pH-Dependent Motion of Self-Propelled Droplets due to Marangoni

Jan 31, 2013 - ABSTRACT: Oil droplets loaded with surfactant propel themselves with a velocity up to 6 mm s. −1 when they are placed in an aqueous p...
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pH-Dependent Motion of Self-Propelled Droplets due to Marangoni Effect at Neutral pH Takahiko Ban,*,† Tomoko Yamagami,‡ Hiroki Nakata,† and Yasunori Okano† †

Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan ‡ Department of Chemistry and Chemical Engineering, Yamagata University,Yamagata 992-8510, Japan S Supporting Information *

ABSTRACT: Oil droplets loaded with surfactant propel themselves with a velocity up to 6 mm s−1 when they are placed in an aqueous phase of NaOH solution or buffer solution. The required driving force for such motion is generated on the interface of the droplets by the change in interfacial tension, due to deprotonation of the surfactant. This force induces Marangoni convection, which gives rise to a circulating flow inside the droplets. The droplets begin to move when the axis of this circulation deviates from the vertical line. This motion depends on the pH condition of the aqueous phase. When the initial value of pH is adjusted such that the pH exceeds the threshold at the equilibrium state, the droplets move spontaneously. It was seen that the droplets were independent of the material of the solid substrates because the droplets were not directly in contact with the surface of the substrate. The condition for the onset of this spontaneous motion was verified by comparing the prediction from the linear stability analysis with experiments. The stability analysis overestimates the value of the driving force, causing instability.

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INTRODUCTION A surface having a spatial gradient in wettability is capable of causing liquid droplets to be transported on it. Such a flow can be created several ways, including the thermal,1−3 electrostatic,4,5 electrochemical,6 optical,7,8 and chemical methods.9−18 Among them, the chemical methods can induce droplet motion without any external forces and control its motion with stimulus-responsive functions. Moreover, nano/micro synthetic solid objects have been developed on the basis of combing the concepts of autonomous chemical power generation and asymmetrical catalytic reaction over the past decade.19−22 Therefore, chemical methods are considered to be the most preferable method in the development of self-propelled objects for accomplishing particular tasks in microscopic spaces beyond the control of external forces.23−25 Liquid droplets can be moved by using two chemical means; the dewetting effect and the Marangoni effect. In the case of dewetting, the driving force can be generated passively using a surface with spatial variations in its surface free energy9,10,16,17 or actively using adsorption or desorption of a solute, rendering a change in wettability of the solid substrate underneath the droplets.11−15,18 There are two types of active motions: (Case I) after the droplet has passed, the substrate is changed in an irreversible way and (Case II) it recovers its initial state due to diffusion of the solute from the surrounding media to the surface. In each case, however, the substrate has to be capable of being adsorbed by solutes on its surface for producing the driving force. Thus, the range of application of these systems is © 2013 American Chemical Society

limited because the droplets can move only on specific substrates having pretreated surfaces. The other chemical method is the use of the Marangoni effect which is induced due to the change in interfacial tension on a liquid surface. The change in interfacial tension results from adsorption/desorption of solutes due to mass transfer across the interface. The resulting Marangoni effect induces convection in the liquid, giving rise to a net mass transport of liquids. Thus, the Marangoni convection allows the droplets to move in another liquid media without the above restriction because the movement requires no surface energy on the surface of a solid substrate.26−38 However, the spontaneous motion of free droplets by the Marangoni effect requires a reduction in the size of the droplets from 10 to 300 μm28,29,33,36,37 or a reduction in the drag force by floating the droplets on the surface of water.27,35 In this study, we show the pH-dependent motion of the oil droplets loaded with di(2-ethylhexyl) phosphoric acid (DEHPA) in the size of the droplets from 500 μm to 1 cm in an aqueous solution. The droplets moved randomly by the Marangoni effect due to the change in the surface activity of DEHPA. DEHPA became deprotonated as the pH level increases. Thus, the mobility of the droplet can be switched on/off as a function of pH. The droplets moved at neutral pH Received: December 3, 2012 Revised: January 21, 2013 Published: January 31, 2013 2554

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RESULTS First, we explain how to move the nitrobenzene droplets loaded with DEHPA in the aqueous phase of the NaOH or buffer solutions. A driving force for spontaneous motion arises from the deprotonation of DEHPA (Figure 1). The deprotonation of

in the buffer solution. The Marangoni convection drew the aqueous liquid of the surrounding media into the bottom of the droplets. The droplets were slightly levitated above the liquid film. Thus, the droplets moved regardless of the material of the solid substrates. Finally, we compared the experimental onset condition of the droplet motion with that of the linear stability analysis.

