Mapping Anisotropic and Heterogeneous Colloidal Interactions via

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Mapping Anisotropic and Heterogeneous Colloidal Interactions via Optical Laser Tweezers Dong Woo Kang, Kyu Hwan Choi, Seong Jae Lee, and Bum Jun Park J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 25 Mar 2019 Downloaded from http://pubs.acs.org on March 27, 2019

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The Journal of Physical Chemistry Letters

Mapping Anisotropic and Heterogeneous Colloidal Interactions via Optical Laser Tweezers Dong Woo Kang†a, Kyu Hwan Choi†a, Seong Jae Leeb, and Bum Jun Parka*

aDepartment

of Chemical Engineering, Kyung Hee University, Yongin 17104, South Korea

bDepartment

of Polymer Engineering, The University of Suwon, Hwaseong, Gyeonggi 18323,

South Korea

Corresponding Author *E-mail: [email protected]; Phone: +82-31-201-2429; Fax: +82-31-204-8114

†These

authors contributed equally to this work.

1 ACS Paragon Plus Environment

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ABSTRACT: Heterogeneity among particles is an inherent feature that allows nondeterministic prediction of the properties of assembled structures and materials composed of many particles. Here, we report a promising strategy to quantify the heterogeneous and anisotropic interactions between ellipsoid particles using optical laser tweezers. The configuration and separation between two particles at an oil-water interface were optically controlled, and the capillary interaction behaviors were directly observed and measured. As a result, the optimal particle configurations at energetically favorable states were obtained, and the interaction forces between the particles were identified accurately by determining the trap stiffness in the direction of major and minor axes of the particle. Visualization of the capillary field around individual particles confirmed that the capillary interactions were quadrupolar, anisotropic, and heterogeneous. The measurement method presented here can be widely used to quantify interaction fields for various types of anisotropic particles.

TOC GRAPHIC

KEYWORDS. Heterogeneity, Quadrupolar interaction, Anisotropic capillarity, Fluid interface, Optical tweezers 2 ACS Paragon Plus Environment

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Heterogeneity in interparticle interactions is both an inherent feature and a serious hindrance to prediction of the properties of assembled structures and materials with higher dimensions. However, if the degree of heterogeneity can be measured experimentally in individual particle units, then the macrostructure features organized by them could also be predictable. The close hierarchical relationship of these microscopic-macroscopic properties of colloidal particles becomes more important when there are strong interactions between particles or when the particles have large geometric or chemical anisotropy (e.g., non-spherical or Janus particles).1-8

When all kinds of colloidal particles are adsorbed to a fluid-fluid interface, the strength of the interparticle interactions (i.e., electrostatic and capillarity) is amplified tens to thousands of times compared to when the same particles are dispersed in a single fluid medium.3,9,10 In general, the electrostatic interaction is caused by dipole 3 ACS Paragon Plus Environment


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formation that results from asymmetric charge distribution,11-15 and the capillary interaction is caused by the increase in surface free energy due to interfacial deformation around particles.16-21 Notably, since Ramsden and Pickering in the early 1910s reported irreversible adsorption of conventional colloidal particles to the fluid interface and their utility as an interface stabilizer,22,23 these particle-interface systems have

been

applied

in

diverse

industrial

fields,

including

cosmetics,24,25

pharmaceuticals,26,27 separation processes,28-30 and catalysts.31 Many researchers have also investigated the colloidal interactions, microstructures, and microdynamics of two-dimensional (2D) suspensions.2,3 The properties of the particles at the interface enabled formation of various types of crystalline assemblies and production of welldefined colloidal microcrystals or capsules.32-38 In all applications where colloidal materials are processed, a detailed understanding of colloidal interactions is required for predictive control of the resulting structures and their properties.

There is no doubt that colloidal interactions are heterogeneous, according to many previous reports.2,5,6,14,39,40 For example, heterogeneity was elucidated by measuring the pair interaction of spherical polystyrene (PS) particles at an oil-water 4 ACS Paragon Plus Environment

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interface using optical laser tweezers, in which the electrostatic repulsive interactions were different for each particle pair.39,40 The results demonstrated that a clear understanding of heterogeneity in the pair interaction strength would be useful for modeling the structure, stability, and surface rheology of 2D suspensions. For attractive interactions, it has been reported that non-spherical particles at fluid-fluid interfaces exhibited a dominant capillary interaction, forming aggregates and percolated networks, in which the capillary interactions were anisotropic and heterogeneous, depending on interparticle configurations and particle pairs.16,41-46 The capillary interactions could be measured indirectly by tracking the motions of two attractive particles and converting the drift velocity to the Stokes drag force that corresponds to the capillary force.7,19,47,48 This method, however, is extremely timeconsuming because one has to wait for two random particles to approach each other spontaneously.

