Article pubs.acs.org/Langmuir

Contact Angles of Microellipsoids at Fluid Interfaces Stijn Coertjens,† Paula Moldenaers,† Jan Vermant,†,‡ and Lucio Isa*,§ †

Department of Chemical Engineering, KU Leuven, B-3001 Leuven, Belgium Department of Materials, ETH Zürich, CH-8093 Zürich, Switzerland § Laboratory of Interfaces, Soft Matter and Assembly, ETH Zürich, CH-8093 Zürich, Switzerland ‡

S Supporting Information *

ABSTRACT: The wetting of anisotropic colloidal particles is of great importance in several applications, including Pickering emulsions, filled foams, and membrane transduction by particles. However, the combined effect of shape and surface chemistry on the three-phase contact angle of anisotropic micrometer and submicrometer colloids has been poorly investigated to date, due to the lack of a suitable experimental technique to resolve individual particles. In the present work, we investigate the variation of the contact angle of prolate ellipsoidal colloids at a liquid−liquid interface as a function of surface chemistry and aspect ratio using freeze-fracture shadow-casting cryo-SEM. The method, initially demonstrated for spherical colloids, is extended here to the more general case of ellipsoids. The prolate ellipsoidal particles are prepared from polystyrene and poly(methyl methacrylate) spheres using a film stretching technique, in which cleaning steps are needed to remove all film material from the particle surface. The effects of the preparation protocol are reported, and wrinkling of the three-phase contact line is observed when the particle surface is insufficiently cleaned. For identically prepared ellipsoids, the cosine of the measured contact angle is, in a first approximation, a linearly decreasing function of the contact line length and thus a decreasing function of the aspect ratio. Such a trend violates Young−Laplace’s equation and can be rationalized by adding a correction term to the ideal Young−Laplace contact angle that expresses the relative importance of line effects relative to surface effects. From this term the contribution of an effective line tension can be extracted. This contribution includes the effects that both surface chemical and topographical heterogeneities have on the contact line and which become increasingly more important for ellipsoids with higher aspect ratios, where the contact line length to contact area ratio increases.

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INTRODUCTION

particle will reduce the interfacial energy. Equation 1 shows a general expression for the change in the interfacial free energy ΔF in a three-phase system, with two liquid phases plus solid particles adsorbing at the liquid−liquid interface:

Particles at fluid−fluid interfaces are used in a wide range of applications (e.g., food, cosmetics, pharmaceutical formulations, etc.) in the stabilization of emulsions, filled foams, or even liquid marbles.1 They may also serve as model systems for biological membranes.2 These applications concern mostly spherical particles, although in the past decade interest in nonspherical particles has been rapidly increasing. In addition to surface chemistry, particle geometry has a large effect on system properties as demonstrated by previous research dealing with ellipsoidal particles at fluid−fluid interfaces, including emulsion stabilization,3 drug delivery,4,5 membrane transduction,6,7 nanocomposites,8 and transport during droplet evaporation.9 The key factor behind this geometry dependence is the reduction of interfacial energy when a particle adsorbs at the interface. Knowledge of the wetting (three-phase contact angle) is crucial, since it is directly related to the extent by which the © 2014 American Chemical Society

ΔF = F(T , V , N1 , N2 , Sint , S1 , S2 , L) − F0(T , V , N1 , Sint , S)

(1)

with F the free energy of the adsorbed state and F0 the free energy of the particles completely immersed in the bulk of liquid 1. These free energies are dependent on temperature T, total volume V, the number of particles Ni exposed to phase i, the interface surface area Sint (between phase 1 and phase 2), the particle surface area S, the particle surface area Si exposed to phase i, and the length of three-phase contact line L. Received: March 7, 2014 Published: March 19, 2014 4289

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Figure 1. FreSCA cryo-SEM images of PS ellipsoids (AR = 4.8) after (top left) single cleaning and (top right) double cleaning, with corresponding AFM images after (a) single cleaning and (b) double cleaning. Scale bars: SEM: 200 nm; AFM: (top) 20 nm; (bottom) 1 μm.

The surface tensions γi between the particle and fluid phase i and the line tension τ are related to free energy according to eqs 2 and 3, respectively: ⎛ ∂F ⎞ γi = ⎜ ⎟ ⎝ ∂Si ⎠T , V , N , N , S 1

τ=

2

⎛ ∂F ⎞ ⎜ ⎟ ⎝ ∂L ⎠T , V , N , N , S 1

2

int , Si , L

(2)

int , S1 , S2

(3)

where τ is the line tension at the three-phase contact line. The particle cross section at the interface S12, the three-phase contact angle θ, L, S, and S1 all depend on Δh, the particle immersion depth into phase 1. Minimization of the free energy in eq 4 with respect to Δh determines the equilibrium position of the particle at the interface and leads to a generalized version of the Young− Laplace equation, where arbitrary shapes of the particle and of the contact line are considered, along with the contributions coming from surface and line tension. Several considerations can be made on eq 4. One of the main points is that the theoretical equilibrium contact angle of a particle with homogeneous surface properties at a fluid−fluid interface is a unique material property, which depends solely on the surface chemistry of the particle and on the properties of the two fluid phases. Experimentally, this condition is rarely valid for real colloidal particles; heterogeneities of the particle surface as well as the details of how the particle reaches the interface frequently cause the experimentally measured contact angles to deviate from the predictions of the Young−Laplace

