arXiv subjects

An-Chang Shi

Publications and source records attributed to An-Chang Shi.

At least 19 recordsLinked to original sources

arXiv2026

Structure and energetics of grain boundaries in self-assembled double-gyroid block copolymer networks

Grain boundaries (GBs) are ubiquitous defects in crystalline materials. However, they remain less explored in block copolymer ordered phases. Here, we develop a self-consistent field theory framework to investigate GB structure and energetics in double-gyroid (DG) diblock copolymer networks. The GB energy landscape is obtained as a function of GB orientation, which reveals multiple local minima representing distinct network-switching GBs. Remarkably, the global minimum is a previously unidentified asymmetric-tilt network-switching GB (ATNS), exhibiting a lower energy than the experimentally observed $(422)$ twin boundary (TB). Comparative analyses of representative low- (ATNS, $(422)$ TB) and high-energy twist ($(0\bar{1}\bar{1})$, $(100)$ TNSs) GBs reveal that, unlike enthalpy-dominated hard matter, GB stability in DG networks is predominantly entropy-driven. Twist-type GBs generate new nodes and disrupt nodal coplanarity, causing chain packing frustration and large entropy penalties. Conversely, the ATNS preserves favorable network connectivity and minimizes conformational constraints on polymer chains, making it the energetically preferred GB.

cond-mat.soft↗

arXiv2026

Phason-Driven Diversity of Nucleation Pathways in Icosahedral Quasicrystals

The nucleation of quasicrystals remains a fundamental puzzle, primarily due to the absence of a periodic translational template. Here, we demonstrate that phasons - hidden degrees of freedom unique to quasiperiodic order - drive diverse nucleation pathways in icosahedral quasicrystals (IQCs). Combining a Landau free-energy model with the spring pair method, we compute distinct critical nuclei and their corresponding minimum energy paths. At low temperatures, a direct, symmetry-preserving pathway dominates. In contrast, higher temperatures promote a "symmetry detour" that reduces the nucleation barrier via a lower-symmetry critical nucleus. Remarkably, while the resulting bulk IQCs exhibit distinct real-space symmetries, they remain thermodynamically degenerate with identical diffraction patterns. We resolve this paradox within the high-dimensional projection framework, showing that phason shifts modulate real-space symmetry without altering bulk thermodynamics. Our findings establish phasons as the structural origin of pathway diversity, offering a new physical picture for the emergence of quasiperiodic order.

cond-mat.soft↗

arXiv2025

Exploring transition pathways in the Landau-Brazovskii model

The Landau-Brazovskii model provides a theoretical framework for describing various phases arising from competing short- and long-range interactions in many physical systems. In this work, we investigate phase transitions among various ordered phases within the three-dimensional Landau-Brazovskii model. We construct the phase diagram of this model, which encompasses eight distinct phases, and systematically compute the transition pathways connecting various metastable and stable states using the Landau-Brazovskii saddle dynamics. Along each transition pathway, the critical nucleus is identified with some detailed analyses of its shape, energy barrier, and Hessian eigenvalues. Furthermore, we explore how the transition state is influenced by model parameters, revealing systematic trends in critical nucleus sizes and energy barrier heights. Our results provide a comprehensive characterization of the nucleation mechanisms within the Landau-Brazovskii model and offer valuable insights into the structural transformations of modulated-phase systems.

cond-mat.mtrl-sci↗

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

Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules

Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can result in a great variety of quasicrystals that could be realized by the self-assembly of liquid crystalline molecules. In this study, we introduce three self-similar dodecagonal tilings, including a novel Diamond-Square-Triangle pattern, composed of triangular and quadrangular tiles and examine their thermodynamic stability by using the self-consistent field theory applied to T-shaped liquid crystalline molecules. Specifically, we detail the inflation rules for the construction of these dodecagonal tilings and analyze their self-similarity, and show that these tilings can be viewed as projections of higher-dimensional periodic lattice points with projection windows. Using these dodecagonal tilings as initial configurations of the SCFT results in solutions corresponding to quasicrystals that could form from the T-shaped liquid crystalline molecules. The relative stability of these aperiodic phases is analyzed to obtain design rules that could stabilize quasicrystals. Meanwhile, we provide two criteria for distinguishing three dodecagonal quasicrystals and their approximants by analyzing their diffraction peaks. These findings shed new lighten on the discovery of new quasicrystals in soft materials.

cond-mat.soft↗

arXiv2024

Designing a minimal Landau theory to stabilize desired quasicrystals

Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging problem. To address this challenge, we propose an intelligent screening method (ISM) to design a Landau theory with a minimal number of length scales -- referred to as the minimal Landau theory -- that includes only the essential length scales necessary to stabilize quasicrystals. Based on a generalized multiple-length-scale Landau theory, ISM first evaluates various spectral configurations of candidate structures under a hard constraint. It then identifies the configuration with the lowest free energy. Using this optimal configuration, ISM calculates phase diagrams to explore the thermodynamic stability of desired quasicrystals. ISM can design a minimal Landau theory capable of stabilizing the desired quasicrystals by incrementally increasing the number of length scales. Our application of ISM has not only confirmed known behaviors in 10- and 12-fold quasicrystals but also led to a significant prediction that quasicrystals with 8-, 14-, 16-, and 18-fold symmetry could be stable within three-length-scale Landau models.

cond-mat.mtrl-sci↗

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

Nucleation and phase transition of decagonal quasicrystals

In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely the nullspace-preserving saddle search method. Specifically, we focus on nucleation and phase transitions of the decagonal quasicrystal (DQC) based on the Lifshitz-Petrich model. We present the nucleation path of DQC from the liquid and demonstrate one- and two-stage transition paths between DQC and periodic crystals. We provide a perspective of the group-subgroup phase transition and nucleation rates to understand the nucleation and phase transition mechanisms involving DQC. These results reveal the one-step and stepwise modes of symmetry breaking or recovery in the phase transition from DQC, where the stepwise modes are more probable.

