Langmuir 2007, 23, 9559-9562
9559
SANS Study of Polymer-Linked Droplets S. Maccarrone,†,* H. Frielinghaus,† J. Allgaier,† D. Richter,† and P. Lindner‡ Institut fu¨r Festko¨rperforschung, Forschungszentrum Ju¨lich, 52428 Ju¨lich, Germany, and Institut Laue LangeVin, 38042 Grenoble Cedex 9, France ReceiVed July 9, 2007. In Final Form: July 30, 2007 We report experimental results obtained from SANS on microemulsion droplets connected by a telechelic polymer. Thanks to its ability to anchor droplets through its short stickers, the addition of this polymer leads to the formation of transient aggregates. Measurements were performed on samples at low surfactant content in such a way that the droplets appear to be isolated with a separation distance longer than the end-to-end distance of the polymer. The locally spherical structure of the micelles is unchanged in size upon polymer addition whereas the large rise in scattered intensity at low Q is due to the induced effective attractive interaction between droplets. The fitting model that we propose allows a quantitative description of the bridging effect.
Introduction Microemulsions are thermodynamically stable, homogeneous mixtures of two nonmiscible components,1,2 namely, oil and water, which are mediated by the surfactant. Control of the emulsification behavior and/or the structural properties is fundamental because nowadays these systems find a wide range of applications. For example, they are used in the food industry and cosmetics and in the production of detergents, paints, and soaps. On the molecular scale, oil and water form domains, and the surfactant, consisting of amphiphilic molecules with hydrophilic and hydrophobic parts, is arranged at the water-oil interface. Microemulsions show a huge variety of microstructures, depending on the chemical composition, temperature, and concentrations of the constituents. In particular, if there is a strong tendency for the interface to bend toward either a water or an oil domain, then the structure is generally that of (spherical and cylindrical) droplets for small volume fractions of oil in water or water in oil.3 Moreover, the use of polymer additives can modify the phase behavior and the structural properties of such systems. Historically, rheological studies were initially reported.4 It was found that the addition of a class of telechelic polymers, namely, hydrophobically end-capped poly(ethylene oxide), affects the intermicellar interaction in oil-in-water droplet microemulsions, leading to increasing ordering of the micelles.5 Recently, an oil-in-water droplet microemulsion linked by triblock telechelic polymers was proposed as a model in order to study the viscoelastic properties of transient network-forming systems.6,7 Such a telechelic polymer consists of a water-soluble middle chain (PEO) with two short “stickers” (i.e., hydrophobic chains (alkyl chains)) by which we are able to create loops anchoring at two points on the same droplet or eventually bridging two * Corresponding author. Present address: Laboratoire des Colloı¨des, Verres et Nanomateriaux, UMR 5587, CNRS et Universite` Montpellier II, c.c. 26, 34095 Montpellier Cedex 5, France. E-mail: maccarrone@ lcvn.univ-montp2.fr. † Institut fu ¨ r Festko¨rperforschung. ‡ Institut Laue Langevin. (1) Kahlweit, M.; Strey, R. Angew. Chem., Int. Ed. Engl. 1985, 24, 654. (2) Strey, R. Colloid Polym. Sci. 1994, 272, 1005. (3) Safran, S. A. Phys. ReV. A 1991, 43, 2903. (4) Odenwald, M.; Eicke, H. F.; Meier, W. Macromolecules 1995, 28, 5069. (5) Bagger-Jo¨rgensen, H.; Coppola, L.; Thuresson, K.; Olsson, U.; Mortensen, K. Langmuir 1997, 13, 4204. (6) Filali, M.; Ouazzani, M. J.; Michel, E.; Aznar, R.; Porte, G.; Appell, J. J. Phys. Chem. B 2001, 105, 10528. (7) Molino, F.; Appell, J.; Filali, M.; Michel, E.; Porte, G.; Mora, S.; Sunyer, E. J. Phys.: Condens. Matter 2000, 12, A491.