By assuming that both surface and line tensions are independent of contact area and contact line length, an explicit version of eq 1 is obtained by integrating eqs 2 and 3 and using Young’s equation (cos θ = (γp1 − γp2)/γ12), with γpi the interfacial tension between phase i and the particle and γ12 the interfacial tension between the two fluids): ΔF(Δh) = γ12[(S1 − S) cos θ − S12] + τL

(4) 4290

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equation.10−12 Additionally, the requirement that the contact angle should be the same everywhere on the particle surface implies that noncircular contact lines, such as for ellipsoidal particles, have to bend out of the interface plane to satisfy such condition (see e.g. Oettel and Dietrich13). This issue is central to the wetting of anisotropic colloids and has been explored by a number of studies in the literature. Previous work has mainly focused on theoretical calculations,14−17 and explicit expressions of the generalized Young− Laplace equation for ellipsoidal particles have been developed.18 Aside from theoretical studies, several experimental techniques19−25 have been applied to determine the shape of the contact line around nonspherical particles and/or to measure their contact angle. Interferometry, for instance, has been successfully employed to visualize and measure the deformations of the contact line around ellipsoidal particles, ranging from several micrometers22,26 to several millimeters.27 The technique offers high resolution in the vertical direction, as is needed to quantify the curvature of the interface close to the particle. However, it lacks the in-plane resolution required to measure accurately the geometry of the contact area and contact line. As discussed in a recent paper by Pouligny and Loudet,27 the relation between interface deformation and contact angle is not univocal for ellipsoids, and thus measurements of the particle cross section at the interface beyond optical resolution are needed. This issue is partially solved by gel-trapping (GT) in combination with SEM,21,24,28 which allows visualizing the particle and the interface deformation with higher lateral resolution, but which presents limitations in the time scales necessary to trap and measure the particles. Moreover, the gelling agents may adsorb onto the surfaces. A more reliable method to characterize the wetting of anisotropic colloidal particles is needed, allowing to calculate the contact angle with high accuracy and being applicable to a large range of liquids. For this purpose, freeze-fracture shadowcasting (FreSCa) combined with cryo-scanning electron microscopy (cryo-SEM) is used in this work. This technique overcomes previously mentioned difficulties and has already been applied to determine the three-phase contact angle of spheres down to 10 nm in diameter.10 In this work, we extend it to the investigation of the wetting of prolate ellipsoids and its dependence on surface chemistry and aspect ratio.

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Supporting Information furthermore demonstrate that the stretching corresponds to a constant-volume deformation and that the particles maintain an ideal prolate shape. For the fluorescent PS particles, this procedure was sufficient to yield a smooth particle surface, while for the nonfluorescent sulfate latex colloids, single cleaning turned out to be insufficient for complete PVA removal, as visualized by cryo-SEM in the top left part of Figure 1. This difference can be ascribed to the different hydrophilicity of the starting spheres and thus the different affinity for PVA coating. These PVA residues greatly affect the local contact angle and cause the contact line to wrinkle with wavelengths between 10 and 100 nm, which makes it difficult to determine the contact line shape or to quantify the contact angle. Therefore, modifications with respect to this step are needed in order to completely remove residues from the particles. After the washing cycle with Milli-Q water, an additional heating step is performed, in which the aqueous particle suspension is heated to 50 °C with subsequent ultrasonication for 30 min. After centrifugation and decantation, Milli-Q water is added to redisperse the particles. This second procedure is referred to as double cleaning. Cryo-SEM and AFM measurements, presented in Figure 1, show a substantial improvement of the surface smoothness, which allows for the measurement of both contact line shape and contact angle. The number of cleaning steps required to eliminate PVA residues varies between the different types of the initial spherical particles but is consistent for all different batches of ellipsoids produced starting from the same spheres. In particular, PVA residues are more difficult to remove from more hydrophilic spheres. Moreover, contact angle measurements of spheres that underwent the same preparation procedure but without stretching still show a reduced contact angle by about 20° as compared to the original beads (see Table 2 in the Results section), which indicates that the surface has changed during the procedure. These facts emphasize the importance of controlled surface preparation on particle properties at interfaces, as already highlighted by Park et al.30 In addition to PS ellipsoids, some more hydrophobic prolate poly(methyl methacrylate) (PMMA) ellipsoids were also prepared, starting from monodisperse PMMA spheres stabilized by short polyhydroxystearic acid (PHSA) chains (synthesized by Schofield31). Some of the PMMA ellipsoids have also been regrafted with PHSA after stretching to investigate the effect of stabilizer removal during preparation. The stretching is applied following the method described by Ho et al.,32 in which the PMMA spheres are embedded in a polydimethylsiloxane (PDMS) film. Subsequently, this film is prestretched in air and put into an oven for 6 h at 160 °C, which is above the glass transition temperature of matrix and particles but below the melting temperature of either. As the system heats up, all spheres slowly undergo a controlled uniaxial plastic deformation to prolate ellipsoids of a given aspect ratio depending on the stretching ratio. After allowing the stretched film to cool down, the PDMS matrix is degraded using a mixture of sodium methoxide, hexane, and isopropanol.33 Finally, the particles are removed from this mixture by centrifugation and decantation and then redispersed into the desired organic solvent, which is cis-decalin in this work (more details on the solvent choice for the PMMA ellipsoids are given in the Supporting Information). The final particle size distribution of each PMMA sample, which is tabulated in Table 2, is analyzed during the cryo-SEM measurements. Freeze-Fracture Shadow-Casting Cryo-SEM. FreSCa cryo-SEM is used here to visualize the wetting of individual particles at the interface between water and n-decane (PS) or water and cis-decalin (PMMA). In brief, in this procedure a macroscopically flat particleladen liquid−liquid interface is created, then vitrified by means of a liquid propane jet, and subsequently exposed via fracture at the interface with a sharp blade under cryogenic and ultrahigh-vacuum conditions. Two series of samples were prepared for the PS ellipsoids to account for the effects of equilibration time after interface formation: a first one where the interface was vitrified immediately after preparation, i.e. approximately after 10 s, and a second one where we waited 60 min before freezing. The second set of samples was kept under water to prevent evaporation during equilibration and then

