AC Electrophoresis of Microdroplets in Anisotropic Liquids: Transport, Assembling and Reaction

We describe the realization and controlled transport of water-based microreactors dispersed in a nematic liquid crystal and transported by application of an alternating electric field through the mechanism of induced charge electrophoresis. We characterize the propulsion speed of these microreactors in terms of droplet size, strength and frequency of the applied field and show how to use them to transport microscale colloidal cargoes and coalesce water miscible chemicals. Controlled motion of microdoplets in anisotropic fluids is a rich field of research which unveils new perspectives in the transport of water miscible chemicals or drugs.


Introduction
Water based microemulsions in oil phases are of fundamental importance in chemical and analytical sciences, due to the 15 possibility to encapsulate and deliver chemical or biological entities otherwise immiscible in the dispersion medium. The controlled transport of these microdroplets is of crucial importance for many applications related with lab-on-a-chip, 1 drug delivery, 2 or the realization of remotely addressable 20 micromotors. 3 In contrast to simple oils as dispersion media, anisotropic fluids like liquid crystals offer the advantage of showing a variety of phases and structures which can be easily controlled and changed via temperature or external fields. These features, in turn, could be used to manipulate the physical or 25 chemical properties of the dispersed droplets. 4 In this context, nematic liquid crystals (NLC) are complex fluids massively used in display technology, and characterized by rod shaped molecules which tend to orient their long axis along one direction, called director field. When a microscale particle is 30 dispersed in a nematic medium, the distortion of the director field caused by the inclusion leads to the formation of defects around the particle, which will mainly depend on the anchoring conditions at the particle surface. 5 For homeotropic anchoring, i.e. when the nematic molecules align preferentially perpendicular 35 to the surface of the particle, two main defects can arise: a point defect known as hyperbolic hedgehog, 6 or an equatorial Saturnring like defect 7 [ Fig. 1(a)-(c)]. A recent breakthrough in electric field transport of colloidal microspheres 8 showed that colloidal particles with point defects can be transported in a NLC by using 40 alternating current (AC) electric fields through the mechanism known as induced-charge electrophoresis (ICEP). 9 The electrophoretic motion of the particles is due to the fact that the point defect, in contrast to the symmetric Saturn ring, breaks the spatial symmetry, unbalancing the ionic flows created by the field 45 around the particle. The main advantage of this technique, compared to the standard capillary electrophoresis methods based on the use of a direct current (DC) field, is the absence of ion migration, avoiding electrochemical processes and steady flows, 10 thus making it suitable to transport also liquid rather than solid 50 inclusions. It is worth remarking that for ICEP to occur, the system must feature broken symmetries. For instance, this phenomenon has been also reported for Janus particles in aqueous solution, where the contrast between metallic and dielectric half surfaces results in unbalanced ionic flow and in particle motion 55 under AC fields. 9 In this respect, the use of NLC provides a more versatile strategy, compatible with droplets of any nature, since the introduction of structural anisotropies in liquid droplets is a technically challenging process. 11 We here demonstrate the controlled motion of water 60 microdroplets dispersed in a NLC and propelled in this medium via AC electric fields. Point defects generated by the microdroplets in the NLC break the fore-aft symmetry and enable controlled motion of the water droplets in the direction of the defect, even if the field is symmetric in time and space.
Moreover, we employ a NLC with negative dielectric anisotropy, which induces motion of the inclusions perpendicular to the electric field. We characterize the droplets velocity in terms of droplet size, frequency and strength of the applied field, and show that these droplets can be used as microreactors to transport in the 70 nematic medium nanoscale particles or to mix femtosized volumes of chemicals, ranging from 10 -14 to 10 -16 L.

