Reciprocating Motion of a Self-Propelled Object on a Molecular Layer

Mar 4, 2013 - Π at States I and II is equal to that in States III and IV, respectively. Under compression from A = 0.4 nm2 molecule–1 to Amax, the ...
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Reciprocating Motion of a Self-Propelled Object on a Molecular Layer with a Local Minimum and a Local Maximum Isotherm Satoshi Nakata,* Tatsuya Miyaji, Tomoaki Ueda, Taisuke Sato, Yumihiko S. Ikura, Shunsuke Izumi, and Masaharu Nagayama †

Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0812, Japan

‡

S Supporting Information *

ABSTRACT: The mode change of a simple autonomous motor depending on the nature of an N-acyl-p-nitroaniline, (CnANA, CH3(CH2)n−2CONHφNO2, n = 8, 14, 16, 18, or 22) monolayer on water was investigated. A camphor disk was floated on a molecular layer of CnANA, which gave a characteristic surface pressure (Π) vs area (A) isotherm. The nature of the camphor motion changed depending on the Π vs A isotherm, and in particular reciprocating motion was observed for C14ANA, C16ANA, and C18ANA, which gave a Π vs A isotherm with a local minimum and a local maximum. The characteristic motion of a camphor disk is discussed in relation to the Π vs A isotherm of CnANA and the influence of the interaction between molecules on the driving force of motion. Reciprocating motion was qualitatively reproduced by numerical calculation.

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floated on a molecular layer of CnANA, the features of motion changed characteristically depending on the Π vs A isotherm. In particular, one-dimensional reciprocating motion was observed for A lower than that at the local minimum of Π, and could be qualitatively reproduced by a numerical calculation based on the Newtonian equation, the surface pressure of camphor and CnANA as a driving force, and the phase-field model. This characteristic change in self-motion is discussed in relation to the Π vs A isotherm and the molecular properties of CnANA.

INTRODUCTION The creation of autonomous motors, which can transport and manipulate matter on a small scale while sensing and adapting to the environment, is an important challenge in industrial and medical fields.1 Because the features of bacterial motion can change in response to changes in the environment, such as in taxis, we must learn how to mimic living organisms to overcome this challenge. All motor organs or organelles in living organisms work under almost isothermal and nonequilibrium conditions.2 Although several artificial autonomous motors have been studied under almost isothermal and chemical nonequilibrium conditions,3−17 changes in the features of motion depending on the molecular properties have not yet been investigated. We have previously investigated the mode-switching of selfmotion for a camphor system18,19 depending on the internal conditions (e.g., the scraping morphology and the chemical structure of camphor derivatives),20 external conditions (e.g., surface tension, chemical stimuli, shape of the water chamber, and coupling),21−25 and a chemical reaction26−28 as a novel autonomous motor that is driven by a difference in surface tension. In addition, the essential features of self-motion have been qualitatively reproduced by numerical calculations.20,21,24,26,27 In the present study, we introduce a novel type of selfmotion that depends on the surface pressure (Π) vs area per molecule (A) isotherm of an N-acyl-p-nitroaniline (CH3(CH2)n−2CONHφNO2, CnANA) monolayer. Several CnANA (n = 14, 16, and 18) molecular layers exhibit large nonlinearity; i.e., a local minimum and local maximum are present in the Π vs A isotherm.29,30 When a camphor disk was © 2013 American Chemical Society

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EXPERIMENTAL SECTION Camphor was purchased from Wako Chemicals (Kyoto, Japan). Water was first distilled and then purified with a Millipore MilliQ filtering system (pH of the obtained water, 6.3; resistance, >20 MΩ). A camphor disk (diameter, 3 mm; thickness, 1 mm; mass, 5 mg) was prepared using a pellet die set for FTIR. The movement of the camphor disk was monitored with a digital video camera (SONY HDR-CX590, minimum time-resolution: 1/30 s) and then analyzed by an image-processing system (ImageJ, National Institutes of Health, USA). The surface pressure depending on the surface area was measured with a surface pressure meter (Kyowa Interface Science Co. Ltd., HMB, Saitama, Japan). For the water phase, 200 mL of 2 mM CaCl2 aqueous solution was poured into a trough of the surface pressure meter (surface area, 0.005−0.021 m2; standard water level, 6 mm). To prepare a molecular layer on the aqueous phase, N-acyl-p-nitroaniline (CH3 (CH2 )n−2CONHφNO2 , Received: January 29, 2013 Revised: March 4, 2013 Published: March 4, 2013 6346

