Experimental Investigation of the Self-Propelled Motion of a Sodium

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Experimental investigation of the self-propelled motion of a sodium oleate tablet and boat at an oil-water interface Yasuhito Watahiki, Tomonori Nomoto, Luca Chiari, Taro Toyota, and Masanori Fujinami Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01090 • Publication Date (Web): 25 Apr 2018 Downloaded from http://pubs.acs.org on April 26, 2018

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Experimental investigation of the self-propelled motion of a sodium oleate tablet and boat at an oilwater interface Yasuhito Watahiki,† Tomonori Nomoto,† Luca Chiari,† Taro Toyota,‡ Masanori Fujinami*,† †

Department of Applied Chemistry and Biotechnology, Chiba University, 1-33 Yayoi, Inage,

Chiba 263-8522, Japan ‡

Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-

8902, Japan

ABSTRACT

The self-propelled behavior of macroscopic inanimate objects at surfaces and interfaces are ubiquitous phenomena of fundamental interest in interface science. However, given the existence of a large variety of systems with their own inherent chemical properties, the kinematics of the self-propelled motion and the dynamics of the forces driving these systems often remain largely unknown. Here, we experimentally investigated the spontaneous motion of a sodium oleate tablet at a water-nitrobenzene interface, under non-equilibrium and global isothermal conditions, through measurements of the interfacial tension with the non-invasive, quasi elastic laser scattering method. The sodium oleate tablet was self-propelled due to an imbalance in the interfacial tension induced by the inhomogeneous adsorption of oleate/oleic acid molecules. The kinetics of the self-propelled motion of a boat-shaped plastic sheet bearing sodium oleate tablets

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at a sodium oleate aqueous solution-nitrobenzene interface was also studied. The interfacial tension difference between the front and rear of the boat was quantitatively identified as the force pushing the boat forward, although the Marangoni flow due to the uneven distribution of the interfacial tension behind the boat tended to decelerate the motion.


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INTRODUCTION Chemical oscillations and spontaneous motion in non-equilibrium systems1 are some of the most astonishing, and yet, so puzzling phenomena in natural science. A common feature in these systems is the conversion of locally available chemical energy into mechanical energy that triggers the motion.2 A noticeable example of such kind of systems is the self-propelled motion of inanimate macroscopic objects at gas-liquid surfaces and liquid-liquid interfaces.2–5 For example, it has long been known that, when camphor fragments or tablets are laid onto a water surface, they exhibit self-driving properties.6–11 More complex objects, such as centimeter-sized plastic sheets bearing camphor tablets, i.e. so-called camphor boats, move on the surface of an aqueous solution with speeds of up to tens cm/s and at distances of up to several tens meter.3,12–17 In all these systems, it is understood that the driving force of the motion is the imbalance in the interfacial tension around those objects due to the non-uniform distribution of adsorbed molecules at the surface. It is well known that whenever an interfacial tension gradient arises as the result of the heterogeneous concentration of a substance at an immiscible interface, a solutal Marangoni convection also develops at the same time.18 When floating alcohol/oil droplets or liquid marbles on a solution surface, they move in one direction with concomitant deformation of their shape.19–24 Similarly, a solid/liquid composite made of an oil droplet attached to solid soap shows a combination of rotational and translational motion when placed on the surface of a water phase.25 In these systems, the spontaneous motion is induced by the chemical Marangoni effect. Hence, both the interfacial tension difference and the Marangoni flow need to be considered. The clarification of the mechanism of the self-propelled motion and deformation of those objects is usually based on numerical simulations through mathematical modeling.9,16,26–29 Nonetheless, recent progress in instrumental techniques, such as the development of the quasi-


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elastic laser scattering (QELS) method,1 a non-invasive method for interfacial tension measurements, enabled us to tackle the fundamental interactions driving the dynamics of those systems also from an experimental perspective. In particular, our earlier experimental studies on the self-propelled motion of camphor boats12,30 revealed that the surface tension difference between the front and the rear of the boat is the active driving force and that there is a positive correlation between the speed of the boat and the surface tension difference. In alcohol droplets,19 the imbalance in the Marangoni convection caused by the imbalance of the surface tension gradient was found to be the driving force of the motion, confirming that both the surface tension difference and the Marangoni flow play an important role in the propulsion mechanism. Given the relevance of the self-propelled behavior of nanoscale and macroscopic devices in interface science research, in our earlier studies we have successfully investigated the mechanism of motion through measurement of the interfacial tension distribution around different objects using the QELS method.1,12,19,30 Self-propelled systems with different physicochemical properties are known to exhibit dissimilar motion features depending on their nature and the environment.31 Consistent with this line of research, in this study we focus on the characteristics of the self-propelled motion of a sodium oleate tablet and a plastic sheet bearing sodium oleate tablets, i.e. a sodium oleate boat. These systems are considered to be useful models for the understanding and modelling of the spatio-temporal regulation of motility in biological cells under nonlinear and global isothermal conditions.32 A tablet of sodium oleate, an anionic surfactant, is known to show self-propulsion abilities only at liquid-liquid interfaces such as water and oil.32 However, to the best of our knowledge a fully quantitative evaluation of this behavior has not been carried out, with only one earlier study being available.32 This previous study qualitatively interpreted the self-propelled motion of a sodium oleate tablet in terms of the


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continuous desorption of oleate/oleic acid molecules and their adsorption at the oil-water interface, which was studied by spectroscopy and interfacial tension measurements using the Wilhelmy method.33 Here, we elucidate the kinetic mechanism of this system by quantitatively examining why sodium oleate tablets are only self-propelled at liquid-liquid interfaces. We prove that the interfacial tension imbalance is the driving force of this motion through measurements of the time- and space-resolved interfacial tension distribution around a sodium oleate tablet at airwater and water-nitrobenzene interfaces using the non-invasive QELS method. Furthermore, in order to easily control the direction and speed of the motion and conduct a systematic study of its dynamics, we also designed a self-propelled sodium oleate boat floating on an aqueous solutionnitrobenzene interface in a loop.

