Nematic Ordering of Anisotropic Nanoparticles in Block Copolymers

Investigation of structural frustration in symmetric diblock copolymers confined in polar discs through cell dynamic simulation

Nanotechnology has opened new avenues for advanced research in various fields of soft materials. Materials scientists, chemists, physicists, and computational mathematicians have begun to take a keen interest in soft materials due to their potential applications in nanopatterning, membrane separation, drug delivery, nanolithography, advanced storage media, and nanorobotics. The unique properties of soft materials, particularly self-assembly, have made them useful in fields ranging from nanotechnology to biomedicine. The discovery of new morphologies in the diblock copolymer system in curved geometries is a challenging problem for mathematicians and theoretical scientists. Structural frustration under the effects of confinement in the system helps predict new structures. This mathematical study evaluates the effects of confinement and curvature on symmetric diblock copolymer melt using a cell dynamic simulation model. New patterns in lamella morphologies are predicted. The Laplacian involved in the cell dynamic simulation model is approximated by generating a 17-point stencil discretized to a polar grid by the finite difference method. Codes are programmed in FORTRAN to run the simulation, and IBM open DX is used to visualize the results. Comparison of computational results with existing studies validates this study and identifies defects and new patterns.

Sublimation of isolated toric focal conic domains on micro-patterned surfaces

Toric focal conic domains (TFCDs) in smectic liquid crystals exhibit distinct topological characteristics, featuring torus-shaped molecular alignment patterns with rotational symmetry around a central core. TFCDs have attracted much interest due to their unique topological structures and properties, enabling not only fundamental studies but also potential applications in liquid crystal (LC)-based devices. Here, we investigated the precise spatial control of the arrangement of TFCDs using micropatterns and sublimation of TFCDs to estimate the energy states of the torus-like structures. Through simulations, we observed that the arrangement of TFCDs strongly depends on the shape of the topographies of underlying substrates. To accurately estimate the energetic effects of non-zero eccentricity and evaluate their thermodynamic stability, we propose a geometric model. Our findings provide valuable insights into the behavior of smectic LCs, offering opportunities for developing novel LC-based devices with precise control over their topological properties.

Nanoparticle anisotropy induces sphere-to-cylinder phase transition in block copolymer melts

Block copolymer nanocomposites including anisotropic nanoparticles have been previously found to co-assemble into complex structures with nanoparticle alignment. Anisotropic nanoparticles with large aspect ratios are found to modify the morphology of block copolymers at modest concentrations, inducing a sphere-to-cylinder phase transition by breaking the local symmetry in the vicinity of a solid particle. This transition takes place over a wide range of NP lengths comparable with the BCP spacing. Controlling the orientation of uniaxial nanoparticles provides additional control over the global orientation of the block copolymer, as previously reported by experiments.

Hybrid Time-Dependent Ginzburg–Landau Simulations of Block Copolymer Nanocomposites: Nanoparticle Anisotropy

Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer–particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg–Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg–Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg–Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles.