Characterization of 2D colloids assembled by optically-induced electrohydrodynamics.

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Soft Matter View Article Online

DOI: 10.1039/C5SM00184F

optically-induced electrohydrodynamics Andrew H. Work, Jr., and Stuart J. Williams*

KEYWORDS: colloids, self-assembly, electrokinetics, microfluidics

ABSTRACT We report the results of a study characterizing the behavior of colloid aggregations under manipulation of a technique known as Rapid Electrokinetic Patterning (REP) - this technique is capable of dynamically manipulating the crystallinity of 2D colloid aggregations, potentially enabling dynamically tunable photonic crystals. Herein, aggregations of spherical polystyrene particles 1.0 µm in diameter suspended in a low conductivity aqueous solution were collected at the surface of an indium-tin oxide coated glass slide. The uniform AC field coupled with laserinduced heating produced electrothermal hydrodynamics which is responsible for the selfassembly characteristics of the planar colloidal aggregation. REP was characterized experimentally by analyzing the mutual particle spacing within the aggregation as a function of the AC signal and laser power. Numerical simulations justified the assumption that the primary forces responsible for colloidal patterning herein are Stokes drag forces and dipole-dipole repulsive forces.

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Published on 10 April 2015. Downloaded by University of Connecticut on 15/04/2015 16:01:26.

Characterization of 2D colloids assembled by

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INTRODUCTION Colloid self-assembly is a subject of ongoing research, there are a variety of commercially

Precise control over colloid trapping, positioning, and overall aggregation organizing is of significant interest in constructing specialized nanostructures [2-4]. In particular, understanding the close-packed nature of particle aggregations enables optical characterization of selfassembled colloidal crystals for photonic applications [5-7]. There exist a variety of techniques for precise colloidal positioning and aggregation assembly including optical trapping [8], electrophoresis [9], dielectrophoresis [10, 11], thermophoresis [12], and sedimentation [13]. Rapid electrokinetic patterning (REP) is a technique that collects and organizes liquid suspended microparticles in a 2D aggregation on the surface of an electrode [14-16] (Fig. 1a). The underlying physics of REP will be briefly discussed here in order for the reader to better comprehend the interaction of electrokinetic mechanisms with hydrodynamics, though a more extensive description is found in literature [17, 18]. First, a sample of liquid-suspended polystyrene microparticles is injected in a microchannel between two parallel plate electrodes. Next, a non-uniform temperature field is generated within the microchannel, either through external optical illumination [15] or embedded resistive heaters [14]. An applied AC electrical field induced electrothermal microfluidic motion [19] that is toroidal in nature; this circulating microvortex carries colloids towards the surface of the electrode (Fig. 1a). Frequency-dependent electrokinetic particle-electrode interactions, including localized electrohydrodynamics [20], cause the colloids to be retained on the electrode surface. Bulk microfluidic motion aggregates the surface-bound colloids at the vortex’s center, though repulsive dipole-dipole forces influence their mutual spacing [21].

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available colloids [1] that can be used as building blocks to develop such artificial architectures.

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REP exhibits a number of advantages over other colloidal-assembly techniques. Optical trapping is limited to trap and position a few particles simultaneously, whereas REP can aggregate a relatively larger number of colloids, including nanoparticles [22]. Some electrokinetic methods,

requires parallel-plate electrodes. Optically-based REP also provides a great degree of freedom in controlling the particles as the user can define and dynamically reconfigure the illumination patterns that translate and pattern colloid aggregations [15]. The shape and crystallinity of the colloid aggregation can be changed rapidly by varying the illumination properties or altering the AC signal. Other electrokinetic colloid assembly techniques, though, are limited by the fixed nature of their electrode geometry. REP is simplistic in its implementation and powerful in its application, yet this technique has not been methodically characterized experimentally. The fundamental nature of its mechanics is understood, but the specific influence of these mechanisms on the aggregation’s crystallinity has not been extensively quantified. Herein, we will demonstrate that the mutual spacing between particles for the AC frequencies tested was governed primarily by dipole-dipole repulsive forces and the bulk hydrodynamic drag exerted on the colloids by the microfluidic vortex. This manuscript characterizes REP interparticle spacing as a function of the AC signal properties and applied illumination power. Experimental results were qualitatively similar to a simplified numerical simulation incorporating dipole-dipole repulsive forces and hydrodynamic drag. Information herein provides the foundation for future development of dynamically reconfigurable electrohydrodynamic colloidal crystals using REP or similar electrokinetic mechanisms.