EXPERIMENTAL SECTION Self-propulsion of the sodium oleate tablet. Sodium oleate (>97.0%) was obtained from Tokyo Chemical Industry Co. Ltd. Sodium oleate tablets (3 mm diameter, 1 mm thick) were prepared using a hand-press die set (PIKE Technologies, USA). A Petri dish (glass, 120 mm diameter) was filled with 90 ml of water up to a height of ~10 mm. Water was purified with a Millipore Milli-Q Integral 3 filtering system. A sodium oleate tablet was laid on the water surface, and time and space-resolved surface tension measurements were carried out around the tablet at room temperature (~23 °C). A second Petri dish of the same size was first filled with 90 ml of nitrobenzene and then 90 ml of water on top of it. Nitrobenzene (>99.5%) was obtained from Kanto Chemical Co. and was used without further purification. After the formation of the water-nitrobenzene interface, a sodium oleate tablet was directly placed at that interface with the aid of tweezers so as to float on the oil phase. The self-propelled motion of the tablet at that


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interface was recorded from the top using a video camera (CASIO, EXILIM EX-100). Similarly, time and space-resolved measurements of the water-nitrobenzene interfacial tension were carried out around the tablet. Self-propulsion of the sodium oleate boat. The sodium oleate boat is made of pentagonal polyester film (12 × 15 mm width and length, 0.1 mm thickness) (Fig. 1a). Three sodium oleate tablets molded into the shape described above are glued onto the rear side of the boat and stick out of the back edge by 1.5 mm. As in our earlier studies on the motion of camphor boats,12,30 the number of tablets and the protrusion margin were selected in order to maximize the desorption of surfactant and consequently the interfacial tension difference between front and back of the boat. Geometry of the boat path. The path geometry used to study the motion of the sodium oleate boat is shown in Fig. 1(b). Two Petri dishes of 82 and 125 mm diameter, respectively, were stacked on top of each other in a concentric geometry to form a unidirectional circular track with a length of 325 mm and a width of 22 mm. The track was filled with 50 ml of nitrobenzene up to a height of ~9 mm and 50 ml of a 1 mM aqueous solution of sodium oleate on top of it reaching a total height of ~18 mm. After the formation of the aqueous solution-nitrobenzene interface, the sodium oleate boat was directly placed at that interface with the aid of tweezers so as to float on the oil phase (Fig. 1c). As soon as the sodium oleate boat was placed at that interface, its continuous, self-propelled motion was observed. Time-resolved measurements of the aqueous solution-nitrobenzene interfacial tension were carried out at a fixed position along the loop during the boat motion. Here, an aqueous solution of sodium oleate was used instead of pure water in order to control the speed of the boat. Various concentrations of sodium oleate in the range of 0.01-10 mM were tested and a value of 1 mM was selected for a more systematic study because it yielded boat speeds compatible with our measurement system. In addition, the surface


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tension measurements with this concentration exhibited very good reproducibility. All measurements were performed at room temperature (~23 °C).

Figure 1. Geometry of (a) the sodium oleate boat and (b) the circular loop used to study the motion of the boat. (c) Cross section of the sodium oleate boat floating at the interface between the sodium oleate aqueous solution and nitrobenzene phases in the loop. (d) Optical system of the QELS method for the interfacial tension measurements. Legend: AOM = acousto-optic modulator, APD = avalanche photodiode. Not drawn to scale.


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QELS method. Interfacial tension measurements at the air-water, water-nitrobenzene and sodium oleate aqueous solution-nitrobenzene interfaces were carried out using the QELS method. The optical and measurement systems of the QELS method (Fig. 1d) have already been explained in detail in our previous studies.1,12,19,30 Hence, for conciseness we provide here a brief summary of the main features of this technique. The QELS method enables to measure the interfacial tension by analyzing the frequency shifts in the light scattered by the thermally excited capillary waves propagating at the interface and measured at a certain scattering angle. In this study, a Nd:YVO4 laser (JUNO100, Showa Optronics Co., 532 nm) was used as the incident light source. The laser light was spilt into two beams using a beam splitter: one beam was used as the pump for the light scattering excitation (incident beam), whereas the second beam was input into an acousto-optic modulator (ISOMET 1205C-2) that shifted the original light frequency by 80 MHz (reference beam). The incident and reference beams were focused onto the interface of interest, as shown in Fig. 1(d). Although separated by a small angle, both beams were as perpendicular as possible to the interface in order to minimize the Doppler shift effect induced by any flows in the liquids. The transmitted reference beam and the scattered beam were directed into the respective avalanche photodiode detectors (Hamamatsu Photonics, C5331-11) as the input signal and the local oscillator, respectively, of an optical heterodyne detection system. A spectrum analyzer (RSA5103A, Tektronix, USA) carried out a Fourier transformation of the output signal in real time in order to obtain a frequency spectrum of the capillary waves. The interfacial tension was calculated from the frequency shifts of the capillary waves using the dispersion relations of capillary waves. The uncertainty in the interfacial tension measurements was estimated to be within 0.2 mN/m (at one standard deviation level).


