Spontaneous Rotation of Nonlinear Pattern Formed by Aqueous

May 18, 2017 - Colloidal Suspension between ITO Electrodes during Electrolysis ... Takeo Sakawa,. ‡ ... sandwiched between two parallel ITO electrodes...
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Spontaneous Rotation of Nonlinear Pattern Formed by Aqueous Colloidal Suspension between ITO Electrodes during Electrolysis Perpendicular to Gravity Kazuya Sasaki,‡ Shuichi Sato,‡ Takahiro Shindo,‡ Takeo Sakawa,‡ Hiromu Sasaki,‡ and Masahito Sano*,‡ ‡

Department of Organic Materials Science, Yamagata University, 4-3-16 Jyonan, Yonezawa, Yamagata 992-8510, Japan S Supporting Information *

ABSTRACT: A colloidal fluid is found to rotate spontaneously during electrolysis when gravity acts perpendicular to the direction of an applied electric field. An aqueous dispersion containing charged colloidal particles is placed inside an O-ring sandwiched between two parallel ITO electrodes. A clip is used to hold the assembly together to prevent the liquid from leaking out. The assembly is positioned such that the electrodes stand vertically, i.e., the electric field during electrolysis points perpendicular to gravity. When a direct-current voltage is applied to initiate the electrolysis of water, a nonlinear colloidal pattern is formed by electroconvective flow. Moreover, the entire fluid rotates spontaneously about the O-ring center with a constant angular velocity. The rotational dynamics are governed by how strong and where the assembly is clipped relative to the gravitational direction. A new phenomenological relationship between the angular velocity, compression vector, and gravity is derived. Coupling of an electrochemical reduction reaction of the ITO film with electroconvection during electrolysis is proposed as a mechanism for the rotational motion.

1. INTRODUCTION Nonlinear patterns may form in a liquid under an external electric field when the liquid has properties sensitive to the electric field. A well-known example includes electrohydrodynamic convection induced in electrolytes, 1−3 dielectric liquids,4−8 and liquid crystals.9 In a standard configuration of the thin-layer geometry, a liquid is confined in a shallow space between two parallel plate electrodes. When an electric field is applied, a convective flow is induced across two plates. If the flow is made visible, for instance, by an addition of dye or an observation under a polarized light, various self-organized patterns such as cells, ribbons, rolls, and so forth are recognized. These nonlinear patterns emerge from the interaction of the electric field with an excess charge density of electrolytes or with uniaxially oriented liquid crystalline molecules. When a simple liquid contains colloids, either colloidal particles organize themselves or an electric-field-induced convective flow carries them to form self-organized patterns. An alternating-current electric field applied on colloidal suspensions has been known to produce highly ordered patterns under various conditions.10−17 Although the conditions are relatively limited, a direct-current (dc) electric field also produces selforganized patterns.18−26 All the patterns reported to date remain stationary once a stable pattern is established. In this paper, we use electroconvection to refer to a convective flow induced by dc electrolysis when a fluid contains electrically charged colloidal particles.18 A standard setup used to study electroconvection consists of two flat transparent electrodes and a thin O-ring. Indium tin oxide (ITO) is used as © XXXX American Chemical Society

an electrode material. An aqueous solution containing charged colloidal particles, such as black ink or milk, is poured inside an O-ring sandwiched between the electrodes (Figure 1a). A clip is used to hold the assembly together so that the liquid does not leak out. When a dc voltage is high enough to cause electrolysis of water, electroconvection is induced in the colloidal fluid. The electroconvective flow places colloidal particles in a nonlinear pattern consisting of packed nearly hexagonal cells over the electrode surface, resembling Rayleigh-Bénard convection.27 This pattern formation has been explained as follows. The charged colloidal particles are moved toward the countercharged electrode by electrophoresis. At the same time, they disturb the ionic flux produced by electrolysis, inducing an electroconvective flow of water around them.21 This flow produces hydrodynamic pressure around the colloidal particles, causing them to draw near one another.22,23 The enlarged colloidal aggregates further disturb the ionic flux and induce stronger electroconvective flow. As a result, the particles are gathered at the edges of electroconvective rolls near the electrode surface.24 In the standard configuration, in which the assembly is laid horizontally (the electrode’s face up), the pattern changes its shape, but remains stationary.26 There are many similarities between electroconvection and Rayleigh-Bénard convection. The size of the nearly hexagonal cells formed under each type of convection is determined uniquely by the depth of the fluid, or the distance between the Received: April 28, 2017 Published: May 18, 2017 A