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like dielectrophoresis, require patterned electrodes to generate non-uniform fields whereas REP

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EXPERIMENTAL

The REP devices used were constructed using commercially available indium tin oxide (ITO) coated glass slides and cover slips (SPI Supplies, West Chester, PA) separated with a microfluidic features created manually using 50 µm double-sided adhesive tape (Adhesives Research Inc., Glen Rock, PA). Holes were manually drilled in the glass slide to provide fluidic access. A low-conductivity aqueous solution of potassium chloride was prepared with a measured conductivity, σm, of 2.5 mS/m. Red-fluorescent 1.0 µm polystyrene particles (FluoroMax, Thermo Fisher Scientific Inc., Waltham, MA) were suspended in this solution before being injected into the REP microfluidic chip.

The REP system is composed of a highly focused laser being delivered to the microfluidic platform (Fig. 1b) and has been previously described [15]. A Nikon Eclipse Ti inverted microscope was used with a 60x water-immersion objective (1.2 NA). An infrared laser diode (975 nm, PL980P330J, ThorLabs, Newton, NJ) was controlled with a temperature controller (TED200, ThorLabs) and current controller (LDC220C, ThorLabs). The diode had stable performance above ~70 mW power which was too powerful for REP operation and characterization; therefore, an absorptive filter (NENIR05, ThorLabs) was incorporated to reduce the received laser power. All laser powers reported herein are with respect to measurements acquired immediately before the objective lens using a laser power meter (1918-C, Newport, Irvine, CA).

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Materials and Methods

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Figure 1. (a) Illustration of REP using a parallel-plate electrode. (b) Schematic of the hardware used for optically-induced REP.

Particle Identification and Image Processing Digital images were processed with MATLAB; the color images were converted to grayscale and individual particle locations were identified assuming a Gaussian distribution of fluorescence by each particle. Figure 2 shows an experimentally acquired image (Fig. 2a) and an artificial image (Fig. 2b) created by extracted particle locations. Particles that were identified far from the bulk aggregation were omitted from the subsequent analysis. Once the particles were identified, the center of the assembly was determined using a 2D center-of-mass calculation. Next, the radial distance for each particle was determined with respect to the aggregation center. This extracted location data was used for subsequent analysis to quantify colloid aggregation and crystallinity.

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DOI: 10.1039/C5SM00184F

Soft Matter


Figure 2. (left) Acquired experimental image of REP aggregation of 1.0 µm fluorescent particles. (right) Software-identified particle locations. First, the three closest neighbors for each particle was identified and used to calculate its each individual particle’s average interparticle distance. Next, the local particle density was obtained for by counting the number of colloids within an arbitrarily chosen 5 µm radial shell surrounding each particle. Last, a local bond orientational order parameter was implemented with

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(1)

where Nb is the number of nearest neighbors to the particle and θn is the angle between some fixed axis and the bond joining the colloid with a neighboring nth particle. The aggregation represents a perfect crystal as approaches a value of 1 but, otherwise, is more representative of a fluid for ≪ 1. For this analysis, Nb was defined as the number of particles within a radial shell value of 1.4 times the average distance of the closest three particle neighbors; this definition

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seemed to satisfy the identification of neighboring particles within the closest shell while excluding the next-nearest neighbors, this characteristic is critical regardless of the definition

For studies involving a range of parameters (i.e. throughout a range of AC frequencies and voltages), the overall assembly was characterized as a whole by averaging the particle-to-particle distance of all particles within the aggregation. However, this led to a relatively large standard deviation due to the radially-dependent distribution of interparticle spacing demonstrated for a typical REP aggregation (Fig. 2); in general, particles closer to the center were more compact than those near the aggregation perimeter. However, a reduction in this standard deviation corresponds to a more consistent, compact colloidal crystal. Numerical Simulation It was hypothesized that the crystallinity of the colloidal aggregation is governed primarily by the dipole-dipole repulsive force and microvortex-induced hydrodynamic drag. Therefore, an iterative dimensionless 2D numerical simulation was conducted that incorporated these two forces only and results were compared to experimental observations. The dipole-dipole interacting force between neighboring polarized particles is given by [24]

3 2 $ # %&3 cos * − 1,"̂ + &sin 2*,*12 4 "

(2)

where a is the particle radius, α is the particle’s polarizability, r is the center-to-center spacing between particles, and θ is the angle between the particles with respect to the direction of the electric field (E). For REP, particles are aligned orthogonal to field (θ = 180o) and are thus

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chosen for Nb [23].