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A significant improvement in the signal acquisition system was achieved in the present study with respect to our previous investigations employing the QELS system1,12,19,30. The utilization rate of the data acquired by the spectrum analyzer was increased up to 50%. Each measured spectrum was collected 40 times in a time interval of 0.1 s and then averaged over that period of time. As a result, the signal-to-noise ratio was improved by a factor of 1.7 and the time resolution of the measurements was just 0.2 s. This upgrade allowed us to obtain more accurate data and increase the time sampling interval of the interfacial tension change. This is particularly critical to achieve high-precision measurements when the speed of the boat becomes high. In addition, without this improvement, measurements of the interfacial tension difference between the front and the rear of the boat would have not been possible.

RESULTS AND DISCUSSION Self-propulsion of the sodium oleate tablet. First, we investigated the self-propelled motion of a sodium oleate tablet at the air-water and water-nitrobenzene interfaces. When the sodium oleate tablet was laid on the water surface, it initially moved just slightly and shortly after that it stopped (see Video S1). On the other hand, when the sodium oleate tablet was placed at the water-nitrobenzene interface, it continuously moved around at that interface (see Video S2). These results are in agreement with earlier observations.32 In order to understand the reason behind the different behavior of the sodium oleate tablets at the air-water and water-nitrobenzene interfaces and to clarify the origin of the self-propelled motion, we measured the time dependence of the surface and interfacial tensions at different distances from the sodium oleate tablet (Fig. 2). The water surface tension was measured at 7, 15 and 45 mm away from the tablet, but for clarity in Fig. 2a we omit the data measured at 15 mm


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as they are identical to those measured at 7 and 45 mm. Note that it was not possible to measure the interfacial tension at distances within 5 mm from the tablet because of the interfacial deformation induced by the meniscus around the tablet. As soon as the tablet was laid on the surface, the surface tension rapidly decreased from the initial value of water (72 mN/m) and stabilized at an asymptotic value of about 25 mN/m. This behavior is consistent with the continuous desorption of sodium oleate molecules from the tablet and the absorption of those anionic surfactants at the water surface. No dependence of the time change in the surface tension on the distance from the tablet was observed. This suggests that at any time the surface tension is identical at any point throughout the surface as the surfactants are evenly distributed. On the other hand, time-resolved measurements of the water-nitrobenzene interfacial tension were carried out at distances of 7, 10, 12, 15 and 25 mm away from the tablet. However, for clarity in Fig. 2b we omit the data measured at 10 and 15 mm as they lie in between the adjacent data. To inhibit the spontaneous motion of the tablet, in this case the tablet was held stationary while measuring the surrounding interfacial tension. At distances of up to 15 mm from the tablet, the interfacial tension suddenly dropped from ~25 mN/m to around 10 mN/m as soon as the tablet was placed at the interface and then rapidly recovered to >20 mN/m within a couple of seconds, followed by a slower monotonic decrease. This dip in the interfacial tension can be ascribed to the desorption of oleate/oleic acid molecules from the tablet and their immediate adsorption to the interface through a redistribution of the surfactants in the oil phase. However, this behavior was not observed at a distance of 25 mm, where a smoother monotonic decrease took place. In fact, the further away from the tablet the interfacial tension change became smaller and smaller. This result points to an uneven interfacial tension distribution due to an inhomogeneous adsorption of the surfactants at the interface. The different behavior of sodium oleate at the two


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interfaces can be traced back to its chemical nature. While sodium oleate is soluble in water, oleic acid is insoluble. However, oleic acid can dissolve in the oil phase and get unevenly adsorbed to the interface.

(a)

(b)

Figure 2. Time dependence of the interfacial tension of (a) the water surface and (b) the waternitrobenzene interface at various distances from the sodium oleate tablet ranging from 7 to 45 mm. The tablets were placed at each interface at 0 s.

(b)

(a)

Figure 3. Interfacial tension distribution of (a) the water surface and (b) the water-nitrobenzene interface measured as a function of the distance in the radial direction from the sodium oleate tablet 20 s after it was placed at the interface.


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To corroborate the results shown in Fig. 2, we measured the interfacial tension distribution as a function of the distance in the radial direction from the tablet 20 s after it was placed on the interface (Fig. 3). This time delay was chosen because Fig. 2 shows that the interfacial tension after that time was almost constant and, therefore, suitable for these measurements. Fig. 3(a) shows that the interfacial tension distribution around the tablet was uniform at the water surface. This supports the conclusion that oleate/oleic acid molecules were homogeneously adsorbed on the water surface. On the other hand, an uneven interfacial tension distribution was observed around the tablet at the water-nitrobenzene interface (Fig. 3b): the closer to the tablet, the lower was the interfacial tension.