points on different droplets. The advantage of using this system is based on the possibility of independently controlling important parameters such as the concentration of the droplets and the connectivity of the network through the number of polymers per droplet that defines the structural properties. In this letter, we report the experimental results obtained by performing small-angle neutron scattering on polymer-modified microemulsions in the droplet phase. The aim of our work was to quantify the bridging effect by the use of a simple model introduced for the analysis of SANS spectra from which one extracts important information about not only the average size of the droplets but also the separation distance between linked droplets. This last quantity related to the size of the polymer can tell us in which range the bridging takes place. Experimental Section Materials. Our investigation concerned microemulsions consisting of oil, water, and surfactant with small amounts of a telechelic polymer. As the oil, we employed decane C10H22 in the hydrogenated form (Sigma-Aldrich). We used n-decyltetraoxyethylene C10E4, a linear nonionic surfactant purchased from Bachem and used without further purification, in its hydrogenated form. For contrast reasons, we substituted H2O with D2O, which was purchased from Chemotrade with a purity of 99.8%. The triblock telechelic polymer is made by a hydrophilic middle block of PEO (of 4000 g/mol) and two hydrophobic ends called stickers of relatively low molar mass (alkyl chains of 12 carbon atoms). It was synthesized in our laboratory at the Forschungszentrum Ju¨lich according to the work of Kaczmarski and Glass8 by generating the terminal short hydrophobes by direct addition of dodecyl isocyanate to PEO. We intended to measure three samples of decane droplets in D2O with C10E4 as a surfactant, and two of those were prepared with different polymer mass fractions φδ )
mP m P + mS + m O + m W
The idea was to have isolated droplets with separation distance 4 times larger than the end-to-end distance of the polymer. Therefore, we fixed the surfactant/water volume fraction ω)
VS VS + V W
at 0.012 and the oil mass fraction, defined as wB )
mO m P + m S + mO + m W
10.1021/la7020353 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/18/2007
9560 Langmuir, Vol. 23, No. 19, 2007
Letters
was chosen to be 0.036. The large asymmetry introduced into the oil/water volume fraction is the condition from which to obtain oil-in-water droplets. The next step was to construct the phase diagram. Usually this measurement is carried out in a thermal water bath. One test tube containing our microemulsion is put into the bath, and we observe by visual inspection how the light from a lamp is scattered or depolarized by the sample when the temperature is varied. At each temperature, the sample is stirred, and after waiting for a while, an eventual phase separation is detectable. Because the quantity of oil was very low, it was not possible to determine the lower phase boundary between the 1 and 2 phases by simple visual inspection. Then, to get an idea of where it was located, we performed static light scattering at a fixed angle while varying the temperature. Starting from a temperature within the 2h phase region characterized by oilin-water droplets with a water phase excess, the scattering intensity stays constant; after crossing the upper boundary, it starts to decrease by several orders of magnitude, signifying the shape transition from cylindrical to spherical droplets. When the lower boundary was crossed, we observed a rapid, steep increase, and then a plateau was reached: we are in the 2 phase in which a phase of spherical oilin-water droplets coexists with an oil excess phase. Small-Angle Neutron Scattering. SANS experiments were performed on the D11 machine at ILL in Grenoble, France. We measured the samples at three detector distances (2, 5, and 20 m) and at different temperatures. The collimation was set at 5.5 m for the first short detector distances and at 20 and 50 m for the 20 m distance; the wavelength (λ) was chosen to be 6 Å. The scattering curves were put on an absolute scale by using water as a standard with intensities in absolute units (cm-1) with an accuracy of 10%. To calculate the experimental spectra correctly, all of the model spectra were convoluted by the instrumental resolution function.9 We made experiments under bulk contrast by substituting H2O with D2O so that the contribution of the scattering comes from the whole hydrogenated droplet made by the oil core and the surfactant shell. With D2O being the major component, the incoherent background is widely reduced.
Theoretical Model Ternary Microemulsion. We modeled the sample without polymer by considering the droplets to be like colloidal particles. In this way, the scattering intensity as function of the scattering vector has the following form
I(Q) ) ΦV(∆F)2 P(Q) S(Q)
(1)
where Φ is the volume fraction of the droplets, V is the volume, and ∆F is the contrast (i.e., the difference in the scattering-length density of our droplet (oil + surfactant) and the solvent (deuterated water)). P(Q) is the form factor that for Q f 0 is 1, and S(Q) is the structure factor that expresses the interaction between the particles. The low surfactant content yields the formation of droplets with large separation distance, and this allows us to simplify the expression for the intensity by considering S ≈ 1. The form factor for spherical objects is
P(Q) )
[
]
3[sin(QR) - QR cos(QR)] (QR)3
2
(2)
with R being the radius of the sphere. Furthermore, one has to take into account that the particles are not uniform in size and therefore the form factor should be averaged over the particle distribution: (8) Kaczmarski, J. P.; Glass, J. E. Macromolecules 1993, 26, 5149. (9) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321.