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repelled from each other. Dipole-dipole forces are proportional to a6 and are frequency independent (except for the polarization term, α).

drag coefficient (f) which, for a sphere in Stokes flow, is 6πµa where µ is the fluid viscosity. For microfluidic experimental observations greater than a few milliseconds [25], it can be properly assumed that the colloid is translating at its terminal velocity with vp = F/f. The microfluidic vortex resembles inward sink-like flow on the surface of the electrode where the inward fluid velocity (vf) is characterized by vf = c1/R, where c1 is a constant and R is the radial location from the center of the vortex, corresponding to the center of the colloidal aggregation. Microfluidic particle image velocimetry [26] confirmed this trend for radial positions greater than an identified radial position, Ro, from which fluid velocity decreased linearly until the fluid reached its stagnation point at R = 0. A numerical simulation was conducted in MATLAB modeling these two forces with massless particles using a characteristic length scale L and time scale T. The 2D fluid velocity for the model was 345 &6 /895 ,8 5 for 8 5 < 895 and 345 &6 895 ,/8 5 for 8 5 > 895 ; here, C1 is a constant (C1 = 1, in units of L/T), 8 5 is the radial position (in units of L), and 895 is the characteristic radial position where the fluid velocity profile transitions (895 10 >). A dipole-dipole repulsive force is applied from each neighboring particle, i, resulting in a velocity given by 35 ∑ 6 &5 ,@ / &" 5 ,$, where C2 is a constant (0.1 to 20, in units of L/T), 5 is the dimensionless particle radius (5 >), and " 5 is the dimensionless interparticle spacing for each particle, i (units of L).

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For an applied force, the velocity of a particle (vp) can be determined by dividing the force by the

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The simulation was initialized with the placement of a square grid, centered about the origin, comprised 441 points (21 x 21 grid) spaced 3L apart with an additional randomized offset of up

calculated with >A, ∆DE345 + 35 F. The simulation was conducted for 4,000 time steps (for a total of 200 T). The interparticle distance and local particle density (using a local shell of 5 L) was obtained similarly as previously described in the colloid experiments. There are inherent weaknesses associated with this simplistic model. First, the particles are modeled as points as opposed to rigid spheres. Second, the coefficient of drag will be altered as it laterally translates parallel with the electrode surface [27]; hydrodynamic drag is further complicated with the influence of neighboring particles, especially for compact aggregations. The velocity of the flow around the particles is on the order of 100 µm/s with a corresponding Reynold’s number on the order of 10-4, justifying the Stokes flow assumption. However, Stokes drag interaction in groups of spheres is not so simplistic [28-30]. Further complicating matters is the interaction between the colloid and the electrode boundary. Data suggests that the presence of a boundary leads to an underprediction of drag in Stokes flow [31] and, though solutions exist in limited cases (i.e. [27, 32]), they ignore important effects such as Brownian motion and particle-particle interactions. Third, other electrokinetic mechanisms including DLVO theory [33], localized AC electro-osmosis [34], etc. where not included in this model. Despite these weaknesses, this model will provide qualitative and semi-quantitative results to determine if hydrodynamic drag and dipole-dipole repulsive forces are the primary mechanisms responsible for REP crystallinity and, therefore, enable a modeling-based approach for future studies. RESULTS AND DISCUSSION

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to ±1.5 L. For an iterative step of ∆T = 0.05 T the finite displacement for each particle (LP,i) was