Figure 4. Schematic diagram of the interfacial tension distribution of (a) the water surface and (b) the water-nitrobenzene interface when a sodium oleate tablet is placed at each interface. The interfacial tension distribution of (c) the water surface and (d) the water-nitrobenzene interface as the tablet is just slightly displaced is also shown.


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Based on these results, we examined the mechanism behind the self-propelled motion of the sodium oleate tablets on the water surface and at the water-nitrobenzene interface. Whenever a tablet is placed at an interface, there is inevitably some degree of inclination with respect to that interface and the tablets are never perfectly cylindrically symmetric in shape. Owing to this symmetry breaking, a surface tension difference at the water surface and an interfacial tension difference at the water-nitrobenzene interface such as those shown in Figs. 4(a) and 4(b), respectively, typically arise around the tablet. Because of these surface/interfacial tension differences, the tablets start to move in both systems. However, as the tablets are just slightly displaced, new interfacial tension distributions are generated as shown in Figs. 4(c) and (d). Oleate/oleic acid molecules are uniformly adsorbed at the water surface. Hence, no surface tension imbalance is induced around the tablet after the displacement and the tablet consequently stops. As the shape of the oleate/oleic acid molecules distribution does not change over time, the tablet no longer moves. On the other hand, the oleate/oleic acid molecules are unevenly adsorbed at the water-nitrobenzene interface and, even after the displacement, the concentration of surfactants is smaller in the forward direction of motion than in the backward direction. This means that the interfacial tension is constantly higher in the forward direction of motion. Therefore, the tablet spontaneously moves. This continuous interfacial tension difference represents the driving force of the self-propelled motion of the tablet. This observation is in agreement with earlier studies on a similar system, i.e. a camphor tablet floating on an aqueous solution, whose self-propelled motion was also attributed to differences in surface tension.34,35 In turn, this interfacial tension gradient generates a Marangoni flow around the sodium oleate tablet. Similar to camphor tablets,35 this flow occurs both at the advancing and receding sides of the sodium oleate tablet: the former tends to accelerate the tablet, whereas the latter tends to


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decelerate it. The effect of the former flow is anticipated to be greater than that of the latter because the tablet moves in the direction of the former flow. In other words, the Marangoni flow behaves as an additional force that pushes the tablet in the same direction of the interfacial tension difference. We note here that, although the experiments were conducted at a constant temperature, the presence of thermo-capillary Marangoni effects cannot be excluded. They can arise, for instance, from the heterogeneous diffusion of heat from the dissolution of the oleic acid/oleate molecules at the interface or into the bulk phases. In principle, these thermal Marangoni flows might affect the self-propelled motion.36,37 However, given that they are an effect of local non-isothermal conditions, they are expected to play a minor role compared to the interfacial tension difference and the Marangoni flow around the tablet. In conclusion, we have proven that the self-propelled motion requires the generation of an uneven interfacial tension distribution caused by the inhomogeneous adsorption of oleate/oleic acid molecules at the interface. Self-propulsion of the sodium oleate boat. Although the study of the sodium oleate tablet allowed us to clarify the origin of its self-propelled motion, the inherently random nature of the motion prevented us from conducting a systematic study on its kinematics and dynamics using the QELS technique. In order to circumvent this limitation, we designed a controllable model system, as similar as possible to the sodium oleate tablet, that allowed us to quantify the magnitude of the driving force of the self-propelled motion and elucidate its role. Similar to our previous studies on the self-propelled motion of camphor boats,12,30 we constructed a sodium oleate boat with three sodium oleate tablets glued to a plastic sheet (Fig. 1a) so as to deliberately generate an interfacial tension difference in the direction of motion. We used a circular track filled with a layer of an aqueous solution on top of a nitrobenzene layer (Fig. 1b) to create a


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continuous unidirectional motion of the sodium oleate boat. In order to adjust the speed of the boat, a 1 mM sodium oleate aqueous solution was used as the aqueous phase in this part of the study. The significant advantage of this system with respect to the mere tablet lies in the fact that it is controllable (e.g. direction of motion, speed of the self-propelled object, etc.) just by changing the parameters of the boat and its surrounding environment (e.g. number of sodium oleate tablets attached to the boat, geometry of the track, sodium oleate concentration of the aqueous solution, etc.). As soon as the sodium oleate boat was placed at the aqueous solution-nitrobenzene interface, it spontaneously moved around the loop (see Video S3). We measured the time change in the interfacial tension of the aqueous solution-nitrobenzene interface at a fixed position along the loop during the self-propelled motion of the boat (Fig. 5a). Fig. 5(b) shows an expanded view of a selected time interval of Fig. 5(a) spanning about four laps. The dashed lines indicate the times when the boat passed through the measurement point: that is, the plot between two dashed lines represents one lap. The interfacial tension sharply dropped at each passage of the boat through the measurement point because of the continuous adsorption of oleate/oleic acid molecules and then slowly recovered to nearly the original value due to the desorption of those surfactants to the oil phase. The overall trend in the interfacial tension is to decrease with time. However, a slight increase towards the end of the measurement is observed and it might be ascribed to the whole system approaching the equilibrium. The average speed of the boat in each lap was calculated from the time interval of each lap and is also shown in Fig. 5(a). In agreement with the observed behavior of the interfacial tension, the speed of the boat also decreases with time.


