (= 4πR3n/3). However, this equation gives a negative value for φ > 0.125. Fournet solved this problem by taking account of the three-body interaction,13 SðqÞ ¼
2. Theoretical Background The small-angle neutron scattering intensity, I(q), of a colloidal dispersion is given by the following equation, IðqÞ ¼ KnV 2 PðqÞ SðqÞ Z
¥
SðqÞ ¼ 1 þ 4πn 0
sinðqrÞ 2 r dr ½gðrÞ - 1 ðqrÞ
SðqÞ ¼ SPY ðq, R, φÞ ¼ ð2Þ
where Fi, bi, and vi are the scattering-length density, the scattering length, and the volume of component i (= s (sample) and 0 (the solvent)). The form factor for spherical objects with radius R is simply given by ð4Þ
1 1 þ 24φ½HPY ð2qRÞ=2qR
ΦðqRÞ ¼
ðqRÞ3
ð5Þ
Now we will discuss several types of structure factors. 2.1. Percus-Yevick Equation. To describe the structure factor, one needs to evaluate g(r) of the system. Debye introduced a hard-core potential and derived the following function,12 SðqÞ ¼ 1 - 8φΦð2qRÞ (12) Debye, P. Phys. Z. 1927, 28, 135.
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ð6Þ
ð8Þ
The explicit form of HPY(2R) is given in Supporting Information. 2.2. Modified Percus-Yevick Equation. The PY equation is modified to the case where two characteristic lengths are necessary to describe the system (i.e., the core radius, R, and the minimum interparticle distance determined by a hard-core potential with a length of D). Such a case is found in block copolymer systems having spherical microdomain structures,15 ionomers,16 and colloid systems stabilized by strong electrostatic repulsive interactions.17 In such a case, the PY equation is modified by SðqÞ ¼ SmPY ðq, D, φ0 Þ ¼
1 1 þ 24φ0 ½HPY ð2qDÞ=2qD
ð9Þ
In this case, the volume fraction of the spherical colloid particles is given by 3 R 4 φ¼φ ¼ πR3 n D 3 0
3½sinðqRÞ - qR cosðqRÞ
ð7Þ
where ς is a constant close to unity. A more rigorous calculation was carried out by Percus-Yevick (PY).14 According to PY theory, S(q) is given by
ð1Þ
Here, K is the scattering contrast and n and V are the number density of the colloid particles and the volume of the particle, respectively. P(q) and S(q) are the form and structure factors, respectively. g(r) is the radial distribution function. In the case of neutron scattering, K is given by bs b0 2 ð3Þ K ¼ ðΔFÞ2 ¼ ðFs - F0 Þ2 ¼ vs v0
PðqRÞ ¼ Φ2 ðqRÞ
1 1 þ 8ζφΦð2qRÞ
ð10Þ
2.3. Hayter-Penfold Equation. Hayter and Penfold developed an analytical structure factor for macroion solutions.18 They took account of repulsive Coulombic interaction and solved the (13) Fournet, P. G. Acta Crystallogr. 1951, 4, 293. (14) Percus, J. K.; Yevick, G. J. Phys. Rev. 1958, 110, 1–12. (15) Kinning, D.; Thomas, E. L. Macromolecules 1984, 17, 1712–1718. (16) Yarusso, D. J.; Cooper, S. L. Macromolecules 1983, 16, 1871–1880. (17) Shibayama, M.; Kawada, H.; Kume, T.; Sano, T.; Matsunaga, T.; Osaka, N.; Miyazaki, S.; Okabe, S.; Endo, H. J. Chem. Phys. 2007, 127, 144507. (18) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109–118.