〈P(Q)〉 )
∫0∞ P(Q,R) f(R) dR
(3)
The function f(R) is described by the Schulz-Zimm distribution
f(R) )
(z + 1)z+1Rz z+1
R0
Γ(z + 1)
[
exp -
]
(z + 1)R R0
(4)
where R0 is the average radius and Γ(x) is the gamma function. The normalized standard deviation or polydispersity is connected with parameter z by
)
〈(R - R0)2〉1/2 1 ) R0 x1 + z
(5)
Addition of Telechelic Polymers. When the telechelic polymer is added, an effective attractive interaction is introduced that brings the droplets together. To calculate the structure factor S(Q), one needs to solve the Ornstein-Zernike equation for the direct correlation function C(R) using a known interaction potential.10 An expression for the potential U(R) can be built by considering the droplets to be hard spheres and the polymer chains to introduce a parabola-shaped attractive interaction (Figure 1):
{
+∞ R eσ A ˆ (σ - R)(R - σ - 2Re) σ < R e σ + 2Re U(R) ) Re2
(6)
R > σ + 2Re
0
Re is the position where the minimum occurs, and σ is the radius of the colloids. When the potential consists of a hard core plus an attractive tail, the direct correlation function can be obtained under the mean spherical approximation
C(R) )
{
CHS(R) R eσ Catt(R) R > σ
(7)
with CHS(R) being a known direct correlation function for the simple hard sphere system. C(R) is then the sum of two parts: A hard core contribution that involves the colloid diameter σ and its volume fraction Φ
CHS(R) ) -R - β - 0.5RΦR3 where R and β are defined as follows:
R)
(1 - 2Φ)2 + Φ3(Φ - 4) (1 - Φ)4
and
β ) -Φ
18 + 20Φ - 12Φ2 + Φ4 3(1 - Φ)4
An attractive part represented by the parabola of the potential
Catt(R) )
U(R) kBT
The amplitude Aˆ and the range parameter Re are the coordinates (10) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic Press: London, 1991.
Letters
Langmuir, Vol. 23, No. 19, 2007 9561
Figure 1. Model of the potential made by a hard core plus an attractive parabola tail.
of the parabola vertex indicating the depth and the position of the minimum of the potential, respectively. By calculating the Fourier transform C(Q) of C(R),12 the structure factor can be easily obtained by
S(Q) )
1 1 - nC(Q)
Figure 2. Scattering-intensity profiles at different temperature for the sample DROP1 without polymer. In the inset, there is an enlargement of the high-Q regime.
(8)
where n is the number density of hard spheres. Our parabola model is a phenomenological model that reflects three properties. At smaller distances R J σ, the potential is usually slightly repulsive. There is a broad minimum (here at R ) Re+σ), and the attractive interaction has a finite range (here at R ) 2Re + σ). Potentials calculated from first principles give a deeper physical insight especially when varying more parameters, but the fit quality was worse.11
Results and Discussion Before SANS measurements, the samples were characterized in terms of phase behavior. The upper phase boundary that delimits the morphological transition from cylindrical to spherical droplets was detected by visual inspection and was found to be 19.4 °C for the ternary microemulsion, 14.8 and 11.9 °C for the two sample respectively, with 0.072 and 0.147% of polymer. The samples were observed when immersed in a thermal bath. The oil-in-water droplet phase coexisting with a water excess phase appears to be turbid while the one phase of a cylinder-to-spherical droplet is transparent with no optical birefringence. From the static light scattering, we learned that an approximate estimation of the lower phase-transition boundary is around 10 °C. In fact, the surfactant monolayer spontaneous curvature is very sensitive to temperature variation. In particular, by decreasing the temperature, the preferred curvature toward oil increases, leading to a reduction in the size of the droplet phase coexisting with the oil phase excess phase. We measured each sample at different temperatures starting from a value in the one-phase region. For example, in the case of ternary microemulsion, by starting at 18.26 °C and continuing to go down in temperature it was possible to follow the transition from cylindrical to spherical droplets, as can be clearly seen from the scattering intensity profiles shown in Figure 2. With decreasing temperature, the intensity for small angles changes from a Q-1 dependence typical of cylinders to a plateau indicating the presence of spherical droplets. At the same time, a small hump is observed to grow at high Q values, defining the size of (11) Porte, G.; Ligoure, C.; Appell, J.; Aznar, R. J. Stat. Mech. 2006, P05005. (12) Ye, X.; Narayanan, T.; Tong, P.; Huang, J. S.; Lin, M. Y.; Carvalho, B. L.; Fetters, L. J. Phys. ReV. E 1996, 54, 6500.