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CnANA, n is number of carbons in the acyl chain equal to 8, 14, 16, 18, and 22) was dissolved in chloroform, and the chloroform solution was dropped on the aqueous phase with a microsyringe (volume: several tens of microliters). The amount of CnANA dropped on water was 84 × 10−9 mol, and the area per molecule (A) was obtained from this amount and the surface area of water phase. The temperature was maintained at 293 ± 1 K throughout the experiments. C16ANA was prepared by the following general procedure.29,30 A mixture of p-nitroaniline (10 mmol) and the appropriate acyl chlorides (10 mmol) was treated with triethylamine (1.01 g) in tetrahydrofuran (40 mL) at room temperature for 3 h. The reaction mixture was carefully neutralized with dilute hydrochloric acid (2 M) and then filtered. The filtrate was concentrated at reduced pressure, and the residue was recrystallized from chloroform. C16ANA: prepared as pale yellow needles in 70% yield; mp 93−94 °C; 1H NMR (500 MHz, CDCl3) δ = 8.20 (d, J = 9.03 Hz, 2H), 7.72 (d, J = 9.03 Hz, 2H), 7.63 (s, 1H), 2.42 (t, J = 7.49 Hz, 2H), 1.74 (quin, J = 7.44 Hz, 2H), 1.20−1.39 (m, 24H), 0.88 ppm (t, J = 6.87 Hz, 3H).

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RESULTS Figure 1 shows the surface pressure (Π)−area (A) isotherms for CnANA molecular layers (n = 8, 14, 16, 18, and 22). The

Figure 2. Surface pressure (Π)−area (A) isotherm for a molecular layer of C18ANA. The barrier was scanned for compression (from A = 0.43 to Ar nm2 molecule−1; blue line), expansion (from A = Ar to 0.43 molecule−1; red line), and compression (from A = 0.43 to 0.09 nm2 molecule−1; green line). Ar = (a) 0.33, (b) 0.24, and (c) 0.09 nm2 molecule−1. The scan rate for A was 0.052 nm2 molecule−1 min−1.

initial compression disappeared under the second compression, as seen in Figure 2b,c. Figure 3 shows (b) snapshots of the motion and (c) time variation of L for the trajectory of a camphor disk on molecular layers of (1) C14ANA (θ = 0.81π rad, A = 0.12 nm2 molecule−1) and (2) C18ANA (θ = 0.44π rad, A = 0.15 nm2 molecule−1). R(θ) is the axis obtained by rotating the x-axis, θ is the angle between the R- and x-axes, and L is the displacement from a given point, (x, y) = (0, 0), to the point on the R-axis that is nearest to the camphor disk, as defined in Figure 3a. In this experiment, a camphor disk was placed on the molecular layer of CnANA (n = 14 or 18) after A reached 0.12 for C14ANA or 0.15 nm2 molecule−1 for C18ANA by compression. For C14ANA, the reciprocating motion of the camphor disk, which followed an almost linear trajectory, started when the camphor disk was placed on the molecular layer of C14ANA. After this reciprocating motion (frequency, 0.4 Hz; amplitude, 10 mm) had proceeded for 2 min, it changed to irregular motion. For C18ANA, 30 s after no motion in the initial state, reciprocating motion of the camphor disk started (frequency, 0.6 Hz; amplitude, 8 mm). After this reciprocating motion had proceeded for 5 min, it finally changed to irregular motion within a circular area at ∼2000 mm2. Figure 4 shows the two-dimensional trajectory of camphor motion as observed from above, and the average amplitude of L depending on θ for molecular layers of CnANA (n = 8, 14, and 18) at a constant area (A = 0.15 nm2 molecule−1). The lengths of the error bars in the individual figures reflect the irregularity of camphor motion. As indicated in Figure 4b-1, the amplitude was maximum at θ = 4π/9 rad; i.e., the motion for C18ANA was considered to be reciprocating motion on the axis at θ = 4π/9 rad. For C14ANA, irregular motion within a circular area of ∼1600 mm2 was observed (Figure 4a-2), and the amplitude of L was independent of θ (Figure 4b-2). For C8ANA, a camphor

