Article pubs.acs.org/Langmuir
Propulsion of Active Colloids by Self-Induced Field Gradients Alicia Boymelgreen,† Gilad Yossifon,*,† and Touvia Miloh‡ †
Faculty of Mechanical Engineering, Micro- and Nanofluidics Laboratory, Technion − Israel Institute of Technology, Haifa 32000, Israel ‡ School of Mechanical Engineering, University of Tel-Aviv, Tel-Aviv 69978, Israel S Supporting Information *
ABSTRACT: Previously, metallodielectric Janus particles have been shown to travel with their dielectric hemisphere forward under low frequency applied electric fields as a result of asymmetric induced-charge electroosmotic flow. Here, it is demonstrated that at high frequencies, well beyond the charge relaxation time of the electric double layer induced around the particle, rather than the velocity decaying to zero, the Janus particles reverse direction, traveling with their metallic hemisphere forward. It is proposed that such motion is the result of a surface force, arising from localized nonuniform electric field gradients, induced by the dual symmetry-breaking of an asymmetric particle adjacent to a wall, which act on the induced dipole of the particle to drive net motion even in a uniform AC field. Although the field is external, since the driving gradient is induced on the particle level, it may be considered an active colloid. We have thus termed this propulsion mechanism “self-dielectrophoresis”, to distinguish from traditional dielectrophoresis where the driving nonuniform field is externally fixed and the particle direction is restricted. It is demonstrated theoretically and experimentally that the critical frequency at which the particle reverses direction can be characterized by a nondimensional parameter which is a function of electrolyte concentration and particle size.
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particles are restricted to travel to regions of high electric field strength where they become trapped9,10 and may not be considered active. In the current work, we demonstrate that when the insulating wall in refs 5, 8, and 10 is replaced with a conducting wall, active motion of metallodielectric Janus particles parallel to the wall is still attained at high frequencies (tens of kHz to MHz), although the velocity direction is reversed compared to that of ICEP.5,6 Specifically, whereas under ICEP, Au-Ps Janus particles travel with their dielectric hemisphere forward due to stronger induced-charge electroosmosis (ICEO) around the metallic hemisphere, at high frequencies, the JPs translate in the direction of their metallic end. In both frequency domains, the interface between the conducting and insulating hemispheres remains approximately parallel to the electric field (and perpendicular to the conducting wall). While the interaction of uniform particles with insulating11,12 and conducting walls13 and Janus particles with insulating walls14,15 have previously been examined, to the best of the authors’ knowledge, the current reversal and lateral translation has only been previously mentioned in an unpublished paper by Suzuki et al.16 with no explanation regarding the underlying physical mechanism.
INTRODUCTION Applications for the precise manipulation of active colloids in microfluidic systems range from separation and targeted delivery to bottom up manufacture of smart-materials.1 Recently, the combination of such colloids with externally applied fields has been used to successfully restrict the degrees of freedom of their motion with demonstrated outcomes including precise alignment, directed control of micromotors along predetermined pathlines, and cargo transport (see, for example, refs 2 and 3 and references therein). In applications where external fields are already present or deemed necessary for enhanced control, it is worthwhile to consider that, beyond alignment, low frequency (kHz) uniform AC electric fields have also been used to induce self-propulsive behavior (wherein particles are not restricted to specific field lines and are capable of exhibiting group behavior4) of metallodielectric Janus particles (JPs) via “induced-charge electrophoresis” (ICEP)5,6in which case the necessity for catalytic propulsion and the accompanying reliance on fuels which are potentially bioincompatible can be circumvented. As the frequency of the applied field exceeds the charge relaxation time of the electric double layer (EDL), the induced charge flows and thus the ICEP mobility decays to zero5−7although particles in close proximity have been observed to form chains due to dielectrophoretic forces.8 Introduction of nonuniform fields can result in positive dielectrophresis (pDEP) of Au-Ps JPs at high frequency, although in contrast to ICEP, the © XXXX American Chemical Society
Received: May 8, 2016 Revised: August 10, 2016
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Figure 1. Experimental setup. (a) Side view. (b) Cross section A−A from part a corresponding to the view from the microscope. Across all frequencies, JP motion occurs in the x−y plane, while the interface between metallic and dielectric hemispheres is parallel to the electric field.
