ArticleOctober 29, 2025

Self-Propulsion of a Soap at an Oil/Aqueous Interface Depending on pH
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Takahito Arai
Takahito Arai
Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan
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Masakazu Kuze
Masakazu Kuze
Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan
Meiji Institute for Advanced Study of Mathematical Sciences (MIMS), Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo164-8525, Japan
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Muneyuki Matsuo*
Muneyuki Matsuo
Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan
Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo153-8902, Japan
*Email: [email protected]
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https://orcid.org/0000-0002-2559-3522
Satoshi Nakata*
Satoshi Nakata
Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan
*Email: [email protected]
More by Satoshi Nakata
https://orcid.org/0000-0002-7290-1508

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Langmuir

Cite this: Langmuir 2025, 41, 44, 29759–29766

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https://doi.org/10.1021/acs.langmuir.5c04037

Published October 29, 2025

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Abstract

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A self-propelled sodium oleate (OleNa) disk was investigated at an oil/aqueous interface prepared in an annular channel to induce characteristic features of self-propulsion. When the pH of the aqueous phase was changed, three types of motion were observed, i.e., unidirectional motion at 3.0 ≤ pH ≤ 6.0, motion with inversion at 8.0 ≤ pH ≤ 9.0, and no motion at 11.0 ≤ pH ≤ 12.0. At pH = 8.0, the interfacial tension and complementary contact angle of the meniscus oscillated simultaneously. The mechanism of the three types of motion is discussed in relation to the acidity constant (pK_a) between protonated and deprotonated oleic acids, their distribution ratios in the oil and aqueous phases, and the driving force of motion. The present study suggests that the mode of self-propulsion is determined by the nature of the energy-source molecule, specifically its pK_a, interfacial tension, and adsorption/desorption of protonated and deprotonated oleic acid molecules at the interface.

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Introduction

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Self-propelled motion driven by the difference in chemical potential, for example, interfacial tension, has been widely studied to develop novel chemomechanical transducers as well as artificial mimics of biological motors. (1−14) Inanimate self-propelled objects generally exhibit random motion owing to external fluctuations or unidirectional motion determined by their shapes or an external force. (1) Introducing nonlinearity into self-propelled systems can induce characteristic features of motion, for example, oscillatory motion, (15−22) bifurcation, (7,15,19,23−27) and collective motion. (28−36) In other words, the introduction of nonlinearity enhances the autonomy and diversity in self-propulsion.

Maintaining heterogeneous distribution of energy-source molecules around an object is essential for sustainable self-propulsion. For example, a soap disk floating at an air/aqueous interface immediately ceases self-propulsion because soap molecules are distributed homogeneously at the aqueous surface owing to the adsorption/desorption equilibrium. Consequently, the driving force for self-propulsion cannot be obtained from the homogeneous distribution of soap molecules at the interface, that is, the homogeneously reduced surface tension around the solid soap. In contrast, at the oil/aqueous interface, the sodium oleate (OleNa) soap disk maintains self-propulsion. (37,38) Such sustainable self-propulsion is realized by the continuation of the spatially imbalanced adsorption and desorption of OleNa molecules at the oil/aqueous interface.

The soap system at the oil/aqueous interface reflects the nonequilibrium nature of the adsorption and desorption of soap molecules at the interface. In addition, the self-propulsion of oleic acid droplets, OleNa, and their combination at the aqueous surface or in the aqueous phase has been extensively investigated. (39−46) However, studies on self-propelled motion at oil/aqueous interface remain scare as far as we know, (37,38) and characteristic features, such as responsiveness to chemical enviroments, have yet to be achieved. In addition, the relationship between self-propelled motion and the nonequilibrium nature of oleic acid adsorption and desorption at the oil-aqueous interface as a function of pH has not yet been clarified.

In this study, a pH-sensitive self-propelled OleNa disk was examined at the oil/aqueous interface. Three types of motion were observed as a function of pH of the aqueous phase, i.e., unidirectional motion at 3.0 ≤ pH ≤ 6.0, motion with inversion at 8.0 ≤ pH ≤ 9.0, and no motion at 11.0 ≤ pH ≤ 12.0. We discuss the mode switching mechanism of the self-propelled OleNa disk as a function of pH in relation to the interfacial tension, the dissociation equilibrium between protonated and deprotonated oleic acids, and their oil/aqueous distribution ratios. The present study suggests that the spatiotemporally spontaneous and heterogeneous distribution of energy-source molecules in the nonequilibrium condition plays an important role in inducing characteristic motion.

