Adhesion of Particles with Sharp Edges to Air–Liquid Interfaces

Article pubs.acs.org/Langmuir

Adhesion of Particles with Sharp Edges to Air−Liquid Interfaces Javed Ally,* Michael Kappl, and Hans-Jürgen Butt Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany ABSTRACT: In order to study the effect of sharp edges on solid particle adhesion to air−liquid interfaces, spherical colloidal probes were modified with a circumferential cut by focused ion beam milling. The interaction of the modified particles with water drops and bubbles was studied using the colloidal probe technique. When the modified particles were brought into contact with air−liquid interfaces, the contact line was pinned at the edge of the cut. Contact hysteresis between the approach and retraction components of the measured force curves was eliminated. The contact angle at the edge takes a range of values within the limits defined by the Gibbs inequality. These limits determine the adhesion force. As such, the adhesion force is a function of the particle wettability and edge geometry.

distance δ that the particle protrudes into the air phase (Figure 1b):15

1. INTRODUCTION Particle interactions with air−liquid interfaces are important for a variety of applications, such as mineral flotation,1 drug delivery to the lung, 2 and stabilization of Pickering emulsions.3−5 In previous theoretical and experimental studies, ideal spherical particles were commonly assumed,6−9 for which the correlation between wetting behavior of the particles and attachment forces is well understood. In real systems, however, edges and surface asperities may lead to contact line pinning, which in turn may change their behavior at air−liquid interfaces.10,11 In this study, spherical particles modified to have a defined circumferential edge (Figure 1a) are used to directly study the effect of edge pinning on particle adhesion to air−liquid interfaces by atomic force microscopy. Little work has been done on the effect of edge pinning on particle-interface interactions. The effect of roughness on particle−particle interactions at air−liquid interfaces was first investigated by Stamou, Duschl, and Johannsman.12 Surface roughness was identified by Maestro et al.13 as a factor that affects particle contact angles, particularly as particle size decreases. The focus of ref 13, however, is on the interplay of roughness and the solvent used to spread particles at the interface. Princen14 presents a theoretical treatment of flotation of long prismatic cylinders at interfaces; however, there are no corresponding adhesion force measurements in the literature. Also, in previous measurements using solid particles, the degree to which sliding of the contact line affects the measured force curves is unclear. An additional motivation of this study is to eliminate contact line sliding by edge pinning, and thus identify the extent of its effect in experiments with spherical particles. For a small, spherical particle (i.e., negligible weight and buoyancy), the interaction with an air−liquid interface is characterized by the three-phase contact angle and the adhesion force between the particle and the interface due to capillary force. The particle contact angle θ can be determined from the equilibrium position of the particle at the interface based on the © 2012 American Chemical Society

cos θ =

R−δ R

(1)

The contact angle may be advancing or receding, depending on whether the particle goes from the air into the liquid phase (advancing) or the liquid into the air phase (receding). When a particle is pushed or pulled away from its equilibrium position at an interface (Figure 1a), the resulting capillary force can be calculated based on the contact line location and wetting angle:16 F = 2πγR cos α cos β

(2)

where the angles α and β are as shown in Figure 1a. If the capillary force, particle radius, and contact line position (i.e., angle α) are known, the angle β and thus the contact angle can be calculated. Normally, however, this is not the case, and some assumption about the contact line position and contact angle is required to use eq 2. Princen assumed that the angle β is determined solely by the equilibrium contact angle of the particle and contact line position.14 Scheludko and Nikolov calculated the adhesion force between a particle and interface by assuming that the contact line is free to move, the contact angle remains constant, and that particle detachment occurs at the contact line position that yields the maximum force value:17

F = 2πγR cos2(ϑ/2)

(3)

Here, ϑ takes the value of θ if the particle is pulled from the liquid into the air phase (i.e., from a drop), or π − θ if the particle is pulled from the air phase into the liquid phase (i.e., from a bubble). There is no corresponding theoretical Received: October 19, 2011 Revised: June 27, 2012 Published: July 2, 2012 11042

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Figure 2. SEM image of typical completed colloidal probe modified by making a cut using the FIB.