watercan be obtained to MHz while the change in direction offers an extra degree of control for directed motion. The greatest potential impact, however, becomes apparent when we look beyond the induced gradients as a novel propulsion mechanism and recognize that their translation with the JP effectively transforms it into a mobile floating electrode which can be activated on demand and externally controlled. Such a phenomenon has immediate applications toward cleaning separation, analysis, and targeted delivery, including the potential to transform the widespread technique of DEP based sorting.33,34
Recently, at low frequencies, reversal of dielectric dimers has been attributed to asymmetric electrohydrodynamic flow over the conducting substrate.17 Although such flows are shown to decay to zero at high frequencies,17,18 high frequency flow reversal has been previously observed in both alternating current (ACEO)19,20 and traveling wave (TWEOF) electroosmosis21,22 (including in low conductivity electrolytes) over active electrodes as well as in electrothermal flow.23,24 In the latter case, the reversal can be predicted from the expression for the electrical body force,23 whereas, in the former, additional nonlinear mechanisms including Faradaic reactions25−27 and steric effects due to ion crowding19,28 within the EDLs are necessary to explain this phenomenon. However, as will be discussed in the sequel, the current experimental conditions do not seem to satisfy the scaling necessary to induce such effects. Additionally, measurement of flow fields around stagnant particles using μPIV as in ref 7 shows a notable absence of hydrodynamic flow at high frequencies. Previously, it has been shown that a homogeneous ideally polarizable particle adjacent to a conducting wall will experience an attractive force in the vertical direction (perpendicular to the wall) as a result of symmetry breaking.29 In the case of a Janus particle, the symmetry is also broken in the horizontal direction and it is proposed that the localized, asymmetric nonuniform electric field, induced by the dual asymmetry of the particle and the wall, acts on the induced dipole within the particle to drive net motion. We have termed this unique propulsion mechanism “self-dielectrophoresis” (sDEP), to reflect the fact that, despite the external applied field, the gradients necessary to induce motion arise from the proximity of the particle itself to the conducting channel wall, rather than being an inherent part of the system, produced by either channel or electrode geometry as in traditional DEP.30 Accordingly, in contrast to DEP, particles driven by sDEP may be considered active colloids, since although there is an external field, the gradients necessary for motion are induced locally on the particle level and, as a result, particles are not restricted to traveling toward geometric regions of high (pDEP) or low (nDEP) field strength2,4,31 but may translate along individual pathlines and exhibit group behavior. The critical frequency (ωcr) at which the particle is observed to switch direction is presumed to represent the point just after the dipolphoretic (DIP) velocity32an umbrella term used to encompass the generally opposing DEP and ICEP velocitiesequals zero. It is shown both theoretically and experimentally that ωcr depends on the electrolyte concentration C0 and particle radius a. A number of important outcomes arise from the current study. First, we extend the frequency range under which finite motion of JPs in electrolytes of low conductivityand even DI