Experimental Section

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Sodium oleate was purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). Toluene, benzene, H₃PO₄, NaH₂PO₄, Na₂HPO₄, and Na₃PO₄ were purchased from Nacalai Tesque, Inc. (Kyoto, Japan). An OleNa disk (thickness: 1 mm, diameter: 3 mm, mass: 6 mg) was prepared based on a previously reported method. (37) Figure 1a shows a schematic representation of the experimental system composed of an annular glass channel (inner diameter: 30 mm, outer diameter: 46 mm), the oil/aqueous interface, and the disk. An annular channel was used to reproduce the periodic boundary conditions. Water was purified by filtering through activated carbon, ion-exchange resin, a water distillation apparatus (RFD24ONC, ADVANTEC Co., Ltd., Tokyo, Japan), and a Millipore Milli-Q filtering system (Merck Direct-Q 3UV, Germany; resistance: 18 MΩ cm). As for the preparation of the oil/aqueous interface, phosphate buffer solution (PBS, pH range: 3.6–12.0, ionic strength: 0.5, volume: 10 mL) was poured into the annular channel as the aqueous phase (depth: 10 mm), and toluene (volume: 10 mL) as the oil phase was poured over the aqueous phase (depth: 10 mm). The relative densities of the solid disk, oil phase, and aqueous phase were 1.1, 0.86, and 1.0, respectively. Therefore, the disk was balanced at the oil/aqueous interface by gravitational and interfacial tension forces. The motion of the disk was monitored from the top view using a digital video camera (HDR-CX560, SONY, Tokyo, Japan; minimum time resolution, 1/30 s), and the images were analyzed using an image processing system (ImageJ, National Institute of Health, Bethesda, Maryland, USA). The experiments were performed in an air-conditioned room at 298 ± 2 K. At least three examinations were performed under each experimental condition to confirm the reproducibility of the results.

Figure 1. Schematic illustration of (a) the experimental apparatus for observing a self-propelled OleNa disk placed at an oil/aqueous interface, (b) the measurement of the interfacial tension, and (c) the simultaneous measurement of the interfacial tension and movie around the OleNa disk fixed at the oil/aqueous interface. In (a), θ and θ = 0 were defined to analyze the motion in the polar coordinates.

To clarify the adsorption and desorption dynamics of the OleNa and oleic acid molecules at the oil/aqueous interface, the time variation of the interfacial tension was measured by using a surface tensiometer (DY-300; Kyowa Interface Science Co., Ltd., Saitama, Japan). To measure the interfacial tension, PBS (volume: 40 mL) was poured into a glass beaker (inner diameter: 72 mm) as the aqueous phase (depth: 10 mm), and toluene (volume: 40 mL) as the oil phase (depth: 10 mm) was poured over the aqueous phase (Figure 1b). Interfacial tension measurements using the Wilhelmy method were initiated at t = 0 with a platinum plate (contact length: 47 mm) positioned at the center of the beaker 10 mm away from the disk at its minimum distance. At t = 10 s, the OleNa disk was brought in contact with the oil/aqueous interface from the air phase and then moved back into the air phase at t = 30 s using a Z-stage system (GSC-01 and OSMS20-35(X), OptoSigma Corp., Costa Mesa, California, USA).

To clarify the relationship between the speed of the OleNa disk and the driving force of its motion, the interfacial tension at the equilibrium state was measured at different pH values for the aqueous phase. OleNa (200 mg) was placed in the toluene (40 mL)/PBS (40 mL) phase at 25 °C for 24 h, and interfacial tension was measured after the complete dissolution was confirmed.

To understand the nature of self-propulsion, simultaneous measurements of the interfacial tension and a movie of the OleNa disk fixed at the oil/aqueous interface were performed (Figure 1c). A rectangular glass container (length: 94 mm, width: 43 mm) filled with 40 mL of PBS (depth: 10 mm) and 40 mL of toluene (depth: 10 mm) was placed on a jack. An OleNa disk was fixed to one end of a platinum wire (diameter: 0.5 mm) located at the center of the container, and the other end was connected to the surface tensiometer. The height of the container was adjusted by the jack, the disk was brought into contact with the oil/aqueous interface, and the temporal change in the interfacial tension was measured along with the observation of the disk motion. The meniscus of the OleNa disk was monitored using a digital video camera from a slanted view, and images were analyzed using ImageJ.