Figure 3. Scattering-intensity profiles for the three samples with different polymer concentrations and relative fitting curves. The spectra of DROP2 and DROP3 were multiplied by factors of 10 and 100, respectively, for a better view. Errors are approximately the same as or less than the size of the symbols. Table 1. Parameters of the Droplet Samplesa system
ω
wB
φδ (%)
DROP1 DROP2 DROP3
0.011 0.010 0.010
0.0037 0.0033 0.0035
0 0.072 0.146
a ω Is the surfactant to water ratio, w is the total oil fraction, and B φδ is the total polymer fraction.
the small droplets. At 6.54 °C, we were sure to have a spherical droplet microemulsion sample. In Figure 3, the scattering intensity profiles for all the three samples at a fixed temperature of 6.54 °C are shown. At first look, the unchanged position of the minimum at high Q is the sign that the average size of the droplets is not influenced by the polymer whereas the upturn of the intensity at low Q indicates the presence of large objects (Figure 3), which likely are linked droplet aggregates that become larger with increasing polymer concentration: the bridging induces an effective attractive interaction, and the bump at moderate Q, which is more visible for the sample with the highest polymer content, shows that there is a preferred distance between droplets in the transient clusters. Quantitative analysis of the scattering data based on eq 1 permits us to extract the mean radius of the spherical droplets σ equal
9562 Langmuir, Vol. 23, No. 19, 2007
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Table 2. Fit Parameter Values Obtained for the Droplet Samples system
Φ
DROP1 DROP2 DROP3
(0.01329 ( 5.0) × (0.01356 ( 5.2) × 10-5 (0.01317 ( 6.9) × 10-5 10-5
Φcorr
σ (Å)
z
Re (Å)
Aˆ
0.01538 0.01426 0.01501
43.03 ( 0.06 42.8 ( 0.07 43.6 ( 0.1
41.4 ( 1.1 39.9 ( 0.9 40.7 ( 1.2
77.6 ( 2.0 79.7 ( 1.3
(-1.45 ( 1.7) × 10-4 (-2.81 ( 0.8) × 10-4
to 43 Å and the volume fraction of droplets around 0.013 in the case of DROP1 (bottom curve in Figure 3). Because of the low surfactant content, the droplets in the pure microemulsion should be well separated, making the assumption of S ≈ 1 reasonable. Indeed, the estimated average distance is quite large, about 295 Å, considering a droplet arrangement on a cubic network with volume fraction and radius values as from the fitting. For the other two samples, the fitting of the SANS spectra (middle and top curves in Figure 3) gave us the same values for the mean radius and volume fraction of the droplets that we did not expect to vary. Moreover, the fitting parameters that determine the position and the amplitude of the attractive well potential are consistent between the two sample with different polymer concentrations. In particular, sample DROP3 with twice the amount of the polymer has an amplitude that is 2 times larger than that for the sample with half of the polymer DROP2. The depth of the minimum Aˆ is equal to -1.45kBT in the case of DROP2 and 2 times larger (-2.81kBT) for DROP3. These values are in reasonable agreement with the work of Bathia and Russel.13 All of the important fit parameters and their resulting values are summarized in Table 2. The calculation of the Φ values from the sample composition should take into account the solubility of the C10E4 surfactant not only in oil but also in water. In fact, these corrected values Φcorr compare quite well with those obtained from the fit. Counting the number of polymers per droplet via
φp Vsphere np ) ndrop Φ Vp with
φp )
npVp Vtot
and
Φ)
ndropVsphere Vtot
we find that in the sample DROP2 there is one polymer chain per droplet so two polymer chains keep two droplets together whereas in DROP3 the droplet pair is linked by four polymers (np/ndrop ) 2). In our model, we chose R and σ to take the same values whereas for an ideal hard sphere model σ ) 2R. The real microemulsion droplets do have contacts and exchange material.14 For this intermediate stage, two droplets merge into one with a relatively large excess surface. This intermediate stage is covered by our (13) Bathia, S. R.; Russel, W. B. Macromolecules 2000, 33, 5713. (14) Mays, H.; Pochert, J.; Ilgenfritz, G. Langmuir 1995, 11, 4347.
model as two intersecting spheres. Thus, we can use the hard sphere model with the attractive interaction being a small perturbation. Filali et al.6 found monophasic behavior over a large range of Φ and np/ndrop values, but according to the rheological properties, it is possible to define a percolation line. Beyond this threshold, the system passes from liquid-like to gel-like behavior. The initial clusters become an infinite viscoelastic transient network. For a volume fraction of