MATERIALS AND METHODS

Preparation of Ellipsoids. Prolate ellipsoidal particles are prepared by uniaxial stretching of monodisperse yellow-green fluorescent (FluoSpheres) and nonfluorescent polystyrene (PS) sulfate latex spheres (1 μm in diameter, Invitrogen). The stretching is applied according to the method described by Keville et al.29 The PS spheres are first embedded in a poly(vinyl alcohol) (PVA) film, subsequently put into an silicon oil bath at 145 °C, which is above the glass transition temperature (Tg) of both matrix and particles, but below the melting temperature of either, and then stretched inside the bath. During the stretching, all spheres undergo a controlled uniaxial plastic deformation to prolate ellipsoids with a given aspect ratio. Afterwards, the film strips are removed from the oil bath and then cooled against air while remaining stretched. Finally, the strips are dissolved and the particles are washed, performing several centrifugation steps. In the original method described by Keville et al.,29 a three-step washing procedure is used, involving three cycles of centrifuging and redispersing the particles in an isopropanol−water mixture (volume ratio 9/21) and one additional cycle with Milli-Q water. This washing procedure is further referred to as single cleaning. Ordinary SEM is used to analyze the final particle size distribution for each sample, which is found in Table 2 in the Results section. Additional data reported in the 4291

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Figure 2. Schematic representation of the elliptic cross section of an ellipsoid, for all three possible wetting situations: (a) θ ≥ 90°, (b) α < θ < 90°, and (c) 0°< θ ≤ α.

Figure 3. Representation of the cutting plane along the sputtering direction under a secondary shadowing angle α′ on (a) a SEM image and (b) schematically of a hydrophobic PMMA ellipsoid. The dark blue part in (a) represents a top view of the cross section visible on (b) and in Figure 2. The origin of the x−y−z coordinate system coincides with the ellipsoid center, but this is not the case in (b) for clarity of the schematics. Scale bar in (a): 2 μm. vitrified. Vitrification happens on the millisecond scale. After vitrification, the samples are kept under liquid nitrogen; thus, no further changes take place for the remainder of the procedure. In a subsequent step, a 2−5 nm thick tungsten layer is deposited on the exposed interface with a fixed angle α = 30° (see Figure 2), casting shadows from each particle protruding from the interface. Finally, the metal-coated surface is imaged with SEM in cryogenic mode. In this sample preparation procedure, particles are either initially trapped at the interface between air and the particle-containing fluid (water or cisdecalin) prior to the addition of the second liquid and then exposed to the liquid−liquid interface, or they adsorb directly to the oil−water interface from one of the bulk phases, without using a spreading solvent. The length of the shadow contains information about the particle height relative to the interface. Since the shape and dimensions of individual particles are directly measurable, the three-phase contact angle of single particles at the interface can be calculated applying

simple geometrical relations. This method is applicable to spherical particles as small as 10−20 nm and easily reaches accuracies of ±2−5° (depending on pixel size and shadowing angle) and thus far surpasses other measurement techniques. More detailed information about the technical procedure can be found in ref 10. Measuring the Three-Phase Contact Angle θ. There are three possible situations for the equilibrium position of an ellipsoid positioned horizontally at the interface, depending on its immersion depth Δh. The latter determines directly the procedure for contact angle measurements, analogously to the case of spherical particles.34 All three possibilities with all relevant dimensions are represented schematically in Figure 2. In the paragraph below, these cases are considered in order of increasing particle hydrophilicity, subdivided as hydrophobic (θ ≥ 90°), hydrophilic with a shadow (α < θ < 90°), and hydrophilic without a shadow (0° < θ ≤α). 4292

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Hydrophobic Ellipsoids, θ ≥ 90°. In the case of hydrophobic ellipsoidal particles (see Figures 2a and 3b), the length of the long semiaxis a and short semiaxis b (which is equal to b′ in this case) can be directly measured in the cryo-SEM images because they are above the interface and thus fully visible; using the measured particle length, width, and shadow length k, the contact angle can directly be determined. As illustrated in Figure 3, the relative orientation of the ellipsoid to the shadowing direction, expressed by defining a secondary shadow angle α′, determines the cross section along which the contact angle is calculated. As every cross section of an ellipsoid is an ellipse, and defining this cross section at the origin of the coordinate system, the short axis of the resulting ellipse is equal to the short axis of the ellipsoid. With this, all dimensions necessary to extract the contact angle from the image are known. We emphasize here that the metal coating thickness is negligible compared to the sizes of the measured particles but needs to be taken into account when measuring particles smaller than 50 nm. The resulting formula from which the contact angle is calculated using the quantities defined in Figure 2a is given by

