Langmuir 2000, 16, 9117-9120
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Resolving the Puzzle of Ferrofluid Dispersants Rafael Tadmor,† Ronald E. Rosensweig, Joseph Frey,‡ and Jacob Klein* Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Received June 30, 2000. In Final Form: September 6, 2000 Oleic acid and stearic acid are similar surfactants which, however, lead respectively to stability and to precipitation of ferrofluid suspensions: to understand this, the forces between layers of oleic-like surfactants and between layers of stearic-like surfactants across a hexadecane (HD) medium were measured using a surface force balance (SFB). Separate measurements reveal that only the oleic layers are solvated by HD, while the SFB results reveal that for both surfactants a marked net attraction is present between the surfaces. Simple considerations based on these observations explain why, despite this attraction, ferrofluid dispersions are stabilized by oleic but not by stearic surfactants.
Ferrofluids are colloidal suspensions of ferroparticles (Fe3O4 or Fe2O3), forming magnetizable fluids that remain liquid in the most intense magnetic fields,1 and find widespread applications.2,3 Such suspensions, frequently dispersed in hexadecane (HD: C16H34) as the carrier medium, may be stabilized by various long-chain surfactants, the classic example being oleic acid, (CH3(CH2)7CHdCH(CH2)7CO2H), which has a C18 (oleic) tail with a cis-double-bond in the middle, forming a kink. Such kinks have been postulated as necessary for effective stabilization, and indeed stearic acid, (CH3(CH2)16CO2H), with no double-bond in its C18 (stearic) tail, cannot stabilize ferrofluid suspensions.4-6 This is a puzzle insofar as molecules such as C9H18dC9H18 and n-octadecane (C18H38), which are identical in structure to the tails of the respective surfactants, are both readily soluble in HD and so would be expected to provide similar stabilizing properties. To try to resolve this, we studied directly, using a mica surface force balance (SFB), the force versus distance profiles between layers of oleic-tailed and of stearic-tailed surfactants, and the wettability of these layers by HD. Our results lead to a simple model which can account for both the stabilization of the ferrofluid dispersions by the oleic tails and their aggregation when coated with stearic tails. The mica surfaces were coated with either stearic trimethylammonium iodide (STAI: CH3(CH2)17N+(CH3)3I-) or oleic trimethylammonium iodide (OTAI: CH3(CH2)7CHdCH(CH2)8N+(CH3)3I-) by immersing in a 0.4 mg/mL water solution of the surfactants.7 The surfaces were withdrawn dry following rinsing in pure water, showing both surfactants form a hydrophobic coating. X-ray photoelectron spectroscopy (XPS) measurements showed † Present address: Department of Chemical Engineering, University of California at Santa Barbara, CA. ‡ Present address: Chemical Laboratories, University of Cambridge, U.K.
(1) Rosensweig, R. E. Sci. Am. 1982, 247, 136. Rosensweig, R. E. Chem. Eng. Commun. 1986, 19, 437. Rosensweig, R. E. Annu. Rev. Fluid Mech. 1987, 19, 437. (2) Raj, K.; Moskowitz, B.; Casciari, R. J. Magnetism Magnetic Mater. 1995, 149, 174-180. (3) Bailey, R. L. J. Magnetism Magnetic Mater. 1983, 39, 178-182. (4) Rosensweig, R. E. Ferrohydrodynamics; Cambridge: 1985. (5) Scholten, P. C. Thermodynamics of Magnetic Fluids; Hemisphere: Washington, DC, 1978. (6) Rosensweig, R. E.; Nestor, J. W.; Timmins, R. S. Mater. Assoc. Direct Energy Convers. Proc. Symp. AIChE-I. Chem. Eng. Ser. 1968, 5, 104. (7) The STAI was prepared according to Kodawa et al., J. Phys. Chem. 1990, 94, 815, and the OTAI was prepared according to Annby et al., Chem. Scr. 1987, 27, 445; both were recrystallized twice from a methanol-acetone mixture. Elemental matches for both were confirmed with NMR analysis.