To estimate the concentrations of oleic acid in the oil and aqueous phases, Co(III)-5-Cl-PADAP (Ponalkit-ABS, Dojindo Molecular Technologies, Inc., Tokyo, Japan) and a UV–vis spectrometer (UV-1650PC, Shimadzu Co., Kyoto, Japan) were used at different pH values. Since Ponal Kit ABS responds only to the deprotonated form of anionic surfactant, all aqueous samples obtained at various pH values were basified with NaOH in the measurement, i.e., protonated oleic acid was converted to a deprotonated one. Thus, the measured value is the sum of the concentrations of the protonated and deprotonated oleic acids. Co(III)-5-Cl-PADAP was used as an indicator of deprotonated oleic acid, and the procedures (1)–(5) were performed. (1) OleNa (6 mg) was dissolved in toluene (40 mL)/PBS (40 mL), and the oil/aqueous interface was allowed to stand for 1 h. (2) Solution A (50 mL) was prepared by mixing a 2.8 mM Co(III)-5-Cl-PADAP aqueous solution (49.65 mL), a 1 M NaOH aqueous solution (250 μL), and the extracted solution from the aqueous phase in (1) (100 μL). (3) Solution A (50 mL) and benzene (4 mL) were mixed for 2 min and allowed to stand for 15 min. (4) Solution B (4 mL) was obtained by extracting from the benzene phase of solution (3). (5) The absorbance of solution B was measured at 560 nm by using a UV–vis spectrometer. The concentration of oleic acid in the aqueous phase was estimated using a calibration curve (Figure S1). The concentration of oleic acid in the toluene phase was estimated by subtracting concentration of oleic acid in the aqueous phase from total concentration of oleic acid (0.5 mM).

Results and Discussion

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Mode Switching of an OleNa Disk at the Oil/Aqueous Interface Depending on pH

First, we examined the self-propulsion of an OleNa disk placed at an oil/aqueous interface at different pH values, as shown in Figure 2. The disk was placed on the interface at t = 0. When the pH of the aqueous phase changed, three types of motions were observed. Unidirectional motion, i.e., unidirectional rotation during self-propulsion, was maintained for approximately 9 min at pH = 6.0 (Figure 2a). The direction of rotation was random in the present system. After t = 9 min, the disks dissolved completely in the oil or aqueous phase. Motion together with inversion, i.e., a change in the direction of rotation during self-propulsion, was maintained for approximately 10 min at pH = 8.0 (Figure 2b). No motion was observed at pH = 12.0 (Figure 2c). At pH 8.0 and 12.0, the disk remained on the interface for 10 min.

Figure 2. Time variations of θ for self-propulsion of an OleNa disk at pH = (a) 6.0, (b) 8.0, and (c) 12.0. θ and θ = 0 are defined in Figure 1. The movies of motion in parts (a) and (b) are provided in the Supporting Information as Movies S1 and S2, respectively.

Figure 3 shows the phase diagram of self-propulsion, the absolute value of the angular speed of motion (|ω|), and the ratio of unidirectional motion per 1 min (R) as a function of pH of the aqueous phase at 30 ≤ t ≤ 90 s (see Figure 2). R is the relative value of the self-propelled distance during unidirectional motion (l_u) divided by the total self-propelled distance (l_total), i.e., R = l_u/l_total. Here, we defined unidirectional motion at 0.8 < R ≤ 1, motion with inversion at 0 < R ≤ 0.8. No motion was defined as a mode when the speed was less than 1 mm s^–1. Unidirectional motion, motion with inversion, and no motion were observed at 3.6 ≤ pH ≤ 6.9, 6.9 ≤ pH ≤ 9.8, and 9.8 ≤ pH ≤ 12.0, respectively. With an increase in pH, |ω| was increased, reached the maximum at pH = 8.0, and was decreased at 8.0 ≤ pH ≤ 9.8 (Figure 3b). R was decreased with an increasing pH (Figure 3c).

Figure 3. (a) Phase diagram of self-propelled motion, (b) absolute value of angular speed, |ω|, and (c) ratio of unidirectional motion per 1 min, R, depending on pH of the aqueous phase. Error bars represent the standard deviations obtained from three or four examinations. In the boundary regions at pH 6.9 and 9.8 in (a), both unidirectional motion and motion with inversion were observed, and both motion with inversion and no motion were observed, respectively.

