Non-equilibrium Self-assembly Of Confined Ellipsoids Induced By A Dynamic Boundary

liquid crystal(LC)is widely applied in displays,optical switches and many other electro-optical devices among which different functions are achieved by steering the orientation of LC.Accordingly,the orientation control of LC phases is essential for fundamental studies as well as practical applications.Surface treatment and topographic confinement have emerged as two of the most effective tools to control ordering and orientation of various types of LC phases.Highly complex and tunable spatial arrangements can be acquired by defects on topologically constrained geometries,which can drive assembly of intriguing higher-order hierarchical materials.The combination of soft materials with topological constraints has appeared as a prospective field for organizing matter on micrometer length scales.In our works,activity generated by topology boundary endows the nematic defects with motility.As a result,the complex spatial defect structure becomes dynamic.By controlling the oscillation frequency and amplitude,our simulation suggests a route for designing soft materials with controllable defects.Active energy input provided by boundary drives the nematic ellipsoids far from equilibrium,yielding surprising dynamics.In chapter 1,we briefly introduce the development and characteristics of liquid crystal.We describe three types of liquid crystal phase: nematic,smectic and cholesteric phase.Further,Elastic continuum theory,Landau-de Gennes theory and Maier-Saupe mean field theory are introduced to study the general behavior of the phase transitions in liquid crystal systems.Lastly,recent investigations on the equilibrium and non-equilibrium self-assembly of the liquid crystals and the colloids are introduced,and the active matter is also investigated.In chapter 2,we present the method of Brownian dynamics and the Gay-Berne potential used in our studies.Firstly,the basic theory of Brownian motion,Langevin equation and Brownian motion of a particle in a potential field are introduced.The Brownian motion of isolated ellipsoidal particles in water confined to two dimension is also studied.Finally,we describe the Gay-Berne potential,which is shown to contain the essential features of the intermolecular interaction between the ellipsoid particles.In chapter 3,a typical Gay-Berne ellipsoid is studied by means of Brownian dynamics both in the two-dimensional bulk state and under confinement in circular geometry.This GB system exhibits four different phases as a function of density in the bulk state,which are isotropic(I),Nematic(N),smectic(Sme)and glass.We mainly focus on studying the phase behavior at high area fractions.We analyse in detail the structural order,correlations and self-diffusion properties in the formed various phases of ellipsoids.When the nematic is confined to the circular plane,the particles close to the boundary align along the boundary.The radial distribution of the density and the orientational order parameters as a function of the distance to the wall are calculated.As a result,the phase behavior of the confined system strongly differs from its bulk counterpart.Confinement induces spatial inhomogeneities within the pore volume.Furthermore,the spatial confinement provides a unique opportunity to study the dynamics of a few isolated interacting defects in a controlled way.In chapter 4,to further probe the confinement with a dynamic boundary,we design a simple 2D system comprising ellipsoids confined in a circular periodically stretching and contracting boundary.Brownian dynamics simulations of the system reveal novel dynamic steady structures,which are not available in equilibrium but only under the conditions of appropriate boundary motion.The collective motion of particles,induced by the input energy owing to the boundary motion,is the key to form ordered steady structures,as well as the evolution of dynamic self-assembly.The change of symmetry in steady structures results from the competition between concentric circle due to the circular confinement and lamellar structure owing to the inward aggregation of confined ellipsoids driven by the dynamic boundary.Both slow and fast dynamic evolutions are observed depending on whether the structural rearrangements happen or not.Our results not only show a new way to achieve dynamic self-assembly structures by the confinement with a dynamic boundary,but also inspire us to better understand the self-assembly within the living organisms.In chapter 5,we systematically investigate the several factors influencing selfassembly behaviors of boundary motion.We consider the effects of boundary roughness,the viscosity of the solvent in the large confined circular area,and the confined oscillating boundary geometry.As the boundary smoothness increases to a certain degree,the formed structure does not change and the average energy also reach a fixed value at low frequency and small amplitude.In the solvent of small viscosity,core-shell structure appears under appropriate amplitude and frequency of the moving boundary.Particularly,three structures come into being,including nematic,smectic hexagon and smectic B as packing increases at fixed frequency and amplitude.The geometry of the system restrict the topology of the defects.Confined to a vibrated slit,either increasing the amplitude or the frequency,the ellipsoidal orientation first tends to align with the boundary,then perpendicular to the boundary,lastly align with the slit for the particles at the center.Boundary vibrated ellipsoid-shaped colloid materials confined to quasi-2D square containers self-organize into distinct patterns.Our results not only show the effects of moving boundary on the self-organization of confined ellipsoids,but also suggest a new way to achieve novel steady structures of ellipsoids,which are inaccessible in equilibrium.Finally,we give a summary of the thesis and an outlook for future works on nonequilibrium self-assembly of confined ellipsoids.