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Article

EXPERIMENT

DEHPA was purchased from Sigma-Aldrich. Phosphate buffers of reagent grade were purchased from Wako Pure Chemical Industries, Ltd. All chemicals were used without further purification. We used nitrobenzene with various concentrations of DEHPA as the droplet phase. The buffer solutions were used as the continuous phase without dilution. We measured the interfacial tension as a function of pH under equilibrium by the drop weight method. The experimental procedure of equilibrium interfacial tension is described elsewhere.39 An aqueous solution was prepared over a pH range 8−13.5 at initial condition by addition of NaOH. The prepared aqueous solution was in contact with an equal volume of nitrobenzene solution containing 0.1 M DEHPA. After the equilibrium was attained, the oil solution in the lower phase was drawn up using a highly regulated pump. An oil droplet was formed in the upper phase. Measurements then were carried out as a function of equilibrium pH. The values of pH change significantly in the equilibrium state because of the deprotonation of DEHPA. For example, the initial pH values 11.0 and 12.0 decreased to 2.9 and 5.3 in equilibrium, respectively (Table 1). The initial pH values did not change in equilibrium beyond pH 13.0.

Table 1. Relation between the Initial pH and Equilibrium and the Effect of pH on Droplet Motion in NaOH Solutions initial pH

equilibrium pH

movement

13.3

− 2.9 3.5 4.3 4.5 4.8 5.1 5.3 5.8 6.1 13.0 −

No No No Yes Yes Yes Yes Yes Yes Yes Yes No

Figure 1. Top: Deprotonation of DEHPA due to a change in pH. Bottom: Schematic representation of a self-propelled droplet. The deprotonated DEHPA decreases interfacial tension, inducing a circulating flow inside the droplet. The deprotonated DEHPA transfers to the aqueous phase. Pristine DEHPA is supplied to vacant sites of the interface.

DEHPA proceeds as pH is increased. The resulting DEHPA has a higher surface activity and decreases interfacial tension. When the oil droplet having DEHPA is formed in alkaline solution, the deprotonated DEHPA induces Marangoni convection along the droplet interface. This convection gives rise to a circulating flow inside the droplet, propelling the droplet. Sustained motion arises from the renewal of the interface. The deprotonated DEHPA transfers from the interface to the aqueous phase. Pristine DEHPA is abundant in the oil droplet and supplied to vacant sites of the interface. We measured the interfacial tension as a function of pH under equilibrium by the drop-weight method. The liquid/ liquid system consisted of water and nitrobenzene containing 0.1 M DEHPA. The pH value of solution was adjusted by adding NaOH. A neutralization reaction occurs between DEHPA and NaOH. The range from pH 7 to 12 is inaccessible because of the vicinity of the equivalence point. We show the equilibrium interfacial tension in the nitrobenzene containing 0.1 M DEHPA/water system. Figure 2 shows the effect of the equilibrium value of pH on equilibrium interfacial tension, γ. The interfacial tension suddenly decreased from 20 to 3 mN/m beyond pH 4 and leveled off beyond pH 6. DEHPA becomes deprotonated as pH is increased. The increase in the amount of the deprotonated DEHPA decreases the interfacial tension. Therefore, this experimental result yields a direct relation

Dynamic interfacial tension was measured by a pendant droplet method under nonequilibrium chemical conditions (Dataphysics Instruments, OCA35). Oxalate (pH 1.68), phthalate (pH 4.01), phosphates I and II (pHs 6.86 and 7.41), tetraborate (pH 9.18), and carbonate (pH 10.1) buffers were used as an aqueous phase without dilution. A nitrobenzene droplet containing 0.1 M DEHPA was formed in the different buffer solutions. The shape of the droplet changed due to the deprotonation of DEHPA. We then estimated dynamic interfacial tension from the droplet shape. The droplet behavior was recorded for 600 s at 25 frames per second. The aqueous phase of NaOH (or buffer solutions) was poured into a Petri dish of 6 cm diameter. The solution height was adjusted to 1 cm. The nitrobenzene containing 0.1 M DEHPA was used as the oil phase. A 0.1−200 μL oil droplet was formed in the Petri dish. The oil droplets sunk into the aqueous phase because of their own weight. We observed the motion of the oil droplets using a high-speed video camera (Keyence, VW-6000) at 60 frames per second. 2555