Force measurements were performed with both air bubbles in water and water drops in air with typical volumes of 0.3 μL. Air bubbles were deposited in water at the bottom of a polystyrene dish. Experiments with drops were performed in an enclosed cell to limit evaporation. Deflection sensitivity of the AFM was determined by pressing the cantilever against the solid polystyrene surface used to hold the drops/ bubbles. For each measurement, 50 force curves were collected. All measurements were carried out with cantilever approach/retraction speeds of 30 μm/s. Comparison with measurements at 1 and 5 μm/s showed that hydrodynamic effects were negligible, as no difference in the force curves was observed. The spring constants of the cantilevers were measured by the thermal noise method18 using the thermal tune function of a Veeco MultiMode TUNA TR AFM with Nanoscope V controller after all processing of the colloidal probes (FIB, silanization) was completed. Thermal tuning and force measurements were carried out at a temperature of 25 °C. To facilitate comparison, forces and distances were normalized. The particle position x was normalized with respect to the particle diameter, x* = x/(2R), where R is the particle radius. The force F (vertical axis) was normalized with respect to the maximum possible capillary force on the particle F* = F/(2πγR). Here, F is the measured force, and γ = 0.072 N/m is the surface tension of water. The zero position of the axis is set at the equilibrium point of the approach curve (i.e., point 3 in Figure 3).

Figure 1. (a) Schematic of a modified colloidal probe used in this study at an arbitrary position. The probe is comprised of an AFM cantilever and a spherical particle with a cut around its circumference at a given distance h from the tip of the probe. The interface shown is of an air bubble; in the case of a liquid drop, the air and liquid phases would be reversed. (b) A spherical particle at the equilibrium (i.e., zero force) position as it is advanced into a bubble. The distance δ corresponds to the receding contact angle θ. If the particle was being pulled out of the bubble, then the values for δ and θ would be replaced by those for the advancing contact angle.

expression for particle adhesion force when the contact line is pinned at an edge.

2. MATERIALS AND METHODS An atomic force microscope (AFM) was used to measure the force on a microscopic particle (Bangs Laboratories, silica, 3.5 μm nominal diameter) mounted on the end of a tipless cantilever (Mikromasch NSC12, 3.5 N/m nominal spring constant). The particles were attached to the cantilever using a micromanipulator and epoxy glue (Epikote 1004). Actual particle diameters were measured by scanning electron microscopy (SEM). The cantilever position was controlled by a piezoelectric actuator. The particle position was determined by adding the cantilever deflection to the position of the base of the cantilever. Plotting the force as a function of the particle position gives a force curve (Figure 3). The particles were modified by cutting with a focused ion beam (FIB, FEI Nova 600 Nanolab) after they were attached to the cantilevers. A beam current of 10 pA and a voltage of 30 kV was used. The cantilevers were mounted in the FIB apparatus with their long side perpendicular to the beam. An edge was produced by etching a cut in the particle, typically 500 nm wide and 500 nm deep, at a 10° angle to compensate for the tilt of the cantilever when mounted in the AFM. The cantilevers were then removed and turned over. The other side of the particle was etched using the previously cut edges for alignment, producing a circumferential cut around the particle (Figure 2). On the basis of SEM images of the modified particles, the radius of curvature of the edge was on the order of 10 nm. The probes were plasma cleaned after processing to remove contamination. To give the particles consistent wetting properties, they were silanized using a fluorosilane vapor for 4 h (1H,1H,2H,2H-perfluorooctyltrichlorosilane, Sigma Aldrich).