Measurement of Interfacial Tension as the Driving Force of Motion

The time variation of the oil/aqueous interfacial tension at different pH values was measured to evaluate the driving force of self-propulsion, as shown in Figure 4. At pH 6.0, the interfacial tension decreased slightly upon contact of the disk with the interface, and the decrease was maintained after removal of the disk from the interface to the air phase (Figure 4 and Figure S2). At pH 8.0, the interfacial tension was slowly decreased by about 2 mN m^–1 during contact of the disk to the interface. When the disk was removed from the interface, the interfacial tension decreased (amplitude: ∼1 mN m^–1) and then slowly increased by ∼2 mN m^–1. At pH 12.0, the interfacial tension was rapidly decreased by about 30 mN m^–1 during contact of the disk. When the disk was removed from the interface, the interfacial tension increased; however, a lower value was maintained.

Figure 4. Time variation of the oil/aqueous interfacial tension at pH 6.0 (red line), 8.0 (blue line), and 12.0 (green line). The downward and upward arrows denote the time when the OleNa disk is placed in contact with the interface from above (t = 10 s) and when it is moved upward away from the interface to the air phase (t = 30 s), respectively.

To clarify the relationship between the speed of the OleNa disk and the driving force of the unidirectional motion (3.6 ≤ pH ≤ 6.0), the interfacial tension at the equilibrium state was measured at different pH values of the aqueous phase. OleNa grains (200 mg) were placed at the oil/aqueous interface for 1 h. Subsequently, it was completely dissolved by mixing for 5 min, and the interfacial tension was measured. Figure 5 shows the difference in the interfacial tension Δγ (= γ₀ – γ_s), where γ_s and γ₀ are the interfacial tensions at the oil/aqueous interface with and without OleNa in the aqueous and toluene phases, respectively. γ_s and γ₀ are shown in Figure S3. Δγ increases with an increasing pH.

Figure 5. Difference in the interfacial tension, Δγ (= γ₀ – γ_s), at the equilibrium state, depending on the pH of the aqueous phase, where γ_s and γ₀ are the interfacial tension at the oil/aqueous interface with and without OleNa in the aqueous and oil phase, respectively. Error bars represent the standard deviation obtained from three examinations.

To elucidate the mechanism of motion with inversion, simultaneous measurements of the interfacial tension and complementary contact angle around the OleNa disk fixed at the interface were performed at pH 8. The meniscus on the left side of the disk expanded from state i to ii and contracted from state ii to iii, as shown in Figure 6a. The complementary contact angle was calculated from the spatiotemporal plot of the meniscus (Figure S4a). The complementary contact angle (θ_c) oscillated as shown in Figure 6b. The vertical force measured by the electronic balance (F_v) is defined by eq 1

F_{v} = γ_{v} l = (γ_{s / w} - γ_{o / s} - γ_{o / w} \cos θ_{c}) l

(1)

where γ_s/w, γ_o/s, and γ_o/w denote the interfacial tension at the solid/water, oil/solid, and oil/water interfaces, respectively. γ_v and l are the sum of γ_s/w, γ_o/s and γ_o/w in the vertical direction and the contact length of the OleNa disk, respectively. Equation 2 is obtained from eq 1.

γ_{v} = γ_{s / w} - γ_{o / s} - γ_{o / w} \cos θ_{c}

(2)

Both θ_c and γ_v oscillated simultaneously. The correlation coefficient between γ_v and θ_c was 0.94. In contrast, no oscillations were observed at pH 6.0 and 12.0 (Movies S4 and S5 (10 ≤ t ≤ 510 s)).

Figure 6. (a) Snapshots of the OleNa disk fixed on the interface at pH 8.0 at t = (i) 680, (ii) 700, and (iii) 760 s (slanted view). The movie at pH 8.0 is provided in the Supporting Information as Movie S3 (500 ≤ t ≤ 900 s). (b) Simultaneous measurement of the time variation of the sum of γ_s/w, γ_o/s, and γ_o/w in the vertical direction (γ_v) and the complementary contact angle (θ_c). The data were smoothed by a seven-point moving average (corresponding to ±3 frames, total ∼1.2 s) to reduce noise. The original time resolution was 0.167 s per frame. The vertical position of the disk was adjusted so that the upper surface of the disk almost coincided with the oil/aqueous interface. We confirmed the reproducibility of the oscillatory phenomena.

