# Influence of Asymmetry and Driving Forces on the Propulsion of Bubble-Propelled Catalytic Micromotors

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials and Experimental Setup

_{2}solution (Wako Pure Chemical Industries) (Figure 1c). Figure 1d shows the synthesizing process for the propeller-shaped micromotor with double catalytic sites. First, three types of polymer solutions were introduced into different compartments of the septuple-barreled glass capillary (Figure 1d-I). These solutions were a mixture solution of 2% (w/w) agarose (Sigma-Aldrich, Type IX-A Ultra-low Gelling Temperature, A2576, St. Louis, MO, USA) and 2% (w/w) sodium alginate with 0.5% (w/w) 1 μm polystyrene nanoparticles (PSNPs) (Polysciences, Polybead carboxylate 1.0 micron microspheres, 07310, Warminster, PA, USA) in the A″ part, a mixture solution of agarose and sodium alginate with platinum nanoparticles (PtNPs) (Sigma-Aldrich, platinum powder, ≤10 µm, 327476) in the B″ part, and 3% (w/w) sodium alginate solution in the C″ part. The PSNPs were used only for microscopic observations and the PtNPs were used as catalysts. In addition, all mixture solutions contained 0.1% (w/w) TritonX-100 (Wako Pure Chemical Industries) to prevent aggregations of the PtNPs and the PSNPs, and to balance surface tension [37]. Through the centrifugation of the CDSD, all polymer solutions were dripped from the tip of the capillary (Figure 1c). Then, the detached droplet was solidified at the bottom of the microtube because of the gelation of the sodium alginate solutions in all compartments. After the centrifugation, the droplets were cooled at ~4 °C for ~20 min. The obtained multi-compartmental gel microparticles (Figure 1d-II) consisted of three parts: A′, an interpenetrating network (IPN) gel of a calcium alginate and an agarose gel with the PSNPs; B′, the IPN gel of the calcium alginate and the agarose gel with the PtNPs; and C′, the calcium alginate gel. The calcium alginate gel in all parts was dissolved away by removing Ca

^{2+}ions with a calcium-chelating agent, ethylenediamine-tetraacetic acid (EDTA) (Wako Pure Chemical Industries). The final concentration of the EDTA was 0.25 M. As a result, the propeller-shaped micromotors with PtNPs were produced; as shown in Figure 1d-III, they consisted of agarose gel with the PSNPs (A part) and agarose gel with the PtNPs (B part).

_{2}O

_{2}(Wako Pure Chemical Industries), 0.0005% (w/w) benzalkonium chloride (Wako Pure Chemical Industries), and 1% (v/v) isopropanol (Wako Pure Chemical Industries) (Figure S2a). The catalyst, PtNPs, in the micromotors decomposed hydrogen peroxide molecules in the solution and generated oxygen bubbles: 2H

_{2}O

_{2}$\stackrel{\mathrm{Pt}}{\to}$ 2H

_{2}O + O

_{2}. The motions of micromotors were observed using a digital microscope (KEYENCE, VHX-2000, Osaka, Japan) (Figure S2a). Trajectories of the micromotors were manually tracked in steps of 0.2 s using Image J (National Institutes of Health, New York, NY, USA, 2015, 1.50a). To exclude the effects of an unintended flow of surrounding H

_{2}O

_{2}solution, the tracked coordinate of a floating bubble irrelevant to motor propulsion was subtracted from the tracked coordinate of the self-propelled micromotor.

#### 2.2. Numerical Simulation and Numerical Model

_{2}bubble is detached from the catalytic surface of a micromotor, a pushing force acts on the surface [24]. The motions of the micromotors are considered in a two-dimensional plane (xy-plane). The bubble-propelled motion of the propeller-shaped micromotor with a single catalytic site (Figure 1e) is described by the following over-damped equations of motion for translation and for rotation:

**r**(t) = (x(t), y(t)) is the position of a micromotor (the initial position:

**r**(0) = (0, 0)); $\mathsf{\phi}\left(t\right)$ is the rotational angle of the micromotor ($\mathsf{\phi}\left(0\right)=0$); t is time;

**F**

_{1}(=

**F**

_{side1}+

**F**

_{arc1}) is the net pushing force from the catalytic surfaces;

**F**

_{side1}and

**F**

_{arc1}are the pushing forces from the side and the arc of the blade, respectively; F

_{1rot}is the rotation-direction component of

**F**

_{1}; l (~7.0 × 10

^{−5}m) is the arm length; η

_{tra}(~1.3 × 10

^{−6}kg·s

^{−1}) and η

_{rot}(~8.5 × 10

^{−15}m

^{2}·kg·s

^{−1}) denote coefficients of viscous resistance for translation and rotation, respectively. The force strengths of

