Data_Sheet_1_Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects.PDF

Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.</p

Video_1_Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects.MP4

Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.</p

Deck the Walls with Anisotropic Colloids in Nematic Liquid Crystals

Nematic liquid crystals (NLCs) offer remarkable opportunities to direct colloids to form complex structures. The elastic energy field that dictates colloid interactions is determined by the NLC director field, which is sensitive to and can be controlled by boundaries including vessel walls and colloid surfaces. By molding the director field via liquid-crystal alignment on these surfaces, elastic energy landscapes can be defined to drive structure formation. We focus on colloids in otherwise defect-free director fields formed near undulating walls. Colloids can be driven along prescribed paths and directed to well-defined docking sites on such wavy boundaries. Colloids that impose strong alignment generate topologically required companion defects. Configurations for homeotropic colloids include a dipolar structure formed by the colloid and its companion hedgehog defect or a quadrupolar structure formed by the colloid and its companion Saturn ring. Adjacent to wavy walls with wavelengths larger than the colloid diameter, spherical particles are attracted to locations along the wall with distortions in the nematic director field that complement those from the colloid. This is the basis of lock-and-key interactions. Here, we study ellipsoidal colloids with homeotropic anchoring near complex undulating walls. The walls impose distortions that decay with distance from the wall to a uniform director in the far field. Ellipsoids form dipolar defect configurations with the colloid’s major axis aligned with the far field director. Two distinct quadrupolar defect structures also form, stabilized by confinement; these include the Saturn I configuration with the ellipsoid’s major axis aligned with the far field director and the Saturn II configuration with the major axis perpendicular to the far field director. The ellipsoid orientation varies only weakly in bulk and near undulating walls. All configurations are attracted to walls with long, shallow waves. However, for walls with wavelengths that are small compared to the colloid length, Saturn II is repelled, allowing selective docking of aligned objects. Deep, narrow wells prompt the insertion of a vertical ellipsoid. By introducing an opening at the bottom of such a deep well, we study colloids within pores that connect two domains. Ellipsoids with different aspect ratios find different equilibrium positions. An ellipsoid of the right dimension and aspect ratio can plug the pore, creating a class of 2D selective membranes

Deck the Walls with Anisotropic Colloids in Nematic Liquid Crystals

Nematic liquid crystals (NLCs) offer remarkable opportunities to direct colloids to form complex structures. The elastic energy field that dictates colloid interactions is determined by the NLC director field, which is sensitive to and can be controlled by boundaries including vessel walls and colloid surfaces. By molding the director field via liquid-crystal alignment on these surfaces, elastic energy landscapes can be defined to drive structure formation. We focus on colloids in otherwise defect-free director fields formed near undulating walls. Colloids can be driven along prescribed paths and directed to well-defined docking sites on such wavy boundaries. Colloids that impose strong alignment generate topologically required companion defects. Configurations for homeotropic colloids include a dipolar structure formed by the colloid and its companion hedgehog defect or a quadrupolar structure formed by the colloid and its companion Saturn ring. Adjacent to wavy walls with wavelengths larger than the colloid diameter, spherical particles are attracted to locations along the wall with distortions in the nematic director field that complement those from the colloid. This is the basis of lock-and-key interactions. Here, we study ellipsoidal colloids with homeotropic anchoring near complex undulating walls. The walls impose distortions that decay with distance from the wall to a uniform director in the far field. Ellipsoids form dipolar defect configurations with the colloid’s major axis aligned with the far field director. Two distinct quadrupolar defect structures also form, stabilized by confinement; these include the Saturn I configuration with the ellipsoid’s major axis aligned with the far field director and the Saturn II configuration with the major axis perpendicular to the far field director. The ellipsoid orientation varies only weakly in bulk and near undulating walls. All configurations are attracted to walls with long, shallow waves. However, for walls with wavelengths that are small compared to the colloid length, Saturn II is repelled, allowing selective docking of aligned objects. Deep, narrow wells prompt the insertion of a vertical ellipsoid. By introducing an opening at the bottom of such a deep well, we study colloids within pores that connect two domains. Ellipsoids with different aspect ratios find different equilibrium positions. An ellipsoid of the right dimension and aspect ratio can plug the pore, creating a class of 2D selective membranes

Deck the walls by tunable energy fields for colloidal particles (Data)

<p>The ability to dictate colloid motion is an important challenge in fields ranging from materials science to living systems. Here, by embedding energy landscapes in conned nematic liquid crystals, we design a versatile platform to dene colloidal migration. This is achieved by placing a wavy wall with alternating hills and wells in a nematic liquid crystal to impose a smooth elastic energy field with alternating splay and bend distortions. This domain generates (meta) stable loci that act as attractors and unstable loci that repel colloids over distances large compared to the colloid radius. Energy gradients in the vicinity of these loci are exploited to dictate colloid trajectories. We demonstrate several aspects of this control, by studying transitions between defect configurations, propelling particles along well defined paths and exploiting multistable systems to send particles to particular sites within the domain. Finally, we demonstrate the ability of a colloid in motion, like \Goldilocks", to select from wells of different sizes for preferred docking. Such tailored landscapes have promise in reconfigurable systems and in microrobotics applications.</p

Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials

Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraintthe requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as “line slips”. More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. These results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nanomaterials

Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials

Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraintthe requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as “line slips”. More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. These results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nanomaterials

Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials

Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraintthe requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as “line slips”. More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. These results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nanomaterials

Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials

Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraintthe requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as “line slips”. More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. These results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nanomaterials

Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials

Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraintthe requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as “line slips”. More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. These results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nanomaterials