⎛ Δh ⎞ θ = π − tan−1⎜ ⎟ ⎝ Δy ⎠

⎛ b2 − (Δh)2 ⎞ θ = tan−1⎜ ⎟ ⎝ b1Δh ⎠

(7a)

⎛ b ⎞2 Δh = b 1 − ⎜ 1 ⎟ ⎝b⎠

(7b)

with b the short ellipsoid semiaxis and Δh the immersion depth as defined in Figure 2c; b1 represents the short semidistance at the interface measured in this plane along the direction of the short semiaxis b, as indicated in Figure 4.

(5a) b

Δh = l tan(α) −

( (

sin tan

⎛ Δy = a⎜⎜1 − ⎝

surface and interface, using the equation of a tangent to an ellipse going through the contact line. The following equations are used:

1−

−1

(Δh)2 b2

b a tan(α)

))

⎞ ⎟ ⎟ ⎠

(5b)

Figure 4. FreSCa cryo-SEM visualization of a hydrophilic ellipsoid (0° < θ < α) at a decane−water interface. Distance b1 is used in the contact angle calculation procedure for this wetting case. Scale bar: 200 nm.

(5c)

Hydrophilic Ellipsoids, α < θ < 90°. When particles are hydrophilic (see Figure 2b,c), the actual length and width of the particle are not directly measurable because the principal axes of the ellipsoid are located below the interface (vitrified water surface). Therefore, the particle dimensions are obtained by fitting the particle cross section at the interface to an ellipse, whose dimensions are then used to calculate the contact angle. For geometric reasons, if the contact angle is larger than the shadowing angle, the particle still casts a shadow as seen in Figure 2b. Consequently, the same measuring procedure as for the hydrophobic ellipsoids can be used, with comparable resolution. The geometrical relations to determine θ in this case are

(6d)

The single-particle resolution is lost using this procedure, since a given particle size distribution is assumed, rather than measuring the size of each particle directly, similarly to the procedure used by Arnaudov et al.25 However, combining this approach with the direct shadow measurements for less hydrophilic particles allows covering the whole range of possible contact angles. The broader the distribution of sizes is, the higher the error in the contact angle measurement will be. Very uniform stretching is therefore essential to ensure shape monodispersity and, thus, high measurement accuracy. Moreover, a varying thickness of the PVA layer over the particle surface can lead to slight shape distortions and thus induce a small systematic error in fitting the ellipsoidal shape. An additional source of systematic errors is the fact that due to contact line deformations, the cross section of the particle at the interface is no longer an ellipse, but the projected shape of a saddle. Given the data reported later in Table 2, this situation applies only for the fluorescent PS ellipsoids, which have a contact angle of ≈30° and aspect ratio ≈ 4. Previous calculations27 have shown that in this case the maximum deformation of the contact line is below 10% of the unstretched sphere radius. For monodisperse samples, individual particle errors as small as ±3−5° were achieved, making the method as accurate as the one used for ellipsoids with θ > α in terms of relative errors.

Hydrophilic Ellipsoids, 0° < θ ≤ α. Hydrophilic particles with a contact angle below or equal to the shadowing angle (see Figure 2c) do not cast any shadow after metal deposition. This issue can be circumvented by using shallower deposition angles or by using another approach to calculate the contact angle. The latter option is preferred for two reasons. First, errors in contact angle calculation by FreSCa increase for small shadow lengths,10 and second, too shallow angles may cast overlapping shadows between neighboring particles. Therefore, an optimal shadow angle of 30° is retained here and all images of particles with contact angles too small to allow clear shadowcasting are processed as follows: initially, the average particle length and width are acquired separately via regular SEM imaging. Then, assuming monodisperse ellipsoids of such average dimensions, the contact angles are extracted by measuring the dimensions of each particle’s cross section and defining the angle between the particle

RESULTS Effects of (Physicochemical) Surface Heterogeneity. The aforementioned nanoscale resolution makes it possible to investigate directly the effects of surface heterogeneity. In particular, we noticed severe differences in the wetting behavior of ellipsoids depending on the applied cleaning procedure (see Materials and Methods section). Single cleaning leaves significant PVA residues on the surface of the sulfate PS particles, as is clearly visible in Figure 1 (left side), opposed to the smooth particle surface shown in Figure 1 (right side) and Figure 6 resulting from a double cleaning procedure. The inhomogeneous layer of PVA causes the contact line to wrinkle, making it impossible to determine the three-phase contact

⎛ b2(l − k) ⎞ θ = tan−1⎜ ⎟ ⎝ a′2 Δh ⎠

Δh =

− b sin ϕ b sin(ϕ)α

− a′ cos ϕ

(6a)

(l − a′cos ϕ) + b sin ϕ

⎛ b ⎞ ⎟ ϕ = tan−1⎜ ⎝ a′ tan α ⎠ a′ =

(6b)

