arXiv subjects

Zhijuan He

Publications and source records attributed to Zhijuan He.

4 recordsLinked to original sources

arXiv2024

Phase Behaviour of X-Shaped Liquid Crystalline Molecules

X-shaped liquid crystalline molecules (XLCMs) are obtained by tethering two flexible end A-blocks and two flexible side B-blocks to a rigid backbone (R). A rich array of ordered structures can be formed from XLCMs, driven by the competition between the interactions between the chemically distinct blocks and the molecular connectivity. Here, we report a theoretical study on the phase behaviour of XLCMs with symmetric and asymmetric side blocks by using the self-consistent field theory (SCFT). A large number of ordered structures, including stable smectic-A, triangle-square, pentagon and giant polygon, are obtained as solutions of the SCFT equations. Phase diagrams of XLCMs as a function of the total length and asymmetric ratio of the side chains are constructed. For XLCMs with symmetric side blocks, the theoretically predicted phase transition sequence is in good agreement with experiments. For XLCMs with a fixed total side chain length, transitions between layered structure to polygonal phases, as well as between different polygonal phases, could be induced by varying the asymmetry of the side chains. The free energy density, domain size, side-chain stretching , and molecular orientation are analyzed to elucidate mechanisms stabilizing the different ordered phases.

cond-mat.soft↗

arXiv2024

High-accurate and efficient numerical algorithms for the self-consistent field theory of liquid-crystalline polymers

Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT encompass efficiently solving plenty of six dimensional partial differential equations (PDEs), precisely determining the subtle energy difference among self-assembled structures, and developing effective iterative methods for nonlinear SCF iteration. To address these challenges, this work introduces a suite of high-order and efficient numerical methods tailored for SCFT of liquid-crystalline polymers. These methods include various advaced PDE solvers, an improved Anderson iteration algorithm to accelerate SCFT calculations, and an optimization technique of adjusting the computational domain during the SCF iterations. Extensive numerical tests demonstrate the efficiency of the proposed methods. Based on these algorithms, we further explore the self-assembly behavior of liquid crystalline polymers through simulations in four, five, and six dimensions, uncovering intricate three-dimensional spatial structures.

math.NA↗

arXiv2024

Phase behavior of symmetric diblock copolymers under 3D soft confinement

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using the self-consistent field theory. The soft confinement is realized in binary blends composed AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in the homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particle to square SL. When the C homopolymers are strongly selective to the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement.

cond-mat.soft↗

arXiv2024

Theory of polygonal phases self-assembled from T-shaped liquid crystalline molecules

Extensive experimental studies have shown that numerous ordered phases can be formed via the self-assembly of T-shaped liquid crystalline molecules (TLCMs) composed of a rigid backbone, two flexible end chains and a flexible side chain. However, a comprehensive understanding of the stability and formation mechanisms of these intricately nanostructured phases remains incomplete. Here we fill this gap by carrying out a theoretical study of the phase behaviour of TLCMs. Specifically, we construct phase diagrams of TLCMs by computing the free energy of different ordered phases of the system. Our results reveal that the number of polygonal edges increases as the length of side chain or interaction strength increases, consistent with experimental observations. The theoretical study not only reproduces the experimentally observed phases and phase transition sequences, but also systematically analyzes the stability mechanism of the polygonal phases.

cond-mat.soft↗