**F**

_{side1}and

**F**

_{arc1}have fluctuation as |

**F**

_{side1}| = f

_{side1}+ ξ

_{side1}and |

**F**

_{arc1}| = f

_{arc1}+ ξ

_{arc1}. f

_{side1}(=2 × 10

^{−10}N) and f

_{arc1}(=0.75 f

_{side1}) are constant. ξ

_{side1}and ξ

_{arc1}are Gaussian noises, where the means of ξ

_{side1}and ξ

_{arc1}are 0, and their standard deviations are σ

_{side1}and σ

_{arc1}, respectively. We define normalized magnitude of fluctuation as $\widehat{\mathsf{\sigma}}$

_{side1}= σ

_{side1}/σ

_{0}and $\hat{\mathsf{\sigma}}$

_{arc1}= σ

_{arc1}/σ

_{0}(normalization constant σ

_{0}= 3 × 10

^{−11}N). When f

_{side1}+ ξ

_{side1}< 0, we set |

**F**

_{side1}| = 0. Similarly, when f

_{arc1}+ ξ

_{arc1}< 0, we set |

**F**

_{arc1}| = 0. When σ

_{side1}is small (~0 N), an approximately steady force |

**F**

_{side1}| ~ f

_{side1}acts on the micromotor. This corresponds to the situation in which generated bubble size is relatively uniform. When σ

_{side1}is large (>f

_{side1}), |

**F**

_{side1}| often has the force value ‘0’ and sometimes has a large force value (>2 f

_{side1}) (Figure S3). The value ‘0’ corresponds to the waiting time to grow a large bubble, and the large value corresponds to the large force due to the large bubble sometimes generated, because a larger bubble generates a stronger force but requires a longer waiting time to grow until it reaches the detachment radius [24]. These situations are the same in the case of |

**F**

_{arc1}| (Figure S3). All numerical calculations were carried out for 2000 steps with a step interval of 0.05 s using the numerical computation software MATLAB (MathWorks Inc., Natick, MA, USA).

**F**

_{2}(=

**F**

_{side2}+

**F**

_{arc2}) is the net pushing force from the catalytic surfaces; F

_{2rot}is the rotation-direction component of

**F**

_{2};

**F**

_{side2}(|

**F**

_{side2}| = f

_{side2}+ ξ

_{side2}, f

_{side2}= f

_{side1}) and

**F**

_{arc2}(|

**F**

_{arc2}| = f

_{arc2}+ ξ

_{arc2}, f

_{arc2}= f

_{arc1}) are the pushing forces from the side and the arc of the blade, respectively. ξ

_{side2}and ξ

_{arc2}are Gaussian noises: their means are 0, and their standard deviations are σ

_{side2}and σ

_{arc2}, respectively. We define a set of normalized magnitudes of fluctuation Σ = ($\hat{\mathsf{\sigma}}$

_{side1}, $\hat{\mathsf{\sigma}}$

_{arc1}, $\hat{\mathsf{\sigma}}$

_{side2}, $\hat{\mathsf{\sigma}}$

_{arc2}) = (σ

_{side1}/σ

_{0}, σ

_{arc1}/σ

_{0}, σ

_{side2}/σ

_{0}, σ

_{arc2}/σ

_{0}). All numerical calculations were carried out for 2000 steps with a step interval of 0.05 s using MATLAB.

## 3. Results and Discussion

#### 3.1. Experimental Observation of Bubble-Propelled Motions of Propeller-Shaped Micromotors

_{2}O

_{2}solution, the micromotors were spontaneously propelled near an interface of the solution due to generated bubbles (Figure S2b,c). Figure 2b shows time-series images of the bubble propulsion of the micromotor motion; its schematic illustration is shown in Figure 2c. The micromotor produced various-sized bubbles and was propelled by those bubbles. Figure 2d shows the whole trajectory of the micromotor of Figure 2b (see also Supplementary Video S1). A trajectory of another micromotor is shown in Figure 2e (see also Supplementary Video S2). Both trajectories show circular trajectories, but they are perturbed and not true circles. |

**r**(t)| and $\mathsf{\phi}\left(t\right)$ of the trajectory of both the micromotors are shown in Figure 2f,g. The time courses of |

**r**(t)| in Figure 2f suggest that both the micromotors had about 1–2 s of circular periods, although the periods were perturbed. In addition, $\mathsf{\phi}\left(t\right)$ time courses in Figure 2g indicate that the circular motions were accompanied by monotonic rotations of the micromotors.

**r**(t)| and $\mathsf{\phi}\left(t\right)$ of the trajectory of both the micromotors are shown in Figure 3f,g. Since the catalytic sites were allocated symmetrically, the rotations of the micromotors were observed as expected (Figure 3g). In addition, the fluctuated translational motions were also observed (Figure 3f); the case of the black solid line of Figure 3f seems to be a perturbed circular motion with a period of about 1 s.