Experimental part
The experimental cell was composed of two 0.7 mm thick microscope slides of size 15 × 25 mm 2 , coated with a layer of 75 indium-tin oxide (ITO), with surface resistivity = 100Ω/square (VisionTeck Systems). The slides were cleaned with a Micro-90 (Sigma-Aldrich) solution, dried and spin-coated with polyimide (PI-2555, HD-Microsystems), baked at 300 o C, and then rubbed with a velvet cloth to obtain planar alignment in one direction. The two plates were then separated by a polyethylene terephtalate spacer (Mylar, Goodfellow, nominal thickness 23 µm) and glued together along two sides with the ITO layers facing inwards. showing the typical population of particles with hedgehog defects in an experimental cell. The fraction of observed particles featuring a Saturnring was below 1%. Subsequent measurements were done for droplet size between 1 -6 µm, as indicated in the image.
Actual thickness of cells was measured via interferometric 15 techniques. Electrical contacts were made by eliminating part of the polyimide coating on the slides by using a suitable solvent (T9039, HD-Microsystems) and gluing wires with colloidal silver. Dispersions of aqueous microdroplets were created by adding 1 µL of Milli-Q water-based aqueous solution to 10 µL of 20 a nematic liquid crystal (MLC-7029, Merck) with a negative dielectric anisotropy, ∆ε = -3.6 at 1 kHz, followed by vortex agitation (IKA MS3 basic) for 3 minutes. Some tests were performed also by using the nematic liquid crystal MLC-2037 from Merk (∆ε = = -3.1 at 1kHz) and MBBA from Synthon 25 Chemicals (∆ε = = -0.53 at 1kHz). The emulsions were stabilized using 0.01-0.05 M Sodium Dodecylsulphate (SDS, Sigma-Aldrich) which, in turn, induced homeotropic alignment of the nematic molecules at the LC/water interface. The experimental cells were then filled by capillarity with freshly prepared 30 dispersions and sealed with glue. With this protocol we obtained suspensions of polydispersed water droplets with sizes ranging from 1 to 20 µm in diameter and a distribution peaked at a diameter of 3µm (Fig. 1). Sinusoidal electric fields were applied to the experimental cell by using a function generator (ISO-35 TECH IFA 730) feeding a power amplifier (TREK model PZD700). The voltages were monitored by a multimeter (HP 34401A) and were in the range 0 to 30 Volts peak to peak, while the applied range of frequencies varied from 0 to 100Hz. Experimental observations were performed with an optical 40 microscope (Nikon Eclipse 50iPol). Images and videos were captured with an AVT Marlin F-131C CMOS camera controlled with the software AVT SmartView 1.10.2. They were then treated and analyzed using the software packages ImageJ and IgorPro.

Results and discussion
In Fig. 1(a) and 1(c), we show optical micrographs of droplets featuring hedgehog (a) or Saturn-ring (b) defects. As shown in the corresponding schematics [ Fig. 1(b) and 1(d)], the hedgehog defect is observed as a dark circular spot which appears on one 50 side of the microdroplet, and oriented along the nematic director. As a result, the symmetry of the nematic director resembles that of an electric dipole. In contrast, the Saturn-ring defect displays a circular ring surrounding the microdroplet and features quadrupolar symmetry. In most of the experimental cells used in 55 this work, we find that the distribution of defects around the microdroplets was predominantly of the hedgehog-type, while only a small fraction of inclusions (<1%) feature Saturn-ring defects. For the studies reported below, we restrict our analysis to droplets of diameter less than 6 µm. These constitute the majority 60 of hedgehog particles [ Fig. 1(e)] and are less prone to buoyancy effects, which tend to pin larger droplets.