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EXPERIMENTAL SECTION Janus particles 3, 5, 10, and 15 μm in diameter were manufactured by coating green polystyrene spheres (Fluoromax) with 10 nm Cr followed by 30 nm Au according to the protocol outlined in ref 35. To enable selective illumination, the 300 nm Ps particles (Fluoro-max) used in Figures 4 and S1 are red. For each electrolyte concentration, particles were rinsed three times with KCl electrolyte of the desired concentration before being entered into a cell containing the desired electrolyte solution. For the experiments on mobile particles (Figures 2, 3, and 5), a small quantity (∼9 × 10−5 M) of nonionic surfactant (Tween 20 (Sigma-Aldrich)) was added to the stock DI solution used to make all the electrolyte concentrations in order to minimize adhesion to the ITO substrate.36 On the other hand, μPIV measurements were taken without the addition of surfactant to the solution according to the protocol outlined in ref 7. To decrease error due to slight variations in concentration and cell conditions, measurement of the critical frequency for each conductivity (Figure 5) was performed for all particle sizes in a single cell. The experimental chamber consisted of a 120 μm high silicone reservoir (GraceBio) sandwiched between an ITO coated glass slide (Delta Technologies) and an ITO coated coverslip (SPI systems), as illustrated in Figure 1. The AC electric forcing was applied using a signal generator (Agilent 33250A) and monitored by an oscilloscope (Tektronix-TPS-2024) and kept constant unless otherwise noted at 5Vp−p ± 2% corresponding to a field of 42 kV/m. Observation of the electric field gradients between the substrate and the JP (Figure 3) was performed on a Nikon Eclipse Ti-E inverted microscope equipped with a Yokagawa CSU-X1 spinning disk confocal scanner and Andor iXon-897 EMCCD camera, coverslip side down, and images were magnified with a ×60 oil immersion lens. Mobile particles were observed under a Nikon TI inverted epi-fluorescent microscope and recorded on a Andor Neo sCOMS camera for a minimum of 30 s at a rate of 5 frames/s with either ×10, ×20, or ×40 magnification depending on the particle size. Particle B
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Figure 2. (a) Sample frequency dispersion of 5 μm (in diameter) Janus suspended in KCl electrolyte of varying concentration. For convenience, JPs translating with Ps hemisphere forward have been designated as positive while Au hemisphere forward is negative. Superimposed microscope images showing the path of 15 μm JPs in 5·10−4 M KCl at (b) 50 kHz (forward ICEP dominated motion) and (c) 1 MHz (backward, sDEP dominated motion). The applied voltage is 5Vp−p. Error bars indicate the standard deviation of the average velocity of multiple particles in the same experimental cell.
velocities for the frequency dispersion (Figure 2) were extracted by tracking particle displacement in Matlab and averaging the velocity over the number of mobile particles, where the error bars represent the standard deviation of the average velocity. Accuracy of the code was initially verified by comparing the velocities obtained using this method with that used in ref 35. The critical frequencies were recorded manually.
particles can turn and change direction but the stable orientation and linear translation are rapidly recovered. Finally, it is noted that, as the frequency increases, in the sDEP domain, a percentage of the Janus particles tend to remain immobile despite the presence of Tween 20, until, at frequencies beyond 5 MHz, there is no apparent motion. Further examination of the velocity of the backward translating particles indicated that it scales quadratically with the strength of the applied field (Figure 3), commensurate with nonlinear electrokinetic behavior. For comparison, we have also measured particles under identical experimental conditions at frequencies which are characteristic of ICEP and note that as expected the velocities also scale with the square of the applied voltage.5,35,38 One potential explanation for the particle reversal could be a change in direction of the ICEO flow. At moderate frequencies, it is possible that symmetry-breaking could engender this reversal even under the weak-field approximation,39 (see the Supporting Information) but since the velocity is still dependent on the formation of the induced double layer, it is expected to decay rapidly with frequencies above the charge relaxation time of the induced EDL and is