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(b)

Figure 5. (a) Time change in the interfacial tension of the aqueous solution-nitrobenzene interface measured at a fixed position along the loop of the self-propelled sodium oleate boat. The average speed of the boat during each lap is also shown. (b) Extended view of a selected time range of (a). The dashed lines indicate the times when the boat passed through the measurement point.

It is important to note that the results shown in Fig. 5 are given in the laboratory frame of reference. However, in the boat frame, the interfacial tension measured immediately after the boat passage is the interfacial tension behind the boat. Similarly, as seen from the boat, the interfacial tension measured just before the boat transit represents the interfacial tension at the front of the boat. Hence, from Fig. 5 it can be inferred that the interfacial tension is smaller at the rear and higher at the front of the boat. The results of the time-resolved interfacial tension measurement, in conjunction with the speed of the boat, can be converted into the space-resolved interfacial tension distribution around the boat. Fig. 6 shows an example of the space-resolved interfacial tension γ(x) distribution at the front and behind the boat calculated in this manner from the time-resolved data of the second and third laps shown in Fig. 5(b), where the average boat speed was 20.7 and 20.0 mm/s, respectively. The measurement point, i.e. the boat, is located


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at the origin and the horizontal axis indicates the distance from it: the data at positive and negative positions represent the interfacial tension at various distances at the front and back of the boat, respectively. The solid lines in Fig. 6 are exponential fits to the data obtained using the function given in Eq. (1): = − ⁄ ,

(1)

where x is the distance from the boat and x0 is the position of the boat (x0 ≈ -323 mm for the first lap in Fig. 6, while x0 ≈ 0 for the second lap), and γ0, A and l are free parameters. The interfacial tension values at the front and back of the boat obtained from these fits amount to ~3.1 and ~1.6 mN/m, respectively. Therefore, the interfacial tension difference between the front and rear of the boat is ∆γ ≈ 1.5 mN/m during the laps shown in Fig. 6. This interfacial tension difference represents the force pulling the boat forward. Similar to the sodium oleate tablet and as we observed in our earlier studies on the self-propelled motion of camphor boats,12,30 this interfacial tension gradient, in turn, generates a Marangoni flow which also affects the boat motion. However, unlike for the sodium oleate tablet, this surface flow behaves as a force in the opposite direction of motion of the boat, i.e. it tends to decelerate it. In conclusion, there are two competing forces acting on the boat: the interfacial tension gradient between the front and back of the boat, which pushes the boat in one direction, and the Marangoni flow which pulls the boat in the opposite direction. The magnitude of the imbalance between these two forces is expected to determine the speed of the boat.


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Figure 6. Space-resolved interfacial tension at the front (positive position values) and back (negative positions) of the sodium oleate boat calculated from the time-resolved data of the second and third laps shown in Fig. 5(b). The solid lines are the fits to the data of each lap using Eq. (1). The vertical dashed line indicates the position of the measurement point, i.e. the boat.

In order to investigate the dynamics between the front-back interfacial tension gradient and the Marangoni flow we studied the kinematics of the sodium oleate boat. We obtained the speed of the boat at each value of the interfacial tension difference between the front and rear of the boat (Fig. 7), simply by repeating the procedure outlined above for all the laps shown in Fig. 5(a). This result shows that the higher the speed, the larger is the interfacial tension difference required to push the boat. However, the increasing rate of the speed tends to slow down as the interfacial tension difference rises. This is thought to be due to the decelerating effect of the Marangoni surface flow generated behind the boat. As the front-back interfacial tension difference rises, and the boat speed consequently increases, the Marangoni flow also becomes gradually faster and faster. Hence, the net driving force of the motion, i.e. the interfacial tension


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gradient minus the Marangoni flow, is gradually reduced. As a result, the boat speed increases but at a slower pace.

Figure 7. Speed of the sodium oleate boat as a function of the interfacial tension difference between the front and back of the boat.

As the Marangoni flow becomes faster when the interfacial tension gradient behind the boat becomes larger, the effect of the Marangoni flow can be quantitatively estimated from the shape of the space-resolved interfacial tension distribution (Fig. 6). In fact, the slope of the tangent line to the interfacial tension profile right at the back of the boat corresponds to the rate of change in the interfacial tension. By taking the derivative of Eq. (1), one obtains:

= − ⁄ .

(2)

In. Eq. (2), the A/l ratio represents precisely the rate of the interfacial tension change. Hence, by determining this ratio from the fits of the space-resolved interfacial tension data using Eq. (1), we can estimate the magnitude of the Marangoni flow. Fig. 8 shows the A/l ratio as a function of


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the boat speed. It is manifest that the faster the boat the larger is the A/l ratio and that this relationship is not linear. This quantitatively proves that the Marangoni flow becomes faster and, therefore, increasingly decelerates the boat as the boat speed increases.

Figure 8. A/l ratio, obtained from the fits of the space-resolved interfacial tension profiles using Eq. (1), as a function of the speed of the sodium oleate boat.