In Fig. 2(a), we show the geometry of our experimental system. Water microdroplets were stabilized in the NLC matrix with sodium dodecyl sulphate (SDS). This surfactant provides strong 65 homeotropic anchoring at the water/NLC interface, i.e. the NLC molecules tend to orient perpendicular to the surface of the inclusions. We observe that, once dispersed in the NLC, most of the water droplets display a point defect (hedgehog), arranged on one side of the particle, while few feature Saturn rings. The 70 suspensions of SDS stabilized aqueous microdroplets were enclosed between two transparent electrodes, treated in order to induce planar (i.e. parallel) anchoring of the nematic molecules at the surface of the cell along a direction determined by the buffing of the polyimide layer. The cell spacing (23 µm) was 75 chosen as a compromise to minimize the interactions with the cell substrates and to guarantee that most of the droplets where in the same observation plane. In order to completely decouple the AC electrophoresis from any residual linear (DC) electrophoretic contribution, we choose to 80 use a NLC characterized by a negative dielectric anisotropy, so the nematic director orients perpendicular to the direction of the applied field. 12,13 With this strategy, we transport the microdroplets always perpendicularly to the direction of the oscillating field. This has the further advantage that the motion 85 can be controlled along any arbitrary predesigned in-plane track in the NLC matrix. In our system application of an external AC electric field between both electrodes sets the droplets in motion always in the direction 15 towards the point defect, Fig. 2(a). As it was reported by Lavrentovich and co-workers, 8 depending on the LC used the motion could be towards or against the point defect for the same particles and under the same conditions of applied field. After testing different liquid crystals, we found that the motion of the 20 microdroplets was towards the point defects for MLC-7029 or MLC-2037, and against the point defect for MBBA. We characterize the transport properties of the microdroplets by measuring their average speed as a function of the strength E (Figure 3(a)) and frequency f (Figure 3(b)) of the applied field, 25 and as a function of the diameter φ for a fixed value of Ε and f (Figure 3(c)). In the first case, we observe that the droplets start to move above a threshold field E 0 ~ 0.5 V/µm and that the speed increases quadratically with the field, v ~ E 2 . This electrophoretic behavior in a nematic medium is in agreement with previous 30 work, 8,12 where it was found that the first nonlinear term in the speed was quadratic rather than cubic like in isotropic fluids. A quadratic term allows using a symmetric AC field to move the particles in the medium, since changing the field polarity does not affect the particle speed. We confirm this quadratic behavior by 35 fitting the experimental values with v=β(Ε−E 0 ) 2 , and we find E 0 = 0.49 V/µm. Also, we find that the dependence of the droplets velocity on the frequency of the applied AC field can be well described by invoking the induced-charge electro-osmosis (ICEO) model, which was originally developed for isotropic 40 fluids. 14 This model is based in the electro-osmotic flow that appears when a tangential electric field is applied to a charged surface. If the surface charge is fixed, the electro-osmotic flow is linear with the applied field. In contrast, if the surface charge is induced by the same applied electric field, the nonlinear 45 phenomenon of ICEO takes place. In ICEO, the first nonlinear term is quadratic with the electric field, thus allowing the use of AC and not only DC fields to generate electro-osmotic flow. If we have a spherical polarizable inclusion immersed in a liquid electrolyte and subjected to an electric field, a quadrupolar 50 electro-osmotic flow is formed around the inclusion, from its poles to its equator. The electric field first generates the inducedcharge screening cloud on the inclusion, and then it drives the resultant electro-osmotic flow, so the dependence on the electric field is quadratic. When using AC fields, it must be noted that 55 ICEO will only take place if the frequency of the field is low enough to let the induced-charge screening cloud form, but high enough to avoid screening of the electric field by the diffuse-layer charging at the electrodes. Following the model developed in Ref. [14], the velocity of the induced flow can be described by the following equation: (1) 5 being ω = 2πf. As proposed in Ref.
[8], this equation can be also used to describe the velocity of a particle in ICEP, where v 0 contains a quadratic dependence with the amplitude of the applied electric field, consistently with the data trend shown in Fig. 3(a). In Eq.
(1), τ c = λ D φ/2D is the droplet charging time and By varying the size of the microdroplets, we observe a linear increase of v with φ, at fixed strength and frequency of the applied field, which is consistent with the fact that larger droplets 25 induce stronger distortion of the nematic director and thus enable larger electrophoretic speed.