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The threshold of the initial pH value for spontaneous motion is 11.2 in our system. Lagzi et al. also reported that the floating droplets containing 2-hexyldecanoic acid on KOH solution can move spontaneously beyond pH 12 in a homogeneous concentration field.35 The propulsion requires the deprotonation of the surfactant because the deprotonation enhances surface activities of the surfactants. Thus, the pH of the solution has to be high. From a technical viewpoint, however, it is preferable that a droplet can move in a low pH field. The experimental results in our system indicate that the droplets should move spontaneously under the condition that the initial pH of the solution was prepared in to the pH range of drastic change in interfacial tension at equilibrium. Thus, the propulsion does not necessarily require such a high pH field. To verify the working hypothesis, we carried out the experiments using buffer solutions instead of NaOH solutions. Figure 4a shows an example of droplet motion in the phosphate buffer with pH 7.41. The droplet with a volume of

Figure 2. Effect of pH on equilibrium interfacial tension in the nitrobenzene containing 0.1 M DEHPA/water system.

between surface concentration of surface-active matter, Γ, and interfacial tension, γ. We can calculate the Marangoni coefficient of the system M = |dγ/dΓ| from this experimental result. The Marangoni coefficient is an important factor to estimate the driving force. The calculation procedure of the Marangoni coefficient is given in detail in the Discussion section. To confirm that there are no spurious effects on the movement of the droplets, we observed the behavior of 10 μL droplets in NaOH solution at pH 12.0, when the oil droplets did not contains DEHPA. The oil droplets settled to the bottom of the Petri dish and never moved. Next, we observed the behavior of 10 μL droplets containing 0.1 M DEHPA in NaOH solutions of various pH values. Figure 3 shows the

Figure 4. (a) Typical behavior of 0.1 μL droplet containing 0.1 M DEHPA in the phosphate buffer solution. The green arrows represent the direction of droplet motion. Time passes with increasing the number in the figure. (b) Trajectory of droplet motion at various sizes of the droplets. Observation times of 0.1, 1.0, 10, and 100 μL droplets are over 10, 4.0, 3.0, and 3.0 s, respectively.

0.1 μL showed irregular translational motion. A jetlike flow of material erupted out of the droplet and interfacial turbulence occurred. The material is considered as deprotonated DEHPA. One can see the range of change in concentration around the droplet due to the difference in the refractive index. The shape of the 0.1 μL droplet did not change within the resolution of the camera during the movement. Random occurrence of interfacial turbulence caused irregular motion of the droplet. The droplet yielded a white turbidity as the deprotonation of DEHPA proceeded. It indicates the formation of emulsion inside the droplet. The generated emulsion inhibits the renewal of the droplet interface, disturbing the development of convection. Thus, the movement of the droplets ceased after the droplets were filled with emulsion. A similar motion was observed in the other phosphate, the tetraborate and the carbonate buffers with pHs 6.86, 9.18, and 10.01, respectively, and the NaOH solutions at a higher pH than 11.2. The relation between pH values of the buffer solutions and droplet motion is summarized in Table 2. The equilibrium pH of these buffers lies in the pH region where the droplet can move in NaOH solutions. Note that droplets cannot move in the NaOH solutions adjusted to the same pH values at initial condition as these buffers. The droplets in the NaOH solutions cannot gain enough energy to move because the interfacial tension does not change due to a low amount of deprotonated DEHPA. The

Figure 3. Trajectory of droplet motion in NaOH solutions in the pH range from (a) 11.2 to 11.9 and (b) 12.0 to 13.3.

trajectories of droplet motion over 2 s as a function of initial pH. The droplets started to move randomly beyond pH 11.2, whereas the droplets remained immobile beyond pH 13.3. For a lower pH than 12.0, the moving distance is less than 1 mm for 2 s (Figure 3a). For a higher pH than 12.0, it stretches beyond 10 mm (Figure 3b). The relation between pH values of the solutions and droplet motion is summarized in Table 1. The initial pH range where droplets move spontaneously corresponds to the equilibrium pH where the interfacial tension decreases drastically. The self-propelled objects at nanoscale may move not due to self-propulsion but due to spurious effects, such as Brownian motion, convection, sedimentation, and bacterial contamination.40 The experimental result in our system provides a clear evidence that the motion is due to selfpropulsion. 2556

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droplet. A water pool was formed underneath the droplet. Thus, the droplet was not in direct contact with the surface of the substrate. The droplet was slightly levitated above the liquid film of the continuous phase. When the axis of the circulating flow deviated from the vertical axis, the droplet started to move in the inclined direction. Thus, the droplets in our system are independent of the physicochemical properties of the substrate. We investigated the relation between the speed and the size of the droplets. Figure 5a shows the instantaneous speed as a