Figure 1. Surface pressure (Π) under the compression of a molecular layer of CnANA (n = 8, 14, 16, 18, or 22) at a rate of 0.052 nm2 molecule−1 min−1.

surface pressure for C8ANA remained at zero with a decrease in A. Π vs A isotherms with a local minimum and a local maximum were observed for C14ANA, C16ANA, and C18ANA. The area per molecule at the local minimum, Amin, and that at the local maximum, Amax, both increased with n. The Amin values for C14ANA, C16ANA, and C18ANA were 0.20, 0.21, and 0.28 nm2 molecule−1, and those for Amax were 0.26, 0.27, and 0.31 nm2 molecule−1, respectively. The surface pressure for C22ANA clearly increased at A = 0.25 nm2 molecule−1 without a local minimum and a local maximum under compression of the monolayer. Figure 2 shows the surface pressure (Π)−area (A) isotherm for a C18ANA molecular layer under an initial compression, expansion at Ar, and a second compression, where Ar is the area at which the initial compression of the monolayer is changed to expansion. The Π vs A isotherm in compression was almost similar to that in expansion at Ar ≥ 0.31 nm2 molecule−1, as seen in Figure 2a. In contrast, that in the initial compression was larger than that in expansion at Ar < 0.31 nm2 molecule−1; i.e., Π decreased to zero when expansion began, and the local maximum of Π at around A = 0.3 nm2 molecule−1 under the 6347

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Figure 3. (a) Definitions for R, θ, and L for the analysis of camphor motion. (b) Snapshots of camphor motion (time interval: 1/3 s) and (c) time variation of L along the trajectory of a camphor disk on a molecular layer of (1) C14ANA at A = 0.12 nm2 molecule−1 and (2) C18ANA at A = 0.15 nm2 molecule−1. All of the trimmed snapshots were of the same space and size. t is the elapsed time after the camphor disk is placed on the molecular layer of C14ANA or C18ANA. θ = 0.81π rad (b-1, blue line of c-1) and 0.44 rad (b-2, blue line of c-2). (c-1) θ = 0.81π rad (blue line) and 0.31π rad (red dotted line), and (c-2) θ = 0.44π rad (blue line) and 0.94π rad (red dotted line).

nm2 molecule−1, respectively. For C22ANA, continuous motion was observed at A > 0.23 nm2 molecule−1, and no motion was observed at A ≤ 0.23 nm2 molecule−1 (data not shown). No reciprocating motion was observed for C8ANA or C22ANA under the present conditions.

