The glass transition is often thought as decoupled from any structural change. I show in this thesis that local order of two types can be detected in a simple experimental glass former. This order increases when approaching the glass transition and is spatially correlated with the dynamic heterogeneities in of the supercooled liquid.

Approaching the glass transition temperature Tg, the temperature dependence of the viscosity or the relaxation time follows at least the Arrhenius law. Glass formers that have a super-Arrhenius behaviour are called fragile, as opposed to strong. It was suggested recently that the fragility of glass formers could be related to the frustration against crystallisation. The glass transition temperature is not a well-defined thermodynamic quantity ; it depends on the cooling rate and on the time scale accessible to the experimentalist. Rather than Tg, some theories use a temperature T0, which corresponds to the temperature where the dynamics (viscosity, relaxation time, etc.) diverge.

Nothing spectacular happens in the positional order of the system at the glass transition: no breaking of symmetry, no drastic structural change. In critical phenomena a static correlation length (the characteristic size of the critical fluctuations) diverges, which are responsible for the dramatic slowing down of the system. No diverging static correlation length could be found for decades in glass forming liquids.

The glass is a non ergodic state of matter where the system is stuck in one configuration, unable to rearrange. By contrast, a supercooled liquid is ergodic even if metastable with respect to the crystal. Supercooled liquids show characteristic dynamical signatures, which include a plateau in the mean square displacement of the particles, a two step relaxation process, non gaussianity of the dynamics and stretching of the decay of correlation functions.

For more than a decade, it is known that the non gaussianity and the stretching are due to dynamic heterogeneities. At a given time, some regions of the supercooled liquid are fast and others are slow. Dynamic heterogeneities are transient and temporally fluctuating. Their size could be characterised using a four-point correlation function and this dynamic length scale diverges toward the glass transition.

Is then the glass transition a purely dynamic phenomenon ? To answer this question Widmer-Cooper and Harrowell ran many simulations from the same initial configuration but with different initial velocities. In this way, they obtained the propensity to move of the different places of this initial configuration independently of the initial dynamic. This propensity was heterogeneous, so some places have a higher probability to move than others. It was then shown by Berthier and Jack that the propensity has a predictive power on the actual dynamic of a given run, but only on medium range scale. Propensity does not predict the dynamic of a given particle but of a mesoscopic region. Nevertheless these works show that dynamic heterogeneities do have a static structural cause - at least in the most common systems.

We are faced with an apparent contradiction: supercooled liquids seem to be amorphous but have some sort of transient local or medium range structure that cause dynamic heterogeneities. This contradiction resolves when considering a structural order criteria catching the local symmetry rather than the long range positional order. An ordered particle is then a particle with a highly symmetric neighbourhood, even if this symmetry is distorted or non existent over a longer range.

This type of structural order is not obtainable experimentally by usual scattering techniques. However if one has the coordinates of the individual particles, like in a simulation, one can use an order parameter taking into account the angles between the bonds linking particles. For example the bond orientational order developed by Seindhart and co-workers is used to study quasi-crystals, crystals and crystallisation. Seindhart bond orientational order is a tensorial order parameter that can be defined for all l-fold symmetry with even l. The rotational invariants of the tensor are called ql and wl. ql describes the strength of the l-fold symmetry. For example icosahedra and crystals (BCC, FCC, HCP) have a strong 6-fold symmetry and thus high values of q6. wl takes a precise value for a given symmetry group. For example the icosahedral symmetry gives w6=-11/√4199~-0.169, whereas the values of all crystals symmetry groups collapse to almost zero.

At finite temperature, the structures are distorted by vibration. This makes the distributions of the ql and wl broad, noisy and overlapping. One can characterise a sample as a mixture of two or three structures, but it is impossible to identify the structure of a single particle. If one takes into account the symmetry of the second shell around a particle and not only the nearest neighbours, the distributions of the coarse-grained Ql and Wl are more robust to thermal fluctuations and less noisy. Structures with a small amount of periodicity (crystal-like) can be resolved at the particle level. Moreover, the signal of the non-periodic structures like icosahedron shrinks to zero. The coarse-grained Q6 is thus a very good indicator of local crystallinity, and local crystallinity only.

Using this technique to analyse simulations of particles close to hard-spheres, Kawasaki and Tanaka showed recently that the fluctuations of the local crystalline order are closely related to dynamic heterogeneities. Moreover, the length scale of these fluctuations show an Ising-like power-law divergence toward the glass transition point. These results suggest a far more direct link than thought before between the glass transition and critical phenomena. Indeed, the glass transition may be a new type of critical phenomenon where a structural order parameter is directly linked to slowness. Moreover, this structural ordering accompanies little change in density, which explains why it has not been detected by the static structure factor so far.