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Figure 1. (a) Experimental assembly. (b) Clip position. (c) Relative orientation of flows. Electroconvective rolls occur perpendicular to the electrode surface as the entire pattern rotates along the surface. The compression vector is directed from the clip toward the center of rotation on the vertical plane.

electrode was shown to be a possible source of the rotational motion.

two parallel electrodes in the present case. Whereas a temperature gradient, which is a common variable in controlling Rayleigh number, is a threshold parameter for Rayleigh-Bénard convection, it is the applied voltage that determines whether electroconvection will occur. In RayleighBénard convection, as a part of the fluid is moved closer to the upper surface, its density increases due to a decrease in temperature. The inverted density gradient leads to gravitational instability, resulting in downward flow. In contrast, there is no temperature gradient throughout the fluid in electroconvection, and gravity does not enter as a relevant parameter. This description holds for the case in which the assembly is laid horizontally, i.e., gravity is parallel to the electric field. In this study, the assembly was held vertical so that gravity acted perpendicular to the electric field (Figure 1a). In this study, we show that the result is the rotation of the entire fluid. First, the motion was analyzed with a focus on finding relevant physical parameters to derive a phenomenological relationship. We found that these parameters included not only gravity but also a kind of nonuniformity caused by clipping the ITO electrodes. After excluding electrical and hydrodynamical effects as the nonuniformity, an inhomogeneous electrochemical reduction reaction of the negative ITO

2. METHODS As a standard procedure, a Teflon O-ring with inner and outer diameters of 21 and 37 mm, respectively, and a thickness of 1.0 mm was sandwiched between two ITO (Geotec Inc., 10 Ω/sq) flat plates (25 × 50 × 1 mm3). For the spacing dependence study, Teflon O-rings with the same ring size but having varying thicknesses were used. A colloidal suspension was poured inside the O-ring to fill the entire space. A metal clip with a spring constant of 2.2 N/mm was used to hold the entire assembly together so that no liquid leaked out when the assembly was positioned vertically (Figure 1a). The clip was positioned so that its contacting edge aligned tangentially to the inner circumference of the O-ring through the ITO plates (Figure 1b). The largest source of error came from setting the direction to which the clip points, corresponding to the clipping angle (θ), which might be as large as ±2°. The colloids used in this study included carbon nanotubes, black ink, milk, and fluorescent polystyrene particles of controlled sizes. A dc voltage of 4.0 V was applied to initiate electrolysis at room temperature in an ambient environment. No other electrolytes B

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Figure 2. Images of rotating pattern. The width of a cell is about 1 mm, which agrees with the electrode spacing. The number in each image indicates the amount of time (in seconds) elapsed after the voltage was turned on. An arrow is drawn to illustrate the trajectory of a point.

were added so that the current remained approximately 1 mA during the entire process. Because all colloidal materials were colored, nonuniform distributions of colloidal particles were directly observable by an optical microscope. Any changes in the particle distribution over the entire O-ring area were recorded by a video camera attached to a vertical microscope. The angular velocity was calculated by measuring the angle that an arbitrary point in a pattern made over a given period.

3. RESULTS AND DISCUSSION 3.1. Rotational Dynamics. Figure 2 is a series of images showing the temporal development of the electroconvective pattern when polystyrene particles (average size 1.0 μm, concentration 0.1 mg/mL) were used (also see SI Video for black ink). White regions correspond to regions of high particle density. Initially, the colloidal particles were uniformly distributed. Upon the application of a dc voltage, they moved toward the counter-charged electrode surface by electrophoresis and remained near the surface, as confirmed by microscopic observations made through the side face of the electrodes. In this experiment, all colloids were negatively charged and a pattern appeared on the positive electrode side. A certain amount of time (in this case, 30 s) is required to develop the full electroconvective pattern. The pattern characteristics were found to be identical to those in the case in which the assembly was laid horizontally.26 In the horizontal orientation, the pattern thickened gradually as more particles were gathered but remained stationary. In the vertical orientation, the entire pattern rotated about a common center. For a symmetric geometry, as shown in Figure 1a, the rotation center was close to the center of the O-ring. Every electroconvective cell rotated with the same angular velocity synchronously such that the entire pattern was maintained without randomization. Figure 3 shows temporal changes in the angle that an arbitrary point of a pattern made