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DISCUSSION On the basis of the present experimental results and related studies,20,22,23 we discuss the mechanism of reciprocating motion of a camphor disk on a molecular layer with a local minimum and a local maximum Π vs A isotherm. Figure 1 suggests that a Π vs A isotherm with a local minimum and a local maximum is obtained for an acyl group of a proper length, i.e., n = 14, 16, and 18. The Π vs A isotherm for n = 8 remains zero under compression because it is difficult to create a monolayer due to the small number of hydrocarbons. In contrast, hydrophobic interaction on a C22ANA monolayer may reduce the local minimum and a local maximum of the Π vs A isotherm under the present conditions. Figure 2 suggests that the Π vs A isotherm was reversible at A that was higher than that in the local maximum of Π (∼0.3 nm2 molecule−1) but was irreversible at A that was lower than that in the local maximum of Π. In addition, disappearance of the local maximum of Π in the second compression is due to the first compression at A
Amax, the speed of camphor motion decreases and finally reaches zero due to the decrease in the difference in surface pressure between camphor (∼20 mN m−1) and CnANA as the driving force.30 The continued absence of motion of the camphor disk is due to the reversibility of the CnANA molecular layer to maintain a surface pressure that is higher than that for camphor. Under compression at A < Amax, the camphor disk moves again due to the decrease in Π of CnANA. As shown in Figure 4-2, camphor motion within a restricted area at around the local minimum of Π suggests that a condensed CnANA molecular layer exists around the area of camphor motion and the camphor disk cannot move on the condensed molecular layer. Under further compression, the camphor disk does not move in the initial stage, because Π for camphor is lower than that for CnANA. However, after a rest period, the camphor disk exhibits reciprocating motion. The motion of the camphor disk can fluctuate due to the instability of camphor molecules that have accumulated around the settled disk and the slight heterogeneity in the initial floating state.23 The surface density of the CnANA molecular layer is increased due to further compression by camphor motion. The camphor disk cannot move further due to the condensed CnANA molecular layer with a higher surface pressure. The surface density of the molecular layer of CnANA along the trajectory of camphor motion remains low due to irreversible condensation, and that of the molecular layer of camphor is also decreased due to the sublimation of camphor molecules. The camphor disk starts to move in the opposite direction due to inversion of the surface pressure around the camphor disk22 and moves along the same trajectory. Because the CnANA molecular layer on the opposite side is condensed by camphor motion in a similar manner, onedimensional reciprocating motion along the same trajectory is repeated. The compressed CnANA molecular layer does not expand to reduce the heterogeneity of the surface density due to the irreversible condensation of CnANA molecules. The change from reciprocating motion for 5 min to irregular motion within a circular area suggests that irreversible condensation proceeds slowly with time while the camphor disk reciprocates. A difference in the surface tension in self-propelled systems induces Marangoni flow.15−17 We have previously reported the relationship between self-motion and Marangoni flow.25,31 Although the effect of Marangoni flow should be considered, we discuss the difference in surface tension to clarify the mechanism, because the magnitude of Marangoni flow depends on the difference in the surface tension. To confirm the mechanism of reciprocating motion, we introduce a mathematical model for one-dimensional system based on the related works.20−24 First, motion of a camphor

Figure 5. Schematic illustration to discuss the nature of the Π vs A isotherm with a local minimum and a local maximum. Amax is the area per molecule at the local maximum of Π. The horizontal dotted line at Π = 20 mN m−1 corresponds to the maximum surface pressure of the molecular layer of camphor.

isotherm with a local minimum and a local maximum for CnANA (n = 14, 16, or 18). Π at States I and II is equal to that in States III and IV, respectively. Under compression from A = 0.4 nm2 molecule−1 to Amax, the response of the molecular layer of C n ANA is reversible to maintain a homogeneous distribution, and therefore Π is increased (see States I and II). The area per molecule in State II is close to the crosssection of the CnANA molecular layer based on the molecular orbital method. When A becomes lower than Amax by compression, the interaction between CnANA molecules is increased. We previously reported the interaction of a CnANA molecular layer; i.e., we spectroscopically confirmed that a molecular layer of C18ANA is condensed by hydrogen bonding and π−π 6349

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disk on a CnANA (n = 14, 16, or 18) molecular layer can be expressed by a Newtonian equation, eq 1:20,22,24 mxc̈ = r0(Γ(ur ,wr) − Γ(ul ,wl)) − μxċ

s=

a(u ,w ,α(s)) u − a7 ⎧ + α (s ) w ≥ w b ⎪ a6ϕ(α(s);w0) tanh a 8 ⎪ ⎪ =⎨ u − (a 7 + a 9w) w < wb ⎪ a6ϕ(α(s);w0) tanh a8 ⎪ ⎪ + α (s ) ⎩