Only a few experimental systems allow access to the individual coordinates of the particles of a supercooled liquid and thus to the bond orientational order. Recently such analysis was performed on two dimensional driven granular matter. For the third dimension, we had to switch to colloids. Confocal microscopy enables us to image colloids in three dimensions. A colloidal suspension is a realistic yet simple system that is able to model many features of condensed matter physics. To our knowledge, colloids were the best choice to investigate experimentally the influence of local order on the glassy dynamics.

Our colloids were designed to behave like hard spheres, one of the most well-studied systems of statistical physics. In particular, it was shown that a system of identical hard spheres has a well-defined freezing transition upon increasing density, driven by purely entropic effects. Hard sphere-like colloids exhibit this transition. Crystallisation can be frustrated by some amount of size polydispersity of the particles, allowing supercooling and a glass transition.

We tracked our colloids to obtain the coordinates of each particle at each time step and following them in time. In order to track tens of thousands particles in a reliable way over extended periods of time, we had to develop a new tracking software with extended capabilities and a gain of speed of between one and two orders of magnitude compared to existing implementations.

From the coordinates linked into trajectories, we were able to compute dynamic quantities (intermediate scattering function, mean square displacement, etc.), both globally and locally. We confirmed that our system exhibits the dynamical signature of supercooled liquids, including the dynamical heterogeneities.

We analysed the local structure of our samples, using both the coarse grained and non coarse grained version of Steinhardt bond orientational order parameter. Surprisingly, the non coarse-grained w6 revealed a strong tendency toward icosahedral order. Particles interacting with an attractive potential have a preferred bond length and naturally form highly symmetric structures at low enough temperatures. For example 13 Lennard-Jones particles in isolation form an icosahedron. For purely repulsive particles, only packing and entropy effects can act to promote local order. Fragments of icosahedra have been detected before in hard-sphere systems, but it was at very high volume fractions, even higher than the glass transition. Icosahedral order was not expected in this proportion in moderately supercooled liquid of hard spheres.

This result was confirmed by re-analysing Kawasaki's simulation data of a similar polydisperse hard-sphere-like system. Icosahedra are detected even in simulations of truly monodisperse systems. The short lived supercooled state contains icosahedra in a proportion similar to polydisperse systems. They are not an effect of polydispersity but may be stabilised by it. The presence of icosahedral clusters is an intrinsic source of frustration to crystallisation in the system. This may explain why hard spheres show some amount of fragility even at zero polydispersity.

We could also confirm experimentally the results of Kawasaki about the local crystalline order parameters Q6. We also detect transient medium range crystalline order reminiscent of critical fluctuations. The high Q6 regions have a strong 6-fold symmetry, but should not be confused with crystal nuclei. Their density is basically the same as the disordered parts. Moreover, they lose their periodicity after the second shell. We could extract a characteristic decay length ξ6 from its spatial correlation function. Volume fraction dependence of ξ6 agrees quantitatively with simulations, diverging toward T0 in a Ising-like fashion.

We could also observe heterogeneous nucleation of crystal at a flat wall. The wall induces layering that promote hexatic plane formation. Even if the equilibrium structure should be Face Centered Cubic crystal (FCC), some planes misalign, forming a random hexagonal compact structure (RHCP). This effect is said to be due to the low free energy difference between FCC and HCP in hard spheres. We could observe this phenomenon during crystal growth an monitor the crystal structures at the particle level using the coarse grain W4. We were also able to see how growing crystals interact with the symmetrically-inconsistent icosahedra.

Despite an extensive exploration of the various parameters exposed by Steinhardt bond orientational order, we could not find other relevant structures in our experimental system or in the simulations. BCC order is absent and dodecahedra are extremely short-lived. The structure of hard sphere systems can then be summarised by a map in the (w6;Q6) plane. Q6 monitors the tendency toward crystallisation (HCP or FCC crystal), whereas w6 follows the formation of icosahedra. We showed that both tendencies are present in hard spheres supercooled liquids and are mutually exclusive.

With this simplified map, we were able to correlate the dynamics of individual particles to their local symmetry. Statistically, ordered particles are slower than the average and rearrange less. On larger length scales, we confirm a mutual exclusion between theses two types of ordered clusters and the fast dynamics regions.

Our results suggest that the dynamical arrest of glass is due to the presence of two types of incompatible local order in the system. One of the two is related to the (crystalline) ground state of the system. The other frustrates crystallisation and is locally stable. The local crystalline order parameter presents critical-like fluctuations growing toward the glass transition. The diverging length scale of theses fluctuations explains the global slowing down of the dynamics. Without the very stable local patches of the second type of order, the crystal would just fill space.