#### 3.2. Numerical Analyses of Bubble-Propelled Motions of Propeller-Shaped Micromotors

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 0). Since no fluctuation disturbs the motions of the micromotor, the trajectory exhibits a true circle, which is due to the asymmetric allocation of the catalytic sites. As $\hat{\mathsf{\sigma}}$

_{side1}and $\hat{\mathsf{\sigma}}$

_{arc1}increase, the trajectories are perturbed by the fluctuation of the force strength: $\hat{\mathsf{\sigma}}$

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 1 (Figure 4b); $\hat{\mathsf{\sigma}}$

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 5 (Figure 4c); $\hat{\mathsf{\sigma}}$

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 10 (Figure 4d). Figure 4e,f show the time courses of |

**r**(t)| and $\mathsf{\phi}\left(t\right)$. Periodic increase and decrease in |

**r**(t)| is observed when the fluctuation of the force strength is small; as the fluctuation increases, the increase of the basal value of |

**r**(t)| in addition to the periodic increase and decrease is observed, which indicates that translational displacements of the micromotors occur. Periodic rotations of the micromotors are also observed (Figure 4f). From these results, we guess that the experimentally observed perturbed trajectories of the micromotors (Figure 2d,e) were induced by the fluctuations in the force strength.

_{side1}= f

_{side2}and f

_{arc1}= f

_{arc2}) because the catalytic sites are allocated symmetrically, but the magnitudes of fluctuation of the pushing forces are not identical. In Figure 5a–e, the sides and the arcs that generate a pushing force with large fluctuation are drawn with red lines/curves, and those that generate a pushing force with small fluctuation are drawn with blue lines/curves. The motion patterns vary depending on Σ values as shown by the trajectory in Figure 5a–e and |

**r**(t)| in Figure 5f, but the micromotors in all cases periodically rotate as shown by $\mathsf{\phi}\left(t\right)$ in Figure 5g. In the cases of Figure 5a,d,e, the magnitude of fluctuation of pushing forces are translationally and rotationally symmetric. Thus, the bubble-propelled motions of micromotors seem to be approximately random motions as confirmed by the linear relationship between MSD and Δt (Figure 5h). In the case of Figure 5b, the magnitude of fluctuation of pushing forces is translationally asymmetric; as a result, a circular motion emerges due to the fluctuation asymmetricity even though the basal values of pushing forces are translationally and rotationally balanced. The circular motion is observed as a periodic change of |

**r**(t)| (Figure 5f) and ${G}_{MSD}\left(\mathsf{\Delta}t\right)$ (Figure 5h). In the case of Figure 5c, the magnitudes of fluctuations in pushing forces are rotationally asymmetric; this case also shows the emergence of a circular motion due to the fluctuation asymmetricity. In the cases of Figure 5a,d,e, ${G}_{MSD}\left(\mathsf{\Delta}t\right)$ (Figure 5h) shows approximate linear time variation, which indicates that the motion is approximately random. On the other hand, in the cases of Figure 5b,c, ${G}_{MSD}\left(\mathsf{\Delta}t\right)$ shows time variation with periodic increase and decrease (Figure 5h), which indicates that the circular motions emerge as statistically predominant. The emergent circular motion (Figure 5b) corresponds to the experimental data as shown in Figure 3d,e.

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Schematic illustrations of the propeller-shaped micromotor and synthesizing methods. (

**a**) 3D sketch of the micromotor; (

**b**) 2D sketch of the micromotor with diameter d ~140 μm and an angle of propeller θ ~50°; (

**c**) Schematic illustrations of centrifuge-based droplet-shooting device (CDSD); (

**d**) Synthesizing diagram of the propeller-shaped micromotors. A cross sectional image of the glass capillary (I), the spherical microparticles (II) and the propeller-shaped micromotors with PtNPs (III) are shown; (

**e**,

**f**) Designs of a propeller-shaped micromotor used in our experiments and numerical simulation with a single catalytic site (

**e**) and with double catalytic sites (

**f**).

**Figure 2.**Experimental results of bubble propulsion of the propeller-shaped micromotors with a single catalytic site in the H

_{2}O

_{2}solution. (

**a**) A microscope image of a propeller-shaped micromotor with a single catalytic site; (

**b**) Time series from t = 5.6 s to t = 8.0 s of a propeller-shaped micromotor with a single catalytic site propelled by bubbles; (

**c**) Schematic illustration of the trajectory of (

**b**); (

**d**) The whole trajectory of the micromotor in (

**b**); Cyan arrow: t = 0 s; magenta arrow: t = 10 s; (

**e**) Trajectory of another micromotor. The notation of arrows is the same as in (

**d**); (

**f**) The time variation of |

**r**(t)|. Black solid line: For trajectory of (

**d**); red dashed line: For trajectory of (

**e**); (

**g**) The time variation of $\mathsf{\phi}\left(t\right)$. The notation of each line is the same as in (

**f**).

**Figure 3.**Experimental results of bubble propulsion of the propeller-shaped micromotors with double catalytic sites in the H