(6c)

ab 2

(b cos α′) + (a sin α′)2

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Finally, the possibility of working with submicrometer objects fully eliminates the influence of gravity on the deformation of the interface. In fact, even if interface deformations due to gravity may be negligible for low density polymeric particles up to the millimeter scale,22,27,40 they can start to play a role for heavier inorganic particles (e.g., silica or metals) in the size range of several micrometers or at interfaces between liquids with lower interfacial tension. Measuring the Three-Phase Contact Angle. As commented in the Introduction, the validity of Young− Laplace’s equation implies that the contact angle has to be uniform along the particle surface. Therefore, measurements of the contact angle should give equal results at the particle’s side and tip. Table 1 shows the values of the contact angle at the side and the tip of fluorescent PS particles of two aspect ratios. For the more monodisperse sample (AR = 4), the two quantities coincide within the statistical errors, while significant differences arise for the other batch, which shows higher shape polydispersity. We recall that for hydrophilic particles without a shadow the calculation of the contact angle relies on the assumption of monodispersity. Polydispersity introduces errors which can lead to the discrepancy reported here. Moreover, since relative errors are larger along the long axis, the distribution is broader if the contact angle is measured at the tip. To minimize calculation errors, the contact angle for this type of particles is always measured at the side. In addition to those factors, if the stretching modifies the particle surface in a nonhomogeneous way, the condition of uniform contact angle may no longer hold, and different contact angles may be measured in different positions along the contact line. For instance, local alignment of the polymer chains after stretching may modify the wettability of the tips compared to the sides.41 It is reasonable to assume that a local alignment of the polymer chains will lead to a higher local surface energy, enhancing therefore water wettability at the tips (lower contact angle). Our data may hint toward these effects for some particle batches but currently does not show systematic evidence, and further investigation is required. We characterized the wetting behavior of different particle types, covering a wide range of possible contact angles. The contact angle calculations are performed in one of the three ways as described in the Materials and Methods section. For hydrophilic ellipsoids like those in Figures 4 and 6 (except for Figure 6g), eq 6a or eq 7a is used, where the latter is employed only for the ellipsoids that do not possess a shadow. Contact angles of hydrophobic ellipsoids are calculated using eq 5a. The results for all particles under investigation are summarized in Table 2, where we report the average aspect ratio and contact angle for each stretched batch; Figure 6 shows some examples of FreSCa cryo-SEM images of some of the particles for which the contact angles were determined. SEM images of all remaining ellipsoids in Table 2 are available in the Supporting Information. From the data in Table 2, it is apparent that all samples are characterized by a large contact angle distribution (±10°). In particular, this variation is larger than the measurement accuracy, the latter ranging from 2° for the PS AR3.6 ellipsoids to 4° for PMMA−PHSA AR5.1, as calculated according to the formulas of Isa et al.,10 extrapolated to the ellipsoidal case. This finding is emphasized by the full contact angle distributions reported in Figure 5. The evidence for wide distributions of contact angles is particularly robust for particles where true FreSCa imaging is possible (with clear and measurable

angle. The top left image in Figure 1 clearly shows contact line wrinkling with both amplitude and wavelength ranging from 10 to 100 nm, where the parts covered with PVA are preferentially wetted relative to the underlying PS surface. Surface smoothness and homogeneity upon the double cleaning are confirmed by performing AFM on the particles, which is shown in Figure 1 (bottom). This is the first direct imaging of the link between surface heterogeneity and nonuniform wetting, which has been proposed theoretically35,36 and observed indirectly, through capillary-induced aggregation of spherical microparticles at interfaces.35,37−39 Possibly, even a smooth PVA layer could be heterogeneous in thickness along the particle surface, altering particle dimensions to a greater extent at certain locations, which could contribute to the contact angle mismatch when measured at the particle tip or side, as reported in Table 1, but this needs further characterization before drawing a conclusion. Table 1. Three-Phase Contact Angles of Two Groups of Single-Cleaned Hydrophilic PS−PVA Particles, both at the Tip and Sidea surface chemistryb

aspect ratio

initial sphere diam [μm]

θside [deg]

θtip [deg]

PS−PVA fluo PS−PVA fluo

2.9 ± 0.4 4.0 ± 0.2

1.0 ± 0.03 1.0 ± 0.03

50 ± 8 32 ± 3

28 ± 9 35 ± 10

The first sample shows significant deviations, mostly caused by a limited shape monodispersity. bfluo = fluorescent. a

As mentioned in the Materials and Methods section, even without the presence of PVA residues on the surface, Park et al.30 reported a variability in particle interaction forces at the interface after applying the single cleaning procedure. These authors speculated that synthesis byproducts may leach toward the particle surface, changing the surface energy. Visualizing the Contact Line. Figure 4 shows a cryo-SEM image of a hydrophilic fluorescent PS ellipsoid that underwent single cleaning, as described in the Materials and Methods section, and therefore some PVA residues are present on the surface. In this specific case, the excess PVA is present as a smooth layer on the surface, avoiding any wrinkling. When single cleaning is performed on these fluorescent PS particles, PVA seems to stick harder to the particle surface, resulting in a smooth PVA layer instead of wrinkles. This observed higher affinity is probably caused by the higher hydrophilicity of the original fluorescent beads in comparison with the nonfluorescent beads which are more hydrophobic. Since a PS− PVA particle possesses a smooth and hydrophilic surface, the particle three-phase contact line is clearly visible. Because of the change in particle curvature along the contact line and in order to ensure a uniform contact angle, the interface is no longer flat in the direct vicinity of the particle. Instead, it is pulled upward at each side and is showing a dip at the tips, confirming earlier theoretical calculations and experiments on larger particles.14,15,19−22,24,25 This phenomenon can also be clearly observed in Figure 6h. FreSCa cryo-SEM allows to visualize the contact line of smaller colloids compared to previous studies. The only setbacks are the lack of accurate quantification of the interface deformation as in interferometry and the fact that the contact line of a hydrophobic particle is not directly visible, even though the contact angle is measurable. In the Supporting Information we report detailed calculations of the contact line length, including the deformations, as a function of the contact angle for all measured particles. 4294