unlikely to continue to the MHz range in accordance with experimental observations. Alternatively, it has previously been suggested that the onset of steric effects can result in high frequency reversal when high voltagesgreatly exceeding the thermal voltageare applied, generating a breakdown of the Poisson− Nernst−Planck (PNP) formulation by violating the fundamental assumption of dilute solution.19 However, previously, such a reversal has only been observed on active electrodes with voltages at least on the order of 100RT/F (where RT/F ≈ 25 mV is the thermal voltage), whereas a simple scaling analysis of the current setup indicates an induced zeta-potential of ξi ≈ E02a for the smallest particle examined (3 μm in diameter) of 5RT/F. Faradaic (redox) reactions at floating electrodes, acting as a bipolar electrode (BPE), are possible only when a sufficiently large driving electric field, E0, is applied across the chamber such that the potential drop induced between the solution and the end of the floating electrode is greater than the standard potential (1.23 V) of water electrolysis.40−42 However, in the current case, the induced potential drop (for even the largest 15 μm particle) is sufficiently small, i.e., |ΔVBPE| = |E0·2a| = 0.625 V < 1.23 V, so as to neglect such effects. Another
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RESULTS AND DISCUSSION Initially, the mobility of Janus spheres translating near the wall with diameters from 3 to 15 μm in electrolytes of varying KCl concentration across a broad range of frequencies was examined and a sample of a typical frequency dispersion is illustrated in Figure 2 for 5 μm (in diameter) particles in KCl of varying concentration. Two distinct domains are revealed: At low frequencies, the dispersion of the mobility takes on the typical form of induced-charge electrokinetic phenomena37 decaying toward both the DC and high frequency limitand the particles are observed to travel with their dielectric end forward in accordance with previously established ICEP of JPs.5,6,35 However, as the frequencies increase beyond the characteristic charge relaxation, ω (Hz) = Ds/(2πλ0a) (where Ds is the diffusion coefficient of the KCl electrolyte, λ0 is the dimensional Debye length, and a is the particle radius), rather than the velocity simply decaying to zero in accordance with ICEP, the particles are observed to switch direction and travel with the metallic hemisphere forward (Figure 2). In both cases, the orientation of the Janus particle is dominated by the alignment of the dipole with the electric field, which results in the interface between the metallic and dielectric hemispheres being roughly parallel with the electric field. After aligning, the particles translate parallel to the wall and are observed to travel along individual pathlines in a manner similar to that exhibited by autonomous self-propelling particles. For the micrometer size particles examined here, the electrostatic alignment and ballistic translation dominate random Brownian motion, although such fluctuations as well as nonuniformities in the surface coating could be responsible for the slight curvature of some JP pathlines such as that illustrated in the upper inset of Figure 2. Additionally, in the case where departure from ballistic translation is observeddue to particles encountering other particles or obstacles adhered to the substratethe C
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Figure 3. (a) Plot of the velocity of various particles at both frequencies characteristic of ICEP (positive) and sDEP (negative) as a function of the applied field squared illustrating that the velocity scales quadratically in the applied field. Parts b−d compare the scaling of the reversed (i.e., sDEP) velocity for a single set of data (10 μm (diameter) particles in DI water) according to E0, E02, and E04 showing that clearly quadratic scaling represents the best fit. Error bars indicate the standard deviation of the average velocity of multiple particles in the same experimental cell.
