Ellipsometric Study of Monodisperse Silica Particles at an Oil−Water

8888

Langmuir 2003, 19, 8888-8893

Ellipsometric Study of Monodisperse Silica Particles at an Oil-Water Interface Bernard P. Binks,† John H. Clint,*,† Amro K. F. Dyab,† Paul D. I. Fletcher,† Mark Kirkland,‡ and Catherine P. Whitby† Surfactant & Colloid Group, Department of Chemistry, The University of Hull, Hull HU6 7RX, United Kingdom, and Unilever Research, Colworth Laboratory, Colworth House Sharnbrook, Bedford MK44 1LQ, United Kingdom Received June 16, 2003. In Final Form: August 20, 2003 Results are reported for ellipsometric measurements of hydrophobized monodisperse silica particles, with a diameter of about 25 nm, spread at the toluene-water interface. Theoretical values for the ellipsometric parameters are derived by treating the particles as a core-shell model and performing integrations of the refractive index profile through the interface using Drude’s equations. With justifiable choices of the fixed parameters for the system, the agreement is good between measured and calculated values for the ellipsometric parameter ∆ as a function of the amount of silica particles added to the interface. However, the results at high particle concentration at the interface are consistent either with coverage greater than a close-packed monolayer or with a monolayer with corrugations whose amplitude is less than the radius of the particles. The results show that this is not a suitable method for the determination of the contact angle of the particles at the oil-water interface.

Introduction In recent years, there has been increasing interest in the properties of emulsions stabilized solely by solid particles [ref 1 and references therein]. They are usually referred to as “Pickering emulsions”2 although they were described several years earlier by Ramsden.3 All the experimental evidence points to the importance of the contact angle made by the oil-water interface at the surface of the solid particles in determining the type and stability of the emulsions.1 However, there are considerable experimental difficulties associated with measuring such angles on very small particles (often a few tens of nanometers in diameter). The present work was originally undertaken in order to test the possibility of determining the contact angle, and perhaps also the degree of packing, for small (nanometer) silica particles spread at the toluene-water interface using ellipsometry. The technique of ellipsometry involves analysis of the state of polarization of light after reflection from an interface. The ratio Rp/Rs, where Rp is the reflection coefficient for light polarized parallel to the plane of incidence and Rs is the reflection coefficient for light polarized perpendicular to the plane of incidence, is given by Rp/Rs ) tan Ψ exp(i∆) where Ψ and ∆ are ellipsometric parameters measured directly by the instrument and i ) x-1. Ellipsometry is very sensitive to thin layers at interfaces, but the interpretation of data usually involves fitting the experimental results to theoretical calculations of Ψ and ∆ for a model of the layer. It would therefore be useful to have independent evidence for the conformation of particles at the oil-water interface. For the submicroscopic particles used in the present study, it is possible to use * To whom correspondence should be addressed. E-mail: j.h.clint@ hull.ac.uk. † The University of Hull. ‡ Unilever Research. (1) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21. (2) Pickering, S. U. J. Chem. Soc. 1907, 91, 2001. (3) Ramsden, W. Proc. R. Soc. 1903, 72, 156.

scanning electron microscopy (SEM) to examine the interfaces in particle-stabilized oil-water emulsions. Figure 1 shows a freeze-fracture SEM image of an oilin-water emulsion stabilized by partially hydrophobized silica particles with a diameter of approximately 25 nm. Details of the SEM technique are given in the Experimental Section. The surface of the oil droplet can be seen to be completely covered with particles, but it is clear that the interface is not smooth and hence that not all of the particles have the same conformation with respect to the oil-water interface. This point is reinforced by a close-up of the particle arrangement in the enlarged part of Figure 1 and a cross section through the oil-water interface in Figure 2. The thickness of the silica particle layer corresponds approximately to a trilayer. In view of this evidence, it will be necessary in any interpretation of ellipsometric data to consider particle arrangements at the liquid interface that involve more than just a closepacked monolayer. In this paper, we present results and possible interpretations of ellipsometric measurements for monodisperse spherical hydrophobized silica particles spread at the toluene-water interface. The original intention was to determine contact angles for the particles at the interface since the contribution to the ellipsometric parameters should depend on the relative fractions of the particles immersed in the two liquids, as these have very different refractive indices. Experimental Section Ellipsometry. Ellipsometric measurements were carried out in a temperature-controlled room (22 ( 0.5 °C) using a Plasmos 2300 ellipsometer operating with a helium-neon laser of wavelength 632.8 nm. The Plasmos ellipsometer operates by constantly switching in and out a quarter-wave plate, and this mechanical action causes ripples on liquid interfaces mounted directly on the normal X-Y stage. The normal X-Y stage of the ellipsometer (for sample mounting) was therefore removed and replaced with an electronic antivibration table (JRS Instruments, Zwillikon, Switzerland). The antivibration table was mounted on blocks astride the base unit of the ellipsometer in order to isolate the experimental cell from the vibrations due to the