γ_o/w at state i is higher than that at state ii, as supported by both the experimental results and the theoretical estimation (see chapter 4 in the Supporting Information (SI)). This is reasonable since the adsorbed amount of oleate ions at the oil/water interface is higher in state i rather than that in state ii.

Based on the experimental results and related studies, we discuss the mechanism of the mode switching in the self-propelled motion of the OleNa disk as a function of the pH of the aqueous phase. Deprotonated oleic acid, which develops from the disk to the oil/aqueous interface, is rapidly converted to protonated oleic acid at pH < pKa (5.35). (47) Unidirectional motion in the lower pH range (3.6 ≤ pH ≤ 6.0) suggests that deprotonated oleic acids, which induce the driving force of self-propulsion, are continuously supplied from the disk (Figures 2 and 3). Here, the driving force of the disk is the difference in the interfacial tension around the disk induced by the heterogeneous distribution of deprotonated oleic acid. Symmetry breaking around the disk to the initial floating state induces the direction of the disk. Once unidirectional motion starts, symmetry breaking is maintained; therefore, unidirectional motion without inversion is obtained. (48) A slight change in γ was observed when the OleNa disk was brought into contact with the interface and then removed at pH 6.0 (Figure 4), and the interfacial tension remained at its initial value in comparison with pH 8 and 12. This result suggests that the adsorption and desorption of protonated oleic acid at the interface more readily reach equilibrium at lower pH. In other words, the spatial difference in γ on the interface is locally generated near the disk at pH 6.0. The increase in |ω| depending on pH at 3.6 ≤ pH ≤ 6.0 (see Figure 3b) is due to the increase in Δγ as the driving force of self-propulsion (see Figure 5). The collapse pressure of fatty acid monolayers at the air/water interface depends on the pH of the water phase corresponding to the adsorption of ionized and nonionized species. (49) This supports our observation that Δγ increases with the pH in Figure 5.

Motion with inversion (Figures 2 and 3) and slow change in γ upon the contact of the OleNa disk with the interface and its removal at middle pH (∼8.0) (Figure 4) suggest that the adsorption and desorption rates of deprotonated oleic acid at the interface are locally and inhomogeneously changed around the disk. In other words, the interfacial tension around the disk, which is affected by the distribution of deprotonated oleic acid, fluctuates during self-propulsion. The pulsation decreased and increased γ after the removal of the disk (Figure4, pH 8 at t = 33 s), suggesting that deprotonated oleic acids accumulated at the base of the disk were rapidly adsorbed onto the interface and then desorbed from the interface by the removal operation. Simultaneous oscillations of the interfacial tension and complementary contact angle for the fixed disk at pH 8.0 (Figure 6) suggest that the deprotonated oleic acid discontinuously absorbs on the interface from the disk. It has been reported that the force working around a self-propelled object oscillates when the object is fixed. (48,50,51) Pulsating changes in γ and slower adsorption/desorption (see Figure 4) and oscillatory changes in γ_v (see Figure 6) may enhance the heterogeneous distribution of deprotonated oleic acids at the interface. Therefore, motion with inversion is generated by a local change in the spatial gradient γ around the disk induced by the heterogeneous distribution of deprotonated oleic acids.

No motion (Figures 2 and 3) at the higher pH range (11.0 ≤ pH) suggests that the driving force of self-propulsion is not obtained around the disk since the interfacial tension is very low (see Figure 4). In addition, the adsorbed deprotonated oleic acids almost occupied the interface and no spatial gradient of γ on the interface was achieved.

Estimation of the Total Concentration of Oleic Acid in the Oil and Aqueous Phases

Co-5-CI-PADAP was used as an indicator of deprotonated oleic acid to estimate the total concentration of oleic acid in the oil and aqueous phases at equilibrium as a function of pH, as shown in Figure 7. If protonated and deprotonated oleic acid molecules exist only in the toluene phase, then the total concentration of oleic acid in the toluene phase is calculated as 0.5 mM. The total concentration of oleic acid in the oil and aqueous phases decreased and increased, respectively, depending on the pH.

Figure 7. Total concentration of oleic acid in the oil (filled circles) and aqueous (empty circles) phases estimated at different pH values.

Numerical Calculation of Oleic Acid Concentrations

We calculated the occupancy ratios of deprotonated oleic acid (X) and protonated oleic acid (Y) at the oil/aqueous interface as functions of pH.