Figure 3. Angle that an arbitrary point makes after the voltage is turned on. The number listed on the right is the voltage. The constant angles at longer times are artifacts produced by the inability to follow the point due to particles settling downward.

with respect to the initial position at the time of voltage application (t = 0) at various voltages. The linear relationship between angle and time indicates a constant angular velocity. Previous studies on electrohydrodynamic convection of dielectric fluids in the vertical configuration have demonstrated pattern formation but without any rotational motion.28,29 Figure 1c indicates the geometrical relationship between the flows. Electroconvection occurred perpendicular to the electrode surfaces, and the hexagonal cells (Actually, the cells are composed of heptagons, hexagons, and connected ribbons. They are idealized to be hexagons in Figure 1) appeared at the edges of electroconvective rolls. A pattern composed of closepacked cells filled the entire electrode surface and rotated about the O-ring center in the vertical plane. The fluid was at rest when the voltage was turned on. Presently, we do not know how the motion evolves. By the time the pattern is fully developed such that we can follow its C

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The Journal of Physical Chemistry B movement, the motion is already in a steady state. Even during this steady state, particle aggregation continues. At some point, these aggregates grow large enough to start settling downward. The following subsection discusses the dynamics that occur after the angular velocity has become constant and before the settling motion has taken place. Under the present condition, the settling motion started before gas bubbles produced by electrolysis became large enough to be visible. Thus, the appearance of gas bubbles is not relevant. 3.2. Voltage Dependence. As shown in Figure 3, the time required for a pattern appear decreased with increasing voltage, as in the horizontal case.26 The slopes corresponding to the angular velocities were nearly constant among all voltages within an experimental error. If the voltage is turned off during rotation, the self-organized pattern continues to rotate for a short while, but gradually disappears as the small particles diffuse apart or the larger aggregates start settling downward. Particle motions indicate that the whole rotation seems to cease. Inertia alone is not enough to maintain the organized rotation. Electrolysis is required for both electroconvection and spontaneous rotation. 3.3. Spacing Dependence. We found that the size of each nearly hexagonal cell depended only on the distance between the electrodes, and their magnitudes coincide. Thus, for a 1mm-thick O-ring, the pattern consisted of 1 mm hexagons or connected ribbons as shown in Figure 2. This result is identical to that observed in the horizontal case,26 indicating that the pattern formed in the vertical configuration is due to electroconvection. The dependence of the electrode spacing on angular velocity is shown in Figure 4. The magnitude of the angular velocity

Figure 5. Effect of clipping angle on angular velocity. The electrode spacing was fixed at 1.0 mm. The solid curve is the sine function.

from the anode surface, when the clip is attached on the righthand side (θ > 0), the rotation is counterclockwise (ω > 0) for negatively charged colloids. The direction of rotation changes sign when the clip crosses the direction of gravity. The curve drawn in Figure 5 represents the function sin θ, which agrees with the data reasonably well. Additionally, we noted that when a stronger clip was used, the rotation became faster. In fact, because the clip is found to follow Hooke’s law with a force constant of 2.2 N/mm, the linear spacing dependence depicted in Figure 4 also indicates that ω depends linearly on the compression strength. These results suggest a cross-product relation ω∼C×g (1) where ∼ should be understood as “depends on”, g is the gravity vector, and C represents the compression vector, whose magnitude is equal to the compression strength and whose direction points from the clip toward the rotating center. To date, all attempts to find other variables that enter into eq 1 have failed (see Supporting Information S1). C appears to be the only variable controlling the dynamics. Because both g and C are constant, the time derivative of the right-hand side vanishes, which agrees with the experimental result indicating that the motion has a constant angular velocity. Because C is determined by the selected clip and its position, whereas g remains constant, two initial conditions determine the motion completely. To the best of our knowledge, the motion in a form of eq 1 has never been reported in any rotational dynamics. The fact that the resulting motion is rotational is expressed by the cross-product. If it were given by an inner-product, the motion would be parallel to the electrode plane, as in downward sedimentation or upward convection. In the horizontal configuration, the cross-product points along the electrode surfaces. This is the same direction as the strong electroconvective rolls, which may be one of the reasons that the present rotational motion has not been recognized in all previous horizontal thin-layer experiments. 3.5. Gravity. In order to examine a role of gravity on colloidal particles, their material, size, and concentration were changed. All rotational motions of the colloidal particles made of different materials, polystyrene, carbon nanotubes, black ink, and milk, were found to follow the angular dependence given by Figure 5. There was an optimum size of 1 μm for the polystyrene particles. Particles larger than 2 μm aggregated rapidly and began settling down before steady-state rotation was established, and particles smaller than 1 μm adhered to the