10.1021/la035058g CCC: $25.00 © 2003 American Chemical Society Published on Web 09/17/2003

Monodisperse Silica Particles at an Interface

Figure 1. Freeze-fracture SEM image of an oil drop in an oil-in-water emulsion stabilized by 25 nm diameter hydrophobized silica particles. Note that the drop surface is completely covered but that additional particles are associated with the interface. The bar is 1 µm.

Figure 2. Freeze-fracture SEM image of an oil-in-water emulsion drop stabilized with 25 nm diameter hydrophobized silica particles, showing a section through the oil-water interface. The bar is 500 nm.

Figure 3. Cross section of glass cell used for ellipsometric measurements of particles spread at the toluene-water interface. The polished windows are angled at 45°. quarter-wave plate. The Brewster angle for the toluene-water interface is 41.7°, and so an incidence angle of 45° was chosen and this necessitated the use of a specially constructed cell. The cell used for the measurements is shown diagrammatically in Figure 3 and was obtained from Hellma UK Ltd., Southendon-Sea, U.K. The two polished windows were each at an angle of 45° so that the laser beam passes through the glass-toluene interface without deviation and without any change in polarization. The cell was mounted on a micrometer lab-jack bolted to the antivibration table in order to allow precise control of the vertical position of the liquid-liquid interface. The glass cell was cleaned by soaking in a solution of Hellmanex followed by rinsing in Milli-Q water and drying in an oven. The stainless steel vessel, with an inner diameter of 32 mm, was cleaned using

Langmuir, Vol. 19, No. 21, 2003 8889 acetone. The liquid-liquid interface was produced by introducing 2.6 cm3 of water into the stainless steel inner vessel and filling the remainder of the angled window cell with 144 cm3 of toluene. Because of the contact angle of the toluene-water interface at the stainless steel surface, the liquid-liquid interface tends to be pinned at the inside corner of the steel vessel. This provides a useful method for controlling the flatness of the interface by making small changes to the volume of water. The flatness was judged by observing the reflection of a square grid from the toluene-water interface and controlled by minimizing any distortion by adding or removing water from the steel vessel. A blank experiment was conducted to show that the spreading solvent produced no changes in the ellipsometric parameters, Ψ and ∆. Once a toluene-water interface had been created, Ψ and ∆ were determined over a 5 min period to ensure that the system had stabilized. Small volumes of spreading solvent (either methanol or a mixture of 87% propan-2-ol + 13% water) were then injected directly at the toluene-water interface using a microliter syringe, up to a total of 100 µL. After each addition, the system was allowed to equilibrate for 30 min and the parameters Ψ and ∆ were measured over a period of 2 h. In all cases, the changes in Ψ and ∆ were negligible within the precision of the measurements ((0.06° in both Ψ and ∆), indicating that surface-active impurities were not left at the interface. Measurements with hydrophobized silica particle monolayers were performed by spreading from a 0.1 wt % dispersion of particles in the spreading solvent. The injections were made at a point near the edge of the toluene-water interface, well away from the center where the laser beam is incident. The object of the experiments was to vary the concentration of particles spread at the interface and to observe the changes in ellipsometric parameters. Scanning Electron Microscopy. Freeze-fracture SEM images of emulsions were obtained by placing a drop of the emulsion on a low-temperature SEM stub and plunging it into nitrogen slush. The stub was then transferred into a low-temperature chamber (Oxford Instruments CP2000) maintained under an ultrahigh vacuum where the emulsion was fractured and then etched. The exposed emulsion surface was coated with a mixture of gold and palladium. The stub was then transferred into a FE-SEM (JEOL 6301F) fitted with a cold stage (Cressington Instruments) operating at about -150 °C. Images were captured using Analysis and Soft Imaging ADDA II system software. This protocol is described more fully elsewhere.4 Transmission Electron Microscopy (TEM). To obtain TEM images of the hydrophobized silica particles used, the aqueous dispersion obtained after dialysis of the original ethanolic dispersion was diluted with water. A single drop of the diluted dispersion was placed on a carbon-coated copper grid (300 mesh) and allowed to evaporate. The particles were imaged using a JEOL 100C 80 kV transmission electron microscope. Materials. Toluene (>99.97%) was obtained from Fisher Scientific and passed several times down a column of chromatographic alumina in order to remove traces of polar impurities. Propan-2-ol (>99.7%) was from Aldrich and used without further purification. Methanol (99.995%) was obtained from Fisher Scientific. Water was purified by passing deionized water through a Milli-Q water purification unit. Hydrophobized silica particles (obtained by treating the surface of hydrophilic silica particles with n-octyl triethoxysilane) were obtained from Rhodia Services as an 8 wt % dispersion in ethanol and converted to a 0.75 wt % dispersion in pure water by dialysis. The diameter of the hydrophobized silica particles was determined by TEM, and a typical image is shown in Figure 4. The particles can be seen to be approximately spherical with a fairly narrow size distribution. To confirm the absence of any interfacially active impurities from the particles, the surface tension of the supernatant from the aqueous suspension was measured using the pendant drop method, before addition of the 2-propanol prior to spreading. The aqueous supernatant had a surface tension of 72.1 mN/m compared with 72.7 mN/m for pure water, indicating the absence of any significant amount of surface-active (and hence presumably interfacially active) impurities. (4) Binks, B. P.; Kirkland, M. Phys. Chem. Chem. Phys. 2002, 4, 3727.