α (s ) =

(4)

(5)

The effect to reduce the movement of camphor by CnANA molecular layer is described as

(6)

where Du and a5 are positive constants. The dynamics of surface concentration of CnANA is considered as interface motion accompanied by the density change, and we introduce a modified phase field model with conservation of the volume.32 ∂w ∂ 2w = ε 2 2 + w(w − a)(w0 − w) − ws ∂t ∂x

4

(10)

(11)

Numerical calculation was performed as a control parameter, w0, under the periodic boundary condition and a proper initial condition based on eqs 1−11, as indicated in Figure 6. w0 can be replaced with the area, A, based on Aw0 = 1. Features of motion at A = 2.5, 1.4, 0.77, and 0.58 correspond to uniform, stop, uniform, and oscillatory motion, respectively. The relationship between the velocity of motion and Πw was also calculated with a decrease in A (see Supporting Information). Thus, the experimental results can be qualitatively reproduced by numerical calculation. Equations 2 and 3 suggest that a camphor disk can move at Π1 > Π(w) (or γ1 < γ(w)). Therefore, the camphor disk indicates uniform motion at A = 0.25 and 0.77. In contrast, the camphor disk cannot move at Π1 ≤ Π(w) (or γ1 ≥ γ(w)); i.e., the camphor disk does not move at A = 1.43. However, we discuss the reason why the camphor disk indicates oscillatory motion at A = 0.58 even if Π1 ≤ Π(w) from a numerical point of view. The CnANA molecular layer is irreversible at w > wb and is compressed by the development of the camphor molecular layer from the disk at u ∼ a7. Π(w) is locally lower than Π1 because the area at w = 0 exists when the CnANA molecular layer is compressed by the development of camphor layer. In this interval at w = 0, the disk can move because the surface pressure depends on u. While the camphor disk pushes the CnANA molecular layer, the difference in the surface tension around the disk is inversed due to sublimation.22 Therefore, the camphor disk inverts and pushes the CnANA molecular layer, which exists at the opposite side. The space of the trajectory of motion is enlarged by the repetition of oscillatory motion. Finally, oscillatory motion at a constant

⎪

⎛ w⎞ d(w) = Du exp⎜ − ⎟ ⎝ a5 ⎠

9w0 2 + 72s

⎧ α(s) < w0/2 ⎪ α(s ) ϕ(α(s);w0) = ⎨ ⎪ ⎩ w0 − α(s) α(s) ≥ w0/2

(3)

where k and s0 are the rate on sublimation and supplement of camphor. The first, second, and third terms of the right side correspond to the diffusion depending on w, sublimation of camphor, and supplement of camphor molecules from the camphor disk, respectively. The function, f(u,xc;r0), is expressed as

⎪

5w0 −

And, function ϕ, which plays a role to determine a value of eq 9 in the suitable range, is described as

where ai and bj (i = 1−4, j = 1, 2) are positive constants. Next, we consider u and w. The reaction-diffusion equation on u is given by eq 4.

⎧1 − u |x − xc| < r0 f (u , xc ;r0) = ⎨ |x − xc| ≥ r0 ⎩0

(9)

where ai (i = 6−9) are positive constants and wb is the concentration when the CnANA molecular layer switches between reversibility and irreversibility. Here, wb corresponds to 1/Amax (Figure 5). α′(s) and α″(s) are regarded as two solutions on (w−a)(w0−w) − s = 0 in eq 7. When α′(s) = 2α″(s), α′(s) is regarded as α(s). α(s) is given in eq 10 when s is treated explicitly.