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Ornstein-Zernike equation in the mean spherical approximation. The structure factor is given by SðqÞ ¼ SHP ðqÞ ¼ Sðq, R, φ, ψ0 , K, εÞ ¼
1 1 þ 24φ½HHP ð2qR, ψ0 , K, εÞ=2qR
ð11Þ
where HHP(2qR, ψ0, κ, ε) is a function not only of q, R, and φ but also the electrostatic properties of the system (i.e., the surface potential of the particle), ψ0, the Debye screening length of the medium, κ-1, and the dielectric constant, ε. Though the explicit form of HHP(2qR, ψ0, κ, ε) is given in Supporting Information, HHP(2qR, ψ0, κ, ε) is reduced to the PY hard-sphere results (i.e., eq 8 for κR f ¥, ψ0 f 0). 2.4. Paracrystal Theory. The paracrystal theory developed by Hosemann and Bagchi is suitable for describing the structure of macrolattice.19 The theory introduces the lattice factor, Zk (k = 1, 2, and 3), which is given by SPC ðqÞ Zk ðqÞ ¼
1 - jFðqÞj2 1 - 2jFðqÞjcosðak 3 qÞ þ jFðqÞj2
ð12Þ
where F(q) is the factor describing the degree of distortion, "
# 1 Δa2 2 2 2 fða1 3 qÞ þ ða2 3 qÞ þ ða3 3 qÞ g jFðqÞj ¼ exp 2 a2
ð13Þ
Here, ai (i = 1, 2, 3) is the fundamental vector and Δa is the standard deviation, respectively. The ratio g Δa/a is often called the Hosemann’s g factor, which determines the order of paracrystallinity. In the case of a face-centered cubic (fcc) structure, ai (i = 1, 2, 3) is defined by the orthogonal vector bi, where a1 = (b2þb3)/2, a2 = (b3þb1)/2, a3 = (b1þb2)/2, and |b1| = |b2| = |b3| = a. The scalar products in eq 13 are given by20-22 1 a1 3 q ¼ aqðsin θ sin φ þ cos θÞ 2 1 a2 3 q ¼ aqð - sin θ cos φ þ cos θÞ 2 1 a3 3 q ¼ aqð - sin θ cos φ þ sin θ sin φÞ 2
ð14Þ
Because the macrolattice is randomly oriented in the space, one needs an orientational average as given by ZðqÞ ¼
1 4π
Z
Z
2π
π
dφ 0
dθ Z1 ðq, θ, φÞ Z2 ðq, θ, φÞ Z3 ðq, θ, φÞsin θ
0
ð15Þ
5 wt % fatty acid (N-(hexadecyloxyhydroxypropyl)-N-hydroxyethylhexadecanamide), and 1.5 wt % anionic surfactant (n-stearoyl-L-glutamic acid monosodium) in water. The emulsification was achieved by a high-pressure emulsifier, an M-140K Microfluidizer Processor (Microfluidics, Massachusetts). This system generates high-pressure fluid of ca. 250 MPa. By repeating this emulsifying process more than five times, the mixture reached a stable NE. For neutron-scattering experiments, deuterated water was used instead of light water. A series of samples for rheological measurements and SANS experiments were prepared by diluting this stock solution with deuterated water. In the case of DLS measurements, however, dilution was carried out using the water-phase solution consisting of glycerol, ethanol, and deuterated water in order to evaluate the exact hydrodynamic radius of the droplet. Those samples were coded as NEx, where x is the dilution ratio with respect to the as-prepared NE.