The effects of X and Y on the adsorption of oleic acid and deprotonated oleic acids at the oil/aqueous interface are described in eqs 3 and 4, respectively. The derivatives X and Y are described in the Supporting Information (see chapters 5 and 6 in the SI).

\frac{d X}{d t} = (1 - X - Y) (k_{1} [{Ole}^{-}]_{o} + k_{2} [{Ole}^{-}]_{w}) - (k_{- 1} + k_{- 2}) X

(3)

\frac{d Y}{d t} = (1 - X - Y) (k_{3} [OleH]_{o} + k_{4} [OleH]_{w}) - (k_{- 3} + k_{- 4}) Y

(4)

where k₁, k_–1, k₂, k_–2, k₃, k_–3, k₄, and k_–4 are the rate constants for the adsorption of deprotonated oleic acid from the oil phase to the oil/aqueous interface, desorption of deprotonated oleic acid from the oil/aqueous interface to the oil phase, adsorption of deprotonated oleic acid from the aqueous phase to the oil/aqueous interface, desorption of deprotonated oleic acid from the oil/aqueous interface to the aqueous phase, adsorption of protonated oleic acid from the oil phase to the oil/aqueous interface, desorption of protonated oleic acid from the oil/aqueous interface to the oil phase, adsorption of protonated oleic acid from the aqueous phase to the oil/aqueous interface, and desorption of protonated oleic acid from the oil/aqueous interface to the aqueous phase, respectively. [Ole^–]_w and [Ole^–]_o are the concentrations of deprotonated oleic acids in the aqueous and oil phases, and [OleH]_w and [OleΗ]_o are the concentrations of protonated oleic acid in the aqueous and oil phases, respectively.

Equations 5 and 6 were obtained under equilibrium conditions, i.e., dX/dt = 0 and dY/dt = 0, respectively.

X = \frac{(k_{1} {[{Ole}^{-}]}_{o} + k_{2} {[{Ole}^{-}]}_{w}) (k_{- 3} + k_{- 4})}{(k_{1} {[{Ole}^{-}]}_{o} + k_{2} {[{Ole}^{-}]}_{w}) (k_{- 3} + k_{- 4}) + (k_{3} {[OleH]}_{o} + k_{4} {[OleH]}_{w}) (k_{- 1} + k_{- 2}) + (k_{- 1} + k_{- 2}) (k_{- 3} + k_{- 4})}

(5)

Y = \frac{(k_{3} {[OleH]}_{o} + k_{4} {[OleH]}_{w}) (k_{- 1} + k_{- 2})}{(k_{1} {[{Ole}^{-}]}_{o} + k_{2} {[{Ole}^{-}]}_{w}) (k_{- 3} + k_{- 4}) + (k_{3} {[OleH]}_{o} + k_{4} {[OleH]}_{w}) (k_{- 1} + k_{- 2}) + (k_{- 1} + k_{- 2}) (k_{- 3} + k_{- 4})}

(6)

Because the number of molecules at the oil/aqueous interface was smaller than that in the bulk, [Ole^–]_w, [Ole^–]_o, [OleH]_w, and [OleH]_o were regarded as constants, and the values obtained in Figure 7 were substituted. Figure S8 shows X (solid line) and the decrease in interfacial tension (filled circles, Δγ_d) as a function of pH. By assuming a 1:1 correspondence between X and the decrease in interfacial tension, we fitted X to the experimental data in Figure 4. Based on this fitting, the rate constants were set as k_–1 = k₃ = k_–4 = 0.1, k_–2 = 5, k₁ = k₂ = 10, and k_–3 = k₄ = 1000. Figure 8 shows the calculated values of X and Y as a function of pH. In this model, X starts to increase from zero at pH ≥ 7.0 and reaches approximately 0.5 at 11.0 ≤ pH ≤ 12.0.

Figure 8. Occupancy ratios of deprotonated oleic acids, X, (orange line) and protonated oleic acids, Y, (blue line) at the oil/aqueous interface based on eqs 5 and 6. k_–1 = k₃ = k_–4 = 0.1, k_–2 = 5, k₁ = k₂ = 10, and k_–3 = k₄ = 1000.