We next demonstrate that these liquid droplets can be effectively used as microcarriers to transport, mix or disperse solid particles or femtoliter volumes of aqueous solutions. First, we observe that 30 microdroplets with Saturn ring defects, although immobile, distort the motion of neighbouring droplets with point defects.
The attraction between dipolar and quadrupolar droplets is long range and mediated by the elastic distortion of the nematic medium. 17 We use this property to realize a localized cargo 35 release operation, as shown in Fig. 4(a). In particular, one microdroplet was previously loaded with polystyrene particles having 1.7 µm in diameter, and driven by an AC field towards a larger droplet characterized by a Saturn ring defect. The large droplet attracts the small one, and they coalesce releasing the 40 colloidal cargo into a larger volume of fluid.
Droplets with point defects feature highly anisotropic interactions. In particular, a microdroplet with a point defect can be considered as a dipole, with one charge located on the point defect and the one (φ = 4.3 µm), forming Prussian blue as a precipitate. In this particular example, the field was momentarily switched off to facilitate the assembly of the droplets. The AC field was then used to prompt coalescence and to drive the resulting droplet away from the reaction zone. The corresponding videos (Video 2 and Video 3) can be found in the Supporting Information other, of opposite sign, located inside the droplet. In general, two approaching inclusions in the NLC will thus try to assemble with 55 the defects in opposite sides. 18 In our case, we find that when driven towards each other, the microdroplets deviate from their collision trajectory. After crossing, their dipolar defects are in antiparallel configuration, and the two droplets attract and can coalesce into a larger one. In Fig. 4 The resulting droplet shows the typical dark-blue precipitate of ferric ferrocyanide, and initially features a Saturn-ring defect, which quickly transforms back into a hedgehog defect, allowing 5 to drive the reaction product to a desired location of the experimental platform. The process shown in Figure 4(b) is only an example of localized microreactions which can be performed with this technique. Our system also allows to explore a selfassembly scenario under AC fields. In particular, by modifying 10 the experimental protocol by introducing the ultrasonication of the NLC emulsions, we are able to further reduce the size of the microdroplets. We find that smaller water droplets, with diameters below 1 µm, were less prone to coalesce. In particular, we show in the Supporting Information (Video 4) that application 15 of the AC field was able to accumulate smaller droplets, while decreasing the frequency releases them in the nematic medium covering a larger area.

Conclusions
In conclusion, we have shown several strategies to transport,

SUPPORTING VIDEO FILES.
With the article there are four video files as support of the experimental results.
Video 1 (.AVI): Movie showing a water droplet with 6.5 µm of diameter and propelled at a speed of 1.7 µm/s by an AC field with amplitude, E = 0.7 V/µm and frequency, f = 10 Hz, Fig. 1(b) of the article. The droplets approach and coalesce in a larger one (φ = 4.3 µm), forming Prussian blue as a precipitate. In this particular example, the field was momentarily switched off to facilitate the assembly of the droplets. The AC field was then used to drive the resulting droplet away from the reaction zone, Fig. 3 1 and 4) was that the article did not present enough novelty to be considered as a Communications, while both referees suggest that an extended version could be suitable as a Paper. We follow their recommendations, and provide with this submission an extended version with more details on the experiments and the model employed in the paper. We also ask You to consider this version as a Paper. Moreover, we have addressed the other criticisms, raised by referees 3 and 4, who asked for a better description of eq. 1, and the fitting procedure. We have rewritten the relevant paragraphs in order to improve their clarity.
We hope that with these changes the manuscript is now suitable for Soft Matter.
Sincerely yours, Pietro Tierno Answer: Although droplets in the size range 1 to 20 microns in diameter are produced with our preparation methods, only droplets of 6 microns or less are taken into account in our analysis of the electrophoretic motion. Larger droplets tend to pin on the substrate, probably due to buoyancy effects as suggested by the reviewer. We have included a statistical study of the droplet size distribution in Fig.1 of the revised manuscript.
2. The definitions of tau_c and tau_e on page 2 are misprinted, ad "D" in the denominator should be apparently a subscript, not an independent variable.