Self-propelling phenomenon, especially on the dynamics and collective effects of self-propelling objects, has attracted considerable attention over the past decade for its ubiquity at all kinds of length scales, along with its nonequilibrium nature. However, insights into the physics of such self-propelling objects through experiments have been problematic owing to the difficulty in the realisation of a controllable experimental system, notably at a microscopic level. In this dissertation, self-propelling phenomenon at a microscopic scale is investigated experimentally by use of a novel experimental system consisting asymmetric colloids (Janus particles) under AC electric field, with an additional intention and interest in observing the effect of thermal fluctuations on the self-propulsion of such particles. For this reason, three main topics are studied experimentally; i) general features of particle motion and interaction, ii) application of fluctuation theorem to self-propelling objects, iii) collective behaviour of self-propelling objects at microscopic length scales.

For the experimental system used in the present study, when an AC electric field is applied to a suspension of Janus particles (polystyrene particle of few micrometres in size, half coated with gold), a two-dimensional motion of these particles perpendicular to the direction of the forcing is observed. The confinement of the particle motion to a two-dimensional plane is one of the novelties of the experimental system, where a realistic motion, i.e., translational motion with the ability to change its direction of motion (albeit it not being intentional), is demonstrated and can be tracked simultaneously. The other novelty is the fact that the self-propulsion of the Janus particles can be controlled relatively well. Indeed, the self-propelling velocity of the particles show electric field squared proportionality, which is expected for ICEP (Induced-charge electrophoresis) generated by ICEO (Induced-charge electro-osmosis) flow in the vicinity of the particle surface.

Not only is the present Janus particle system beneficial for the experimental study of selfpropelling objects, it displays a plethora of interesting behaviours that are purely phenomenal. The system shows an AC frequency dependence, having 3 characteristic frequency regions; Aggregation region, Self-propelling (SP) region, and Inverse SP region. Every region has its unique motion and interaction. In the Aggregation region (~500Hz), particles do not self-propel. Strictly speaking, particles do not self-propel in the sense that the polarity of the Janus particle with respect to the direction of motion is random. Aggregation of particles and the motion of particles driven towards the aggregation can be expressed by dielectrophoresis. Whereas, in the SP (500Hz~30kHz) and Inverse SP (30kHz~) regions, particles self-propel and interact among themselves. Nevertheless, particles move in the direction of the polystyrene side and show repulsive interactions for the SP region, while the motion is in the direction of the metal side and the interaction is attractive for the Inverse SP region. Consequently, since the main interest is in the self-propelling objects, the general features of the two self-propelling regions are investigated in depth.

Self-propelling motion of the Janus particles is enhanced with the increase in the applied electric field, where the trajectories become straighter. Moreover, as mentioned above, the self-propelling velocity of the particles is attained via mean squared displacement, demonstrating proportionality to the applied electric field squared, as is expected by theory.

Furthermore, the AC frequency dependence of the particle velocity is examined. Switching of the direction of motion is observed, having no signs of hysteresis. ICEP velocity is calculated for a dielectric sphere with half metal coating, where a compact-layer model is also considered. Using appropriate physical values, the frequency dependence of the particle velocity similar to the experimental result is realised. This particular switching frequency can be estimated by considering a typical time necessary for the charging of the electric double-layer. Since the above frequency depends on the salt concentration of the medium and the particle size, the dependency is tested for different NaCl concentration and particle size, and show that it is sufficient in describing the approximate behaviour of the switching frequency.

In addition, the change in interaction between the SP and Inverse SP regions is scrutinised by regarding that the polarisability of dielectric material cannot follow the AC electric field when the frequency is to a certain degree too fast. At a characteristic frequency, i.e., Maxwell-Wagner frequency, it can be predicated that the dipole configuration of the particle polarisation changes to a quadrupole configuration, which in turn induces attraction between particles. Actually, the Maxwell-Wagner frequency is calculated to be similar to the switching frequency.

Once the general features are known, a variety of experiments can be conducted with the Janus particles.