本研究は、コロイド分散系(剛体球系)のガラス転移点近傍での遅いダイナミクスに焦点を当て、一粒子レベルで個々の運動を追跡可能な3次元共焦点レーザ顕微鏡を用いることで、スローダイナミクスの構造的起源を明らかにすることを目的として行なわれた。

第1章では、研究背景と目的について記されている。ガラス転移にかかわる未解明な現象として、液体の2体の密度相関関数にほとんど変化がないにもかかわらず、緩和時間が10桁以上も増大すること、さらに、過冷却度の増大に伴い系のダイナミクスの空間的な不均一化(動的不均一性)が顕著になることが挙げられる。さらに、この二つの現象の間にどのようなかかわりがあるかも未解明な問題である。静的な構造と動的不均一性の関係に注目した最近の研究例にも触れ、静的な構造と動的不均一性のかかわりを調べることで、ガラス転移に伴う遅いダイナミクスの物理的起源に迫ろうという本論文の中心的な目的が記されている。

第2章では、実験で用いる蛍光標識されたコロイド合成法、3次元共焦点レーザ顕微鏡の原理、密度・屈折率マッチングなどの実験の詳細について、第3章では、共焦点顕微鏡による新たな高速粒子位置追跡手法について、第4章では、ボンド秩序変数を中心とした局所構造の定量的解析方法について、第5章では、これらの処理の高速化について記されている。

第6章では、多分散コロイド系(分散度6%)の実験結果の詳細が述べられている。液体構造の体積分率依存性の解析から、ガラス転移点に近づくにつれ発達してくる構造として、結晶的中距離ボンド秩序(結晶構造に近いボンド対称性をもち、構造緩和時間よりも長い寿命を持つクラスター)と正20面体が重要であることが明らかとなった。またこれらの構造の寿命を直接評価することにより、結晶的ボンド秩序が長い寿命を持つこと、正20面体構造には、寿命の長い孤立した完全に近い正20面体とネットワーク上に連結した構造の乱れを伴う寿命の比較的短いものが存在することが示された。様々な幾何学的データの定量解析の結果、局所的な密度の高い正20面体構造を形成する周囲の粒子は比較的大きな自由体積を有しており、正20面体構造の形成は、系全体のエントロピーの増加に寄与することが示された。したがって、結晶的ボンド秩序、正20面体構造はともに系の相関エントロピーを増大させることにより、自由エネルギーを下げる効果を持つことになり、それが過冷却液体の局所的構造化の起源であることが明らかとなった。

第7章では、コロイド分散系を封入した容器の壁付近からの不均一結晶核形成とその成長についてのダイナミクスの研究結果について述べられている。結晶・液体の界面の付近には正20面体構造が存在し、これらの存在が結晶化に対してフラストレーションとして働く可能性が示された。

第8章では、過冷却液体の遅いダイナミクス、とくに局所的な粒子のダイナミクスを定量的に解析することで、局所構造とダイナミクスの相関について議論され、第9章は全体のまとめである。ここでは、局所的な構造化と遅いダイナミクスに強い相関があることを、それぞれの相関長を直接定量評価し比較することで示すとともに、相関長が理想ガラス転移温度に向かって、臨界現象的に発散することを報告している。これまで、過冷却液体のスローダイナミクスの背景に液体の構造化があるという考え方は、論文提出者の所属する研究室のシミュレーション・理論により提案されていたが、実験的な直接の裏付けはなかった。しかし、本研究で局所的なボンド配向秩序とダイナミクスの相関を一粒子レベルの分解能で直接測定することにより、その間に極めて強い相関があることが初めて実験的に示された。特に、遅いダイナミクスの鍵になるのは、結晶的ボンド秩序であり、正20面体的なボンド秩序ではないことが本研究で初めて明確に示され、これまで論争が続いていたガラス転移の背景にあるフラストレーションが、結晶化に対するフラストレーションなのか、正20面体的な効率的なパッキングへ向かっての構造化に伴うフラストレーションなのかという根源的な問いに、少なくともコロイドガラスにおいて、前者のシナリオが正しいということを強く示唆する証拠が得られた。正20面体構造は、直接遅いダイナミクスをもたらすのではなく、結晶化に対するフラストレーションとして結晶化を阻害する因子として働くことが示された。

以上のように、本研究で得られた成果は、長年の未解明問題であるガラス転移にともなう遅いダイナミクスの起源について、液体の局所構造化による運動の低下という新しい視点を提示しており、物理工学上重要なものである。よって本論文は博士(工学)の学位請求論文として合格と認められる。