In this thesis Moore and Yeo's proposed mapping of the structural glass to the Ising spin glass in a random field is presented. In contrast to Random First Order Theory and Mode Coupling Theory, this mapping predicts that there should be no glass transition at finite temperature. However, a growing correlation length is predicted from the size of rearranging regions in the supercooled liquid, and from this a growing structural relaxation time is predicted. Also presented is a study of the propensity of binary fluids (i.e. fluids containing particles of two sizes) to phase separate into regions dominated by one type of particle only. Binary fluids like this are commonly used as model glass formers and the study shows that this phase separation behaviour is something that must be taken into account.The mapping relies on the use of replica theory and is therefore very opaque. Here a model is presented that may be mapped directly to a system of spins, and also prevents the process of phase separation from occurring in binary fluids. The system of spins produced in the mapping is then analysed through the use of an effective Hamiltonian, which is in the universality class of the Ising spin glass in a random field. The behaviour of the correlation length depends on the spin-spin coupling J and the strength of the random field h. The variation of these with packing fraction and temperature T is studied for a simple model, and the results extended to the full system. Finally a prediction is made for the critical exponents governing the correlation length and structural relaxation time.

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The adhesion at solid/liquid interface plays a fundamental role in diverse fields and helps explain the structure and physical properties of interfaces, at the atomic scale, for example in catalysis, crystal growth, lubrication, electrochemistry, colloidal system, and in many biological reactions. Unraveling the atomic structure at the solid/liquid interface is, therefore, one of the major challenges facing the surface science today to understand the physical processes in the phenomena such as surface coating, self-cleaning, and oil recovery applications. In this thesis, a variety of theory/computational methods in statistical physics and statistical mechanics are used to improve understanding of water adhesion at solid/liquid interfaces. In here, we addressed two separated, but interconnected problems: First, we consider water adhesion on fiber/surface, responsible for the emergence of droplet residue upon droplet detachment. In this project, we study the mechanism of water droplet detachment and retention of residual water on smooth hydrophilic fibers and surfaces using nonequilibrium molecular dynamics simulations. We investigate how the applied force affects the breakup of a droplet and how the minimal detaching force per unit mass decreases with droplet size. We extract scaling relations that allow extrapolation of our findings to larger length scales that are not directly accessible by molecular models. We find that the volume of the residue on a fiber varies nonmonotonically with the detaching force, reaching the maximal size at an intermediate force and associated detachment time. The strength of this force decreases with the size of the drop, while the maximal residue increases with the droplet volume, V, sub-linearly, in proportion to the V2/3. Second, we address the adhesion on conducting graphene. We improved the graphene model by incorporating the conductivity of graphene sheet using the fluctuating charge technique of Constant Potential Molecular Dynamics (CPMD). We evaluated the wettability by measuring the contact angle of cylindrical water drops on a conducting graphene sheet. We found that the CA of a water droplet on a graphene sheet supported by water is lower than in the absence of water under graphene. Our calculations reveal effective attractions between partial charges of equal sign across the conducting graphene sheet. Attractive correlations are attributed to the formation of the highly localized image charges on carbon atoms between the partially charged sites of water molecules on both sides of graphene. By performing additional computations with nonpolar diiodomethane, we confirm that graphene transmits both polar and dispersive interactions. These findings are important in applications including sensors, fuel cell membranes, water filtration, and graphene-based electrode material to enhance the supercapacitor performance. A challenge for future work concerns dynamic polarization response of wetted graphene at alternating (AC) field condition.

Recent years have seen remarkable progress in our understanding of physical aging in nondisordered systems with slow, i.e. glassy-like dynamics. In many systems a single dynamical length L(t), that grows as a power-law of time t or, in much more complicated cases, as a logarithmic function of t, governs the dynamics out of equilibrium. In the aging or dynamical scaling regime, these systems are best characterized by two-times quantities, like dynamical correlation and response functions, that transform in a specific way under a dynamical scale transformation. The resulting dynamical scaling functions and the associated non-equilibrium exponents are often found to be universal and to depend only on some global features of the system under investigation. We discuss three different types of systems with simple and complex aging properties, namely reaction diffusion systems with a power growth law, driven diffusive systems with a logarithmic growth law, and a non-equilibrium polymer network that is supposed to capture important properties of the cytoskeleton of living cells. For the reaction diffusion systems, our study focuses on systems with reversible reaction diffusion and we study two-times functions in systems with power law growth. For the driven diffusive systems, we focus on the ABC model and a related domain model and measure two- times quantities in systems undergoing logarithmic growth. For the polymer network model, we explain in some detail its relationship with the cytoskeleton, an organelle that is responsible for the shape and locomotion of cells. Our study of this system sheds new light on the non- equilibrium relaxation properties of the cytoskeleton by investigating through a power law growth of a coarse grained length in our system. / Ph. D.