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the PS particles. The importance of uniform stretching is especially visible in the case of the ungrafted PMMA ellipsoids that show a bidisperse contact angle distribution with one peak around 95° and the other around 125°. The median being different from the average is already an indication of a nonGaussian distribution. Although, when both peaks are separated, their distributions are narrow, hinting toward two different particle populations after stretching. The present data confirm the earlier observation for spherical particles10 that wetting at the microscale is a heterogeneous process with particle-to-particle variations stemming from surface heterogeneity.37,38 As recently proposed, surface heterogeneities can also cause contact line pinning and slow aging of measured contact angles over long time scales. In particular, previous work by Kaz et al.11 demonstrated that particles adsorb to a fluid interface in two steps: there is first an initial “snap-in”, where the particle breaches the interface, followed by a logarithmic relaxation, where the contact angle slowly increases. In our experiments, we take “a snapshot” of the interface by vitrification, and therefore for the samples vitrified after approximately 10 s, some of the spread in the contact angles may be coming from observing particles at different stages of the adsorption process. In order to test this hypothesis, we have waited 60 min before vitrifying the interface in a second series of measurements. From the data reported in Table 2, we observe that the spread in the contact angles is slightly reduced but that it remains significant. Conversely, we also observe a marked difference in the average values of the contact angles, which have significantly increased after an hour equilibration. Effect of Particle Shape and Dimension on the ThreePhase Contact Angle. Earlier studies performed by Isa et al.10 showed that contact angles can decrease when lowering the size of particles with nominally identical surface chemistry to sizes as small as 100 nm in radius. The same behavior is observed in Table 2 when comparing the wetting of the fluorescent spheres, with a contact angle decrease from 85° to 67° for 1 μm and 200 nm diameter particles, respectively. The PS double-cleaned particles additionally allow for a systematic study of the contact angle when varying the AR and the equilibration time, without strongly altering other properties. Figure 6 contains some FreSCa cryo-SEM images of these particles. For the first three rows, the left column displays electron micrographs taken after immediate vitrification, whereas the images in the right column refer to a waiting time of 60 min between creating and vitrifying the interface. When comparing the two image series, it is evident that the particles on the right have a higher contact angle, i.e., cast a longer shadow. The quantification of this observation is summarized in Figure 7, which reports the contact angles of the PS ellipsoidal particles as a function of contact line length. The data indeed confirm that the average contact angle increases significantly with equilibration time, in agreement with the findings of Kaz et al.11 for spheres. Second, although the effect is convoluted by the aforementioned broad distribution, the measured contact angles decrease with the contact line length for both short and longer equilibration times, showing that more prolate ellipsoidal particles are on average more hydrophilic.42 The fact that the decreasing trend is observed irrespective of the equilibration time indicates that it cannot be solely due to differences in the adsorption kinetics. Moreover, the logarithmic nature of the contact angle relaxation reported by Kaz et al.11 implies that the largest contact angle change takes place close to interface formation.

Figure 5. Distributions of contact angles for PS ellipsoids at the water−decane interface (immediately frozen) with aspect ratio between 4 and 5 (red) and between 3 and 4 (green), respectively. Particles from different batches but with AR falling in the ranges above have been grouped. The width of the bars (5°) indicates the accuracy of the individual measurement, which is significantly smaller than the width of the distributions.

Table 2. Three-Phase Contact Angles of PS Ellipsoids Batches at a Water−Decane Interface (at Different Equilibration Times teq) and of PMMA Ellipsoids at a Water−cis-Decalin Interface with Different Particle Surface Chemistries and Aspect Ratios Ranging from 1 to 7.4a surface chemistryb

spherical sizec [μm]

AR

PS orig PS dc

0.7 0.7

1.0 1.0

PS dc

0.7

3.6 ± 0.5

PS dc

0.7

4.3 ± 0.5

PS dc

0.7

4.8 ± 0.4

PS dc PS dc

0.7 0.7

5.7 ± 0.6 7.4 ± 0.9

PS fluo PS fluo PS−PVA fluo PMMA PMMA−PHSA

0.2 1.0 1.0 1.2 3.0

1.0 1.0 4.0 ± 0.2 2.4 ± 0.2 5.1 ± 0.5

teq [min] 0 0 60 0 60 0 60 0 60 0 0 60 0 0 0 0 0

θav [deg]

θmed [deg]