8890

Langmuir, Vol. 19, No. 21, 2003

Binks et al.

Figure 4. Transmission electron micrograph of hydrophobized silica particles, with a diameter of 25 nm. The bar is 100 nm.

Theory Use of Drude’s Equations with Full Dielectric Profile through the Interfacial Region. We first consider a layer of particles with a core/shell structure adsorbed at the oil-water interface as illustrated in Figure 5. It is clear from the simple sketch in Figure 5a that contact angle should be a factor in determining the ellipsometric response to particles in the interface since the oil and water usually have very different refractive indices. The contribution will then depend on the relative amount of the particle immersed in each phase (i.e., on the contact angle). With reference to Figure 5b, let r1 be the radius of the core and r2 the radius of the outer surface of the hydrophobic shell. The geometry is most simply referred to the plane through the particle centers. The interface between oil and water is then at a height h ) r2 cos θ above this plane, where θ is the contact angle measured in the water phase. For the case where particles are hexagonally closepacked within a monolayer, the volume fraction of core material at a height z is given by

fc )

π(r12 - z2) 2x3r22

and fc ) 0

for -r1 < z < r1 for |z| > r1

π(r22 - z2) fs ) 0

fs )

for r1 < |z| < r2

2x3r22

n(z) ) qfcnc + qfsns + no(1 - qfc - qfs) for z > h (3)

(2)

n(z) ) qfcnc + qfsns + nw(1 - qfc - qfs) for z < h (3′) where q is the fractional coverage of the oil-water interface by particles on a scale where hexagonal close packing is represented by q ) 1. Since we are dealing with optical frequencies and nonabsorbing species, the relative permittivity at this plane (z) ) n(z)2, that of the bulk water phase w ) nw2, and that for the bulk oil phase o ) no2. It is now possible to use Drude’s equation6 to calculate the parameter η:

for |z| > r2

π(r22 - r12) 2x3r22

continuous phase (no for oil or nw for water), scaled by the appropriate volume fraction:

or

(1)

The volume fraction of shell material at the same plane is

fs )

Figure 5. (a) Positions of hydrophilic (low θ) and hydrophobic (high θ) particles relative to a toluene-water interface. (b) Particle with a core-shell structure situated at the oil-water interface with a contact angle θ measured through the water phase. (c) Possible location of particles at the oil-water interface. Following completion of the close-packed monolayer of particles A at the interface, additional particles could be in the preferentially wetting phase (particles B) or in the nonpreferentially wetting phase (particles C). Particles C could be held by capillary bridges (see the text).

η) for |z| < r1

Using the effective medium approximation suggested by Bruggeman,5 the refractive index n(z) of the system in the plane at height z can be taken as a linear combination of the refractive indices of the core (nc), shell (ns), and (5) Bruggeman, D. A. G. Ann. Phys. (Leipzig) 1935, 24, 636.

