Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level.
We report on the identification and quantitative characterization of elementary edge and screw dislocations in a colloidal smectic phase of tip-labeled rods. Thanks to the micrometer layer spacing, direct visualization of dislocations has been performed at the \textit{smectic periodicity scale} by optical fluorescence microscopy. As a result, the displacement field around an edge dislocation has been experimentally established and compared with the profile predicted by elastic theory. Elementary screw dislocations have been also evidenced, for which the core size as well as the \textit{in situ…
Understanding the relaxation dynamics of colloidal suspensions is crucial to identify the elements that influence the mobility of their constituents, assess their macroscopic response across the relevant time and length scales, and thus disclose the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft-repulsive rod-like particles, which are able to self-organise into nematic and smectic liquid-crystalline phases. By performing Dynamic Monte Carlo simulat…
Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetti…
Weakly attractive interactions between the tips of rod-like colloidal particles affect their liquid-crystal phase behaviour due to a subtle interplay between enthalpy and entropy. Here, we employ molecular dynamics simulations on semi-flexible, repulsive bead-spring chains of which one of the two end beads attract each other. We calculate the phase diagram as a function of both the volume fraction of the chains and the strength of the attractive potential. We identify a large number of phases that include isotropic, nematic, smectic A, smectic B and crystalline states. For tip attraction energ…
We perform extensive Monte Carlo simulations to investigate the phase behaviour of colloidal suspensions of hard board-like particles (HBPs). While theories restricting particle orientation or ignoring higher ordered phases suggest the existence of a stable biaxial nematic phase, our recent simulation results on monodisperse systems indicate that this is not necessarily the case, even for particle shapes exactly in between prolate and oblate geometries, usually referred to as self-dual shape. Motivated by the potentially striking impact of incorporating biaxial ordering into display applicatio…
Self-diffusion in isotropic and liquid crystalline phases of fd virus colloidal rods: a combined single particle tracking and differential dynamic microscopy study
Colloids held by optical or magnetic tweezers have been used to explore the local rheological properties of a complex medium and to extract work from fluctuations with some appropriate protocols. However, a general theoretical understanding of the interplay between the confinement and the interaction with the environment is still lacking. Here, we explore the statistical properties of the position of a probe confined in a harmonic trap moving at constant velocity and interacting with a bath of colloidal particles maintained at a different temperature. Interactions among particles are accounted…
Computing stable configurations of confined smectic liquid crystals with a deep variational framework
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Columbia University（哥伦比亚大学）；Center for Applied Mathematics, Renmin University of China（中国人民大学应用数学中心）；School of Mathematical Sciences, Beijing International Center for Mathematical Research, Center for Quantitative Biology, Center for Machine Learning Research, Peking University（北京大学数学科学学院、北京国际数学研究中心、定量生物学中心、机器学习研究中心）
The effective dynamics of a colloidal particle immersed in a complex medium is often described in terms of an overdamped linear Langevin equation for its velocity with a memory kernel which determines the effective (time-dependent) friction and the correlations of fluctuations. Recently, it has been shown in experiments and numerical simulations that this memory may depend on the possible optical confinement the particle is subject to, suggesting that this description does not capture faithfully the actual dynamics of the colloid, even at equilibrium. Here, we propose a different approach in w…
The mechanical properties of crystalline materials can be substantially modified under confinement. Such modified macroscopic properties are usually governed by the altered microstructures and internal stress fields. Here, we use a parallel plate geometry to apply a quasi-static squeeze flow crushing a colloidal polycrystal while simultaneously imaging it with confocal microscopy. The confocal images are used to quantify the local structure order and, in conjunction with Stress Assessment from Local Structural Anisotropy (SALSA), determine the stress at the single-particle scale. We find that …
The structure of finite self-assembling systems depends sensitively on the number of constituent building blocks. Recently, it was demonstrated that hard sphere-like colloidal particles show a magic number effect when confined in spherical emulsion droplets. Geometric construction rules permit a few dozen magic numbers that correspond to a discrete series of completely filled concentric icosahedral shells. Here, we investigate the free energy landscape of these colloidal clusters as a function of the number of their constituent building blocks for system sizes up to several thousand particles.…
Calorimetric study of the nematic to smectic-\textit{A} and smectic-\textit{A} to smectic-\textit{C} phase transitions in liquid-crystal+aerosil dispersions
Composed of microscopic layers that stack along one direction while maintaining fluid-like positional disorder within layers, smectics are excellent systems for exploring topology, defects and geometric memory in complex confining geometries. However, the coexistence of crystalline-like characteristics in one direction and fluid-like disorder within layers makes lamellar liquid crystals notoriously difficult to model - especially in the presence of defects and large distortions. Nematic properties of smectics can be comprehensively described by the Q-tensor but to capture the features of the s…
Understanding the relationship between colloidal building block shape and self-assembled material structure is important for the development of novel materials by self-assembly. In this regard, colloidal superballs are unique building blocks because their shape can smoothly transition between spherical and cubic. Assembly of colloidal superballs under spherical confinement results in macroscopic clusters with ordered internal structure. By utilizing Small Angle X-Ray Scattering (SAXS), we probe the internal structure of colloidal superball dispersion droplets during confinement. We observe and…
Understanding relaxation of supercooled fluids is a major challenge and confining such systems can lead to bewildering behaviour. Here we exploit an optically confined colloidal model system in which we use reduced pressure as a control parameter. The dynamics of the system are ``Arrhenius'' at low and moderate pressure, but at higher pressures relaxation is faster than expected. We associate this faster relaxation with a decrease in density adjacent to the confining boundary due to local ordering in the system enabled by the flexible wall.