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

101 76 97 77 87 68 81 63 93 70 62 80 68 84 33 97 110

97 73 97 78 85 70 81 66 91 71 62 80 67 85 32 103 113

9 9 7 13 7 12 11 12 9 12 10 9 4 7 3 15 7

a

The spherical diameter of the ellipsoids refers to the diameter of the original sphere before stretching. (θav = average contact angle; θmed = median of the contact angle distribution). At least 30 particles are measured for each sample. bAbbreviations: orig = original beads from company without any treatment; dc = double cleaned; fluo = fluorescent; PS−PVA = single-cleaned PS with a smooth PVA layer. c The diameter of the unstretched sphere.

shadows) and thus where contact angles of individual particles can be accurately measured, without any assumption on the particle size. For very hydrophilic particles, for which average dimensions are assumed, the initial size distribution also has an impact on the contact angle measurement accuracy. A good initial sample monodispersity, uniform stretching, and homogeneous PVA removal are vital, the latter only being important for 4295

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Figure 6. Cryo-SEM images of some of the double-cleaned PS ellipsoids from Table 2 at two different equilibration times: (a) spheres after 0 min, (b) spheres after 60 min, (c) AR4.3 after 0 min, (d) AR4.3 after 60 min, (e) AR7.4 after 0 min, (f) AR7.4 after 60 min and some PMMA and fluorescent PS ellipsoids: (g) PMMA AR5.1, (h) PS fluo AR4. Scale bar: 1 μm unless specified otherwise.

closer to 90° after 60 min waiting time, the contact line lengths of these particles are slightly greater than the ones measured after immediate vitrification. Given that the used particle batches have equal dimensions, the only reason for the contact line length to be different from the theory is a change in contact angle. The aspect ratio dependence of the contact angle for ellipsoidal particles has been already experimentally investigated by Loudet et al. In a first paper,22 the authors used interferometry to measure the maximum contact line deformation induced by the ellipsoids (with a spherical

The clear evidence of the contact angle reduction with increasing AR can also be seen by plotting the length of the measured contact line versus measured AR for all particles (see inset to Figure 7). The dashed line represents the analytical relation between L and AR provided that the contact angle does not change as a function of AR and stays equal to the contact angle of the unstretched spheres, as predicted by Young− Laplace’s equation (details of the contact line length calculations are provided in the Supporting Information). The measurements increasingly deviate from this analytical line at higher the aspect ratios. Since the average contact angles are 4296

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Figure 7. Distributions of the cosine of contact angles of PS ellipsoids versus the length of their contact line for two different waiting times between creation and vitrification of the interface (open symbols 10 seconds, filled symbols 60 minutes). The grey data points refer to unstretched spheres. The dashed lines are linear fits to the data points corresponding to the ellipsoids and do not include the spheres. The inset shows the experimentally determined contact line length versus aspect ratio compared to the theoretical curve (dashed line) assuming a constant contact angle for all ARs equal to the contact angle of the spheres after 60 minutes waiting time. The symbols are the same as in the main graph. All errors on both graphs are the standard deviations of the data for each aspect ratio bin.

diameter of 10 μm) and related that to the particle contact angle, showing a marked decrease of the contact angle with increasing AR, which was initially attributed to surface modifications after stretching. In a more recent paper,27 it was demonstrated that the relation between the maximum deformation at the interface and the contact angle is not univocal and that a second branch exists, which only shows a weak decrease of the contact angle in the range of investigated ARs. To elucidate this issue further, the authors measured the contact angles by measuring the cross sections of the particles at the interface and comparing it to the total particle area, identically to what we do in eq 7a. The data in ref 27 did not provide conclusive evidence, possibly due to relatively low statistics and limitations of the optical setup in accurately measuring the particle cross section at the interface. The key unresolved question relates to the cause of the observed trend in the measured contact angles. In fact, the Young−Laplace equation and the notion that the equilibrium contact angle of a particle at a liquid−liquid interface is uniquely a material property for a homogeneous particle imply a θ that is independent of particle size, shape, and position along the contact line. We hypothesize that the experimentally measured deviation from the ideal behavior can be due to a number of factors, including surface chemical heterogeneity and nanoscale surface roughness.37,38 The first contribution can be related to the presence of chemical defects on the particle surface as mentioned by Kaz et al.11 Since these particles contain sulfate groups only on the surface and the stretching procedure increases the particle surface area, the relative contribution of these defects may decrease. The particle surface energy therefore slightly increases, pulling the particle more into the higher surface energy liquid, which in this case is the

water. This is consistent with the observations of Chen et al., who found, combining optical imaging at the interface with AFM studies of the surface of spherical particles, that the charges on a particle surface tend to group together, with PS37 as well as with silica38 particles. The observation of a nonuniform charge distribution was also reported earlier by Feick and Velegol,43 who used rotational electrophoresis. It needs to be emphasized that the surface energy will always increase upon stretching for all particle types since less surfaceactive material comes to the surface. If a molecule or chemical group had lowered the surface energy, it would have been located at the surface from the beginning. It is additionally possible that, as a consequence of stretching, the contact angle is not equal along the edge of the ellipsoid, for instance due to different surface roughness or texture at the tips relative to the particle center. Previous studies have indicated that the surface charge distribution stays homogeneous upon stretching44 (albeit with some small variations see Supporting Information). Regardless of the physicochemical origins of the deviations, in a first approximation, the cosine of the contact angle reported in Figure 7 can be considered a linearly increasing function of contact line length L: cos θ ≃ cos θ0 + kL