We have recognized the absence of an experimental approach to visualize directly the interaction field around diverse individual particles in interparticle interaction systems. In particular, for particles with chemically and/or geometrically 5 ACS Paragon Plus Environment


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anisotropic properties, visualization of interaction strength would provide direct insight into anisotropy and heterogeneity of the interaction force as well as potentially offer further information regarding the structure formation mechanism and kinetics during assembly. The aim of this work was to investigate quantitatively the configurational and rotational behaviors of non-spherical particles (i.e., ellipsoids) caused by heterogeneous and anisotropic interparticle interactions. The interaction field around the individual ellipsoid particles could be clearly monitored in real time by forcing them to rotate using optical laser tweezers,49,50 directly demonstrating the presence of quadrupolar interface deformation. More quantitatively, capillary force was directly measured as functions of azimuthal angle and separation, in which the trap stiffness values for the major and minor axes directions of the particle were determined via the drag calibration method. As a result, the configurations of particle pairs at which the capillary force was strongly attractive or repulsive were found as the particles approached each other. Importantly, the surface plot of the interaction field around individual particles provided clear visualization of the heterogeneous features of the quadrupolar capillarity for each particle pair.


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To investigate the effect of capillary interaction on the configuration behavior of two ellipsoid PS particles at the oil-water interface, the one-two trap method was used, in which one particle was held by a single optical trap and the other was held by two traps. The ellipsoid particles were fabricated by the mechanical stretching method,51 and their aspect ratio was 𝐸 = 𝑐/𝑎 = 4.28, where c and a were the radii of major and minor axes, respectively. As shown in Figure 1A, the double trapped particle (P2) on the right side was rotated from φ2 = 0° to 360° in the counterclockwise direction at intervals of Δφ2 = 30°, and the single trapped particle (P1) on the left was freely rotated under the influence of capillary field changes caused by the forced rotation of P2. P2 was translated by one step toward P1 and then rotated 360°. The same operation was repeated until the two particles attached to each other due to capillary force. Note that the input azimuthal angle (φ2) of P2 was almost identical to the output angle that was measured by the image analysis because P1 was rotated freely. The motion of P1 was found to depend significantly on the separation between the two particles. At relatively large distances, P1 swung to the left and right while remaining approximately vertical with a mean azimuthal angle from 80° to 90° as P2 was forced to rotate 360° (Figure 1B and Movie S1-S3). The φ1 value in this swing mode showed a sinusoidal response as a function of φ2 (Figure 2A), in which the period was ~π, and the node 𝑛

with a minimum amplitude occurred around 𝜑2~2𝜋 (𝑛 = 0,1,2,…). The maximum swing angle (Δmaxφ1), which was the difference in maximum and minimum amplitudes, increased as normalized separation (r/2c) decreased (Figure 2A and Figure 2D). The capillary field affected the configuration of the particles more strongly as the distance between particles decreased. 𝑟

When the two particles became closer than a certain distance (2𝑐 ≈ 5.8), the rotational motion of P1 was coupled with that of P2, and they rotated in opposite directions 7 ACS Paragon Plus Environment


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(Figure 1C and Movie S1-S3). This gear-rotating mode was the decisive clue that the capillary interaction was dominated by quadrupolar interface deformation that has been optically visualized in previous work.20 Theoretically, the capillary force due to quadrupolar deformation was expressed as Fcap~ ― 𝑟 ―5cos (2𝜑1 + 2𝜑2).52 To achieve the maximum capillary interaction, the sum of the azimuthal angles should be 𝜑1 + 𝜑2 = 0, suggesting the presence of gear-rotating mode. As shown in Figure 2B and Figure S1, φ1 in this mode monotonically decreased as φ2 increased, satisfying the relationship of φ1 + φ2 ≈ 0° for quadrupolar capillary coupling. The plot of φ1 + φ2 versus φ2 also showed a sinusoidal function with a 𝑛