(2)

b ⎛ a w − 1⎞ Π(w) = 1 ⎜1 + tanh 1 ⎟ 2⎝ a 2w ⎠

∂u ∂ ⎛⎜ ∂u ⎞ = d(w) ⎟ − ku + s0f (u ,xc ;r0) ⎝ ∂t ∂x ∂x ⎠

(8)

The function, a is the effect on the occupancy of the water surface between CnANA molecular layer and camphor disk is expressed as

where γ1 is the minimum surface tension of camphor, γ(w) is the surface tension of CnANA molecular layer, and β is a positive constant. The surface pressure of w, Π(w), which is equal to γ0 − γ(w) (γ0: the surface tension of pure water), is supposed to be given by eq 3 based on the Π vs A isotherm for CnANA (n = 14, 16, or 18).

⎛ ⎛1 ⎞2 ⎞ + b2 exp⎜ −a3⎜ − a4⎟ ⎟ ⎝w ⎠⎠ ⎝

∫Ω w dx

(1)

where m, r0, xc, and μ are the mass, radius, position of the camphor disk, and the constant of viscosity, respectively. u and w are the surface concentrations of camphor and CnANA, respectively. Subscripts, r and l, are the positions of the right and left edges of the camphor disk, respectively, i.e., ur = u(t,xc+r0), ul = u(t,xc−r0), wr = w(t,xc+r0), and wl = w(t,xc−r0). The surface tension, Γ, depending on u and w may be expressed by eq 2:20,22,24 ⎧ βγ u 2 + γ(w) ⎪ γ1 < γ(w) ⎪ 1 2 Γ(u ,w) = ⎨ 1 + βu ⎪ ⎪ γ(w) γ1 ≥ γ(w) ⎩

∫Ω w(w0 − w)(w − a(u ,w ,α(s))) dx

(7)

where ε (0 < ε ≪ 1) is the constant and w0 is the average value of w at the initial state. s is determined by eq 8. 6350

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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Prof. Seiji Shinkai (Sojo University, Japan) for providing useful suggestions on the interaction of CnANA molecules. This work was supported in part by a Grant-in-Aid for Scientific Research (No. 23111715) to SN, (No. 21340023) to MN, and a Grant-in-Aid for the Global COE Program “Formation and Development of Mathematical Sciences Based on Modeling and Analysis”.

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Figure 6. Numerical calculation of (upper) the time variation of the velocity of self-propelled motion at w0 = (a) 1.7, (b) 1.3, (c) 0.7, and (d) 0.4, and (lower) the Π vs A isotherm based on eqs 1−10. The parameters were μ = 0.5, r0 = 1.0, m = 1.0, γ1 = 55, β = 2.0, γ0 = 72, b1 = 71, a1 = 0.5, a2 = 0.2, b2 = 30, a3 = 5.0, a4 = 1.3, k = 0.5, s0 = 2.0, Du = 1.0, a5 = 0.01, ε = 0.1, a6 = 0.1, a7 = 0.4, a8 = 0.02, a9 = 2.0, and wb = 0.8.

amplitude is maintained while the compression length by camphor motion is balanced to the expansion length of the compressed CnANA molecular layer.

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CONCLUSION The major finding of this study is that a camphor disk shows reciprocating motion on a molecular layer of CnANA (n = 14, 16, or 18) with a local maximum and local minimum values on a Π vs A isotherm. This characteristic Π vs A isotherm was discussed in relation to the interaction between CnANA molecules on water and the irreversible condensed state. The mechanism of reciprocating motion at a lower A was discussed in relation to the property of the CnANA molecular layer and the camphor molecular layer that developed from the solid disk. Reciprocating motion was qualitatively reproduced by a numerical calculation based on the suggested mechanism and the related studies. Our experimental results suggest that an autonomous motor, which can change the features of its motion depending on the chemical structure of the molecular layer on water, can be controlled at a molecular level.

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ASSOCIATED CONTENT

S Supporting Information *

Discussion of experimental results for measurement of disk speed and surface pressure, dynamics of the molecular layer, and numerical results for the change of camphor motion velocity. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel & fax: +81-82-424-7409. E-mail: [email protected]. jp. 6351

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dx.doi.org/10.1021/jp400971h | J. Phys. Chem. C 2013, 117, 6346−6352