3.2. Freeze-Fracture Transmission Electron Microscopy. Freeze-fracture transmission electron microscopy (FFTEM) observation was carried out to confirm the size and packing condition of NE1. The frozen sample of NE1 was used to make FF specimens in the usual way. The specimens were observed using JEOL CX II transmission electron microscope (JEOL Ltd., Tokyo, Japan) in conventional transmission mode using an 80 kV acceleration voltage. 3.3. Rheology. Rheological measurements were carried out on an MCR-301 (Anton Paar, Physica, Austria) with cone-plate geometry at 25 C. The diameter and the cone angle of the cone-plate were changed according to the viscosity of the samples: 25 mm and 1 for NE1, 50 mm and 2 for NE1.25, and 75 mm and 2 for NE1.33-NE54. Dynamic viscoelastic measurements of storage and loss moduli (G0 and G00 ) versus the angular frequency, ω, were carried out in the linear viscoelastic region. 3.4. Small-Angle Neutron Scattering (SANS). SANS experiments were performed on the SANS instrument (SANS-U) at the Institute for Solid State Physics, The University of Tokyo.23,24 The neutron wavelength was 0.7 nm, and its distribution was ca. 10%. The sample-to-detector distances were chosen to be 2 and 12 m, and the corresponding q range was from 0.02 to 1.5 nm-1. Here q is the magnitude of the scattering vector defined by q = (4π/λ)sin θ, where λ is the wavelength of the neutron beam and 2θ is the scattering angle. The necessary corrections were made for air scattering and cell scattering, along with incoherent background subtraction.25 After these corrections, the scattering intensity was normalized to the absolute intensity with a polyethylene secondary standard sample.26 All of the SANS experiments were carried out at 25 C. 3.5. Dynamic Light Scattering (DLS). DLS measurements were carried out using a DLS/SLS-5000 compact goniometer (ALV, Langen) coupled with an ALV photon correlator. A 22 mW helium-neon laser (wavelength, λ = 632.8 nm) was used to deliver the incident beam. The decay-rate distribution functions G(Γ) were calculated from the intensity-intensity-time correlation function using the CONTIN data analysis package. All of the DLS measurements were carried out at 25 C at a scattering angle of 90 unless otherwise noted.
3. Experimental Section
4. Results and Discussion
3.1. Sample Preparation. The nanometer-sized oil-in-water emulsion (nanoemulsion, NE) was prepared by high-pressure emulsification of a solution consisting of 30 wt % glycerol, 3 wt % ethanol, 16 wt % oil (dimethylpolysiloxane with a viscosity of 6 mPa s),
4.1. Concentration Dependence. Figure 3 shows an FFTEM image of NE1. It is clearly resolved that spherical objects are aligned in hexagonal packing as guided by dashed hexagons. The size of the particles and the interparticle distance are roughly
(19) Hosemann, R.; Bagchi, S. N. Direct Analysis of Diffraction by Matter; North-Holland: Amsterdam, 1962. (20) Matsuoka, H.; Tanaka, H.; Hashimoto, T.; Ise, N. Phys. Rev. B 1987, 36, 1754–1765. (21) Matsuoka, H.; Tanaka, H.; Iizuka, N.; Hashimoto, T.; Ise, N. Phys. Rev. B 1990, 41(6), 3854–3856. (22) Okabe, S.; Sugihara, S.; Aoshima, S.; Shibayama, M. Macromolecules 2002, 35, 8139–8146.
(23) Okabe, S.; Nagao, M.; Karino, T.; Watanabe, S.; Adachi, T.; Shimizu, H.; Shibayama, M. J. Appl. Crystallogr. 2005, 38, 1035–1037. (24) Okabe, S.; Karino, T.; Nagao, M.; Watanabe, S.; Shibayama, M. Nucl. Instum. Methods Phys. Res., Sect. A 2007, 572, 853–858. (25) Shibayama, M.; Matsunaga, T.; Nagao, M. J. Appl. Crystallogr. 2009, 42, 621–628. (26) Shibayama, M.; Nagao, M.; Okabe, S.; Karino, T. J. Phys. Soc. Jpn. 2005, 74, 2728–2736.
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Figure 3. FF-TEM image of NE1. The hexagons with dashed lines indicate the crystal lattice.
Figure 5. Viscoelastic properties, G0 (ω) and G00 (ω), of NEx (1 e
x e 54). G0 (ω) of NEx’s (x g 2) were undetectable because of insufficient torque (shear stress).
Figure 4. Shear-rate dependence of the steady shear viscosities of NEx (1 e x e 54). The viscosities of NEx (2 e x e 54) in the lowshear-rate region were undetectable because of insufficient torque (shear stress) and the influence of interfacial tension.