Table 2. Effect of pH on Droplet Motion in the Various Buffer Solutions buffer

initial pH

equilibrium pH

movement

oxalate phthalate phosphate(I) phosphate(II) tetraborate carbonate

1.68 4.01 6.86 7.41 9.18 10.01

1.48 3.65 5.59 5.62 5.52 5.87

No No Yes Yes Yes Yes

crucial condition for droplet motion is not initial pH but equilibrium pH. We investigated the effect of droplet size on droplet motion. We found that the directionality of the motion increased as the size of the droplet was increased and a persistent length became longer (Figure 4b). Droplets become deformable beyond the capillary length [= (γ/Δρg)1/2, where Δρ is the density difference and g the gravitational acceleration].38 The capillary length of the droplet at 0.1 M of DEHPA concentration in the phosphate buffer is about 1 mm. The large droplets changed to a parachute shape and moved unidirectionally. The similar volume-dependent mode change was obtained in the NaOH solutions. The droplet behavior depends not on the type of liquid systems but on the droplet size. Nagai et al. investigated the relation between volume of an alcohol droplet and motion when the droplet floated on water.27 Their result showed that for the droplets smaller than 0.1 μL, irregular translational motion was observed, whereas the droplets of 0.1−200 μL exhibited vectorial motion. The theoretical studies of dynamics of a deformable particle show that its shape changes as the propagating velocity increases, and the shape deformation has the significant effects on the dynamics of the particle.41−45 In general, the motion of self-propelled droplets due to the dewetting effect strongly depends on the physicochemical properties of the surface of a solid substrate.11,14,15,46 We have also investigated the droplet behavior in our system when the oil droplets were placed on the surface of a PTFE substrate in the phosphate buffer solution. We found that the droplets moved on the PTFE substrate, and the speed was almost the same as on the glass substrate, although there are some induction times for the droplets to start to move (data not shown). The droplets first were attached to the PTFE surface and then came unstuck due to the convection generated around the droplets. Thus, it takes time for the droplets to start to move. For the dewetting effect, a droplet can move only on the solid substrate when the droplet changes the wettability of the substrate by adsorption or desorption of molecules. For a cationic surfactant, trimethylstearylammonium chloride (TSAC), a droplet containing anionic molecules can move spontaneously on a glass substrate which charges negatively.11,14,15 The droplet, however, never moves on a PTFE substrate because TSAC cannot be adsorbed on the substrate.46 For the dewetting effect, the droplet motion depends on the physicochemical properties of the substrate. The droplets in our system can move regardless of the material of the substrates. It is an outstanding feature. To visualize the flow pattern of liquid inside the oil droplet, we added a small amount of silica powder to the droplet.38 The visualization experiment of the flow pattern revealed that Marangoni convection near the oil droplet interface gave rise to a circulating flow inside the droplet. The aqueous liquid was drawn out of the surrounding media into the bottom of the

Figure 5. (a) Evolution of instantaneous speed of droplet at various sizes. (b) Effect of droplet size on average speed for one second. The error bar represents standard deviation.

function of time. The speed changed with time. The movement of droplets persisted several seconds from several minutes. We found that the duration of the movement increased with the increase in the size of the droplets. The similar size-dependent behavior was observed in the NaOH solutions. Figure 5b shows the effect of the droplet size on average speed for one second after the droplets start to move. As the droplet size was increased, the speed increased and leveled off. To investigate the kinetics of surface concentration of surface-active matter, we measured time evolution of interfacial tension by a pendant droplet method under a nonequilibrium chemical condition. An oil droplet containing 0.1 M DEHPA was formed in the different buffer solutions. The evolution of interfacial tension was calculated from the fitting of the droplet shape. A typical oscillation in the interfacial tension is shown in Figure 6. Interestingly, regular oscillation of interfacial tension was observed. A sudden decrease appeared in the interfacial tension, and gradual recovery to a certain constant value was followed by a rapid increase in the interfacial tension (the inset of Figure 6). The oscillation period is 55.7 ± 6.7 s. The sudden decrease in the interfacial tension indicates the production of a large amount of deprotonation DEHPA in the interface. The increase in the interfacial tension indicates a desorption process of the deprotonated DEHPA. Therefore, we can calculate the desorption rate of the deprotonated DEHPA from the interface by using the time evolution of the interfacial tension. We will discuss the estimation of the desorption rate in the next section.