∫

{(z) - o}{(z) - w} (z)

dz

(4)

where λ is the wavelength of the light and the integration is performed through the whole interfacial region. Equation 4 refers to measurements at the Brewster angle, φB. In this study, the Plasmos ellipsometer was set to an incidence angle φ (which is a few degrees away from (6) Drude, P. The Theory of Optics; translated by C. R. Mann and R. A. Millikan; Longmans: New York, 1902; p 293.

Monodisperse Silica Particles at an Interface

Langmuir, Vol. 19, No. 21, 2003 8891

the Brewster angle) at which the ellipsometric angles Ψ and ∆ were determined. It is then necessary to use another of Drude’s equations6 to determine ∆ appropriate to this angle from η calculated using the integration in eq 4:

tan ∆ )

cos φ sin2 φ 4π wxo η λ (o - w)  sin2 φ -  cos2 φ o w

(5)

The ellipsometric angle Ψ can then be calculated7 using

tan Ψ ) tan Ψ h

[cos ∆h +cossin∆∆h tan ∆]

(6)

where Ψ h and ∆ h refer to values for the clean liquid-liquid interface. In view of the pictorial evidence presented in the Introduction, it will be necessary to consider the effect of particles accumulating at the liquid-liquid interface in quantities in excess of that needed for a single close-packed monolayer. When a second layer of particles is present at the interface, it could be imagined that they will be sitting within the hollows formed by three touching spheres in the first layer, as shown in Figure 5. Particles may be held in this configuration by dispersion forces between themselves and those anchored in the interface. Then the spacing between the planes through the centers of the two layers is shown by simple geometry to be (8/3)1/2r2. Two possible arrangements will be considered; one with the second layer in the preferentially wetting phase (particles B in Figure 5) and the other with the second layer in the nonpreferentially wetting phase (particles C). The latter situation is not unreasonable since, for systems where there is slight mutual miscibility of the oil and water phases and even with alkane-water mixtures,8 attractive capillary bridges (of preferentially wetting liquid) holding the second layer in place will only form if the particles are in the nonpreferentially wetting phase. These capillary forces will augment the dispersion forces between particles. For the case of two layers, the approach is the same as described above for a single layer but the integration in eq 4 covers both layers. In the simplest model, particles in the second layer are assumed not to be present until the first layer is completely full. In a more refined treatment, particles will be allowed to distribute between the first and second layers. If q1 and q2 are the fractional coverages in layers 1 and 2, respectively, then the Boltzmann distribution of particles is given by

Figure 6. Ellipsometric parameter ∆ for hydrophobized silica particles, with a diameter of 25 nm, at the toluene-water interface plotted against the mass of particles spread. Open circles, particles spread from methanol; filled circles, particles spread from propan-2-ol. The inset shows the ellipsometric parameter Ψ plotted against the mass of particles.

In the ellipsometry experiments, the parameters Ψ and ∆ were determined for different coverages of the interface,

and the results are shown in Figure 6. The parameter Ψ (shown plotted in the inset) did not show any significant changes compared with the value for the clean interface, and as a result we shall confine our attention to changes in ∆. For the particle-free interface, ∆ is close to the theoretical value of 360°. As the particle concentration at the interface increases, ∆ falls to a plateau value in the range 350-353°, there being a slight difference in the data for the two spreading solvents. The start of the plateau in ∆ coincided with the beginning of a visible accumulation of excess particles near the point of injection at the interface, implying that spreading had stopped at this stage. To use eqs 1-7 to compare theoretical calculations with these experimental data, it is necessary to estimate some of the parameters appropriate to the experimental system. Particle Core. The density of fused silica is 2.2 g cm-3, and its refractive index is 1.465 at the wavelength used, 632.8 nm. Particles of precipitated silica have a pore volume of approximately 0.12 cm3 g-1.9 This represents a porosity (fractional pore volume) of 0.209. In our applications, such pores are presumably filled with water and hence the density of the core can be calculated as 0.791 × 2.2 + 0.209 × 1 ) 1.949 g cm-3. The refractive index (at λ ) 632.8 nm) of the core, nc, will be 0.791 × 1.465 + 0.209 × 1.332 ) 1.437. For the Rhodia silica particles, r1 ) 12.5 nm and r2 can be assumed to be 13.3 nm. Particle Shell. The density of the alkyl coating will be taken as 0.70 g cm-3, similar to that of octane, and its thickness as 0.8 nm. This gives an overall particle density (needed to calculate the mass required for hexagonal close packing) of [(12.5)3 × 1.949 + {(13.3)3 - (12.5)3} × 0.7]/ (13.3)3 ) 1.737 g cm-3. The refractive index of the shell will be assumed to be equal to that of n-hexadecane (same ratio of CH2 to CH3 groups as in n-octyl chains), that is, ns ) 1.434. Comparison of Simulations and Experimental Results. To compare the experimental values of Ψ and ∆ with those calculated using eqs 1-7, the parameters θ

(7) Drude, P. Ann. Phys. 1889, 36, 865. (8) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992; p 333.