_{2}O

_{2}solution. (

**a**) A microscope image of a propeller-shaped micromotor with double catalytic sites; (

**b**) Time series from t = 7.8 s to t = 9.4 s of a propeller-shaped micromotor with double catalytic sites propelled by bubbles; (

**c**) Schematic illustration of the trajectory of (

**b**); (

**d**) The whole trajectory of the micromotor in (

**b**); Cyan arrow: t = 0 s; magenta arrow: t = 10 s; (

**e**) Trajectory of another micromotor. The notation of arrows is the same as in (

**d**); (

**f**) The time variation of |

**r**(t)|. Black solid line: For trajectory of (

**d**); red dashed line: For trajectory of (

**e**); (

**g**) The time variation of $\mathsf{\phi}\left(t\right)$. The notation of each line is the same as in (

**f**).

**Figure 4.**Numerical analyses of bubble propulsion of the propeller-shaped micromotors with a single catalytic site. (

**a**–

**d**) Calculated trajectories of the micromotor in each condition of $\hat{\mathsf{\sigma}}$

_{side1}and $\hat{\mathsf{\sigma}}$

_{arc1}. $\hat{\mathsf{\sigma}}$

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 0 (

**a**); $\hat{\mathsf{\sigma}}$

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 1 (

**b**); $\hat{\mathsf{\sigma}}$

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 5 (

**c**); $\hat{\mathsf{\sigma}}$

_{side1}= $\hat{\mathsf{\sigma}}$

_{arc1}= 10 (

**d**); Cyan arrow: t = 0 s; magenta arrow: t = 100 s; (

**e**) The time variation of |

**r**(t)|. Black line: For trajectory of (

**a**); red line: For trajectory of (

**b**); green line: For trajectory of (

**c**); blue line: For trajectory of (

**d**); (

**f**) The time variation of $\mathsf{\phi}\left(t\right)$. The notation of each line is the same as in (

**e**).

**Figure 5.**Numerical analyses of bubble propulsion of the propeller-shaped micromotors with double catalytic sites. (

**a**–

**e**) Calculated trajectories of the micromotor in each condition of Σ = ($\hat{\mathsf{\sigma}}$

_{side1},$\hat{\mathsf{\sigma}}$

_{arc1},$\hat{\mathsf{\sigma}}$

_{side2},$\hat{\mathsf{\sigma}}$

_{arc2}). Red lines/curves: the sides and the arcs that generate a pushing force with large fluctuation. Blue lines/curves: the sides and the arcs that generate a pushing force with small fluctuation. Σ = (1, 1, 1, 1) (symmetric) (

**a**); Σ = (1, 10, 1, 1) (asymmetric) (

**b**); Σ = (10, 1, 1, 1) (asymmetric) (

**c**); Σ = (1, 10, 1, 10) (symmetric) (

**d**); Σ = (10, 1, 10, 1) (symmetric) (

**e**); Cyan arrow: t = 0 s; magenta arrow: t = 100 s; (

**f**) The time variation of |

**r**(t)|. Black line: For trajectory of (

**a**); blue line: For trajectory of (

**b**); purple line: For trajectory of (

**c**); green line: For trajectory of (

**d**); orange line: For trajectory of (

**e**); (

**g**) The time variation of $\mathsf{\phi}\left(t\right)$. The notation of each line is same as (

**f**); (

**h**) The time variation of mean square displacement (MSD) ${G}_{\mathrm{MSD}}\left(t\right)$. The notation of each line is same as (

**f**).

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**MDPI and ACS Style**

Hayakawa, M.; Onoe, H.; Nagai, K.H.; Takinoue, M.
Influence of Asymmetry and Driving Forces on the Propulsion of Bubble-Propelled Catalytic Micromotors. *Micromachines* **2016**, *7*, 229.
https://doi.org/10.3390/mi7120229

**AMA Style**

Hayakawa M, Onoe H, Nagai KH, Takinoue M.
Influence of Asymmetry and Driving Forces on the Propulsion of Bubble-Propelled Catalytic Micromotors. *Micromachines*. 2016; 7(12):229.
https://doi.org/10.3390/mi7120229

**Chicago/Turabian Style**

Hayakawa, Masayuki, Hiroaki Onoe, Ken H. Nagai, and Masahiro Takinoue.
2016. "Influence of Asymmetry and Driving Forces on the Propulsion of Bubble-Propelled Catalytic Micromotors" *Micromachines* 7, no. 12: 229.
https://doi.org/10.3390/mi7120229