In a system of colloidal inclusions suspended in a thermalized bath of smaller particles, the bath engenders an attractive force between the inclusions, arising mainly from entropic origins, known as the depletion force. In the case of active bath particles, the nature of the bath-mediated force changes dramatically from an attractive to a repulsive one, as the strength of particle activity is increased. We study such bath-mediated effective interactions between colloidal inclusions in a bath of self-propelled Brownian particles, being confined in a narrow planar channel. Confinement is found …
Monodisperse rod-like colloidal particles are known for spontaneously forming both nematic and smectic liquid crystal phases, but their self-assembly was typically exploited from the fundamental soft condensed matter physics perspective. Here we demonstrate that depletion interactions, driven by non-adsorbing polymers like dextran and surfactants, can be used to enrich self-organization of photon-upconversion nanorods into orientationally ordered nematic and smectic-like membrane colloidal superstructures. We study thermodynamic phase diagrams and demonstrate polarization-dependent photon upco…
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at the boundary. Using this novel system, we capture the amorphous-order particle clusters and demonstrate the development of a static correlat…
We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in point-like units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showi…
The persistent dynamics in systems out of equilibrium, particularly those characterized by annihilation and creation of topological defects, is known to involve complicated spatiotemporal processes and is deemed difficult to control. Here the complex dynamics of defects in active smectic layers exposed to strong confinements is explored, through self-propulsion of active particles and a variety of confining geometries with different topology, ranging from circular, flower-shaped epicycloid, to hypocycloid cavities, channels, and rings. We identify a wealth of dynamical behaviors during the evo…
We investigate the phase behaviour of a two-dimensional colloidal model system of ultra-soft particles on a substrate which varies periodically along one spatial direction. Our calculations are based on mean-field density functional theory for a system of particles interacting via an ultra-soft potential, that is, the generalized exponential model with index four (\mbox{GEM-4}). For suitable substrate periodicities (with commensurability parameter $p=2$), we find a succession of phase transitions from a modulated liquid to a locked smectic and then to a locked floating solid phase. The appeara…
Chiral crystals consisting of micro-helices have many optical properties while presently available fabrication processes limit their large-scale applications in photonic devices. Here, by using a simplified simulation method, we investigate a bottom-up self-assembly route to build up helical crystals from the smectic monolayer of colloidal helices racemate. With increasing the density, the system undergoes an entropy-driven co-crystallization by forming crystals of various symmetries with different helical shapes. In particular, we identify two crystals of helices arranged in the binary honeyc…
Understanding the correlation between structure and rheology in colloidal suspensions is important as these suspensions are crucial in industrial applications. Moreover, colloids exhibit a wide range of structures under confinement that could considerably alter the viscosity. Here, we use a combination of experiments and simulations to elucidate how confinement induced structures alter the relative contributions of hydrodynamic and repulsive forces to produce up to a ten fold change in the viscosity. We use a custom built confocal rheoscope to image the particle configurations of a colloidal s…
The complex behavior of confined fluids arising due to a competition between layering and local packing can be disentangled by considering quasi-confined liquids, where periodic boundary conditions along the confining direction restore translational invariance. This system provides a means to investigate the interplay of the relevant length scales of the confinement and the local order. We provide a mode-coupling theory of the glass transition (MCT) for quasi-confined liquids and elaborate an efficient method for the numerical implementation. The nonergodicity parameters in MCT are compared to…
We use computer simulations to study the existence and stability of a biaxial nematic $N_b$ phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long ($L$), medium ($M$), and short ($S$) particle axis. For all three shape families, we find stable $N_b$ states provided the shape is not only close to the so-called dual shape with $M = \sqrt{LS}$ but also sufficiently anisotropic with $L/S>9,11,14, 23$ for rhombi, prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-$N_b$ trans…