no traces of iodine on the hydrophobically modified surface, indicating that only the ionized headgroups attached. The thickness L0 of the dry surfactant layers was estimated from XPS measurements to be L0 ) 10 ( 2 Å and L0 ) 5 ( 2 Å for STAI and OTAI, respectively. The STAI layer thickness is thus around half of a close-packed monolayer coverage, corresponding roughly to one hydrophobic tail per negative charge on the mica surface. The OTAI layer is even less densely attached, corresponding to roughly 1/4 of a close-packed monolayer. These values are comparable with surfactant adsorbances on stabilized ferroparticle surfaces.4 An advancing contact angle of 80 ( 2° for a water droplet is measured for both the STAI (stearic)- and the OTAI (oleic)-coated mica surfaces. In contrast, as shown in Figure 1, the HD (Aldrich 99%+ grade, used as received) wets the oleic-coated mica surface but not the steariccoated one. A droplet of HD on the oleic layer spreads readily (Figure 1b), while a stearic-coated mica surface emerges dry from immersion in HD, which has an advancing contact angle of 50 ( 2° on it. Thus, we conclude that (i) both OTAI and STAI form collapsed layers on the surface following adsorption from aqueous solution and rinsing in pure water and (ii) on exposure to HD the oleic layer appears to be solvated and fully wetted by the liquid, while the stearic layer remains collapsed and unsolvated by the HD. This deserves comment, insofar as we have confirmed that n-octadecane (C18H38), which has the same stucture as the stearic surfactant tails, is itself readily soluble in bulk HD. The collapse of the stearic tails on the surface must therefore occur because the (weak) attraction, of van der Waals origin, between the tethered C18 tails on the surface is not compensated by the translational entropy which favors dissolution of the identical C18H38 chains in bulk HD. In oleic tails, on the other hand, the kink induced by the cis-bond at the C9 position presumably weakens the nematic interactions between the tethered chains to the extent that they are solvated by the HD despite being tethered (and so not benefiting from the translational entropy effect noted above). The origin of the partial wetting behavior of HD on the stearic layer also deserves comment: on the basis of van der Waals interactions alone one might expect the HD to fully wet the STAI film on the mica:8 the large contact angle actually observed must therefore reflect short-ranged effects at the surface of the collapsed stearic chains. The SFB used is similar in design to the balance described in detail recently.9 Following calibration of the air-contact position between the bare mica surfaces, the
10.1021/la0009137 CCC: $19.00 © 2000 American Chemical Society Published on Web 10/31/2000
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Figure 1. (a) HD droplets on a STAI-coated mica. On sliding, the drops leave a dry surface behind them. (b) HD spreading on an OTAI-coated mica. The inset (190 µm × 220 µm) shows the spreading edge magnified, revealing interference bands which indicate an advancing contact angle on the order of 0.5° or less. The HD film continues to spread slowly.
Figure 2. Force profiles between surfactant-covered mica surfaces immersed in HD (D ) 0 corresponds to air-contact between the uncoated mica surfaces). Dots: the calculated vdW interaction (F(D)/R ) -(A/6D2), where A ) 9 × 10-21 J) between two bare mica surfaces across HD. Different symbols correspond to different experiments. (a) OTAI layer. (b) STAI layer; the repulsive peaks are obtained on approach, while the attractive wells are observed on separation (and evaluated from the jumpout positions J), suggestive of a quasi-oscillatory force profile. The broken line is the oscillatory profile obtained between surfactant-coated mica surfaces across a similar but purified n-alkane (tetradecane).11 The insets suggest schematically the configurations of the corresponding surfactant layers (end-attached to the mica) and the confined HD.