Information). Finally, in order to further examine the presence of any electrohydrodynamic mechanisms at high frequencies, we analyzed the high frequency flow fields using μPIV (Figure S1 in the Supporting Information) according to the protocol outlined in ref 7. We observed a notable absence of any significant jetting or fluid flow at high frequencies. It is thus suggested that the dominant driving mechanism is not electro-convective in nature but rather electrostatic, so that, similar to dielectrophoresis, the net force is obtained by integrating the Maxwell stress tensor over the particle surface. Specifically, it is proposed that this force is derived from highly localized asymmetric field gradients, produced directly below the particle as a result of the dual broken symmetry of the Janus particle and its proximity to the channel wall, which act on the induced dipole of the particle as in dielectrophoresis. Since direct measurement of the gradient in the gap between the particle and the substrate is unfeasible, the presence of such gradients is verified indirectly by the motion of small (with respect to the JP diameter) 300 nm polystyrene (Ps) “tracer” particles. At low frequencies, the particles will be attracted to regions of high field strength via pDEP, transitioning to nDEP at the crossover frequency which is determined by the particle and electrolyte material properties. Using a standard quadrupole, this crossover frequency was characterized for 300 nm Ps particles suspended in DI as ∼2 MHz. Previously, we have shown that, at low frequency, EHD and ICEO flows compete with DEP forces and the tracers are convected accordingly preventing clear detection of field gradients.7 At high frequencies, however, beyond the relaxation time of the induced electric double layer, such flows decay to zero and we can easily observe the gradient of the field by the trapping of the tracers. For a particle which is facing with the gold side down (interface parallel to the substrate), trapping is uniform
alternative mechanism for reversal is Joule heating or irradiation of the light source, which operate across a broad range of frequencies and can result in both electrothermal (ET) flow (which is also characterized by reversal at high frequencies)23 and in the latter case thermophoresis of Janus particles.43 However, for the low conductivities used in this study, scaling analysis indicates that, even for the highest electrolyte conductivity, σ = 10−1 S/m, studied herein, the temperature increase is only ΔT ∼ 0.3 K based on ΔT ∼ σV02/2k (eq 44 of ref 23), where k = 0.6 W/mK is the thermal conductivity of water and V0 = 1.8 V is the RMS voltage. Additionally, on the basis of eq 54 in ref 23, flow reversal is expected to occur at ω ∼ 2σ/ε0 which corresponds to approximately 90 kHz and 6 MHz for the DI and 1 mM solutions, respectively, greater than an order of magnitude above ωcr (Figure 5). Neglect of electrothermal forces arising from Joule heating is also supported by the quadratic scaling of both forward and backward motion illustrated in Figure 3, since electrothermal flows arising from Joule heating are expected to scale as E04.23 In terms of light-induced electrothermal flow, we show that even a reduction of the intensity of the light source (130 W at its maximum) by a factor of 32 does not affect the measured velocities, supporting the rejection of light induced ET effects as a significant force in the system (Figure S3a in the Supporting Information). Such a result is important, as light induced ET flow cannot be discounted on the basis of the scaling of the velocity with the field, since it would theoretically scale with E02 23 in a similar manner to induced-charge and DEP effects. Additionally, we note that, in the absence of an electric field, no motion is observed, indicating that the light intensity and wavelength (which at 450 nm is well below the infrared wavelength of 1064 nm used in ref 43) are insufficient to drive thermophoresis (Figure S3b,c in the Supporting D
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Figure 4. Trapping of 300 nm Ps particles around stationary particles. (a) JP with the gold hemisphere facing down (interface parallel to the wall) effectively representing a homogeneous Au sphere. (b) JP with the interface aligned with the field corresponding to the stable orientation of a translating particle. Images were taken using a confocal microscope approximately 1 μm above the substrate. The applied voltage is 10Vp−p. Insets are Comsol simulations depicting the electric field gradients (normalized by the maximum of the homogeneous case) for (a) a uniform gold sphere and (b) a Janus sphere with its interface perpendicular to the wall. (c) Transition of 300 nm particles from pDEP (100 kHz) to nDEP (2 MHz) at the metallic hemisphere. Particle orientation is as depicted in part b; the applied voltage is 5Vp−p.