Finally, we compare the two self-propelled sodium oleate systems (tablet and boat) examined in this study in terms of their driving mechanism. It is interesting to note that the space-resolved interfacial tension behind the sodium oleate boat in each of the laps shown in Fig. 6 is similar in shape to that around the sodium oleate tablet at the water-nitrobenzene interface (Fig. 3b). This agreement corroborates our initial assumption that the boat is a suitable model system for the investigation of the kinematics and dynamics of the self-propelled motion. In addition, this result endorses the model of the inhomogeneous adsorption of oleate/oleic acid molecules at the waternitrobenzene interface responsible for the decrease in the interfacial tension around the tablet (Fig. 4). In fact, this model applies behind the boat moving at the aqueous solution-nitrobenzene


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interface as well. On the other hand, it is important to note that the driving mechanism of these two systems is somewhat different. Although, the interfacial tension gradient is the driving force of the motion of both the tablet and boat, the Marangoni convection affects their speed in opposite ways. Overall, the Marangoni flow behaves as an additional, accelerating force on the tablet, whereas it operates so as to decelerate the boat. This result is in agreement with previous studies on the accelerating and decelerating effect of the Marangoni flow on the self-propelled motion of camphor tablets and boats, respectively.35 In conclusion, the investigation of both the sodium oleate tablet and boat aided us in elucidating the important and different role played by interfacial tension gradients and the Marangoni flow in affecting the kinematics of self-propelled systems. This would have not been possible if only one of the systems had been individually studied.

CONCLUSIONS We have experimentally investigated the self-propulsion properties of sodium oleate tablets and boats at different interfaces. In particular, we investigated the spontaneous motion of sodium oleate tablets at air-water and water-nitrobenzene interfaces. Although no motion was observed on the water surface, the sodium oleate tablet was self-propelled at the water-nitrobenzene interface. We quantitatively elucidated the dynamics of this motion through measurements of the interfacial tension distribution around the sodium oleate tablets at both interfaces using the noninvasive QELS method. A uniform interfacial tension distribution at the water surface induced by the homogeneous adsorption of oleate/oleic acid molecules explained the absence of motion. On the other hand, the uneven interfacial tension distribution generated by the inhomogeneous adsorption of oleate/oleic acid was observed at the water-nitrobenzene interface. We


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quantitatively showed through QELS measurements that this interfacial tension gradient was the key factor behind the continued self-propelled motion of the tablet. Thanks to the recent significant improvements in the S/N ratio and time resolution of the QELS measurements, we have also investigated the kinetic mechanism of a self-propelled sodium oleate boat at the water (sodium oleate solution)-nitrobenzene interface. We successfully measured the interfacial tension difference at the front and rear of the boat for different boat speeds. We quantitatively proved that the driving force of the motion of the boat is the interfacial tension difference at the front and rear of the boat using the QELS method. In addition, the greater the interfacial tension difference driving the boat, the faster was the boat. However, the increasing rate of the boat speed was gradually reduced as the interfacial tension gradient became higher. This was thought to be due to the decelerating effect of the Marangoni surface flow generated by the interfacial tension behind the boat, whose flow became progressively faster as the boat speed increased. The present results confirm that self-propelled systems with peculiar physico-chemical properties exhibit different motion features depending on their nature and the surrounding environment. In conjunction with numerical simulations, these experimental results help the understanding of the self-propelled behavior of macroscopic devices in interface science research. This data may also be useful for the understanding and modelling of the spatiotemporal regulation of motility in biological organisms under nonlinear and global isothermal conditions.


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ASSOCIATED CONTENT Video S1. Behavior of the sodium oleate tablet at the water surface. Video S2. Self-propelled motion of the sodium oleate tablet at the water-nitrobenzene interface. Video S3. Self-propelled motion of the sodium oleate boat at the sodium oleate aqueous solution-nitrobenzene interface in the circular track.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (M.F.) Tel: +81-43-290-3503 Fax: +81-43-290-3503

ACKNOWLEDGMENT This work was partially supported by the JSPS (Japan Society for the Promotion of Science) KAKENHI grant No. 15H03824.


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REFERENCES (1)

Nomoto, T.; Toyota, T.; Fujinami, M. Quasi-Elastic Laser Scattering for Measuring Inhomogeneous Interfacial Tension in Non-Equilibrium Phenomena with Convective Flows. Anal. Sci. 2014, 30, 707–716.

(2)

Paxton, W. F.; Sundararajan, S.; Mallouk, T. E.; Sen, A. Chemical Locomotion. Angew. Chemie Int. Ed. 2006, 45 (33), 5420–5429.

(3)

Zhao, G.; Pumera, M. Macroscopic Self-Propelled Objects. Chem. - An Asian J. 2012, 7 (9), 1994–2002.

(4)

Balzani, V.; Credi, A.; Venturi, M. Molecular Machines Working on Surfaces and at Interfaces. ChemPhysChem 2008, 9 (2), 202–220.

(5)

Ismagilov, R. F.; Schwartz, A.; Bowden, N.; Whitesides, G. M. Autonomous Movement and Self-Assembly. Angew. Chemie 2002, 114 (4), 674–676.

(6)

Rayleigh, L. Measurements of the Amount of Oil Necessary in Order to Check the Motions of Camphor upon Water. Proc. R. Soc. London 1890, 47 (286–291), 364–367.

(7)

Tomlinson, C. On the Motions of Camphor on the Surface of Water. Philos. Mag. Ser. 1869, 38 (257), 409–424.