Figure 4. Effect of electrode spacing or compression strength on angular velocity. The clipping angle was fixed at 90°. The straight line is the least-squares fit.

depends linearly on the electrode spacing. A least-squares fit gives a straight line passing through the origin with a slope of 6.6 mrad/(s mm). Because the size of the hexagonal cells depends linearly on the spacing, the angular velocity scales with the cell size. As discussed in the following subsection, the electrode spacing also corresponds to the magnitude of the compressing force applied by the clip holding the assembly. 3.4. Clipping Dependence. The most striking finding is that the rotational dynamics are completely governed by the clip. Figure 5 shows the dependence of the clipping angle (θ) on the angular velocity ω, where θ is defined as the angle the clip makes with the direction of gravity (Figure 1a). Looking D

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identical to the colloidal electroconvection pattern left on the negative ITO electrode after the electrolysis. (We usually viewed the dynamical pattern on the positive electrode where the colloidal particles gathered. The brown pattern on the negative electrode was not visible until the electrodes was disassembled.) Thus, the ITO underwent reduction reaction during electrolysis. To observe the reduction reaction clearly, the same procedure with the present experimental configuration was applied without colloidal particles. Pure water did not conduct and produced no brown color. When 2% NaOH solution containing no colloidal particles, a typical condition to collect O2 and H2 in a school laboratory, was subjected to electrolysis, the ITO was reduced immediately, producing a uniformly brown circular disk over the entire inner area of the O-ring. When an electrolyte concentration was lowered so that the current remained about 1 mA as in the present colloidal solution, a brown colored pattern as shown in Figure 6

electrode surface because they were carried closer by electrophoresis. Similarly, although rotation occurred with a black ink at a high concentration of 0.25 mL/10 mL water, the particles aggregated and started settling downward at an early stage. Lowering the concentration caused an increasing amount of time to start the sedimentation and 0.01 mL/10 mL water was usually chosen as a standard condition. These results indicate that the rotational motion completes with sedimentation. Thus, gravity appearing in eq 1 should be treated differently from one causing the local sedimentation motion of the colloidal aggregates. 3.6. Compression Vector. Since clipping is a kind of the technical process, some kinds of physical or chemical properties must correspond to the compression vector C. The clip material and method were found to have no effects on the rotational dynamics (Supporting Information S1). Most interestingly, applying silicon grease to the entire area where the O-ring touches the electrode surface ceases rotation completely, simply reproducing the same result as the horizontal configuration. Grease eases the compressional force and seals the contact space. This result indicate that the compression vector C represents a type of nonuniformity caused by the contact between the O-ring and the electrode surface. It is conceivable that compressing only a small section of the O-ring causes one electrode surface to tilt with respect to the other. In order to examine possible effects of the tilted electrodes, we purposely sliced an O-ring along the radial direction so that its thickness varied linearly in one direction. Two ITO plates held by this O-ring were tilted in the direction of the sloped thickness. When the clipping angle was varied at a fixed tilt direction or the tilt direction was changed at a fixed clipping angle, the same clipping angle dependence as shown in Figure 5 was obtained regardless of the tilt direction (Supporting Information S2). Thus, the electrode spacing variation is not the nonuniformity. It is not necessary to have the nonuniformity over the entire contacting area. When the contact area of the O-ring and the electrodes was covered by grease but with a small portion left uncovered, typical rotation governed by C occurred irrespective of the position of the grease-free section. Furthermore, it is not necessary to have the entire O-ring space filled with the fluid. If the fluid fills only the bottom half of the space (the other half is filled with air), the fluid rotates as if the fluid−air interface is a part of the O-ring. When we divided the space inside the O-ring into a number of small chambers such that no fluid flowed across the chambers, the fluid in each chamber rotated independently as if the walls dividing the chambers acted as an O-ring. We also observed that the patterns close to either the O-ring or air bubbles that were included accidentally remained stationary. These observations suggest that the nonuniformity is not related to changes in the fluid flow near the O-ring contact area. 3.8. Reduction Reaction of ITO. The above result suggests a model in which the nonuniformity is transmitted through the ITO surface to affect the colloidal fluid. We found that point-by-point mapping of the local resistivity of the ITO surface in air without the colloidal suspension showed no resistivity variation by clipping. Thus, C is not related to stressinduced resistivity. ITO is known to be reduced electrochemically under certain conditions.30 The reduced ITO consists of metallic particles, has a dark brown color, and is less conductive. We have recognized a dark brownish pattern