node position at 𝜑2~2𝜋 and a period of ~π (Figure 2C). The corresponding amplitude difference, Δmax(φ1 + φ2), decreased as 𝑟/2𝑐 decreased, indicating a stronger angular response or a stronger capillary coupling of P1 with P2 rotation at shorter separation distance (Figure 2C and 2D). Notably, in both modes (i.e., swing mode and gear-rotating mode), the shape of the observed sinusoidal functions in Figure 2A and 2C was distorted significantly and was not perfectly consistent with that of a normal periodic function (dotted line). This deviation was an important indicator of the anisotropic capillary force between the particles depending on direction and configuration. In results of similar experiments and analyses for two different particle pairs (Pair-II and Pair-III), the swing mode over large separation distance and the gearrotating mode by strong quadrupolar capillary coupling over relatively shorter separation distance were consistently observed (Figure S2). In addition, heterogeneity of the capillary interaction was confirmed by the differences in the distorted sinusoidal response of φ1 or φ1 + φ2 with φ2 and in the transition separation for mode switching (i.e.,

𝑟 2𝑐

≈ 5.3 and 5.0 for

Pair-II and Pair-III, respectively), depending on each particle pair. As P2 approached P1 in gear-rotating mode (Figure 1C), the position of P1 moved 8 ACS Paragon Plus Environment

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slightly toward the direction of P2. Therefore, the displacement trajectory of P1 in the gearrotating mode was analyzed in more detail. Upon forcibly rotating P2 in the counterclockwise direction, in swing mode where the capillary force was relatively weak, the center position trajectory of P1 did not show any particular tendency (Figure S3 - S5). In gear-rotating mode, however, the center trajectory of P1 tended to move counterclockwise in a polygonal shape (Figure 3 and Figure S6) (note that P1 rotated clockwise). During P2 rotation over 0 ‒ 180° and 180° ‒ 360°, the center of P1 formed two polygons, and the shape of the polygon became increasingly clear as the particle distance decreased. The right shift (X > 0) from the equilibrium position (X = 0) of the P1 trajectory in Figure 3B and Figure S6 indicated that the capillary force between the two particles was attractive. The counterclockwise rotation of the center of P1 could be explained as follows. As illustrated in Figure 3A, the largest capillary attraction occurred in the tip-to-tip (tt) configuration that corresponded to the maximum value of the right shift. The magnitude of the right shift decreased slightly, while P1 rotated clockwise due to the reduced capillary attraction, displacing P1 along the major axis of the particle toward the optical trap position or the equilibrium position (X→0). When the particles adopted a side-to-side (ss) configuration at φ2 = 90° due to capillary coupling, the decreased capillary attraction led to the less right shift. As P2 rotated from 90° to 180°, the attraction increased again; consequently, P1 was displaced back along the major axis toward P2, resulting in a closed polygonal shape. The center of P1 rotated in a similar way when P2 rotated φ2 = 180° ‒ 360°. Notably, the shapes of the two polygons drawn during the 360° rotation were different, and the displaced positions of P1 at φ2 = 0° and 180° (red and blue symbols in Figure 3B) and at φ2 = 90° and 270° (green and purple symbols in Figure 3B) also differed. In addition, the microscopic images in Figure 3C showed that P1 did not form perfectly aligned tt and ss configurations with P2 at φ2 = 0° or 9 ACS Paragon Plus Environment