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Experimental Results Figure 3a shows average interparticle distance for 2D REP colloidal aggregations imaged on the

range of AC frequencies (30 kHz to 89 kHz); the initial aggregation was acquired at a low frequency before subjecting the sample to higher frequencies. The aggregation becomes more compact with (i) increasing laser power and (ii) higher AC frequencies. At higher laser powers, the electrothermal microfluidic vortex increases in velocity, thus increasing the lateral inward hydrodynamic drag induced on the particles; fluid velocity is directly proportional to the applied optical power [26]. Although electrothermal fluid velocity is AC frequency dependent, the frequencies herein are low with respect to the charge relaxation frequency of the fluid (ω < σm/εm = 560 kHz) and, therefore, the microfluidic velocity is constant for the range of frequencies tested (< 90 kHz). Electrokinetic mechanisms, in general, weaken with increasing AC frequencies due to polarization relaxation. Here, the dipole-dipole repulsive force decreases at higher frequencies, resulting in a consistent trend with respect to decreased interparticle spacing (line fit, Fig. 3a). This trend continues until it approaches the characteristic frequency at which the particles are released from the surface (denoted by arrows in Fig. 3a); this is the point at which hydrodynamic lift overcomes a weakened particle-electrode trapping force. Figure 3b further illustrates this phenomenon, showing the rate at which particles are released at higher frequencies. Particles are released at lower frequencies for a larger applied laser power; this result is expected as the aggregation is exposed to larger hydrodynamic lifting forces.

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surface of the ITO electrode at a range of laser powers (8.6 mW to 15.1 mW), 5.4 Vrms, and a

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(a)

(b)

Figure 3. (a) The average particle-particle distance for an REP aggregation at 5.4 Vrms as a function of the applied AC frequency and laser power. (b) The number of trapped particles (normalized) using REP as the AC frequency is increased. The previous result characterized interparticle spacing of the aggregation as a whole; Figure 4 (left column) displays this information as a function of radial position from the aggregation center for a range of frequencies (40 kHz to 75 kHz) at a laser power of 12.1 mW and AC potential of 5.4 Vrms. The microfluidic vortex exhibits a sink-like behavior and, as such, the lateral hydrodynamic drag is weaker at larger radial locations resulting in a less-compact aggregation. The interparticle distance approaches a constant value as you approach the center of the aggregation (~1.1 µm). This lower limit appears to be independent of the range of AC frequencies tested suggesting AC electrokinetic phenomena do not play a role here and, instead, mechanisms like DLVO forces or hard sphere-to-sphere contact may be occurring. More extensive testing is needed to determine the nature of this lower limit value and, more importantly, determine a methodology to dynamically control this characteristic.

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Figure 4. Characterization of REP colloidal aggregations as a function of radial position at various frequencies (40 kHz, 50 kHz, 60 kHz, 70 kHz, 75 kHz) showing (left column) average

column) local bond orientational order parameter, . Each of these figures shows how the aggregation becomes more compact at higher frequencies. The applied voltage was 5.4 Vrms and the laser power was 12.1 mW. The local particle density for each cluster was also obtained (Fig. 4, middle column). These plots demonstrate that there is a distinct compact region (characterized with a low local particle density slope for smaller radial positions) and a diffuse region of greater colloid spacing (characterized with a higher local particle density slope). The transition between one region to the other is clearly pronounced at higher AC frequencies occurring at approximately 8 µm for 70 kHz and 6 µm for 75 kHz).

The diffuse layer of colloids is more pronounced at lower

frequencies, as at lower AC frequencies the particles become more dispersed due to their greater polarizability. As AC frequency increases the interparticle distance throughout the aggregation becomes more compact, demonstrating that the 2D assembly is more crystalline ( ~1, Fig. 4, right column) as the dipole relaxes. At lower AC frequencies the aggregation is more dispersed – though the value with this electrokinetic technique is that the colloidal crystal can be dynamically altered from a near-crystalline state (ex: 75kHz) to a more dispersive state at lower AC frequencies. However, the most consistent crystalline aggregations occur as the AC frequency approaches the value at which the colloids are released from the surface – a counter-productive characteristic with respect to colloid self-assembly processes. Therefore, understanding the nature of the particle-

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interparticle spacing, (middle column) local particle density for a radial shell of 5 µm, and (right

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electrode holding force is crucial for the future development of self-assembly methods that require consistent, compact colloidal crystals.

REP trapping at a constant frequency (35 kHz) and laser power (14.0 mW) as illustrated in Figure 5. The applied forces involved in the lateral interaction between particles (electrothermal hydrodynamic drag, dipole-dipole repulsion) are proportional to the square of the applied field (E2) and, thus, the resultant forces balance accordingly. This observation is consistent with previous results [17, 18] and, thus, crystallinity within an REP aggregation is voltage independent.