(8)

Nakata, S.; Hiromatsu, S. Intermittent Motion of a Camphor Float. Colloids Surfaces A Physicochem. Eng. Asp. 2003, 224 (1–3), 157–163.

(9)

Hayashima, Y.; Nagayama, M.; Nakata, S. A Camphor Grain Oscillates While Breaking Symmetry. J. Phys. Chem. B 2001, 105 (22), 5353–5357.

(10)

Kitahata, H.; Hiromatsu, S.; Doi, Y.; Nakata, S.; Rafiqul Islam, M. Self-Motion of a Camphor Disk Coupled with Convection. Phys. Chem. Chem. Phys. 2004, 6 (9), 2409– 2414.


24

Page 25 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(11)

Schulz, O.; Markus, M. Velocity Distributions of Camphor Particle Ensembles. J. Phys. Chem. B 2007, 111 (28), 8175–8178.

(12)

Karasawa, Y.; Oshima, S.; Nomoto, T.; Toyota, T.; Fujinami, M. Simultaneous Measurement of Surface Tension and Its Gradient around Moving Camphor Boat on Water Surface. Chem. Lett. 2014, 43 (7), 1002–1004.

(13)

Nakata, S.; Yoshii, M.; Matsuda, Y.; Suematsu, N. J. Characteristic Oscillatory Motion of a Camphor Boat Sensitive to Physicochemical Environment. Chaos 2015, 25 (6), 64610.

(14)

Nakata, S.; Kohira, M. I.; Hayashima, Y. Mode Selection of a Camphor Boat in a DualCircle Canal. Chem. Phys. Lett. 2000, 322 (5), 419–423.

(15)

Suematsu, N. J.; Ikura, Y.; Nagayama, M.; Kitahata, H.; Kawagishi, N.; Murakami, M.; Nakata, S. Mode-Switching of the Self-Motion of a Camphor Boat Depending on the Diffusion Distance of Camphor Molecules. J. Phys. Chem. C 2010, 114 (21), 9876–9882.

(16)

Soh, S.; Bishop, K. J. M.; Grzybowski, B. A. Dynamic Self-Assembly in Ensembles of Camphor Boats. J. Phys. Chem. B 2008, 112 (35), 10848–10853.

(17)

Langmuir, I. Experiments with Oil on Water. J. Chem. Educ. 1931, 8 (5), 850–866.

(18)

de Gennes, P.-G.; Brochard-Wyart, F.; Quéré, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves; Springer: New York, 2004.

(19)

Oshima, S.; Nomoto, T.; Toyota, T.; Fujinami, M. Surface Tension Gradient around an Alcohol Droplet Moving Spontaneously on Water Surface. Anal. Sci. 2014, 30, 441–444.

(20)

Toyota, T.; Maru, N.; Hanczyc, M. M.; Ikegami, T.; Sugawara, T. Self-Propelled Oil Droplets Consuming “Fuel” Surfactant. J. Am. Chem. Soc. 2009, 131 (14), 5012–5013.

(21)

Ooi, C. H.; van Nguyen, A.; Evans, G. M.; Gendelman, O.; Bormashenko, E.; Nguyen, N.-T. A Floating Self-Propelling Liquid Marble Containing Aqueous Ethanol Solutions.


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RSC Adv. 2015, 5 (122), 101006–101012. (22)

Bormashenko, E.; Bormashenko, Y.; Grynyov, R.; Aharoni, H.; Whyman, G.; Binks, B. P. Self-Propulsion of Liquid Marbles: Leidenfrost-like Levitation Driven by Marangoni Flow. J. Phys. Chem. C 2015, 119 (18), 9910–9915.

(23)

Hanczyc, M. M.; Toyota, T.; Ikegami, T.; Packard, N.; Sugawara, T. Fatty Acid Chemistry at the Oil−Water Interface: Self-Propelled Oil Droplets. J. Am. Chem. Soc. 2007, 129 (30), 9386–9391.

(24)

Čejková, J.; Novák, M.; Štěpánek, F.; Hanczyc, M. M. Dynamics of Chemotactic Droplets in Salt Concentration Gradients. Langmuir 2014, 30 (40), 11937–11944.

(25)

Takabatake, F.; Magome, N.; Ichikawa, M.; Yoshikawa, K. Spontaneous Mode-Selection in the Self-Propelled Motion of a Solid/liquid Composite Driven by Interfacial Instability. J. Chem. Phys. 2011, 134 (11), 114704.

(26)

Nagayama, M.; Nakata, S.; Doi, Y.; Hayashima, Y. A Theoretical and Experimental Study on the Unidirectional Motion of a Camphor Disk. Phys. D Nonlinear Phenom. 2004, 194 (3–4), 151–165.

(27)

Yoshinaga, N. Spontaneous Motion and Deformation of a Self-Propelled Droplet. Phys. Rev. E 2014, 89 (1), 12913.

(28)

Czirók, A.; Stanley, H. E.; Vicsek, T. Spontaneously Ordered Motion of Self-Propelled Particles. J. Phys. A. Math. Gen. 1997, 30 (5), 1375–1385.

(29)

Chaté, H.; Ginelli, F.; Grégoire, G.; Raynaud, F. Collective Motion of Self-Propelled Particles Interacting without Cohesion. Phys. Rev. E 2008, 77 (4), 46113.