3. RESULTS AND DISCUSSION A force curve from a measurement of an unmodified (i.e., spherical) particle is shown interacting with an air bubble in Figure 3, along with a schematic of the particle and interface position during the measurement. The measurement begins with the probe at its furthest position from the interface, and follows the dashed line shown in section 1 of Figure 3 from right to left as the probe approaches the interface. At 2, the probe makes contact with the interface and jumps into it due to the capillary force. As the probe approaches further into the bubble/drop after contact is made, it reaches an equilibrium position (3), where the interface has returned to its original position before contact, and no force acts onto the probe. Upon further approach, the force on the probe becomes positive and increases as the probe is pushed into the interface (4). During retraction (5), the force on the probe decreases until it reaches an equilibrium position (6). There is normally some hysteresis between the approach and retraction parts of the curve in the contact region, so the equilibrium position during retraction (6) is not the same as that during the approach (3). The probe is retracted until it detaches from the interface (7). The 11043

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The hysteresis typically observed in the contact region of the force curves is attributed to contact angle hysteresis and the motion of the three-phase contact line over the particle surface.11,19 The advancing contact angle during retraction can be determined similarly as during approach, based on the distance between points 2 and 6, using eq 1. Calculation of the advancing and receding angles is performed similarly for a particle interacting with a drop, although in this case, the advancing angle occurs during the particle approach, and the receding angle occurs during retraction. The advancing and receding contact angles for the unmodified particle shown in Figure 3 (probe 1 in Table 1) are 111°and 101° respectively, determined using eq 1. The difference between the advancing and receding contact angles means that the immersion depths of that particle at the equilibrium points on the approach and retraction parts of the curve are different, i.e. the contact line has moved on the particle surface. When measuring forces with FIB-modified particles, the contact regions of the force curves show little or no hysteresis. A typical example for a FIB-modified particle interacting with an air bubble is shown in Figure 4a. Force curves were measured using particles with edges cut at different heights (i.e., different values of h as shown in Figure 1a). For the FIBmodified particles, the jump-in distance corresponds to the location of the edge. This can be seen from the edge positions and jump-in distances for various modified particles (Table 1). Similar results were also obtained in measurements with drops (Figures 4c,d). The correlation between jump-in distances and edge positions shows that the contact line was pinned at the edge in the contact region. Hysteresis in the contact region is eliminated, as seen by comparing Figures 3 and 4. Another feature resulting from the edge pinning is the underdamped oscillation that occurs when a FIB-modified particle jumps into the interface; one example is shown in Figure 4b. The likely reason for the oscillation is that the damping that would otherwise occur due to the contact line sliding on the particle surface is absent. Similar oscillations were observed were observed by McGuiggan et al.20 for colloidal probes interacting with sessile drops. The adhesion force for the unmodified particle and a bubble in Figure 3 was 629 nN, 12% higher than the value of 559 nN predicted using eq 3. In AFM measurements, the accuracy of the force measurement is limited by the error inherent in determining the spring constant, which we estimate to 10% for the thermal calibration method used here.21 Therefore, the

Figure 3. (a) A typical force curve measured at a water/air interface of a bubble with an AFM using a spherical (i.e., unmodified) particle (probe 1). The measurement begins from right to left with the dashed line showing the particle approach to the interface. The measurement continues from left to right with the solid line as the particle is retracted. (b) The position of the particle and interface, corresponding to the numbering in the force curve.

retraction continues (8) until the probe is in its original starting position. When the particle initially makes contact with the air−water interface, it jumps in, deforming both the cantilever and interface. Experimental error aside, the uncertainty inherent in the location of the jump-in position is on the order of 10 nm, due to instability resulting from van der Waals forces between the particle and interface.15 The distance between the jump-in and equilibrium position (2 and 3 in Figure 3) gives the immersion depth of the particle at equilibrium in the air phase (Figure 1b), which can be used to determine the receding three-phase contact angle (since the particle goes from water into air) using eq 1. Additional jumps in and out in the force curve typically indicate pinning of the contact line on surface inhomogeneities. The smoothness of the curves in Figure 3 while the particle is in contact indicates that the surface is homogeneous and there are no such pinning sites. Table 1. Probe and Force Curve Characteristicsa probe

interface

particle radius (μm)

normalized tip-edge distance h

1 2 3 4 5 6 7

bubble bubble bubble bubble bubble drop drop

1.75 1.95 1.85 1.90 1.80 1.85 1.70

0.44 0.18 0.31 0.20 0.24 0.36

normalized jump-in distance

contact angle at detachment (deg)