45 is combined with the imaging method15) can be obtained as a function of the Debye length (see the Supporting Information for a derivation). For simplicity, we have considered only the first order solutions for both ICEP and DEP when solving for ωcr. Although the incorporation of higher order terms will alter the precise value of ωcr, since the aim here is merely to determine the overall scaling, which remains the same, such extension has been left for future work. For moderate frequencies, below the Maxwell−Wagner limit, i.e.,
(Figure 4a), as, from the perspective of the wall, such a particle appears homogeneous. On the other hand, when the interface is perpendicular to the substrate and aligned with the field (corresponding to the stable position for a translating particle), trappingor evidence of strong gradientsis visible only at the metallic hemisphere (Figure 4b). The presence of highly localized field gradients between the particle and wall and the asymmetry induced by the JP is further supported by numerical simulations using COMSOL (inset of Figure 4a,b)see the Supporting Information for details. Moreover, it is noted that the increased intensity around the Janus particle in part b, reflecting greater attraction of the Ps particles, is in qualitative agreement with the numerical simulation which shows stronger gradients in the asymmetric case. That this trapping mirrors gradients of the electric field is further evidenced by switching the forcing frequency between 100 kHz and 2 MHz and observing the transition of the tracers from pDEP to nDEP (Figure 4c). When placed in a high frequency nonuniform electric field, bare Au-Ps Janus particles are always observed to travel toward the direction of high electric field (pDEP), due to the dominant polarizability of the metallic hemisphere.9,10,44 It thus seems reasonable that the electric field gradients illustrated in Figure 4 above would have the effect of propelling the JP in the direction of its metallic hemisphere. Theoretically, the interplay between the two mechanisms of ICEP and sDEP can be described according to the dipolophoretic theory, originally developed in ref 32 and elaborated for the specific case of Janus particles in ref 45, where the critical frequency, ωcr, at which the particles reverse direction occurs just past the point where the dipolophoretic velocity, or equivalently sum of the counteracting ICEP and DEP velocities, UICEP and UDEP, respectively, equal zero. On the basis of the theoretical formulation in ref 45, dimensionless expressions for both UICEP and UDEP (when ref
Ω MW =
ωλ 0 2 Ds
≪ 1, the full expressions can be simplified to
UICEP(Ω) ∝
K K + (A Ω)2 2
UDEP(Ω) ∝ −
where Ω =
ωλ 0a Ds
Ω2 K 2 + (A Ω)2
(1a)
(1b)
= Ω MW a/λ 0, A = 47 is a constant, and K ∝ a/
λ0. In accordance with the experiments, ICEP dominates DEP at low frequencies, while beyond the charge relaxation time of the induced EDL where Ω > 1, ICEP decays to zero according to Ω−2 while the DEP approaches its maximal value. It is emphasized that the simplified expressions in eq 1 are valid only for forcing frequencies which satisfy ΩMW ≪ 1. As the frequency increases, one must consider the full expressions for the symmetry breaking of the induced charge (see ref 45), in which case the DEP velocity begins to decay to zero. However, such decay corresponds with the limit of ΩMW → 1, or the charge relaxation frequency of the liquid which lies beyond the upper limit of the current theoretical formulation. Accordingly, it is emphasized that, although the experimental data in Figure 2 also shows a secondary decay to zero in the high frequency limit, it is uncertain whether this represents a true decay in the DEP mobility or the increased dominance of secondary effects E
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Figure 5. Plot of the critical frequency at which JPs begin to translate with their metallic hemisphere forward (a) for varying electrolyte concentrations, C0, as a function of particle diameter, 2a, and (b) for varying diameters as a function of electrolyte concentration. Experimental data is fit with a single fitting parameter c according to
ωcra1/2γ 3/2 Co3/4Ds
= c = 3·10−4 . Closed symbols stand for the frequency at which the first particle was seen
to translate backward while open symbols for the frequency at which no more particles were observed to move forward.
(characteristic of ICEP), at high frequencies, when moving under sDEP a proportion of particles remained immobile or became immobile after translating for a period of time. The latter phenomena in particular seems to be more pervasive in higher conductivity electrolytes, although we emphasize that such particles were for the most part not actually stuck to the wall; reverting the frequency close to the ICEP maxima or manually pumping the fluid in the channel resulted in the majority of particles moving. It is unlikely that this immobility is due to electrical contact (shorting) between the JP and the wall, since, in the cells with tracer particles, DEP trapping was still observed near the substrate, whereas COMSOL simulations indicate that in the case of full contact (electrical shorting) the contact region would be characterized by a local minimum of the field.