For small objects with length scales of the order of nanometre to submicrometre, precisely the size range in which the Janus particles belong to, the effect of thermal fluctuation cannot be neglected. The relation between such fluctuations and active self-propulsion is scarcely understood, especially from an experimental point of view. Accordingly, fluctuation theorem is applied to the Janus particle system in order to question how self-propelling force of the particles competes with thermal fluctuation and also to examine the validity of fluctuation theorem on self-propelling objects. In consideration of the above aims, experiments using Janus doublets are carried out in the Inverse SP frequency region. Since in this region, particles are able to attract each other and self-propel concurrently, rotating Janus doublet can be produced. The rotation demonstrates a continuous and fluctuating nature, having a probability of rotation counter to the main direction of rotation, i.e., negative rotation. Increasing the applied voltage to the system causes the Janus doublets to rotate faster and the probability of negative rotation to decrease. This result is obvious though on the other hand very interesting. There is a probability of getting instantaneous negative entropy production, although on the average it is of course positive, as is stated by the second law of thermodynamics. Using only the rotation angle θ and fluctuation theorem defined for rotating Janus doublet, the torque acting on the Janus doublet is estimated. To confirm the validity of the estimated torque via fluctuation theorem, it is compared with another torque estimated by the rotating velocity and Stokes equation with near wall correction. Both estimated torques show good agreement with each other, evincing the validity of fluctuation theorem on self-propelling objects.

The other interest concerning self-propelling objects is the collective behaviour. This topic is extremely important especially from the standpoint of nonequilibrium statistical mechanics since collective behaviours exhibit macroscopic order despite having only relatively simple local rules that are under the effect of noises from the environment. Notwithstanding its importance, seldom has it been studied experimentally, for the difficulty in the realisation of controllable experiments. Therefore, it could be said that the present study is the first ever attempt to look into collective behaviour of self-propelling artificial (and controllable) particles at a microscopic scale. In the experiments, a few hundreds of particles self-propel in the region of observation, done in the SP region where the particles are able to move without the attraction of the particles.

Before studying the collective behaviour of the Janus particles in depth, an evaluation on the angular fluctuation with respect to the self-propulsion due to differences in applied electric field is done. Clearly, the fluctuation of the direction of motion weakens as the applied electric field is increased. This is important in the sense that it acts like some sort of noise in the system.

Next, experiments using many Janus particles are conducted. The first set of interest is in the manner in which the particles aligned during self-propulsion. Spatial correlation of the direction of motion is calculated, where it shows a short-range correlation of approximately a few particles' diameter in length. Despite the short-range nature of the correlation, interestingly enough, particles demonstrate the tendency of polar alignment at small distances (between the particles), i.e., particles face more or less in the same direction locally. However, obvious to some extent, when the distance between the particles is large, the direction of motion is random. Such local alignment, though not very strong, induced a swirl-like structure.

The kind of structure mentioned above should in principle be initiated by collective motion, which exhibits anomalous density fluctuations that are not observed in equilibrium systems. For this reason, the next set of interest is in the density fluctuations, or strictly speaking the fluctuation in the number of particles in a given area of observation. In an equilibrium system with a mean number of particles N, the standard deviation of the number of particles ΔN is proportional to √N, as is stated by the central limit theory. Nevertheless, it is known that for a system that demonstrates collective motion, ΔN deviates from the √N proportionality, where the scaling exponent α for ΔN ∝ Nα is larger than 0.5 (theoretically, for collective motion, it should reach the value α = 0.8). Consequently, ΔN and N is experimentally obtained for the many self-propelling Janus particle system for a wide range of area size within the region of observation. When the particle density is moderately high and the self-propulsion is relatively fast, a significant deviation of ΔN from √N is seen, having a value of approximately α = 0.6. On the other hand, when the surface fraction, namely particle density, and/or the particle velocity is low, the deviation is not apparent. The possible reasoning into the aforementioned deviation is scrutinised by discussing the distinctive change in both the spatial correlation and angular fluctuation for the experimental condition where such deviation is unique. However, according to theories, when the system is in the disordered phase, i.e., the majority of the objects are not well aligned, which is the case in the present experiment (in the sense that long-range alignment is absent), ΔN should not deviate from √N. The discrepancy between the experiment and theory may probably be due to the following reasons. Firstly, finite size effect can be considered. Although there are no boundaries anywhere near the particles, some particles are pinned to the bottom electrode (which is inevitable) and they may act as a sort of boundary. Secondly, it may be caused by the complexity of the system, especially the fact that the system is at a microscopic length scale with hydrodynamic effects, which are not considered in the theories. Interestingly, such discrepancy mentioned above was observed experimentally for microscopic biological objects. Since experimental studies at a microscopic scale are extremely rare, all the results including the disagreement with theory is meaningful. Without doubt, more of such experimental investigation into collective behaviours is necessary in the future, especially at microscopic length scales.

The dissertation experimentally explores some of the fundamental aspects of not only nonequilibrium physics but also active and self-propelled matter system. A lot remains unclear, however, it is safe to say that this dissertation adds a new category in the "catalogue of generic behaviours" concerning physics of self-propelled objects, especially in the sense that experimental studies at a microscopic level had not been done prior to the present dissertation. Furthermore, the introduction and initiation of such experimental investigation regarding self-propelled objects seen in this dissertation, will surely benefit in driving the field of self-propelled/active matter to prominence and in appreciating the many wonders that nature displays.