± ± ± ± ± ± ±

101b 136 102 110 111 103 83

0.58 0.452 0.236 0.299 0.22 0.233 0.39

0.02 0.004 0.005 0.007 0.01 0.004 0.02

normalized adhesion force 0.773 0.698 0.602 0.623 0.661 0.291 0.443

± ± ± ± ± ± ±

0.004 0.011 0.008 0.018 0.019 0.011 0.010

a

Unless otherwise noted, all distance and force values are normalized. Jump-in distances and measured adhesion forces were averaged over 50 force curves. Error values shown are the standard deviation for each set of measurements; systematic errors are not included. The contact angles at detachment were calculated from the average values of the adhesion force. btheoretical, based on assumption that detachment from a sphere occurs when α = β = ϑ/2. 11044

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Figure 4. Experimental force versus position curves. The dashed lines show the approach curves, the solid lines show the retraction; directions are indicated by arrows. (a) Normalized force curve for a modified particle (cantilever 4) and an air bubble in water. The circled region showing the oscillation observed upon particle jump into the interface is shown in (b). (c) Normalized force curve for a modified particle (cantilever 6) and a water drop. (d) Normalized force curve for a modified particle (cantilever 7) and a water drop with an extended approach into the interface.

measured force values, described above, may also be the cause of these deviations. Another possible explanation of these deviations may be the effect of line tension, due to variations in the edge geometry. It has been assumed that the edge is perfectly sharp and smooth, thus the contact line is not subject to any distortion. In reality, the edge has a radius of curvature on the order of 10 nm, based on SEM images. This radius of curvature, as well as the edge geometry, would vary around the particle circumference due to the limited resolution and stability of the FIB apparatus. Possible roughness or waviness of the edge would produce a rough or undulating contact line, resulting in line tension contributing to the adhesion force. The magnitude of this contribution is not trivial to estimate, however, due to the large range of values found in the literature for line tension, from 10−10 to 10−6 N.22 As shown by Gibbs,23 when the contact line is pinned at an edge the contact angle can take a range of values, determined by the following inequalities, assuming that the contact angle θ (receding for a drop, advancing for a bubble) is the same for both surfaces comprising the edge:

difference between the adhesion force for the modified particles and the predicted values for unmodified spheres (normalized forces of 0.687 for a bubble and 0.405 for a drop) shown in Table 1 are too large to be explained by experimental error, and are thus a result of pinning at the edge. Since the contact line is pinned, its position and angle α in eq 2 are known and constant. Therefore, the wetting angle β of the pinned three phase contact line at the edge (Figure 1a) can be determined from the force. Note that θ, the contact angle measured with respect to the lower part of the particle beneath the edge, can be calculated directly from β. Detachment from the interface of a bubble occurs approximately when the advancing contact angle value for the particle surface was exceeded. This was observed for particles with edges at various heights (Table 1). Similar behavior was also observed for detachment from a drop, shown in Figure 4d; the particle detaches when the receding contact angle is exceeded (Table 1). Note that in the case of a bubble, the contact angle calculated from β increases, because the particle is being pulled into the liquid phase, whereas for a drop it decreases because the particle is being pulled out of the liquid phase. The contact angles at detachment shown in Table 1 fit this criterion except in the cases of cantilevers 2 and 7. These deviations may be due to the experimental error factors described above. In the case of cantilever 2 in Table 1, the contact angle at detachment was significantly higher (136°) than the advancing contact angle of the surface (111°). In the case of cantilever 7, the detachment angle (83°) was lower than expected (101°). Unlike the particle contact angle and jump in distances, the wetting angle is determined from the force measurements, so the experimental error factors that affect the

cos φa ≤ −cos θ cos φl ≤ cos θ

(4)

Here, φa is the angle filled by the air, and φl is the angle filled by the water. Thus, the wetting angle β at the edge can take any value such that the contact line is within the shaded sectors shown in Figure 5 for a bubble and drop, respectively. This variability in contact angle is known as canthotaxis. For the experiments described in Table 1, the lower boundaries of the shaded sectors in Figure 5 determine the particle detachment, 11045

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wettability and edge geometry. The results also show that the hysteresis typically observed in measurements with spherical particles is due to the motion of the contact line on the particle surface. When the contact line is pinned at an edge, the contact angle changes as the particle moves. As long as the contact line does not move, there is no hysteresis.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; phone: +49-(0)6131-379519.