We discuss the relationship between switching of motion and the physicochemical parameters pKa and X. The switching point between unidirectional motion and motion with inversion, that is, pH = 6–7, is determined by the pKa and a lower value of X. That is, the local existence of deprotonated oleic acid around the OleNa disk at the oil/aqueous interface plays an important role in the unidirectional motion. The pH range of motion with inversion may be related to the remarkable changes in X and Y at pH = 8.0–10.0. On the other hand, the pH range in no motion at pH > 10.0 is due to the constant value of X. In other words, an appropriate amount of deprotonated oleic acid adsorbed at the oil/aqueous interface suppresses the difference in the interfacial tension around the disk; thus, the driving force of self-propulsion cannot be obtained. X did not reach 1 at pH > 11.0 since the supply of deprotonated oleic acid from the OleNa disk was not considered in the numerical calculation. However, Figure 8 suggests that X and Y are determined by the adsorption/desorption kinetics and the oil/aqueous distribution ratios of deprotonated and protonated oleic acid.

Conclusions

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In summary, we observed mode switching of motion for a self-propelled soap at an oil/aqueous interface as a function of pH. Three types of motion were observed depending on pH, i.e., unidirectional motion at 3.6 ≤ pH ≤ 6.0, motion with inversion at 8.0 ≤ pH ≤ 9.0, and no motion at 11.0 ≤ pH ≤ 12.0. At 3.6 ≤ pH ≤ 6.0, the speed of unidirectional motion is increased with increasing pH due to the increase in the difference in the interfacial tension. Motion with inversion at 8.0 ≤ pH ≤ 9.0 is generated by the discontinuous change in the interfacial tension originating from the heterogeneous distribution of deprotonated oleic acids at the interface. No motion at pH > 11.0 is due to zero spatial difference in the interfacial tension. Numerical calculations suggest that the pH-dependent protonation and deprotonation states of oleic acid at the oil/aqueous interface, along with their adsorption and desorption behaviors, determine the type of self-propelled motion of the OleNa disk. In particular, switching of motion is strongly influenced by pKa and the occupancy ratios of the deprotonated oleic acid (X) at the interface, which are determined by the adsorption/desorption kinetics and oil/aqueous distribution ratios. Our results may provide insights into the environmentally responsive locomotion widely observed in biomimetic behaviors. (52)

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.5c04037.

Calibration curve of oleic acid concentration, interfacial tension over time at pH 6.0, steady-state interfacial tension vs pH, spatiotemporal plot on the meniscus around the OleNa disk, pH dependence of deprotonated and protonated oleic acid concentrations, and adsorption behavior of deprotonated and protonated oleic acids at the interface (PDF)
Self-propulsion of the OleNa disk at pH 6.0 (real time) (AVI)
Self-propulsion of the OleNa disk at pH 8.0 (real time) (AVI)
Meniscus around the OleNa disk pH 8.0 (5× speed) (AVI)
Meniscus around the OleNa disk at pH 6.0 (5× speed) (AVI)
Meniscus around the OleNa disk at pH 12.0 (5× speed) (AVI)

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Author Information

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Corresponding Authors
- Muneyuki Matsuo - Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan; Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo153-8902, Japan; https://orcid.org/0000-0002-2559-3522; Email: [email protected]
- Satoshi Nakata - Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan; https://orcid.org/0000-0002-7290-1508; Email: [email protected]
Authors
- Takahito Arai - Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan
- Masakazu Kuze - Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima739-8526, Japan; Meiji Institute for Advanced Study of Mathematical Sciences (MIMS), Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo164-8525, Japan
Notes
The authors declare no competing financial interest.

Acknowledgments

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This study was supported by JSPS KAKENHI (grant nos. JP20H02712, 24KJ1731, 21H00996, and 25K18011), Iketani Science and Technology Foundation (0351181-A), Cooperative Research Program of “Network Joint Research Center for Materials and Devices” (No. 20251018), Research Fund for Young Scientists; Grant-in-aid of Graduate School of Integrated Sciences for Life, the JSPS Bilateral Joint Research Project between Japan and the Polish Academy of Sciences (JPJSBP120204602), JSPS-Hungary Bilateral Joint Research Project (JPJSBP120213801), ExCELLS, National Institute of Sciences, Project Research (25K18011), JST ACT-X (JP24031207), and MEXT Leading Initiative for Excellent Young Researchers (JPMXS0320230007). We would like to thank Editage (www.editage.jp) for English language editing.

References

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This article references 52 other publications.