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180° and φ2 = 90° or 270°, respectively (i.e., φ′1 + φ′2 ≈ 0 but φ′1 + φ′2 ≠ 0). For Pair-II and Pair-III (Figure S7 and S8), the trajectory for the center of P1 drew different polygon shapes to each other and formed one polygon during the 360° rotation of P2 in gear-rotating mode, likely due to the presence of stronger anisotropy (e.g., |FaA| ≫ |𝐹𝑐𝐶|) and heterogeneity in the capillary interaction. The one-two trap method conveniently and simply provided information on rotational motion related to magnitude of capillary force, whereas a more direct method for quantification of the force depending on configuration and separation distance was needed. A more quantitative study of the interfacial capillary interactions and their direct visualization were performed using the two-two trap method (Movie S4). Two particles P1 and P2 were each held by two optical traps, and their rotation and separation were controlled separately (Figure 4A). P2 was rotated from φ2 = 0° to 360° at intervals of Δφ2 = 30° at a fixed azimuthal angle (φ1) of P1. The same procedure was repeated upon 360° rotation of P1 and translation of P2 until the two particles were attached to each other (Figure 4B). Because each particle was fixed by two optical traps, the capillary interaction might cause the output azimuthal angles (φ′1 and φ′2) obtained by the image analysis to be slightly different from the input angles (φ1 and φ2). Note that the contribution of the electrostatic repulsions could be ignored because the measured zeta potential of the spherical seed particles used for fabrication of the ellipsoid particles was very small (-22.5 mV) and the interaction between the spheres at the oil-water interface exhibited the attraction dominant.47 Thus, the net interaction force was assumed to be governed mainly by capillary interactions (𝐹𝑛𝑒𝑡 ≈ 𝐹𝑐𝑎𝑝). Based on the angular dependent drag calibration method (see the detailed description and Figure S9-S11 in SI),49,50,53,54 the interaction forces could be measured quantitatively as functions of 𝜑1, 𝜑2, and r/2c (Figure S12 and S13), enabling the determination of the particle configurations that were energetically favorable (maximum attraction) and unfavorable 10 ACS Paragon Plus Environment

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(maximum repulsion). As shown in Figure 5, the maximum magnitude in the capillary attraction and repulsion were determined as a function of separation distance. The attraction force curve was somewhat consistent with the scaling behavior (Fcap~𝑟 ―5) of quadrupolar capillary attraction (solid curve in Figure 5), whereas the degree of deviation was attributed to rotational motion upon particle approach (Figure S14B). In attraction, the particles tended to adopt the ss–like configuration at long–range separation, whereas they adopted the tt–like configuration at relatively small separation (Figure S14A and S14B). In repulsion, the side-totip (st) configuration was observed as the separation decreased (Figure S14C and S14D). The sum of the two azimuthal angles was approximately 𝜑′1 + 𝜑′2 ≈ 𝑛𝜋 for attraction (Figure S14A) and

(2𝑛 + 1)𝜋 2

for repulsion (Figure S14C), which simultaneously indicated that the

interactions followed the quadrupolar capillary interaction but were not perfectly quadrupolar. Finally, we were able to visualize the capillary field around single particles, clarifying that the capillary interactions were quadrupolar, anisotropic, and heterogeneous. The surface plots in Figure 6A-6L were obtained from the three-dimensional plots in Figure S13, in which the red and blue colors indicate the direction of increasing repulsion and attraction, respectively. To read the surface plot, based on the centrally located P1 with a given azimuthal angle (𝜑1), P2 could be located anywhere in the radial direction on the colored area in the surface plot (Figure 6M). 𝜑2 corresponded to the angle between the horizontal line and the line connecting the centers of P1 and P2, and the center-to-center radial distance indicated the interparticle separation distance (r/2c). The two particles with 𝜑1 and 𝜑2 were translated on a horizontal line without rotation, and the magnitude of the corresponding capillary force was read with the color where P2 was located on the surface plot. For instance, the particles with 𝜑1 = 270° and 𝜑2 = 0° in Figure 6M would be repulsive because the line joining the two particles was located in the red zone, regardless of separation, and P2 with 𝜑2 = 60° or 90° located in the blue zone 11 ACS Paragon Plus Environment


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would be attractive with P1. If the interface deformation around a single ellipsoid was perfectly symmetrical with respect to its major axis, a similar symmetric capillary field could be expected on the surface plot. Notably, the shape of the measured capillary field in Figure 6A-6L displayed four distinctive zones, that is, four deformation poles (quadrupoles) existed, whereas the asymmetry in size and shape of the zones clearly indicated that the capillary force was anisotropic. The capillary interactions were measured for another particle pair using the twotwo trap method, and the shape of the obtained interaction landscapes in Figure S15 was very different from those in Figure 6, demonstrating the interaction heterogeneity. The surface plot of the capillary field could be useful for predicting angular transition behavior when one particle pulls on another. The attraction valley, a path with a relatively strong capillary attraction in the surface plot, could be determined by locating the maximum gradient in the force