Figure 5. Canthotaxis sectors (light gray) for a solid edge with the interface of a (a) bubble and (b) drop, as defined by the Gibbs inequality. Both surfaces of the solid have a contact angle θ. The contact line at the edge may take any angle within these sectors.

Notes

The authors declare no competing financial interest.

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as the particles are pulled upward with respect to the figure. It should be noted that the theory of Gibbs is developed for a straight edge. The correlation of the experimental results and theory suggest that the curvature of the particles is small enough to be neglected. Detachment of the interface from the edge was also observed when a particle was pushed into a drop. In this case, the width of the cut on the particle was 100 nm, much smaller than for the other modified particles used. As shown in Figure 4e, as the particle is pushed into the drop, a second jump-in is observed. The normalized length of this jump is 0.24; added to the length of the initial jump-in of 0.39, this gives a value of 0.63, similar to the length of the jump-in for an unmodified particle. This suggests that the contact line jumps past the edge and is pinned at its “natural” position for an unmodified sphere instead of jumping to the upper edge of the cut. The detachment force was less than that for an unmodified particle, however: 0.550 as compared to 0.773. A possible explanation for this could be that air is trapped within the cut around the particle. For the particles with circular cuts used in this study, the force on the particle at detachment is given by an expression similar to eq 2. On the basis of the geometry shown in Figure 5 for a bubble and drop, respectively, the adhesion force F is given by F = 2πγR cos α cos(ϑ − α)

ACKNOWLEDGMENTS The authors acknowledge the support of the Max Planck Society for funding this work and J.A.'s fellowship, Maren Müller for the SEM images and assistance with the FIB, and Profs. A. Amirfazli and S. Garoff for helpful discussions.

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REFERENCES

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(5)

where α is the angle defining the position of the edge (Figure 1a). As defined previously, ϑ is equal to θ if the particle is pulled from liquid into the air phase, or π − θ if the particle is pulled from air into liquid. In the development of eq 3, Scheludko and Nikolov assume that particle detachment for an unmodified spherical particle occurs at the position where α = β = ϑ/2, where the maximum force would occur. This means that the expected position of the contact line at detachment is below the edge for all of the modified particles used in these experiments. However, in all cases, when the modified particles detach from the interface, there does not appear to be any secondary attachment or indication that passing over this point affects that particle detachment. This may be due to the speed of detachment, i.e., the particle jump out of the interface, or the contact angle not meeting the criteria described by Scheludko and Nikolov for the maximum force to occur.

4. CONCLUSIONS When the contact line is pinned at an edge, the adhesion is governed by the Gibbs inequality, as the particle contact angle at the edge can take a range of values. The force at particle detachment can be calculated based on the particle surface 11046

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(18) Hutter, J. L.; Bechhoefer, J. Calibration of atomic-force microscope tips. Rev. Sci. Instrum. 1993, 64, 1868−1873. (19) Gillies, G.; Kappl, M.; Butt, H. J. Direct measurements of particle−bubble interactions. Adv. Colloid Interface Sci. 2005, 114, 165−172. (20) McGuiggan, P. M.; Grave, D. A.; Wallace, J. S.; Cheng, S.; Prosperetti, A.; Robbins, M. O. Dynamics of a disturbed sessile drop measured by atomic force microscopy (AFM). Langmuir 2011, 27, 11966−11972. (21) Matei, G. A.; Thoreson, E. J.; Pratt, J. R.; Newell, D. B.; Burnham, N. A. Precision and accuracy of thermal calibration of atomic force microscopy cantilevers. Rev. Sci. Instrum. 2006, 77, 083703. (22) Amirfazli, A.; Neumann, A. W. Status of the three-phase line tension. Adv. Colloid Interface Sci. 2004, 110, 121−141. (23) Gibbs, J. W. The Collected Works of J. Willard Gibbs; Yale University Press: New Haven, CT, 1957; Vol. 1.

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