(30)

Karasawa, Y.; Nomoto, T.; Chiari, L.; Toyota, T.; Fujinami, M. Motion Modes of Two Self-Propelled Camphor Boats on the Surface of a Surfactant-Containing Solution. J.


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Colloid Interface Sci. 2018, 511, 184–192. (31)

Nakata, S.; Kawagishi, N.; Murakami, M.; Suematsu, N. J.; Nakamura, M. Intermittent Motion of a Camphor Float Depending on the Nature of the Float Surface on Water. Colloids Surfaces A Physicochem. Eng. Asp. 2009, 349 (1–3), 74–77.

(32)

Nakata, S.; Hiromatsu, S. Self-Motion of Soap at an Oil–water Interface. Chem. Phys. Lett. 2005, 405 (1–3), 39–42.

(33)

Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces; Wiley, 1997.

(34)

Nakata, S.; Nagayama, M.; Kitahata, H.; Suematsu, N. J.; Hasegawa, T. Physicochemical Design and Analysis of Self-Propelled Objects That Are Characteristically Sensitive to Environments. Phys. Chem. Chem. Phys. 2015, 17 (16), 10326–10338.

(35)

Matsuda, Y.; Suematsu, N. J.; Kitahata, H.; Ikura, Y. S.; Nakata, S. Acceleration or Deceleration of Self-Motion by the Marangoni Effect. Chem. Phys. Lett. 2016, 654, 92– 96.

(36)

Brochard, F. Motions of Droplets on Solid Surfaces Induced by Chemical or Thermal Gradients. Langmuir 1989, 5 (2), 432–438.

(37)

Savino, R.; Paterna, D.; Lappa, M. Marangoni Flotation of Liquid Droplets. J. Fluid Mech. 2003, 479, 307–326.


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ABSTRACT GRAPHIC


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Figure 1. Geometry of (a) the sodium oleate boat and (b) the circular loop used to study the motion of the boat. (c) Cross section of the sodium oleate boat floating at the interface between the sodium oleate aqueous solution and nitrobenzene phases in the loop. (d) Optical system of the QELS method for the interfacial tension measurements. Legend: AOM = acousto-optic modulator, APD = avalanche photodiode. Not drawn to scale. 289x248mm (300 x 300 DPI)


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Figure 2(a). Time dependence of the interfacial tension of (a) the water surface and (b) the waternitrobenzene interface at various distances from the sodium oleate tablet ranging from 7 to 45 mm. The tablets were placed at each interface at 0 s. 120x91mm (300 x 300 DPI)


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Figure 2(b). Time dependence of the interfacial tension of (a) the water surface and (b) the waternitrobenzene interface at various distances from the sodium oleate tablet ranging from 7 to 45 mm. The tablets were placed at each interface at 0 s. 121x94mm (300 x 300 DPI)


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Figure 3(a). Interfacial tension distribution of (a) the water surface and (b) the water-nitrobenzene interface measured as a function of the distance in the radial direction from the sodium oleate tablet 20 s after it was placed on the interface. 123x92mm (300 x 300 DPI)


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Figure 3(b). Interfacial tension distribution of (a) the water surface and (b) the water-nitrobenzene interface measured as a function of the distance in the radial direction from the sodium oleate tablet 20 s after it was placed on the interface. 123x93mm (300 x 300 DPI)


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Figure 4. Schematic diagram of the interfacial tension distribution of (a) the water surface and (b) the water-nitrobenzene interface when a sodium oleate tablet is placed at each interface. The interfacial tension distribution of (c) the water surface and (d) the water-nitrobenzene interface as the tablet is just slightly displaced is also shown. 247x148mm (300 x 300 DPI)


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Figure 5(a). (a) Time change in the interfacial tension of the aqueous solution-nitrobenzene interface measured at a fixed position along the loop of the self-propelled sodium oleate boat. The average speed of the boat during each lap is also shown. (b) Extended view of a selected time range of (a). The dashed lines represent the times when the boat passed through the measurement point. 131x90mm (300 x 300 DPI)


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Figure 5(b). (a) Time change in the interfacial tension of the aqueous solution-nitrobenzene interface measured at a fixed position along the loop of the self-propelled sodium oleate boat. The average speed of the boat during each lap is also shown. (b) Extended view of a selected time range of (a). The dashed lines represent the times when the boat passed through the measurement point. 118x90mm (300 x 300 DPI)


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Figure 6. Space-resolved interfacial tension at the front (positive position values) and back (negative positions) of the sodium oleate boat calculated from the time-resolved data of the second and third laps shown in Fig. 5(b). The solid lines are the fits to the data of each lap using Eq. (1). The vertical dashed line indicates the position of the measurement point, i.e. the boat. 118x90mm (300 x 300 DPI)


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Figure 7. Speed of the sodium oleate boat as a function of the interfacial tension difference between the front and back of the boat. 119x95mm (300 x 300 DPI)


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Figure 8. A/l ratio, obtained from the fits of the space-resolved interfacial tension profiles using Eq. (1), as a function of the speed of the sodium oleate boat. 126x91mm (300 x 300 DPI)


Experimental Investigation of the Self-Propelled Motion of a Sodium

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