(9) Kenny, M. B.; Sing, K. S. W. In The Colloid Chemistry of Silica; Bergna, H. E., Ed.; Advances in Chemistry Series 234; American Chemical Society: Washington, DC, 1994; pp 505.

q2 ∆E ) exp q1 kT

(

)

(7)

where ∆E is the energy difference between a particle in layers 1 and 2 and k is Boltzmann’s constant. The effects of corrugations in the layers and of capillary waves at the interface are both discussed in the next section. A Visual Basic module has been written to perform the above calculations in an Excel spreadsheet. The step size for the integration in eq 4 was set equal to 0.002r2. It was checked by step size variation that this gave precision in calculated ∆ values to within 0.005°. Results

8892

Langmuir, Vol. 19, No. 21, 2003

Figure 7. Ellipsometric parameter Ψ for hydrophobized spherical silica particles spread at the toluene-water interface. The points are experimental values for particles spread from propan-2-ol. The lines are for theoretical calculations: full line, contact angle θ ) 60°; broken line, θ ) 120°. Incidence angle φ ) 45°.

Figure 8. Ellipsometric parameter ∆ for hydrophobized silica particles spread at the toluene-water interface. Contact angle θ ) 120°. Open circles, particles spread from methanol; filled circles, particles spread from propan-2-ol. The lines are for theoretical calculations with ∆E ) 10 kT. Full line, second layer of particles in the preferentially wetting phase (in this case toluene since θ > 90°); dotted-dashed line, second layer of particles in the preferentially nonwetting phase (water); dotted line, particle coverage limited to a monolayer.

and ∆E were treated as variables. All others were kept at the values deduced above. Figure 7 shows the results of calculation of Ψ as a function of the mass of particles spread (up to coverage corresponding to a close-packed monolayer) for two different contact angles; the experimental data have been superimposed. The comparison between experiment and theory is good, but it confirms that the parameter Ψ is insufficiently sensitive to contact angle and to coverage of the interface to be used in the determination of either. We shall therefore confine our interest to changes in ∆. Figure 8 shows the results of calculations of ∆ for θ ) 120° and ∆E ) 10 kT for which any second layer would only form when the first layer is essentially complete. Where particles have been spread from propan-2-ol (filled circles), the agreement between theory and experiment is good and consistent with the second layer forming in the preferentially wetting (toluene) phase. Spreading from

Binks et al.

Figure 9. Ellipsometric parameter ∆ for hydrophobized silica particles spread at the toluene-water interface. Contact angle θ ) 60°. Open circles, particles spread from methanol; filled circles, particles spread from propan-2-ol. The lines are for theoretical calculations with ∆E ) 10 kT. Full line, second layer of particles in the preferentially wetting phase (in this case water since θ > 90°); dotted-dashed line, second layer of particles in the preferentially nonwetting phase (toluene); dotted line, particle coverage limited to a monolayer.

methanol produces a plateau in ∆ at slightly higher values than predicted for a full second layer. However, the results for both spreading solvents show plateau values for ∆ that are considerably lower than predicted from a single monolayer. Figure 9 shows the results for θ ) 60° and ∆E ) 10 kT. Here the overall fit is less good and the plateau values for ∆ are intermediate between those predicted for one and two completed layers. The results for high coverage with particles spread from propan-2-ol (filled circles) are close to the model in which the second layer forms in the nonpreferentially wetting phase (in this case the toluene). Comparison between Figures 8 and 9 suggests that agreement between theory and experiment is not sufficiently precise to allow calculation of the contact angle in such systems. The hydrophobized particles used in the present study form preferentially oil-in-water emulsions with equal volume fractions of toluene and water, suggesting that the real contact angle is less than 90°. Better agreement between theory and experiment is shown however if the contact angle is greater than 90° (Figure 8 vs Figure 9). Figure 10 shows the effect of reducing ∆E to 2 kT. Even for this energy difference between the first and second layer, the equivalent to a full monolayer would correspond to 88% completion of the first layer and 12% occupation of the second layer. The difference in the three curves can be seen in the region below monolayer coverage. In fact, such “equilibrium” considerations may not apply to the present systems since the particles are not adsorbed to the interface but spread and left stranded at the interface when the spreading solvent dissolves into the bulk phases. Whatever the intricacies of contact angles and energy differences between first and second layers, the implication from Figures 8-10 is that more than one monolayer is being formed. However, this analysis assumes a perfectly flat liquid-liquid interface. Thermally induced capillary waves are always present at liquid interfaces. Meunier10 has shown that if one allows for mode coupling between (10) Meunier, J. J. Phys. (Paris) 1987, 48, 1819.

