Recent studies show that two low-energy van Hove singularities (VHSs) seen as two pronounced peaks in the density of states could be induced in a twisted graphene bilayer. Here, we report angle-dependent VHSs of a slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows ΔE(vhs)∼ℏν(F)ΔK between 1.0° and 3.0° [here ν(F)∼1.1 × 10(6) m/s is the Fermi velocity of monolayer graphene, and ΔK = 2Ksin(θ/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer]. This result indicates that the rotation angle between graphene sheets does not result in a significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle θ∼1.3°, the observed ΔE(vhs)∼0.11 eV is much smaller than the expected value ℏν(F)ΔK∼0.28 eV at 1.3°. The origin of the reduction of ΔE(vhs) at 1.3° is discussed.

Janus particles exhibit interesting self-assembly behavior and functional performances. In particular, soft and deformable Janus particles, as diverse as Janus micelles, Janus microgels, and Janus dendrimers, should receive more attention due to their unique chemical and physical properties and enormous potential applications. Gaining control over precise and predictable self-assembled structures and understanding the fundamental details of self-assembly remain a formidable challenge.Here we present a novel mesoscale model for soft Janus particles, which successfully reflects their physical nature by directly mapping onto experimentally measurable particle properties. By properly tuning Janus balance and the strength of attraction between attractive patches, soft Janus particles can reversibly self-assemble into a number of fascinating hierarchical superstructures in dilute solutions, such as micelles, wormlike strings, single helices, double helices, bilayers, tetragonal bilayers, and complex supermicelles. Our work demonstrates that soft Janus particles with deformable and noncentrosymmetric characteristics hide many surprises in the design and fabrication of hierarchically selfassembled superstructures.

The Langmuir film balance technique was used to investigate the effects of copolymer composition and subphase pH/temperature on the aggregation behaviors of two stimuliresponsive amphiphilic diblock copolymers poly(2-(dimethylamino)ethyl methacrylate)-block-poly(lauryl methacrylate) (PDMAEMA-b-PLMA) at the air/water interface. The morphologies of their Langmuir−Blodgett (LB) films were characterized by atomic force microscopy. With the rise in subphase pH, the corresponding surface pressure−molecular area isotherms of the two copolymers gradually move to large areas due to the decreased protonation degrees of PDMAEMA blocks. Almost all the LB films of the predominantly hydrophilic copolymer prepared under different subphase conditions exhibit isolated circular micelles. For the predominantly hydrophobic copolymer, however, the dense wormlike aggregates and the large domains appear in its LB films due to the connection of adjacent PLMA cores at low temperature and the local richness of PDMAEMA chains at high temperature, respectively.

We develop a self-consistent-field lattice model for block copolymers and propose a novel and general method to solve the self-consistent-field equations. The approach involves describing the polymer chains in a lattice and employing a two-stage relaxation procedure to evolve a system as rapidly as possible to a free-energy minimum. In order to test the validity of this approach, we use the method to study the microphases of rod-coil diblock copolymers. In addition to the lamellar and cylindrical morphologies, micellar, perforated lamellar, gyroid, and zigzag structures have been identified without any prior assumption of the microphase symmetry. Furthermore, this approach can also give the possible orientation of the rods in different structures.

Considering multi-body systems of monodisperse hard Brownian particles, it remains challenging to predict the forms of order that can emerge in their dense assembled structures. Surprisingly, here, using Monte Carlo simulations, we show that tetratic-ordered phases emerge in a dense two-dimensional system of hard kites that are rotationally asymmetric and have opposite 72° and α ≈ 90° internal angles. We observe a new tetragonal rectangular crystal (TRX) phase possessing (quasi-)long-range fourfold molecular-orientational order. We propose a method based on local polymorphic configurations of neighboring particle pairs (LPC-NPPs) to understand this emergent tetratic order and show that LPC-NPPs can be useful for predicting orientational order in such systems. To examine the dependence of the tetratic order on α, we apply LPC-NPP analysis to other hard kites for 54° ≤ α ≤ 144°. Our work provides insight into the creation of novel ordered materials by rationally designing particle shape based on anticipated LPC-NPPs.

Using a combinatorial screening method based on the self-consistent-field theory for polymers, we study the bulk morphology and the phase behavior of π-shaped ABC block copolymers, in which A is the backbone and B and C are the two grafts. By systematically varying the positions of the graft points, the π-shaped block copolymer can change from a star block copolymer to a linear ABC block copolymer. Thus, the corresponding order−order phase transition due to the architecture variation can be investigated. At two given compositions, we find seven different morphologies (“three-color” lamellar phase, “three-color” hexagonal honeycomb phase, lamellae with beads inside, dodecagon−hexagon−tetragon, hexagon−hexagon, lamellae with alternating beads, and octagon−octagon−tetragon). The hexagon−hexagon morphology has not been reported previously for linear and star triblock copolymers in the bulk state. The phase diagram of the π-shaped ABC block copolymer with symmetric interactions among the three species is constructed. When the volume fractions of block B and block C are equal, the triangle phase diagram shows reflection symmetry. When the shorter block is fixed at the backbone end and the other block moves to the other end along the backbone, the resulting morphology reaches to the same as that of a linear triblock copolymer rapidly. These results may help the design of the microstructures of complex block copolymers.

Effects of subphase pH and temperature on the aggregation behavior of a thermosensitive amphiphilic diblock copolymer poly­(lauryl acrylate)-block-poly­(N-isopropylacrylamide) (PLA-b-PNIPAM) at the air/water interface and the morphologies of its Langmuir–Blodgett (LB) films were characterized with the Langmuir film balance technique and atomic force microscopy, respectively. The surface pressure–molecular area isotherms shift positively with the increase of subphase pH, and there exist two quasi-plateaus under acidic condition but only one under neutral or alkaline conditions. The lower and upper plateaus under acidic condition are attributed to immersion into water for the protonated amide groups and the rest of PNIPAM blocks, respectively. The plateau pressures gradually decrease with the elevation of temperature due to promotion of protonation and solubility of PNIPAM blocks. On the contrary, those under neutral and alkaline conditions gradually increase but exhibit a lower critical solution temperature behavior which is consistent with that of PNIPAM-containing polymers in aqueous solutions. The initial LB films of PLA-b-PNIPAM transferred from different subphases exhibit tiny isolated circular micelles which coalesce and transform into large dense ones upon compression. Furthermore, PLA cores usually coalesce with the elevation of temperature due to the increased molecular thermal mobility as a result of their low glass transition temperature.

Physical gelation in the concentrated Pluronic F127/D2O solution has been studied by a combination of small-angle neutron scattering (SANS) and Monte Carlo simulation. A 15% F127/D2O solution exhibits a sol-gel transition at low temperature and a gel-sol transition at the higher temperature, as evidenced by SANS and Monte Carlo simulation studies. Our SANS and simulation results also suggest that the sol-gel transition is dominated by the formation of a percolated polymer network, while the gel-sol transition is determined by the loss of bound solvent. Furthermore, different diffusion behaviors of different bound solvents and free solvent are observed. We expect that this approach can be further extended to study phase behaviors of other systems with similar sol-gel phase diagrams.