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DISCUSSION We now discuss the onset condition of the droplet motion. The analysis of the onset condition requires the relation between the fluid flow developed by the Marangoni effect and the kinetics of surface-active matter. To evaluate quantitatively the relation, we have to know the value of the Marangoni coefficient of the system, M = |dγ/dΓ|, and desorption rate of 2557

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radius of a droplet. The linear stability analysis gives a critical value where the adsorption amount of the surfactant shows growth in an exponential manner. As Γ0M increases, the expression in brackets is positive and the instability occurs. Assuming that the diffusion within the interface is negligibly small, we obtain the following expression at the lowest mode, m = 1,

Γ0M >

3 kRη 2

(3)

When supply of surfactant by the Marangoni effect exceeds the consumption of surfactant by desorption, the resting state becomes unstable and eventually the droplet starts to move spontaneously. Estimation of the value of the right-hand side of eq 3 requires the value of the rate constant of desorption, k. We estimated k from the experimental result of the dynamic interfacial tension. Figure 6 depicts the regular oscillations in the interfacial tension. Here, we will focus our attention on the rapid increase in the interfacial tension over the first two seconds. We will not go into the mechanism of the oscillation. The increase in the interfacial tension indicates a desorption process of the deprotonated DEHPA to relax to a steady state. Thus, evolution of interfacial tension was fitted by the following equation, γ = (γ0 − γ∞)e−kt + γ∞

The fitting parameter, k, in eq 4 is regarded as the desorption rate in eq 3. We obtained k = 2.2 ± 0.6 s−1 in the carbonate systems. When the volume of a droplet is 0.1 μL, the radius is 0.39 mm. η (= ηoil + ηwater) in our system is 2.7 mPa s. Substituting the values into eq 3, we obtain the value of the right-hand side of eq 3 in the different buffer solutions (Table 3).

Figure 6. Evolution of interfacial tension of nitrobenzene droplet containing 0.1 M DEHPA in the carbonate buffer solution under nonequilibrium. The inset is a magnified view. The top left panel shows the shape of the droplet at t = 440 s and the top right, the shape of the droplet at t = 442.5 s.

surface-active matter, k. The former can be calculated by using the experimental result of the pH dependence of the interfacial tension at equilibrium, and the latter can be calculated by using the dynamic interfacial tension under nonequilibrium. First, we explain the onset condition based on the linear stability analysis developed by Thutupalli et al.36 Assuming that an axisymmetric flow field47,48 was generated inside and outside the droplet by the Marangoni stress, grad γ = M grad Γ. The velocity field u(θ) at the interface is expressed by u(θ ) =

M η sin θ

m=1

∑ ∞

m(m + 1)ΓmCm−+1/2 1 cos θ 2m + 1

Table 3. Criteria of the Onset of the Instability in the Various Buffer Solution Systems buffer oxalate phthalate phosphate(II) tetraborate carbonate

(3/2)kRη (mN/m) 1.8 4.6 1.7 6.0 3.8

× × × × ×

−3

10 10−3 10−3 10−3 10−3

Γ0M (mN/m) ≈0 0.78 24.9 24.3 69.7

Next, we will calculate the left-hand side of eq 3. Estimation of Γ0M for the different buffer solutions requires the relation between the interfacial tension and surface concentration of DEHPA. The overall equilibria during the distribution of DEHPA consists of dimerization in both phases, partition of both monomeric and dimeric DEHPA, and acid dissociation in the aqueous phase. First, we will determine which species of DEHPA has the strongest surface activity. To estimate the concentration of the different species in the aqueous phase, we have to know the equilibrium constants in the water/ nitrobenzene system. Unfortunately, the equilibrium constants in the system are not available. Thus, we used the equilibrium constants in the water/benzene system.49,50 Assuming that only monomeric DEHPA is capable of being distributed in the aqueous phase, we obtain

(1)

where C−1/2 m+1 is the Gegenbauer polynominal of order m and η is a prefactor containing the liquid viscosities outside and inside the droplet. The kinetics of surface concentration of surfaceactive matter, Γ, was described as the advection-diffusion equation with the desorption term. Expanding the surfactant density in spherical harmonics as Γ(θ) = ∑m∞= 0ΓmPm(cos θ), where Pm the Legendre polynominal of order m, Thutupalli et al. obtained36 ⎡ ⎤ ⎛ Γ0M dΓm D⎞ = ⎢m(m + 1)⎜ − 2i ⎟ − k ⎥Γm dt ⎝ (2m + 1)Rη R ⎠ ⎣ ⎦

(4)

(2)

where Γ0 is the equilibrium surface concentration of the surfactant, k the rate constant of desorption, Di the diffusion coefficient of the surfactant within the interface, and R the

2RH ⇔ (RH)2 , 2558

K 2 = [(RH)2 ]/[RH]2

(5)

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RH ⇔ R− + H+,

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Kd = [RH]/[RH]

− P2 exp(P3X)], where Pi is the fitting parameter. We calculated the equilibrium surface concentration of deprotonated DEHPA Γ0 by the Gibbs adsorption isotherm,