estimated to be 20-40 and 50-60 nm, respectively. It is interesting that oil droplets form a crystal-like arrangement over a concentration range (∼0.3) that is much lower than their closepacking concentration (∼0.74). Figure 4 shows the steady shear viscosity, η, of NE1 and its _ Only NEx’s (x e diluted samples as a function of the shear rate, γ. 1.33) exhibit strong shear-thinning behavior, whereas NEx’s (x g 2) show Newtonian behavior. NE1.25 and NE1.33 show a transition around γ_ ≈ 0.1 and 1 s-1, respectively. The shearthinning behavior observed in NEx’s (x e 1.33) was reversible _ Figure 5 shows (a) the storage, G0 (ω), and with respect to γ. (b) loss shear moduli, G00 (ω), of NEx’s. The shear strain was 1% for NEx (1 e x e 1.33) and 100% for NEx (2 e x). NE1 shows the typical rheological behavior of elastic gels (i.e., G0 ≈ ω0, G00 ≈ ω0, and G0 . G00 ). However, NEx’s (x g 2) show undetectable G0 and G00 ≈ ω1 characteristic of viscous fluids. NE1.25 and NE1.33 are in a transition region. To elucidate further the structureproperty relationship of NEx’s, we carried out SANS and DLS experiments. Figure 6 shows SANS curves of NEx. A clear interparticle interference peak and a shoulder appear for each scattering curve. The peak shifts toward lower q by dilution. To determine the structure parameters, we first analyzed NE54, which was expected Langmuir 2010, 26(4), 2430–2437
Figure 6. SANS functions of NEx (1 e x e 54).
to have no or a very small contribution from interparticle interference. 4.2. Assignment of the Structure Factors. Figure 7 shows the SANS curve of NE54. The form-factor fit with eqs 1-5 (S(q) = 1) is shown by the dashed line. Note that the scattering intensity in the low-q region (e0.04 nm-1) is not well reproduced by the fit and the observed intensity is lower than the fit. This indicates that interparticle interference exists even at 54-fold dilution (i.e., φ ≈ 0.005). The presence of such a long-range interference interaction is typical in charged colloid systems. Hence, the Percus-Yevick (PY) function was used to reproduce the observed SANS function of NE54. However, as will be shown in Figure 9a, the fit with the PY function is poor and the evaluated volume fraction with SPY(q) was φ = 0.02, which is not consistent DOI: 10.1021/la902905b
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Figure 7. SANS functions of NE54. The dashed line, dotteddashed line, and solid lines denote P(q), S(q), and I(q), respectively.
Figure 9. Experimentally obtained S(q)’s. (a) PY, (b) mPY, and (c) HP. Note that mPY fitting reproduces the observed SANS curve more effectively than do others, particularly around the peak and the low-q region.
Figure 8. (a) Experimentally obtained ratio, I(q)/P(q) = KnV 2S(q), as a function of x. (b) Value of KnV 2 as a function of the dilution ratio, x.
with the stoichiometric value. We tried to fit the function with the Hayter-Penfold (HP) function as well. It gave a reasonable fit, but the volume fraction was overestimated. As will be discussed later in Figure 9a, HP could not reproduce the observed SANS functions at intermediate φ values. Then, we employed the modified Percus-Yevick (mPY) function. The result is shown by the solid line, which nicely reproduces the observed scattering intensity function with a reasonable value of φ (φ = 0.00425). The structure factor used to reproduce I(q), S(q) = SmPY(q), is shown as a dotted-dashed line. Thus, the radius of the sphere, R, the interparticle distance, D, and the volume fraction of the nanodroplets, φ, are found to be 17.1 nm, 92.3 nm, and 0.00425, 2434 DOI: 10.1021/la902905b
respectively. This means that there is a strong repulsive potential in the NE system due to electrostatic interaction characterized by the interparticle distance D. Further discussion with respect to a suitable structure factor will be given below. To analyze the scattering function of colloidal systems, it is essential to evaluate S(q). Here, we assume that the size of the oil droplets in NE does not change by dilution. The structure factor, S(q), can be simply obtained by taking the I(q)/P(q) ratio. Figure 8a shows I(q)/P(q). According to eq 1, the ratio is related to the number density of the droplets, n, (i.e., I(q)/P(q) = KnV 2S(q)). By knowing S(q f ¥) = 1, the value of KnV 2 can be evaluated with eq 1. The variation of KnV 2 with x is given in Figure 8b, which is an inversely proportional function of x as expected. These results clearly support the assumption that