Figure 6. Pattern formed by the reduced ITO electrode without colloids and its trace. The trace of a smaller spiral region may not be connected correctly and the spiral direction may be opposite. The black arrows indicate gravity (g) and the clip position (C). The vertical line is shifted from the middle position away from the clip side.

appeared gradually on the negative ITO electrode. The pattern consists of two spirals separated by a vertical line. It is difficult to identify the spiral direction (clockwise or counter-clockwise) in each region and we do not know if they share the same direction. We found that, even if a pattern of one side was disturbed externally, for instance, by air bubbles, a pattern of the other side developed fully. In fact, many repetitive experiments have produced two vertically separated regions with an independently developed pattern in each region. The patterns included spirals, circles, and cellular ribbons. In Figure 6, two spirals happen to share the same location at their separating interface, resulting in a brown vertical line. Although there were many cases where we could not specify a separating line as two brown patterns did not share the same location, we could easily recognize different patterns produced on the right and left sides with respect to the gravitational direction. There has been no previous report of the vertically separated reduction of ITO and the mechanism is not known. Since electroconvection has been recognized previously with electrode materials other than ITO,10−26 an inhomogeneous reduction of ITO is not required for electroconvection. Then, it is reasonable to assume that inhomogeneous ionic flows accompanying electroconvective roles affect an extent of the reduction reaction. On the other hand, since the brown part conducts less than the transparent area, electroconvective flow E

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The Journal of Physical Chemistry B will be different over the regions of reduced and unreduced parts of ITO. These considerations suggest that the electroconvective flow can couple with the electrochemical reduction reaction if both processes proceed at similar rates. When the ITO electrodes were set in the horizontal orientation without colloids, a stationary brownish pattern which was identical to the hexagonal pattern of colloidal electroconvection filled the entire region inside the O-ring. In this case of the horizontal configuration, a pattern of the electroconvective roles coincides with a pattern of the electrochemical reduction. In the case of the vertical orientation, the electrochemical reduction is no longer symmetric against the gravitational direction and proceeds independently in each vertically separated region. The electroconvective flow over such composite regions will be affected, but cannot behave independently due to continuity condition. Two processes no longer share the common spacial dependence and their coupling may lead to different outcomes including the rotational motion. An introduction of charged colloidal particles enhances inhomogeneous ionic flows, which have amplifying effects on both electroconvective flow and electrochemical reduction. In this case, the nonuniformity represented by C corresponds to a difference of the reduction pattern between two regions. Also, the vertical separation links gravity to the rotational motion, suggesting that g as depicted in eq 1 originates from a reference direction of the inhomogeneous reduction of ITO. This is consistent with our result that g should be treated independently of gravity causing colloidal sedimentation. The right arrow in Figure 6 indicates the compression vector C. The vertical brown line is shifted horizontally from the middle so that it positions away from the clipping side. Other than this shift, however, there is no symmetry breaking in the spiral pattern directly related to the position of C. When the position of C was varied, both the amount of shift and the pattern in each region changed. In all cases, the changed pattern did not show any symmetry breaking with respect to C. Unfortunately, we could not find the exact location of a separating line in many cases as explained above, and were not able to quantify a relation between the shift and C. The correspondence between the separating line with g, however, suggests a possibility that C controls the shifted amount, which in turn, determines an unbalance between the regional reduction of ITO.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81 238 26 3072. ORCID

Masahito Sano: 0000-0002-9050-5269 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by JSPS Grant-in-Aid for Exploratory Research (21654052).

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REFERENCES

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4. CONCLUSIONS A nonlinear electroconvective pattern made by a colloidal suspension under electrolysis is found to rotate under an electric field applied perpendicular to the direction of gravity. The rotation is characterized by constant angular velocity and is governed by the clip used to hold the assembly together. A new phenomenological relationship is established to describe this result and an inhomogeneous reduction reaction of ITO is proposed as a source of torque causing the rotation. In order to elucidate the mechanism further, the electrochemical reduction reaction of ITO film and its coupling with the colloidal electroconvection need to be examined.

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Effects of physical parameters; effects of tilting one ITO plate relative to the other (PDF) Video showing rotational movement with black ink as the colloid (MPG)

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b04009. F

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