(6)

K a = [R−][H+]/[RH]

(7)

where bar superscript and bracket denote the oil phase and the concentration, respectively. The conservation of DEHPA yields [RH]0 = [RH] + 2[(RH)2 ] + [RH] + [R−]

Γ0 = −

(8)

[R−] dγ RT d[R−]

(9)

where R is the gas constant and T is temperature. We obtain the relation between Γ0 and γ (Figure 8b) and then determine the Marangoni coefficient M = 4.1 × 106 mN·m2/mol from the linear fitting of the data. Eventually, we obtained the values of Γ0M for the different buffer solutions and summarized the results in Table 3. All buffer solution systems except for the oxalate satisfy the condition predicted by eq 3. However, for the phthalate systems, droplets never moved. Using the equilibrium constants in the water/toluene system instead of the benzene system, we found that the value of Γ0M was about 0.6% lower than that of the benzene system. The onset of the instability in the theoretical model is based on the onset of axisymmetric circulating flow. In the experimental system, the droplets start to move when the axis of circulation deviated from the vertical direction. A more precise analysis requires the consideration of this effect.

Inserting the equilibrium constants, K2 = 2.19 × 10 , Kd = 9.33 × 102, and Ka = 1.26 × 10−2, in the benzene system49,50 to these equations, we can calculate the concentration of each species as a function of pH. Figure 7 shows the effect of pH on 7

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CONCLUSION

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ASSOCIATED CONTENT

We have studied the self-propelled droplets containing DEHPA, which become deprotonated in a pH-dependent manner. The droplets moved spontaneously and sustainably when the initial pH was adjusted within a range where the interfacial tension decreased significantly at the equilibrium state. Thus, buffer solutions enable the droplets to move even in the neutral pH. The motion of the droplets can be started or stopped by changing the pH level. We compared our experimentally observed onset condition with that from the linear stability analysis proposed by Thutupalli.36 We found that the stability analysis overestimates the value of the driving force for instability. A more refined analysis is required for the understanding of the development of a circulation flow inside the droplet. In our previous study, we found that the secondary instability, a periodic pore dynamics, occurred when the concentration of DEHPA was sufficiently high to form emulsion at equilibrium and the droplet size was larger than a critical value.38 A hole opened and closed repeatedly in response to the pH level of the surrounding media. The causes of the periodic pore dynamics in the previous study and the sustained motion of the droplet in this study should involve the oscillation of the dynamic interfacial tension. Clarification of the mechanism of the oscillation will be the subject of future work.

Figure 7. Concentration of various chemical species of DEHPA in the benzene system as a function of pH.

concentration of each species of DEHPA. The concentration of deprotonated DEHPA increases with the increase in pH from acidic to neutral conditions, whereas those of the others remain constant. The deprotonated DEHPA is identified as the strongest surface activity because the equilibrium interfacial tension changes in the pH range from acidic to neutral conditions. We should calculate the Marangoni coefficient, M, as a function of concentration of deprotonated DEHPA [R−]. We reproduce the interfacial tension as a function of [R−]. The result is shown in Figure 8a. The data is fitted by Y = P1[1

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author Figure 8. (a) Effect of concentration of deprotonated DEHPA on the equilibrium interfacial tension. (b) Relation between the equilibrium interfacial tension and equilibrium surface concentration of deprotonated DEHPA.