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Abstract
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Figure 1
Figure 1. Schematic illustration of (a) the experimental apparatus for observing a self-propelled OleNa disk placed at an oil/aqueous interface, (b) the measurement of the interfacial tension, and (c) the simultaneous measurement of the interfacial tension and movie around the OleNa disk fixed at the oil/aqueous interface. In (a), θ and θ = 0 were defined to analyze the motion in the polar coordinates.
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Figure 2
Figure 2. Time variations of θ for self-propulsion of an OleNa disk at pH = (a) 6.0, (b) 8.0, and (c) 12.0. θ and θ = 0 are defined in Figure 1. The movies of motion in parts (a) and (b) are provided in the Supporting Information as Movies S1 and S2, respectively.
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Figure 3
Figure 3. (a) Phase diagram of self-propelled motion, (b) absolute value of angular speed, |ω|, and (c) ratio of unidirectional motion per 1 min, R, depending on pH of the aqueous phase. Error bars represent the standard deviations obtained from three or four examinations. In the boundary regions at pH 6.9 and 9.8 in (a), both unidirectional motion and motion with inversion were observed, and both motion with inversion and no motion were observed, respectively.
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Figure 4
Figure 4. Time variation of the oil/aqueous interfacial tension at pH 6.0 (red line), 8.0 (blue line), and 12.0 (green line). The downward and upward arrows denote the time when the OleNa disk is placed in contact with the interface from above (t = 10 s) and when it is moved upward away from the interface to the air phase (t = 30 s), respectively.
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Figure 5
Figure 5. Difference in the interfacial tension, Δγ (= γ₀ – γ_s), at the equilibrium state, depending on the pH of the aqueous phase, where γ_s and γ₀ are the interfacial tension at the oil/aqueous interface with and without OleNa in the aqueous and oil phase, respectively. Error bars represent the standard deviation obtained from three examinations.
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Figure 6
Figure 6. (a) Snapshots of the OleNa disk fixed on the interface at pH 8.0 at t = (i) 680, (ii) 700, and (iii) 760 s (slanted view). The movie at pH 8.0 is provided in the Supporting Information as Movie S3 (500 ≤ t ≤ 900 s). (b) Simultaneous measurement of the time variation of the sum of γ_s/w, γ_o/s, and γ_o/w in the vertical direction (γ_v) and the complementary contact angle (θ_c). The data were smoothed by a seven-point moving average (corresponding to ±3 frames, total ∼1.2 s) to reduce noise. The original time resolution was 0.167 s per frame. The vertical position of the disk was adjusted so that the upper surface of the disk almost coincided with the oil/aqueous interface. We confirmed the reproducibility of the oscillatory phenomena.
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Figure 7
Figure 7. Total concentration of oleic acid in the oil (filled circles) and aqueous (empty circles) phases estimated at different pH values.
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Figure 8
Figure 8. Occupancy ratios of deprotonated oleic acids, X, (orange line) and protonated oleic acids, Y, (blue line) at the oil/aqueous interface based on eqs 5 and 6. k_–1 = k₃ = k_–4 = 0.1, k_–2 = 5, k₁ = k₂ = 10, and k_–3 = k₄ = 1000.
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References
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Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.5c04037.
- Calibration curve of oleic acid concentration, interfacial tension over time at pH 6.0, steady-state interfacial tension vs pH, spatiotemporal plot on the meniscus around the OleNa disk, pH dependence of deprotonated and protonated oleic acid concentrations, and adsorption behavior of deprotonated and protonated oleic acids at the interface (PDF)
- Self-propulsion of the OleNa disk at pH 6.0 (real time) (AVI)
- Self-propulsion of the OleNa disk at pH 8.0 (real time) (AVI)
- Meniscus around the OleNa disk pH 8.0 (5× speed) (AVI)
- Meniscus around the OleNa disk at pH 6.0 (5× speed) (AVI)
- Meniscus around the OleNa disk at pH 12.0 (5× speed) (AVI)
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Self-Propulsion of a Soap at an Oil/Aqueous Interface Depending on pHClick to copy article linkArticle link copied!

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Abstract

Note

Introduction

Experimental Section

Figure 1

Results and Discussion

Mode Switching of an OleNa Disk at the Oil/Aqueous Interface Depending on pH

Figure 2

Figure 3

Measurement of Interfacial Tension as the Driving Force of Motion

Figure 4

Figure 5

Figure 6

Estimation of the Total Concentration of Oleic Acid in the Oil and Aqueous Phases

Figure 7

Numerical Calculation of Oleic Acid Concentrations

Figure 8

Conclusions

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Self-Propulsion of a Soap at an Oil/Aqueous Interface Depending on pH
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