the size of individual oil droplets does not change and is stable upon dilution. From Figure 8a, it is clear that each NEx has an interparticle interference peak for 1e x e 8 and the peak fades by further dilution. Here, we compared the observed S(q)’s with those of the theories. Figure 9 shows S(q)’s evaluated with (a) the Percus-Yevick (PY) theory, (b) the modified Percus-Yevick (mPY) theory, and (c) the Hayter-Penfold (HP) theory. Though all of the theories seem to reproduce well the observed S(q) for NE1, SPY(q)’s and SHP(q)’s deviate from the observed ones for the diluted samples (NEx, x > 1). However, SmPY(q)’s best reproduced the observed S(q)’s up to the samples with the highest dilution (i.e., NE54). Table 1 shows the structure parameters of NEx evaluated with PY, mPY, and HP as well as the sample characteristics. The fittings were carried out by fixing the radius of Langmuir 2010, 26(4), 2430–2437
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NEx
φcalcd
R (nm) σR (nm) D (nm) φR,PY φR,mPY
φR,HP
Z
1 0.250 17.1 3.23 34.8 0.378 0.362 0.370 12.1 1.25 0.200 17.1 3.23 37.3 0.336 0.283 0.325 11.5 2 0.125 17.1 3.23 43.5 0.245 0.151 0.199 21.9 4 0.0625 17.1 3.23 52.9 0.183 0.0673 0.0952 20.3 8 0.0313 17.1 3.23 63.8 0.130 0.0313 0.0421 20.3 16 0.0156 17.1 3.23 73.4 0.0827 0.0152 0.0208 18.6 27 0.00926 17.1 3.23 81.1 0.0482 0.00853 0.0117 18.6 54 0.00463 17.1 3.23 92.3 0.0200 0.00425 0.00631 20.2 a σR is the standard deviation of the Gaussian size distribution of the radius; D is the interparticle distance evaluated by mPY; and Z is the number of charges on a droplet evaluated by curve fitting with HP.
Figure 11. Dilution ratio, x, dependence of the relative interparticle distance, D(x)/D(x = 1).
Figure 12. SANS intensity functions of NE solutions depending with (a) the Percus-Yevick equation, SPY(q), and (b) paracrystal theory, SPC(q).
on the salt effect. The KCl concentration was systematically increased from 0 to 0.05%. Nanoparticle concentrations were the same as that of NE2. The inset shows an expansion of the peak area.
the droplets. Although the evaluated values of the volume fraction of the droplets, φR, are somewhat larger than the calculated (stoichiometric) value, φcalcd, it becomes more similar by dilution. The original PY equation did not reproduce the observed scattering function and overestimated the value of φ by a factor of 2-4. Hayter-Penfold (HP) theory27 did not work either. Because the HP theory was originally derived to describe nanometer-sized macroions, it was expected to describe this nanodroplet system reasonably well. As a matter of fact, the HP function was successfully employed for analyses of silica colloids and polymer-adsorbed silica colloids.28,29 This is probably due to the preparation method of the NE (i.e., high-pressure emulsification). Hereafter, mPY theory was employed in the following analysis for NEx with x > 1. The values of D in the Table were obtained by mPY. Now, let us discuss what kind of structure factor is the most suitable to describe NE1. Figure 10 shows I(q) of NE1 and the fitted results with the modified Percus-Yevick (mPY) and paracrystal theories (PC). Here, we assumed face-centered
cubic (fcc) packing to apply the PC theory. It is reasonable to assume that a system with repulsive interaction or with a hardcore potential has a tendency to form an fcc packing. If there is another interaction, such as a packing problem of block polymer chains in the matrix, then body-centered-cubic (bcc) packing is also possible as reported by Gast et al.30 Though the mPY fitting seems to be satisfactory, evidence of an ordered structure by the FF-TEM photograph (Figure 3) and the selfstanding nature (Figure 1) support the PC theory being more reasonable to describe NE1 for q g 0.1 nm-1. Furthermore, a SAXS study on block copolymers in a selective solvent by Hashimoto et al. supports this conjecture. They investigated the relationship between the rheological behavior and smallangle X-ray patterns for block copolymers in a selective solvent and found that the dissolution of the paracrystal-like ordered structure was responsible for the plastic flow to non-Newtonian flow transition.31 Note that the PC fit has a significant
Figure 10. Comparison of SANS intensity functions curve-fitted
(27) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651–656. (28) Qiu, D.; Cosgrove, T.; Howe, A. M. Langmuir 2006, 22, 6060–6067. (29) Qiu, D.; Dreiss, C. A.; Cosgrove, T. Langmuir 2005, 21, 9964–9969.