surfactant layers were deposited and the new contact separation was determined. Subtraction yields the doublelayer thickness of the surfactant coating: 20 ( 5 Å and 10 ( 5 Å for the STAI and the OTAI double layers respectively, fully consistent for both surfactants with the values of 2L0 from the XPS measurements. A drop of HD was then introduced between the surfaces,10 and the force profiles (F(D)/R versus surface separation D) were measured, as shown in Figure 2. Interactions between the OTAI-covered surfaces (Figure 2a) exhibit, within the scatter, a monotonic attraction comparable with the van der Waals (vdW) forces expected between curved mica surfaces across HD (dotted line in Figure 2), followed by steep repulsion at D j 20 Å (8) Where dispersion forces are dominant, a liquid 3 in equilibrium with its vapor 1 on top of solid 2 will fully wet it whenever the inequality A33 < A22 is obeyed, where Aii is the Hamaker constant of species i. In the present configuration, where HD liquid (3) is on top of the solid substrate (STAI coating on the mica) (2), one expects (from the values of the refractive indices and the Lifschitz relation) that this inequality holds and that for dispersion force dominance the HD should wet the solid substrate. (9) Klein, J.; Kumacheva, E. J. Chem. Phys. 1998, 108, 6996-7009. (10) Janik, J.; Tadmor, R.; Klein, J. Langmuir 1997, 13, 4466.
(indicating the oleic coating is solvated to roughly twice its dry thickness). Such a profile is reminiscent of the interactions between mica coated by rough or fluid surfactant layers across tetradecane;11 however, the solvation of the oleic layers (suggested by the wetting observations) indicates that the origin of the repulsion in our case is due to osmotic effects within the layers. In contrast, forces between the stearic-covered surfaces across HD (Figure 2b) exhibit alternating attractive wells and repulsive regions reminiscent of the oscillating forces observed (due to layering) between solid surfactants across linear alkanes.11 The periodicity of the oscillations is less well defined in our case, possibly because we used asreceived technical grade HD in order to simulate more closely the actual carrier medium used for ferrofluids. Our observations appear to contradict the macroscopic behavior of ferrofluid dispersions: the clear attraction between the oleic-coated mica surfaces across HD, revealed by the SFB measurements (Figure 2a), contrasts with the known stability to aggregation of oleic-coated ferroparticles: If we use the (F(D)/R) profile of Figure 2a to estimate (11) Gee, M. L.; Israelachvili, J. N. J. Chem. Soc., Faraday Trans. 1990, 86, 4049.
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0 the total attractive interaction energy E ) ∫D ∞ F(D) dD, where D0 is the equilibrium separation between the surfaces (bottom of the attractive well), we find E ≈ (-2.5 × 106)kBT for the SFB crossed cylindrical surfaces (R ) 1 cm), corresponding to E ≈ -0.8kBT for spherical particles of R ) 5 nm coated with oleic surfactant. Bearing in mind that the Hamaker constant (A) for Fe3O4 across HD12 is ∼8-fold larger than that for mica across HD,12 we expect, on the basis of the SFB profile, E ≈ -6kBT for oleic-coated ferroparticles, leading us to expect aggregation rather than the stability observed in such ferrofluid dispersions. The origin of this discrepancy is explored below. In our model the overall interaction energy between two particles is E ) EvdW + Es, the vdW attraction and steric repulsion contributions, respectively. Because of their small size, however, we may not assume the Derjaguin approximation (as above) for the ferroparticles. Instead we must use the full Hamaker expression13 to evaluate EvdW between two spherical particles of radius R, with surfaces a distance D apart:
EvdW ) -
{
A 2R2 2R2 + + 2 2 6 (2R + D) - 4R (2R + D)2 (2R + D)2 - 4R2 ln (2R + D)2
[
]}
(1)
We model Es as illustrated in the inset to Figure 3b: the surfaces, radius R and distance D apart, are covered by the solvated surfactant-tail layer of thickness L, and the extent of overlap between them is δ ) (2L - D), as shown. We make here a rough analogy with the osmotic pressure of a dense polymer solution of volume fraction Φ, the mean volume fraction of the stearic segments in the overlap region, writing14
Π)
kBT a
3
[ln(1 -1 Φ) - Φ - χΦ ] 2
(2)