Figure 5. Interparticle spacing as a function of applied voltage for a fixed frequency (35 kHz) and laser power (14.0 mW). Particle spacing is nearly constant (dashed line), demonstrating that the governing physics exhibit the same dependency on the electric field (E2) and, thus, REP crystallinity is voltage independent.

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Varying the applied voltage (2.4 to 5.5 Vrms) did not affect the crystallinity of the aggregation for

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Numerical Simulations Numerical simulations were conducted to assess if electrothermal hydrodynamic drag and

(Fig. 4). Figure 6 shows selected iterations from a simulation sequence showing how aggregation would occur for a value of C2 = 10 (a movie is available in Supplemental Information, Movie 1). Colloids are represented with open circles, though the simulation itself does not account for hard sphere-to-sphere contact. Visually, the results are qualitatively similar to a characteristic REP aggregation (Fig. 2) with it being more compact in the center and less-so closer to its perimeter.

Figure 6. Selected iterations from a simulation sequence modeling 2D REP aggregation only incorporating dipole-dipole forces and sink-like hydrodynamic drag. Numerical simulations were repeated for a range of C2 (0.1 to 20), a variable corresponding, in part, to the polarization of the particle; lowering C2 is qualitatively similar to increasing the applied AC frequency with respect to the magnitude of the dipole’s polarization. The simulation reached a steady state at the end of the iteration period (200 T) and the interparticle distance as a function of their radial position was determined (Figure 7). As C2 decreased, corresponding to dielectric dispersion, the aggregation become more compact and approached a near-constant interparticle value for small radial distances (< 5 L). The particle spacing increased with radial distance, following a polynomial-like trend, especially for larger C2 values. Qualitatively, the

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dipole-dipole repulsive forces were the dominating mechanisms guiding the previous results

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numerical simulation (Fig. 7a) follows the frequency dependent results (Fig. 4, left column), suggesting that the microfluidic vortex and dipole-dipole repulsive forces are the dominant mechanisms governing crystallinity within an REP aggregation. Further, the simulated local

disperse, and thus lower local particle density values, at higher polarizabilities.



particle density (Fig. 7b) qualitatively agrees with the experiments in that it becomes more

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Figure 7. Results from the numerical simulation showing (a) normalized interparticle distance (with respect to L) and (b) local particle density with a shell radius of 5L as a function of radial position for various C2 values. The higher the C2 value, the greater the dipole-dipole repulsive force (corresponding, for this study, to lower AC frequencies). Future numerical simulations will incorporate hard sphere-to-sphere constraints. This simulation, though, provides a good qualitative description of the nature of REP aggregations such that the dynamic electrokinetic tuning of colloidal crystals can be explored. Further, this result suggests that REP could quantify the polarization of colloids trapped within an aggregation, a feature that would aid in the characterization of particles, including biological species. CONCLUSIONS It has been established that optically-induced REP particle aggregation and colloidal crystallinity is a function of laser power, the applied AC signal, and particle characteristics (diameter, surface

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chemistry, etc.). Here, an in-depth look at interparticle spacing, local particle density, and local bond order as a function of radial position within the aggregation was explored as a function of applied AC frequency. Results herein demonstrated that REP has the capability of creating local

AC frequency. Modeling suggests that mutual colloidal spacing within the aggregation for our range of tested AC frequencies is driven primarily by dipole-dipole repulsive forces and lateral hydrodynamic drag. The former is governed by the AC frequency dependent polarizability of the particle; thus, dynamically tunable electrokinetic 2D REP colloidal crystals are feasible. Experimental results further demonstrated that mutual particle spacing within the aggregation is voltage independent for the range tested herein. This work provides the foundation for future research of dynamically tunable colloidal crystals where crystallinity is tuned through the careful balance of hydrodynamics and electrokinetics. This simplified model will be improved, including the incorporation of a hard sphere characteristic – this feature will enable more in-depth modeling that can look at electrokinetic colloidal patterning, translation, and tuning. Ultimately, electrokinetic tuning of 3D colloidal structures may be feasible with a combination of attractive/repulsive dipole-dipole forces and electrokinetically-driven hydrodynamics.

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a 2D colloidal aggregation whose crystallinity and local density can be tuned through the applied

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Reconfigurable swarms of nematic colloids controlled by photoactivated surface patterns.

Hexadecapolar colloids.

Fractal nematic colloids.