𝑑𝐹𝑐𝑎𝑝

( ) 𝑑𝑟

𝑚𝑎𝑥

starting at any position and azimuthal angle. When P2 approached P1 with a

fixed 𝜑1 = 120° (Figure 6N), for example, 𝜑2 initially at positions 1 to 4 would follow the trajectories along the attraction valley indicated by the yellow arrows in Figure 6N (see the angular trajectories in Figure 6O). In other words, the probability of the configuration corresponding to the repulsion ridge (the red zones in Figure 6N) was very low. In conclusion, an in-depth investigation of the capillary forces of ellipsoid particles was carried out using optical laser tweezers. Previous studies have shown that the interface deformation around an ellipsoid particle was a quadrupole, and it has been shown experimentally and theoretically that the capillary force at long-range separation decayed as 𝑟 ―5.17,19,21,53,55 Importantly, we found for the first time that the


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rotational motion between two ellipsoid particles was composed of two unique modes (i.e., swing mode and gear-rotating mode) depending on the strength of capillary coupling, and that the capillary field around individual particles could be visualized and quantified by directly measuring the capillary force of particle pairs. The asymmetric capillary landscapes with the four distinctive zones that differ for each particle pair provided evidence that the capillary interaction was quadrupolar, anisotropic, and heterogeneous. It is believed that heterogeneity could be attributed to the presence of irregular wettability or an undulated interface meniscus likely due to chemical and geometric non-homogeneity.21,56,57 The rotational interval of 𝛥𝜑 = 30° was used when measuring the capillary force in this study; however, by decreasing the interval, it would be possible to improve the accuracy in finding the stable configurations and visualizing the capillary field. In addition, the method of decomposing the force components in the direction of the major and minor axes for drag calibration and determining the respective trap stiffness values would be a great help in quantitatively measuring the interaction forces between particles with various shapes using optical laser tweezers. By combining an automated real-time image analysis process, the



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interaction landscape visualization method presented here will potentially provide a key methodology for easily and accurately displaying the intensity and vector field of interactions (i.e., repulsions and attractions) around all possible combinations of diverse pairs or ensembles of multiple particles with geometric and chemical anisotropies.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: xxx.

Experimental methods and additional results using the one-two trap and two-two trap methods.

AUTHOR INFOMRATION Corresponding Author *E-mail: [email protected]; Phone: +82-31-201-2429; Fax: +82-31-204-8114

ORCID Seong Jae Lee: 0000-0001-5514-3234


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Bum Jun Park: 0000-0002-5567-3523

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT: This work was supported by the National Research Foundation (NRF) of Korea, NRF-2014R1A5A1009799 and NRF-2017R1A2B4003123.

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Figures

Figure 1. The one‒two trap method. (A) Optical microscope images showing the rotation and translation of the two ellipsoid particles. (B,C) Stacked images of the sequences (Pair-I) during rotation and translation, showing swing mode (B) and gear-rotating mode (C). The white lines at each particle position indicate the stacked major axis of the particle during rotational motion of P1 and P2 (see Movies S1-S3).


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Figure 2. Swing mode versus gear-rotating mode of Pair-I with the one-two trap method. Direct observations of the two distinctive rotation modes of P1 upon forced P2 rotation. (A) Swing mode. (B, C) Gear-rotating mode. The different symbols in panels A-C indicate the normalized separation distances (r/2c). (D) The differences in maximum and minimum amplitudes of the plots in panels A and C.



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Figure 3. Double rotation of Pair-I in gear-rotating mode. (A) Schematic illustrating the trajectory of the center of P1 in response to P2 rotation. (B) Trajectories of the center of P1 upon rotating and translating P2. (C) Optical microscope images showing the particle configurations at φ2 = 0, 90, 180, 270°, with various values of r/2c.


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Figure 4. The two‒two trap method. (A) Optical microscope images showing the rotation and translation of the two ellipsoid particles. (B) Example of stacked microscope images at fixed φ1 upon 360° P2 rotation, which is indicated by white lines (see Movie S4). The separation in all of the stacked images was r/2c = 4.28.



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Figure 5. Maximum attraction (negative value) and repulsion (positive value) in the capillary force upon particle approach.


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Figure 6. Direct visualization of capillary interaction fields. (A-L) Surface plots of the capillary interaction depending on configuration and separation between two ellipsoid particles. Each panel indicates a different φ1 value. (M) An example of how to interpret the surface plot. (N) A 3D surface plot at φ1 = 120° showing the prospective paths (yellow arrows) of φ2 at four different initial orientations and positions. (O) The corresponding φ2 values for the four paths upon approach (see Movie S5).



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Mapping Anisotropic and Heterogeneous Colloidal Interactions via

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