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 2559

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(23) Ebbens, S. J.; Howse, J. R. In pursuit of propulsion at the nanoscale. Soft Matter 2010, 6, 726−738. (24) Wang, J.; Gao, W. Nano/microscale motors: Biomedical opportunities and chanllenges. ACS Nano 2012, 6, 5745−5751. (25) Sengupta, S.; Ibele, M. E.; Sen, A. Fantastic voyage: Designing self-powered nanorobots. Angew. Chem., Int. Ed. 2012, 51, 8434−8445. (26) Kitahata, H.; Aihara, R.; Magome, N.; Yoshikawa, K. Convective and periodic motion driven by a chemical wave. J. Chem. Phys. 2002, 116, 5666−5672. (27) Nagai, K.; Sumino, Y.; Kitahata, H.; Yoshikawa, K. Mode selection in the spontaneous motion of an alcohol droplet. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2005, 71, 065301. (28) Toyota, T.; Tsuha, H.; Yamada, K.; Takakura, K.; Ikegami, T.; Sugawara, T. Listeria-like motion of oil droplets. Chem. Lett. 2006, 35, 708−709. (29) Hanczyc, M. M. .; Toyota, T.; Ikegami, T.; Packard, N.; Sugawara, T. Fatty acid chemistry at the oil−water interface: Selfpropelled oil droplets. J. Am. Chem. Soc. 2007, 129, 9386−9391. (30) Ban, T.; Kita, T.; Tominaga, H.; Shioi, A. Droplet motion induced by spontaneous breaking of flow symmetry in aqueous twophase systems. Chem. Lett. 2008, 37, 162−163. (31) Ban, T.; Fujii, T.; Kurisaka, K.; Shioi, A. Ionic control of droplet motion. Chem. Lett. 2006, 35, 1134−1135. (32) Ban, T.; Shioi, A. In Chemical Reactions on Surfaces; Dunkan, J. I., Klein, A. B., Eds.; NOVA Science Publishers: New York, 2008; pp 156−194. (33) Toyota, T.; Maru, N.; Hanczyc, M. M.; Ikegami, T.; Sugawara, T. Self-propelled oil droplets consuming “fuel” surfactant. J. Am. Chem. Soc. 2009, 131, 5012−5013. (34) Ban, T.; Hatada, Y.; Takahashi, K. Spontaneous motion of a droplet evolved by resonant oscillation of a vortex pair. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2009, 79, 031602. (35) Lagzi, I.; Soh, S.; Wesson, P. J.; Browne, K. P.; Grzybowski, B. A.. Maze solving by chemotactic droplets. J. Am. Chem. Soc. 2010, 132, 1198−1199. (36) Thutupalli, S.; Seemann, R.; Herminghaus, S. Swarming behavior of simple model squirmers. New J. Phys. 2011, 13, 073021. (37) Banno, T.; Kuroha, R.; Toyota, T. pH-sensitive self-propelled motion of oil droplets in the presence of cationic surfactants containing hydrolyzable ester linkages. Langmuir 2012, 28, 1190− 1195. (38) Ban, T.; Yamagami, Y.; Furumichi, Y. Transient pore dynamics in pH-responsive liquid membrane. Langmuir 2012, 28, 10682−10687. (39) Ban, T.; Kawaizumi, F.; Nii, S.; Takahashi, K. Study of drop coalescence behavior for liquid-liquid extraction operation. Chem. Eng. Sci. 2000, 55, 5385−5391. (40) Dunderdale, G.; Ebbens, S.; Fairclough, P.; Howse, J. Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes. Langmuir 2012, 28, 10997−11006. (41) Krischer, K.; Mikhailov, A. Bifurcation to traveling spots in reaction-diffusion systems. Phys. Rev. Lett. 1994, 73, 3165−3168. (42) Ohta, T.; Ohkuma, T. Deformable self-propelled particles. Phys. Rev. Lett. 2009, 102, 154101. (43) Hiraiwa, T.; Matsuo, M. Y.; Ohkuma, T.; Ohta, T.; Sano, M. Dynamics of a deformable self-propelled domain. Europhys. Lett. 2010, 91, 20001. (44) Hiraiwa, T.; Shitara, K.; Ohta, T. Dynamics of a deformable selfpropelled particle in three dimensions. Soft Matter 2011, 7, 104007. (45) Itino, Y.; Ohta, T. Dynamics of deformable self-propelled particles with repulsive interaction. J. Phys. Soc. Jpn. 2012, 81, 033001. (46) Shioi, A.; Katano, K.; Onodera, Y. Effect of solid walls on spontaneous wave formation at water/oil interfaces. J. Colloid Interface Sci. 2003, 266, 415−421. (47) LeVan, M. D.; Newman, J. The effect of surfactant on the terminal and interfacial velocities of a bubble or drop. AIChE J. 1976, 22, 695−701. (48) LeVan, M. D. Motion of a droplet with a Newtonian interface. J. Colloid Interface Sci. 1981, 83, 11−17.

ACKNOWLEDGMENTS This work was supported by the Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Exploratory Research (Grant 24656469). The authors thank Professor S. Dost of the University of Victoria, Canada, for constructive criticisms and EKO INSTRUMENTS for measuring the dynamic interfacial tension.