Monodisperse Silica Particles at an Interface

Langmuir, Vol. 19, No. 21, 2003 8893

Figure 10. Details as in Figure 8 but with ∆E ) 2 kT.

capillary waves, the parameter η, due to such roughness of the interface, can be expressed approximately as

ηR ) -

2 3 (o - w) 2 o +  w

xπkT 6γ

(8)

For a clean toluene-water interface, all the parameters in eq 8 are known (interfacial tension, γ ) 36 mN/m) and the value of ηR is calculated to be -0.01921 nm. Inserting this value into eq 5 at the incidence angle used in the present study (45°) gives a value of ∆ ) 359.80°, compared with 360° for a planar interface. Such a small contribution to changes in ∆ is within the range of experimental uncertainty. For a toluene-water interface covered with a layer of silica particles, this analysis would not be accurate but it seems unlikely that the large decrease in ∆ seen experimentally is due to capillary waves. Moreover, it has recently been shown11 that the bending modulus for a close-packed monolayer of particles of radius 13 nm at an oil-water interface can be estimated to be several hundred times kT from calculations of the variations of wetting energy with interface curvature. Such large values for the bending modulus would almost eliminate any contribution to ∆ from capillary waves once the interface was filled with a monolayer of particles. One other possibility should be discussed. Compression of spread monolayers of particles at the oil-water interface12 to the point of collapse results in corrugation (11) Aveyard, R.; Clint, J. H.; Horozov, T. S. Phys. Chem. Chem. Phys. 2003, 5, 2398. (12) Aveyard, R.; Clint, J. H.; Nees, D.; Quirke, N. Langmuir 2000, 16, 8820.

of the monolayer rather than ejection of particles from the interface. In the present experiments, particles are added by injection at the interface and it is assumed that they spread to form a uniform layer, after which no more spreading takes place and further addition results in the accumulation of a dense patch of particles (visible to the naked eye) near the point of injection. At this stage, it is possible that the particles are subjected to a sufficiently high surface pressure to cause small corrugations. Assuming parallel sinusoidal corrugations at a clean toluenewater interface, it is a simple matter to use eq 4 to calculate η for the interface as a function of the amplitude of the corrugations and hence calculate ∆ using eq 5. The result is that corrugations with an amplitude of 11 nm are sufficient to decrease ∆ by 4.75°. This is the difference between the theoretical value of ∆ for monolayer coverage and the experimental value at the plateau for high coverage. Since contributions to ellipticity tend to be additive, one possible conclusion is that the spreading stops at a monolayer of particles but that the layer then corrugates with an amplitude of about 10 nm, which is of course less than the particle radius. Such an analysis of the sinusoidal surface profile using eq 4 is independent of the wavelength of the corrugations, provided they are small compared with the wavelength of light. Corrugations of this amplitude would of course not be seen either visibly or microscopically. Conclusions 1. Ellipsometric measurements for partially hydrophobized silica particles spread at the toluene-water interface indicate large changes in the parameter ∆ with spread amount but very little change (less than the experimental error) in Ψ. 2. Theoretical calculations of changes in ∆, using Drude’s equations integrated through the interface, agree well with experimental measurements up to monolayer coverage. 3. For greater numbers of particles spread, the experiments are consistent either with formation of a second layer of particles in the toluene phase or with the formation only of a monolayer but with corrugations whose amplitude is less than the radius of the particles. 4. In the absence of additional data, it is not possible to use ellipsometric measurements as a method for determining the contact angle of nanometer-sized particles at oil-water interfaces. Acknowledgment. The authors thank Rhodia Services (France) for supplying the hydrophobized silica particles. LA035058G