which cause the sticking (or immobility) of some JPs in the sDEP domain. The exact frequency at which the particles will switch is strongly dependent on the relative magnitudes of the ICEP and DEPthe latter being heavily dictated by the gap width, h, scaling as (a/h)5 (see the Supporting Information). However, qualitatively, on the basis of eq 1, it is clear that the onset of reversal (corresponding to UICEP + UDEP ≈ 0) will always scale according to ωcrλ0a/Ds ∝ √k so that ωcra2/Ds ∼ (a/λ0)3/2. Recalling next that, according to the Debye scale, the dimensional molar concentration of the electrolyte is given by C0 =
2
ε0RT 1/2
( ) where γ = ( ) γ λ0 −1
2F 2
(where ε0 = 80·8.854·10−12 C
V−1 m is the solute permittivity, R = 8.314 J K−1 mol−1 is the universal gas constant, T = 300 K is the temperature, and F = 9.648·104 C mol−1 is the Faraday constant). Thus, we find that ωcra1/2 γ 3/2 · D Co3/4 s
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= const , which provides the proper scaling for the
CONCLUSIONS To conclude, this work aims to rigorously demonstrate and characterize the frequency dependent reversal of active, metallodielectric Janus particles under uniform AC fields. It is proposed that the change in direction of the mobility at high frequencies is dominated by the response of the particle dipole to localized field gradients induced between the substrate and the wall, to produce a propulsion mechanism which we have termed “self-dielectrophoresis”. A dimensionless parameter, which controls the critical frequency at which backward motion is initially observed, is defined, and it is shown that this onset is a function of particle radius and electrolyte conductivity. Practically, this propulsion mechanism extends the frequency regime at which finite mobility may be obtained in electric fields to MHz, well beyond the low-frequency (tens of kHz) domain of previously established induced-charge electrophoresis, and offers an additional degree of control via frequency-dependent directionality. Additionally, the potential for the localized induced fields which drive sDEP to simultaneously exert a force on other components in the system suggests a limitless range of possible microfluidic applications including cleaning, concentration, targeted delivery, and transport.
critical frequency in terms of the solute concentration. For the current electrolyte, using Ds = 2·10−9 m2 s−1, we can evaluate γ3/2/Ds ∼ 2.7·10−6 M3/4 s/m1/2. The constant c, which is related to the permittivity contrast between the hemispheres of the JP (see the Supporting Information) can then be extracted as a fitting parameter. For the current system, we find that c = 3· 10−4 when ω is calcuated in Hz (Figure 5). It is noted that, since the onset of reversal is characterized by a very small velocity, its exact determination experimentally is somewhat complicated, since there exists a not insignificant range (to the order of tens of kHz), where in a given cell, while some particles have transitioned to backward motion, other particles of the same size translate forward while others remain still, exhibiting zero mobility. To account for this variation, in the following figure, we plot both the frequency at which the first particle was seen to translate backward (closed symbol) and the frequency at which no more particles were observed to move forward (open symbol) (Figure 5). Indeed, the existence of such a transition domain is reasonably to be expected due to the presence of small variabilities in the Janus particle geometries or local conditions at the wall such as surface roughness and is similar to the dispersion often encountered when trying to determine the dielectrophoretic crossover frequency (pDEP to nDEP response) due to the small signal-to-noise ratio of the DEP response around the crossover frequency (COF). However, it was also observed overall that while the Tween 20 successfully inhibited sticking that was exploited in ref 7 at low frequencies
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b01758. F
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Numerical simulations, micro-particle-image-velocimetry, supplementary equations, and negation of electrothermal effects (PDF)
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors would like to thank Tov Balli for assistance in executing the experiments and Dr. Sinwook Park in assistance in Janus particle preparation The authors would like to acknowledge US−Israel Binational Science Foundation Grant 2009371 and the RBNI and Gutwirth graduate fellowships. A.B. and T.M. acknowledge partial support from ISF 1945/14. The JP preparation was possible through the financial and technical support of the Technion RBNI (Russell Berrie Nanotechnology Institute) and MNFU (Micro Nano Fabrication Unit).
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