where a is the monomer dimension, χ is the segmental interaction parameter, and we have dropped the term in polymer translational entropy for the surface-attached chains. Integrating the osmotic repulsion over the extent of overlap δ (inset to Figure 3b) to obtain the repulsive interaction energy and setting χ ) 0 (good solvent), we find:15
Es ≈
((
kBT a
3
ln
)(
1 πδ2 [6(R + L) - δ] -Φ 1-Φ 12
)
)
(3)
This model for Es is clearly simplified,16 but we believe it describes approximately correctly the strong steric effects within the dense solvated layers which truncate the vdW attractive well. From eqs 1 and 3 we evaluate E ) EvdW + Es. We evaluate A ) 9 × 10-21 J and 7 × 10-20 J for interactions across the HD/surfactant-layer medium in the gap between mica and between ferroparticles, re(12) A was evaluated for mica and for Fe3O4 across HD from the Lifschitz relation and the known refractive indices of the materials (see e.g. ref 18). (13) Hamaker, H. C. Physica IV 1937, 300, 341. (14) de Gennes, P. G. Scaling concepts in polymer physics; Cornell University Press: Ithaca, NY, 1975; p 74. (15) The result for Es assumes the volume fraction Φ is constant during the compression (and similar to its value within the unperturbed layers). This is a reasonable approximation, since the steric repulsion rises very rapidly once the layers overlap (Figure 2b) so that the extent of compression (and δ) remains small. (16) For example, we use an expressionseq 2sdeveloped for polymer chains while the surfactant layers consist of 18-mers only.
Figure 3. Calculated values of the interaction potential E ) EvdW + Es, from eqs 1 and 3, between two OTAI-coated curved surfaces, according to the model discussed in the text and illustrated in the inset to part b. (a) Crossed cylinders, R ) 1 cm, A ) 9 × 10-21 J (corresponding to mica interacting across HD12). The inset shows the normalized force F(D)/R, deduced from E(D), compared with data from Figure 2a. (b) Spherical particles, R ) 5 nm, A ) 7 × 10-20 J (corresponding to Fe3O4 interacting across HD12). c shows the interaction and shortranged attraction expected between STAI-coated spherical particles (R ) 5 nm) across HD. The long-ranged attraction is similar to that in Figure 3b and is due to vdW forces between the stearic-coated ferroparticles. The adhesive attractive energy (of magnitude ∼10kBT) is due to the short-range forces between the contacting collapsed stearic layers in the HD medium. For further details, see text.
spectively;12 we take the thickness of each solvated OTAI layer as L ) 1 nm and the mean volume fraction of OTAI in the solvated layers as Φ ) L0/L ) 0.5. Figure 3 shows the calculated interactions across HD, based on this simple model, for crossed mica cylinders (R ) 1 cm) and for spherical ferroparticles (R ) 5 nm). From Figure 3a we see that the attractive potential at the equilibrium separation is ∼(2 × 106)kBT, comparable with our estimate (2.5 × 106)kBT based on Figure 2a, while the F(D)/R versus D variation (inset) is in reasonable agreement with the SFB data. Figure 3b reveals that an attractive interaction is expectedsprior to the strong steric repulsionsalso between oleic-coated ferroparticles but that the attractive potential is less than 1kBT.17 Such a weak attraction is not sufficient to cause coagulation of the particles and
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thus accounts for the stability of oleic-acid-stabilized ferrofluids. The origin of the aggregation resulting when stearic surfactants are used to coat ferrofluid particles4-6 is more subtle. In contrast to what is observed between the flat, smooth stearic-coated mica surfaces (Figure 2B), interactions between stearic-coated ferroparticles (radius R ≈ 5 nm) are unlikely to be oscillatory beyond a few angstroms, due to the small radius of the particles. Rather, such particles will likely experience a long-ranged van der Waals attraction, whose magnitude when the stearic films touch each other will be due mainly to the forces between the Fe3O4 cores. The depth of the attractive well will then be comparable to that estimated above for the oleic-coated particles at a similar separation, and thus too weak to cause aggregation. However, once in contact the steariccoated particles will adhere strongly together because of the substantial interfacial energy γHD/Stsof short-ranged origin, as discussed abovesbetween the stearic layer and the HD carrier medium. From the Young equation, we have γHD/St ) γSt - γHD cos θ, where