本論文は7章からなる。第1章は序論であり,研究の背景と目的が述べられている。第2章では本研究で用いたヤヌス粒子(金を半球上に蒸着したポリエチレンビーズ)が交流電場中で電場と垂直方向に動く原理について説明している。第3章ではヤヌス粒子の製造法、実験系の設定について記述している。第4章から6章では、実験結果を示すとともに考察を行っている。第4章では運動の方向と粒子間の相互作用についての周波数依存性を調べている。第5章では、この実験系でゆらぎの定理が成り立つことを示し、回転のトルクを見積もっている。第6章では粒子の集団運動を解析し、高密度において熱平衡状態で見られるランダムな分布とは異なる振る舞いをすることを示した。第7章では、本研究の結論が述べられている。

我々人間を含めて、生き物はエネルギーを消費しつつ、能動的に動いている。このような自己駆動する物体の運動を物理として一般的にとらえよういう機運が非平衡物理の研究者にあり、そのモデル系として自己駆動する粒子の運動が最近、盛んに研究されている。本研究で用いた電場による運動は、化学反応による運動に比べて、運動速度などを容易に制御できる長所がある。また、エネルギーを常に供給しているので長時間の観測も可能である。従って、自己駆動する物体の物理現象を調べるモデル実験系のひとつとして、今後の発展が期待できる。

ヤヌス粒子の電場による運動について、これまでに直線上の運動とその速度依存性については報告されていたが、周波数依存性については調べられていなかった。論文提出者は周波数によって3つの運動モードがあることを発見した。低周波では、運動は行わず、粒子間には引力が働き、凝集する。中間の周波数では金の凝着面の方向に運動し、粒子間には斥力が働く。高周波では運動の方向が逆転し、ポリエチレンの面の方向に運動し、粒子間には引力が働く。これらの運動は電場で誘起された粒子表面上の電荷による電気浸透流によるものである。論文提出者は、金属と誘電体の部分における電気二重層を形成する時間の差を考慮することによって、運動方向の反転も定量的に理解できることを示した。実験で得られる塩濃度、粒子半径依存性も定量的に説明できる。粒子間の相互作用が反転することは誘電体が高周波数では交流電場に追随できなくなることによって説明できる。このように論文提出者は電場周波数を変えることで運動方向と粒子間の相互作用を制御できること示し、そのメカニズムもしっかりと解析している。

第5章において、2つのヤヌス粒子が接着したdoubletを用いて、ゆらぎの定理を検証している。ゆらぎの定理は90年代半ばに提案された非平衡状態でも成り立つ比較的新しい定理である。まだ、実験系での検証例はそれほど多くない。高周波領域において、基板上に接着したヤヌス粒子の周りをその粒子に接着したヤヌス粒子が回転することがあることに見て、論文提出者はゆらぎの定理の検証に適していることに気づき、検証を行っている。回転の前後への遷移確率が、ゆらぎの定理の関係を満たすことを確認し、その大きさから、回転のトルクを見積もった。回転速度と粘性からくる回転の摩擦抵抗から見積もったトルクを誤差の範囲内で一致することを示し、トルクからも、ゆらぎの定理が成り立っていることを明らかにした。また、ゆらぎの定理を用いると回転速度を用いるよりもトルクを精度よく見積もれることが示した。この測定法は細胞運動など複雑な自己駆動物体の解析にも有効であると思われる。

第6章において、ヤヌス粒子の集団運動を解析している。まず、粒子間の運動の相関を調べ、近接粒子では運動方向が揃う傾向があることを示した。密度ゆらぎを、粒子数の測定空間の長さ依存性を調べた。低密度では熱平衡で見られるような中心極限定理が成り立つが,高密度では成り立たないことを示した。このような空間分布の非一様性は自己駆動する物体の集団運動に特徴的なものであると思われる。

以上のように本論文では,非対称基板上を回転する粒子の運動の周波数依存性とその動作原理を明らかにするとともに、この実験系を用いて、ゆらぎの定理の検証、粒子の集団運動の新しい知見も得ている。論文提出者の構築した実験系はエネルギーを消費して運動する粒子の実験系の中でも、制御が容易で長時間観察可能であり、今後の非平衡物理学の発展への寄与が期待できる。なお本論文は指導教員である佐野雅己氏(全般)と佐野研究室ポスドク研究員のHong-Ren Jiang(4章)の共同研究であるが,論文提出者が主体となって研究を行ったもので,論文提出者の寄与が十分であると判断する。

したがって,審査員全員の一致により,博士(理学)の学位を授与できると認める。