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REFERENCES

(1) Cazabat, A. M.; Heslot, F.; Troian, S. M.; Carles, P. Fingering instability of thin spreading films driven by temperature gradients. Nature 1990, 346, 824−826. (2) Biance, A. L.; Clanet, C.; Quéré, D. Leidenfrost drops. Phys. Fluids 2003, 15, 1632−1637. (3) Quéré, D.; Ajdari, A. Surfing the hot spot. Nature Mat. 2006, 5, 429−430. (4) Washizu, M. Electrostatic actuation of liquid droplets for microreactor applications. IEEE Trans. Ind. Appl. 1998, 34, 732−737. (5) Pollack, M. G.; Fair, R. B.; Shenderov, A. D. Electrowetting-based actuation of liquid droplets for microfluidic applications. Appl. Phys. Lett. 2000, 77, 1725−1726. (6) Gallardo, B. S.; Gupta, V. K.; Eagerton, F. D.; Jong, L. I.; Craig, V. S.; Shah, R. R.; Abbott, N. L. Electrochemical principles of active control of liquids on submillimeter scales. Science 1999, 283, 57−60. (7) Ichimura, K.; Oh, S.-K.; Nakagawa, M. Light-driven motion of liquids on a photoresponsive surface. Science 2000, 288, 1624−1626. (8) Berná, J.; Leigh, D. A.; Lubomska, M.; Mendoza, S. M.; Pérez, E. M.; Rudolf, P.; Teobaldi, G.; Zerbetto, F. Macroscopic transport by synthetic molecular machines. Nature Mat. 2005, 4, 704−710. (9) Chaudhury, M. K.; Whitesides, G. M. How to make water run uphill. Science 1992, 256, 1539−1541. (10) Bain, C. D.; Burnett-Hall, G. D.; Montgomerie, R. R. Rapid motion of liquid drops. Nature 1994, 372, 414−415. (11) Yoshikawa, K.; Magome, N. Chemomechanical transduction in an oil-water system. Regulation of the macroscopic mechanical motion. Bull. Chem. Soc. Jpn. 1993, 66, 3352−3357. (12) Dos Santos, F. D.; Ondarcuhu, T. Free-running droplets. Phys. Rev. Lett. 1995, 75, 2972−2975. (13) Lee, S.-W.; Laibinis, P. E. Directed movement of liquids on patterned surfaces using noncovalent molecular adsorption. J. Am. Chem. Soc. 2000, 122, 5395−5396. (14) Sumino, Y.; Magome, N.; Hamada, T.; Yoshikawa, K. Selfrunning droplet: Emergence of regular motion from nonequilibrium noise. Phys. Rev. Lett. 2005, 94, 68301. (15) Ban, T.; Suzuki, S.; Abe, S.; Shioi, A. Anionic control of autonomous motion of oil/water interface with cationic surfactant. Chem. Lett. 2007, 36, 1040−1041. (16) Bliznyuk, O.; Patrick Jansen, H.; Stefan Kooij, E.; Zandvliet, H. J. W.; Poelsema, B. Smart design of stripe-patterned gradient surfaces to control droplet motion. Langmuir 2011, 27, 11238−11245. (17) Yao, X.; Bai, H.; Ju, J.; Zhou, D.; Li, J.; Zhang, H.; Yanga, B.; Jiang, L. Running droplet of interfacial chemical reaction flow. Soft Matter 2012, 8, 5988−5991. (18) Nanzai, B.; Ishikawa, R.; Igawa, M. Spontaneous motion of Otoluidine droplets: Repetitive motion of running and squashing. Chem. Lett. 2012, 41, 609−611. (19) Paxton, W. F.; Kistler, K. C.; Olmeda, C. C.; Sen, A.; St. Angelo, S. K.; Cao, Y.; Mallouk, T. E.; Lammert, P. E.; Crespi, V. H. Catalytic nanomotors: Autonomous movement of striped nanorods. J. Am. Chem. Soc. 2004, 126, 13424−13431. (20) Howse, J. R.; Jones, R. A. L.; Ryan, A. J.; Gough, T.; Vafabakhsh, R.; Golestanian, R. Self-motile colloidal particles: From directed propulsion to random walk. Phys. Rev. Lett. 2007, 99, 048102. (21) Dhar, P.; Fischer, Th. M.; Wang, Y.; Mallouk, T. E.; Paxton, W. F.; Sen, A. Autonomously moving nanorods at a viscous interface. Nano Lett. 2006, 6, 66−72. (22) Gao, Wei; Pei, A.; Wang, J. Water-driven micromotors. ACS Nano 2012, 6, 8432−8438. 2560

dx.doi.org/10.1021/la3047164 | Langmuir 2013, 29, 2554−2561

Langmuir

Article

(49) Miyake, Y.; Matsuyama, H.; Nishida, M.; Nakai, M.; Nagase, N.; Teramoto, M. Kinetics and mechanism of metal extraction with acidic organophosphorus extractants (I): Extraction rate limited by diffusion process. Hydrometallugy 1990, 23, 19−35. (50) Kolarik, Z. Review: Dissociation, self-association, and partition of monoacidic organophosphorus extractants. Solvent Extr. Ion Exch. 2010, 28, 707−763.

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