(8)

where θ0 is the angle of the unstretched spheres and k the slope of this linear approximation. This implies that the deviation from the ideal behavior prescribed by Young−Laplace’s equation is related to line effects and not to surface effects. We point out that eq 8 is a simplified linearized version of the generalized Young−Laplace equation, which for the case of spherical particles can be written as45 4297

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systematic study comparing the contact angle of ellipsoids with different aspect ratio but equal surface properties reveals a small gradual decrease of the contact angle with increasing aspect ratio, although contact angle distributions are broad. This trend can be explained by introducing a correction term to the contact angle determined by the Young−Laplace equation that is linear in the length of the contact line. This correction allows writing a simplified, linearized version of the generalized Young−Laplace equation, including the contribution of contact line heterogeneities and possible surface energy changes into an ef fective line tension, with magnitude comparable to results obtained with other techniques on different systems. The correction becomes more important for particles with higher aspect ratios, for which the length of the three-phase contact line relative to the area is increased. In general, it is expected that the surface energy will tend to increase when deforming a particle plastically, such that the surface area increases, as material comes to the surface which is less surface active, changing the contact angle of the particle. The magnitude of this measured correction term prompts further investigations on the relative contributions of surface chemistry, surface topography, and actual line tension. The flexibility and accuracy of FreSCa cryo-SEM make it potentially possible to separate these effects by investigating colloids with controlled surface roughness and uniform chemistry or particles with smooth surfaces but controlled chemical patches. Systematic investigations of small nanoparticles (e.g., below 100 nm) may also make it possible to isolate pure line tension contributions and compare them with theoretical calculations.

(9)

where θ0 is the macroscopic contact angle obtained from the classical Young’s equation, τ is the line tension, and R is the particle radius. The generalized Young−Laplace equation has also been explicitly formulated for ellipsoidal particles by Faraudo and Bresme,18 under the assumption of flat contact lines, equilibrium conditions, and ideal particle surfaces. Equation 8 gives instead an empirical, simplified model, which includes all deviations from the idealized behavior in the correction to the contact angle. We can estimate that the correction term kL in eq 8 to cos θ is of the order of kL ∼

τ L̃ τ̃ ⇒k∼ γπR2 γπR2

(10)

representing the ratio of line contributions to surface contributions, where τ̃ represents an effective line tension, which takes into account the effects of heterogeneity in the contact line described before. In the estimate we used a typical cross-sectional area of the unstretched sphere, since for prolate ellipsoids stretched at constant volume the corresponding cross section scales with AR1/3, and therefore maximally a factor 2 is missing. From eq 10 we can therefore estimate that the effective line tension contributions amount to ≈1 nN. Theoretical estimates of the pure line tension at three-phase contact lines identify values of the order of 1−100 pN,46 while experimental values for particles at interfaces span a very large range between 1 pN and 1 μN.47 The large discrepancy between theory and experiments suggests that in many experimental studies effects of heterogeneities, and therefore τ̃, and not the pure line tension τ, may be actually measured. The values that we report are within the range of literature values. The effect of a positive ef fective line tension correction on the contact angle can be qualitatively understood as a drive toward the reduction of the three-phase contact line length. For hydrophilic particles this is achieved by pushing the colloid more into the water phase and thus lowering the contact angle. In the case of our ellipsoidal PS particles, this effect becomes more important for increased stretching, as the ratio between line and surface effects grows for more elongated objects.

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ASSOCIATED CONTENT

* Supporting Information S

Additional details about solvent choice in FreSCa experiments, zeta-potential measurements, validity and importance of all assumptions, and contact line length calculations. Furthermore, SEM images of the particles in Table 2 that are not shown in the main text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (L.I.).

■

Notes

The authors declare no competing financial interest.

CONCLUSIONS This work shows the effect of key parameters such as surface chemistry, size, and shape on the wetting of small anisotropic particles at liquid−liquid interfaces. In particular, FreSCa cryoSEM is employed to visualize the contact line of spherical and ellipsoidal particles at a liquid−liquid interface with nanometer resolution and measure their contact angle. Accurate measurements on both hydrophilic (PS) and hydrophobic (PMMA) particles have been performed and highlight the importance of surface preparation protocols. For the former particle type, deformations of the contact lines have been observed. The interface surrounding a hydrophilic particle is pushed down at the tips and pulled up at the sides, confirming earlier theoretical studies and experiments with larger particles. This phenomenon occurs due to a combination of varying curvature and a constant contact angle along the edge, which is confirmed by our observations. To observe the contact line, a homogeneous particle surface is a prerequisite, as surface contaminants induce heterogeneous wetting and corrugations of the contact line. A

■

ACKNOWLEDGMENTS We acknowledge the financial support from SNSF Ambizione Fellowship PZ00P2 _142532/1, FWO projects G.0554.10 & G.0697.11, Hercules AKUL024, IAP programme MICROMAST (financed by BELSPO), and technical support from the Scientific Center for Optical and Electron Microscopy (SCOPEM, ETH Zürich). The authors also thank Zhenkun Zhang and Patrick Pfleiderer for preparing the PMMA ellipsoids and Stef Kerkhofs for providing support with the zeta-potential measurements.

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