cond-mat.mtrl-sci↗

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↗

arXiv2021

Transition pathways connecting crystals and quasicrystals

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz-Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

cond-mat.mtrl-sci↗

arXiv2021

Binary Blends of Diblock Copolymers: An Efficient Route to Complex Spherical Packing Phases

The phase behaviour of binary blends composed of A$_1$B$_1$ and A$_2$B$_2$ diblock copolymers is systematically studied using the polymeric self-consistent field theory, focusing on the formation and relative stability of various spherical packing phases. The results are summarized in a set of phase diagrams covering a large phase space of the system. Besides the commonly observed body-centered-cubic (BCC) phase, complex spherical packing phases including the Frank-Kasper A15 and $σ$ and the Laves C14 and C15 phases could be stabilized by the addition of longer A$_2$B$_2$-copolymers to asymmetric A$_1$B$_1$-copolymers. Stabilizing the complex spherical packing phases requires that the added A$_2$B$_2$-copolymers have a longer A-block and an overall chain length at least comparable to the host copolymer chains. A detailed analysis of the block distributions reveals the existence of inter- and intra-domain segregation of different copolymers, which depends sensitively on the copolymer length ratio and composition. The predicted phase behaviours of the A$_1$B$_1$/A$_2$B$_2$ diblock copolymer blends are in good agreement with available experimental and theoretical results. The study demonstrated that binary blends of diblock copolymers provide an efficient route to regulate the emergence and stability of complex spherical packing phases.

cond-mat.soft↗

arXiv2021

Binary Blends of Diblock Copolymers: An Effective Route to Novel Bicontinuous Phases

The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (DBCPs) is studied using the polymeric self-consistent field theory. The theoretical study predicts that the double-diamond and the "plumber's nightmare" phases, which are metastable for neat diblock copolymers, could be stabilized in block copolymers with designed dispersity, namely, binary blends composed of a gyroid-forming DBCP and a homopolymer-like DBCP. The spatial distribution of different monomers reveals that these two types of DBCPs are segregated such that the homopolymer-like component is localized at the nodes to relieve the packing frustration. Simultaneously, the presence of a local segregation of the two DBCPs on the AB interface regulates the interfacial curvature. These two mechanisms could act in tandem for homopolymer-like diblock copolymers with proper compositions, resulting in larger stability regions for the novel bicontinuous phases.

cond-mat.soft↗

arXiv2019

Pathways connecting two opposed bilayers with a fusion pore: A molecularly-informed phase field approach

A phase field model with two phase fields, representing the concentration and the head-tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta-Kawasaki model (Macromolecules 19, 2621-2632 (1986)). It is shown that this molecularly-informed phase field model is capable of producing various self-assembled amphiphilic aggregates, such as bilayers, vesicles and micelles. Furthermore, pathways connecting two opposed bilayers with a fusion pore are obtained by using a combination of the phase field model and the string method. Multiple fusion pathways, including a classical pathway and a leaky pathway, have been obtained depending on the initial separation of the two bilayers. The study shed light to the understanding of membrane fusion pathways and, more importantly, laid a foundation for further investigation of more complex membrane morphologies and transitions.

cond-mat.soft↗

arXiv2019

Elastic Property of Membranes Self-assembled from Diblock and Triblock Copolymers

The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussian modulus, and line tension of the membranes. The results reveal that the bending modulus of the triblock membrane is greater than that of the diblock membrane. Furthermore, the Gaussian modulus and line tension of the triblock membrane indicate that the triblock membranes have higher pore formation energy than that of the diblock membranes. The equilibrium bridging and looping fractions of the triblock copolymers are also obtained. Implications of the theoretical results on the elastic properties of biologically equivalent lipid bilayers and the bolalipid membranes are discussed.

cond-mat.soft↗

arXiv2019

Self-Consistent Field Theory of Inhomogeneous Polymeric Systems: A Variational Derivation

The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many-body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric systems such as polymer blends and block copolymer melts. The polymeric SCFT is commonly derived using field-theoretical techniques. Here we provide an alternative derivation of the SCFT equations and SCFT free energy functional using a variational principle. Numerical methods of solving the SCFT equations and applications of the SCFT are also briefly introduced.

cond-mat.soft↗

arXiv2016

Computing optimal interfacial structure of modulated phases

We propose a general framework of computing interfacial structures between two modulated phases. Specifically we propose to use a computational box consisting of two half spaces, each occupied by a modulated phase with given position and orientation. The boundary conditions and basis functions are chosen to be commensurate with the bulk structures. It is observed that the ordered nature of modulated structures stabilizes the interface, which enables us to obtain optimal interfacial structures by searching local minima of the free energy landscape. The framework is applied to the Landau-Brazovskii model to investigate interfaces between modulated phases with different relative positions and orientations. Several types of novel complex interfacial structures are obtained from the calculations.

cond-mat.soft↗

arXiv2015

Computing optimal interfacial structure of ordered phases

We propose a general framework of computing interfacial structure. If an ordered phase is involved, the interfacial structure can be obtained by simply minimizing the free energy with compatible boundary conditions. The framework is applied to Landau- Brazovskii model and works efficiently.

physics.comp-ph↗

arXiv2015

Application of Self-Consistent Field Theory to Self-Assembled Bilayer Membranes

Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such surface tension, bending moduli and line tension. Understanding how the molecular property of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.

cond-mat.soft↗