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(30) McConnell, G. A.; Gast, A. P.; Huang, J. S.; Smith, S. D. Phys. Rev. Lett. 1993, 71, 2102. (31) Hashimoto, T.; Shibayama, M.; Kawai, H.; Watanabe, H.; Kotaka, T. Macromolecules 1983, 16, 361–371.
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deviation for q < 0.1 nm-1. This is because PC theory does not include the concepts of excluded volume and hard core potential. Hence, it is necessary to modify the PC theory by taking account of these effects. The relative interparticle distance, D(x)/D(x = 1), is plotted in Figure 11, which also clearly indicates a simple dilution of NE. Hence, it is concluded that the NE system loses its interparticle interaction by dilution without changing the size and shape of the droplet. 4.3. Effects of Salt. Figure 12 shows the salt effect on the structure factor. Here, only the salt concentration was systematically increased from 0 to 0.05%. It was attained by adding a
Figure 13. Shear rate dependence of the viscosities of NE1.33 and NE2 on the salt effect.
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KCl deuterated water solution to NE1, and the NE solutions were prepared in which the nanoparticle concentrations were the same as that of NE2. Hence, the series of samples shows a simple substitution of the solvent by salt solutions. As shown in the Figure, systematic peak broadening takes place by increasing salt concentration without a significant change in the peak position. This result obviously indicates that the mean distance between NE particles does not change but the distance distribution becomes large by adding salt. Hence, it is clear that the dominant interparticle interaction is the electrostatic interaction. Figure 13 shows the shear rate dependence of the viscosities of NEs in the presence of salts. Here, the salt concentration was also systematically increased from 0 to 0.05% for NE1.33 and NE2. The viscosities of NEs decrease abruptly with increasing salt concentration. They also suggest that the electrostatic interaction is dominant. In the case of NE1, the electrostatic interaction is strong enough to form a crystal-like structure, resulting in the NE acquiring a self-standing nature. This is the first system, to our knowledge, that is a nanometer-order emulsion and is capable of self-standing stabilized by electrostatic repulsion even at low concentration. 4.4. Diffusion Coefficient and “Effective” Viscosity. Now, let us examine the dynamics of the NE systems. Figure 14 shows the size distribution functions of NEx’s obtained by DLS. The abscissa and the ordinate denote the characteristic decay time, Γ-1, and its distribution, G(Γ-1), respectively. At low dilution (x e 8), two distinct peaks were observed. However, they seem to merge for x g 16. It is clear that the single peak corresponds to the translational diffusion of individual droplets. However, the assignment of the fast and slow modes appearing in NEx (x e 8) needs further discussion. The
Figure 14. Cluster size distribution, G(Γ-1), of NEx (1 e x e 54) obtained by dynamic light scattering. 2436 DOI: 10.1021/la902905b
Langmuir 2010, 26(4), 2430–2437
Kawada et al.
Article
Figure 16. Dilution ratio, x, dependence of the microscopic effecFigure 15. Dilution ratio, x, dependence of the diffusion coeffi-
tive viscosity of NEx.
cients, Dc. Fast mode (4) and slow mode (O). They seem to merge for x g 16 (0).
in the semidiute concentration regime.32 We conjecture that this fast mode is ascribed to a vibration or a cooperative mode, and it appears exclusively in the case where the colloidal particles are arrested in a strong electrostatic potential. As a matter of fact, the fast mode is strongest in NE1 and decreases with x (Figure 14). Hence, the presence of the fast mode in DLS is another piece of evidence of the presence of long-range interparticle interaction.