High performance natural materials typically employ highly tuned structures spanning the nanoscopic to macroscopic length scales. Synthetically recapitulating this degree of complexity has become a unifying goal connecting the fields of chemistry, nanoscience, biology, and materials science. One common strategy is to direct the bottom up assembly of nanoparticle building blocks into hierarchical structures using stimuli such as electric fields. Despite the promise and great versatility of electric fields, there are many knowledge gaps surrounding their use to assemble highly complex structures. In this thesis, we explore the assembly of nanoparticles into hierarchical structures through dielectrophoresis (DEP), or the motion of polarizable objects in non-uniform electric fields. Critically, through a systematic approach, we study the fundamental polarizability of individual particles, the assembly of particle dimers, and finally the emergence of macroscopic structure from nanoscopic particles. Interweaving these explorations are instrumentation advances that broaden our ability to measure fundamental particle properties and explore hierarchical structures. Initially, we measure the polarizability of nanoparticles in solution using fluorescence microscopy. Specifically, we quantify the polarizability of solution-phase semiconductor quantum dots (QDs) for the first time. Through analyzing the thermodynamic distribution of particles in a microfluidic device with a non-uniform electric field profile, we identify a striking 30-fold increase in polarizability in the presence of low salt conditions due to the Debye screening length being commensurate with the particle size. This increase in polarizability indicates that nanoparticles assemble far more rapidly and easily than previously predicted. Next, we study the assembly of nanoparticles in the vicinity of anisotropic template particles as a path to realizing hierarchical structures. Specifically, we explore eight particle geometries using finite element analysis and find a >10-fold local field enhancement near some shapes, potentially promoting hierarchical assembly. We subsequently introduce a framework for predicting the assembly outcome of particles with multiple distinct sizes and shapes that includes thermodynamic and kinetic considerations. Then, we perform experiments demonstrating the hierarchical assembly of QDs into macroscopic structures. Despite theory predicting the formation of chains, we observe a macroscopic foam-like cellular phase when the QDs experience a combination of alternating current (AC) and direct current (DC) voltages. The resulting materials are both highly hierarchical in that they are 200 µm thick materials comprised of 20 nm particles, but they also represent extremely low-density materials. Finally, we report the invention of a novel instrument for imaging hierarchical materials. Specifically, we describe a massively parallel atomic force microscope with >1000 probes that is made possible through the combination of a new cantilever-free probe architecture and a scalable optical method for detecting probe-sample contact that provides sub-10 nm vertical precision. / 2022-09-28T00:00:00Z

The prediction and analysis of changes in the numbers of biological populations rest on mathematical formulations of demographic events (births and deaths) classified by the age of individuals. The development of demographic theory when birth and death rates vary statistically over time is the central theme of this work. A study of the standard Leslie model for the demographic dynamics of populations in variable environments is made. At each time interval a Leslie matrix of survival rates and fertilities of a population is chosen according to a Markov process and the population numbers in different age classes are computed. Analytical bounds are developed for the logarithmic growth rate and the age-structure of a population after long times. For a two dimensional case, it is shown analytically that a uniform distribution results for the age-structure if the survival rate from the first to the second age-class is a uniformly distributed random quantity with no serial auto correlation. Numerical studies are made which lead to similar conclusions when the survival rate obeys other distributions. It is found that the variance in the survival parameter is linearly related to the variance in the age structure. An efficient algorithm is developed for numerical simulations on a computer by considering a time sequence of births rather than whole populations. The algorithm is then applied to an example in three dimensions to calculate a sequence of births when the survival rate from the first to the second age-class is a random parameter. Numerical values for the logarithmic growth rate and the logarithmic variance for a population and the probability of extinction are obtained and then compared to the analytical results reported here and elsewhere.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19478号 / 理博第4138号 / 新制||理||1595(附属図書館) / 32514 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)講師 市川 正敏, 教授 佐々 真一, 教授 山本 潤 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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