γSt and γHD are the pure component surface tensions and θ ) 50° is the contact angle (Figure 1a). Putting γHD ≈ γSt ≈ 25 mJ‚m-2 yields γHD/St ≈ 9 mJ‚m-2. The adhesion force Fadh between two stearic-coated spheres across HD is then given by18 Fadh ) 2πRγHD/St, and assuming a short-range x ) 1.5 Å for this force,19 the adhesive energy will be Eadh ) Fadhx J 10kBT. It is this adhesive energy which ensures that, once in contact, the adhered stearic-coated ferroparticles are stable against thermal energies and remain aggregated. A number of assumptions are made in applying the conclusions of this model, on the basis of our experiments using model surfactant-coated mica surfaces, to ferrofluid particles. The ferroparticles are assumed to be spherical (in the expression for Fadh); and in particular the nature of short-ranged interactions with HD is taken to be similar between collapsed stearic surfactants on both types of surfaces. Consideration, however, suggests that these assumptions are reasonable.20 The essential point is that the interactions are determined by the stearic and oleic tails which are identical in the two different systems.21 For this reason we believe that differences in the details (17) The reduction in the ∼6kBT attraction estimated earlier from the SFB profiles arises mostly from the use of the full Hamaker expression rather than the Derjaguin approximation, which is valid only at R . D, and partly from the steric contributions. (18) Israelachvili, J. N. Intermolecular and surface forces; Academic: London, 1992.
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of the underlying substrate are unlikely to influence the conclusions of our model. To summarize: we used an SFB to measure the interactions between surfaces coated with oleic-tailed and with stearic-tailed surfactants across HD, mimicking the surfactants used to coat ferroparticles in magnetic fluids, and determined also the wettability of such layers by HD. Attractions were observed for both surfactant types, but while the oleic tails were solvated and fully wetted by the liquid medium, the stearic layers appeared to be collapsed. This is probably due to the kink in the oleic surfactant tails, which weakens their nematic attraction and thus favors their solvation. The stearic layers were only partially wetted by HD, indicating a substantial interfacial energy of short-ranged origin. For the oleic layers, a simple model for the steric repulsion based on their solvation can account for the marked attraction observed with such surfactants in the SFB and at the same time also explain the observed stability of ferrofluids coated by oleic acid surfactants. The origin of the aggregation observed for stearic-coated ferrofluid particles, on the other hand, is probably due to short-ranged adhesive interactions arising from the interfacial energy between HD and the surface of the collapsed stearic surfactant layers. Acknowledgment. We thank the US-Israel BSF, the German Israel Program (DIP), and the Ministry of Science (Tashtiot programme) for support of this project. R.E.R. was a Meyerhoff Visiting Professor at the Weizmann Institute. We thank S. Safran for useful discussions. LA0009137 (19) This value is taken as similar to the effective cutoff separation between surfaces in molecular van der Waals contact, which for a wide range of materials18 is ∼1.65 Å. (20) The actual shape, as determined by electron-microscopy,4 is spheroidal rather than perfectly spherical, but this should not affect Fadh too strongly, while the short-ranged interactions depend essentially on the areal density of the collapsed stearic tails, which are similar for the mica and the ferroparticle surfaces,4 and thus are expected to be insensitive to the underlying substrate. (21) The hexadecane medium is a 99+% grade solvent (Aldrich) and used as received to simulate the HD used in ferrofluid dispersions; it thus probably contains an equilibrium (low) water concentration. Though trace water can have a marked effect on surface forces in hydrocarbon liquids (see e.g. McGown, D. N. L.; Parfitt, G. D. Kolloid Z. Z. Polym. 1967, 220, 56. Christenson, H. K.; Israelachvili, J. N. J. Colloid Interface Sci. 1987, 119, 194-202), this is generally for interacting hydrophilic surfaces and is not expected to affect the results for strongly hydrophobic surfaces, as in the present case or in the case of surfactant-coated ferrofluid particles.