diffusion coefficients, Dc, calculated from the peak position of G(Γ-1) (i.e., Γmax-1) via
Rh ¼
Dc ¼ Γmax -1 q2
ð16Þ
kT , 6πηDc
ð17Þ
ξ ¼
kT 6πηDc
are plotted in Figure 15, where η is the nominal viscosity of the solvent and k is the Boltzmann constant. The validity of eq 16 was examined for NE4 at 25 C in the scattering angle range of 30 to 130, and it was confirmed that two Γmax’s were indeed proportional to q2. The two obtained diffusion coefficients in which the magnitudes differ by a factor of 1000 at x = 1 merge at x = 16 by dilution. At this stage, it is not clear which Dc corresponds to the translational diffusion and which is the other. To answer these questions, we first evaluated Rh at x = 54 by knowing the solvent viscosity (pure solution) (i.e., η = 4.26 mPa s). The hydrodynamic radius of the droplet, Rh, was evaluated to be 15.6 nm, which is very close to the value obtained by SANS. Next, we evaluated the (microscopic) “effective” viscosity of NEx via eq 17 by assuming that Rh (= 15.6 nm) does not depend on x. The thus-obtained effective viscosity (ηeff) is shown in Figure 16. In the case of NE1, 2, 4, and 8, ηeff’s of the “fast” mode are much smaller than the solvent viscosity. Therefore, it is clear that the viscosity evaluated from the fast mode does not correspond to the real viscosity. However, the viscosities obtained from the “slow” mode are decreasing functions of x and approach the value for pure solution η(x = ¥) = 4.26 mPa s. The variation of this “microscopic” viscosity is similar to the macroscopic viscosity _ 103 s-1) obtained by macroscopic shear measurement at high γ(≈ in Figure 4. By dilution, it approaches the value of pure solution η(x = ¥) = 4.26 mPa s. Thus, the slow mode can be assigned to the translational diffusion of the droplets. This, in turn, suggests that the open circles and squares in Figure 15 correspond to the translational diffusion of droplets. However, the triangles obtained from the fast mode in Figure 15, appearing only at low dilution (x e 8), can be assigned to the collective diffusion of which the characteristic length is defined by the correlation length, ξ, as proposed by Tanaka for polymer gels and polymer solutions (32) Tanaka, T.; Hocker, L. O.; Benedek, G. B. J. Chem. Phys. 1973, 59, 5151– 5159.
Langmuir 2010, 26(4), 2430–2437
5. Conclusions Small-angle neutron scattering and dynamic light scattering investigations were carried out to elucidate the nanoscopic origin of the self-standing nature of colloid dispersion consisting of oil droplets, NE1. The following findings were obtained. (1) We succeeded in preparing a stable nanoemulsion with Rh ≈ 17 nm by high-pressure emulsification. (2) The nanoemulsion does not flow and has a yield stress. (3) This nonfluidity is ascribed to colloidal crystal structure consisting of nanodroplets. The colloidal crystal structure was observed from the freeze-fracture surface of the specimen. (4) SANS showed a scattering peak, indicating the presence of long-range order. (5) This long-range order is, in principle, ascribed to the electrostatic potential between charged nanodroplets, which is described by the mPY equation. (6) DLS shows two relaxation modes. The fast mode corresponds to the collective motion of the ordered and/or arrested colloidal particles by the electrostatic potential, and the slow mode corresponds to the translational diffusion of the nanodroplets. These results indicate that the self-standing nature of NE is due to its crystallike ordered structure with strong electrostatic repulsion. Although it is stable against gravity, the structure undergoes a crystal-to-fluid transition by dilution. Acknowledgment. This work was supported by the Ministry of Education, Science, Sports and Culture, Japan (Grant-in-Aid for Scientific Research (A), 2006-2008, no. 18205025, and for Scientific Research on Priority Areas, 2006-2010, no. 18068004). The SANS experiment was performed with the approval of the Institute for Solid State Physics, The University of Tokyo (proposal nos. 6558 and 7622), at the Japan Atomic Energy Agency, Tokai, Japan. Supporting Information Available: Details of the PercusYevick, modified Percus-Yevick, and Hayter-Penfold equations. This material is available free of charge via the Internet at http://pubs.acs.org. DOI: 10.1021/la902905b
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