Tomonari Dotera

Mosaic two-lengthscale quasicrystals

Over the past decade, quasicrystalline order has been observed in many soft-matter systems: in dendritic micelles, in star and tetrablock terpolymer melts and in diblock copolymer and surfactant micelles. The formation of quasicrystals from such a broad range of ‘soft’ macromolecular micelles suggests that they assemble by a generic mechanism rather than being dependent on the specific chemistry of each system. Indeed, micellar softness has been postulated and shown to lead to quasicrystalline order. Here we theoretically explore this link by studying two-dimensional hard disks decorated with step-like square-shoulder repulsion that mimics, for example, the soft alkyl shell around the aromatic core in dendritic micelles. We find a family of quasicrystals with 10-, 12-, 18- and 24-fold bond orientational order which originate from mosaics of equilateral and isosceles triangles formed by particles arranged core-to-core and shoulder-to-shoulder. The pair interaction responsible for these phases highlights the role of local packing geometry in generating quasicrystallinity in soft matter, complementing the principles that lead to quasicrystal formation in hard tetrahedra. Based on simple interparticle potentials, quasicrystalline mosaics may well find use in diverse applications ranging from improved image reproduction to advanced photonic materials.

The diagonal bond method: A new lattice polymer model for simulation study of block copolymers

A new lattice model for Monte Carlo simulations of dense polymer melts, developed in the spirit of Verdier–Stockmayer algorithm on square and simple cubic lattices, is presented. By introducing diagonals of squares and cubes as bonds, the lattice model acquires a large number of configurations and wiggling local moves. While it maintains the excluded volume interactions of monomers, it allows bond crossings and phantom moves, which result in a high mobility of polymers. For an application, we carry out simulations of symmetric A–B block copolymer melts and observe a first‐order transition. We also show the stretching of the chains, namely, the non‐Gaussian character, as a function of temperature. A quicker evolution towards thermal equilibrium enables us to form an ordered tricontinuous double‐diamond (OTDD) phase for linear A–B–C triblock copolymers and a new cylindrical phase for star A–B–C triblock copolymers.

Kaleidoscopic morphologies from ABC star-shaped terpolymers

Star-shaped terpolymers of the ABC type composed of incompatible polymer components give a variety of ordered structures with mesoscopic length scales depending on their composition ratio. Their peculiar features are summarized in this report. Polymer components adopted are polyisoprene (I), polystyrene (S) and poly(2-vinylpyridine) (P), and many monodisperse samples of the I(X)S(Y)P(Z) type were anionically prepared. Firstly our focus is on molecules of the I(1.0)S(1.0)P(x(1)) type, where x(1) is only a variable. The complex but systematic morphology change was displayed within the range 0.2 ≤ x(1) ≤ 10, that is, their structures change from spherical plus lamellae structure for I(1.0)S(1.0)P(0.2) to periodic tilings (0.4 ≤ x(1) ≤ 1.9), then to lamellae-in-lamella (3.0 ≤ x(1) ≤ 4.9) and lamellae-in-cylinder (7.9 ≤ x(1) ≤ 10) structures with increasing x(1). Here if we pay attention to the structural variation of the P domain inclusively, it transforms from sphere to cylinder, lamella and then to matrix, which is the same as that for linear polymers. Among them, several periodic Archimedean tiling patterns can be naturally formed when the relative lengths of the three chains are close to one another. Moreover, it has been found that the tiling zone is spread out widely. For example, the series I(1.0)S(1.8)P(x(2)) (with 0.8 ≤ x(2) ≤ 2.9) and the other series I(1.0)S(y)P(2.0) (with 1.1 ≤ y ≤ 2.7) show mostly Archimedean tilings. Additionally, block copolymer/homopolymer blends with a composition of I(1.0)S(2.7)P(2.5) reveal a quasicrystalline tiling with dodecagonal symmetry. Furthermore, a zinc-blende-type four-branched network structure was created just a little outside of the tiling region for a block copolymer/homopolymer blend of I(1.0)S(2.3)P(0.8). When some more asymmetry in chain length is introduced, hyperbolic tiling on a gyroid membrane has successfully been constructed for the sample I(1.0)S(1.8)P(3.2) and it transforms into a hierarchical cylinders-in-lamella structure with further increase in P content to I(1.0)S(1.8)P(6.4). Thus, kaleidoscopic morphologies have been generated from ABC star-shaped terpolymers and their structural change has turned out to be very sensitive to relative compositions.

Dodecagonal quasicrystal in a polymeric alloy

We report the formation of an approximant of a dodecagonal quasicrystal in a quasi-two-dimensional lattice Monte Carlo simulation of a star-shaped three-component polymeric alloy. It is associated with the recent striking experimental manifestation of the complex Archimedean tiling (32.4.3.4) consisting of triangles and squares, related to the σ phase in the Frank–Kasper family, but whose edge length is about 80 nm. The simulation box with periodic boundary conditions (128 × 128 × 10) can be regarded as the Stampfli inflation of the (32.4.3.4) tiling, an approximant of the dodecagonal quasicrystal. The corresponding edge length of deflated squares and triangles is thought to be about 300 nm. Furthermore, the phason dynamics of the deflated square–triangle tiling is observed at an elevated temperature.

Voronoi space division of a polymer: Topological effects, free volume, and surface end segregation

In order to investigate the topological effects of chain molecules, united-atom molecular dynamics simulations of a 500-mer polyethylene linked by 50 hexyl groups (a grafted polymer having 52 ends) are carried out and analyzed in terms of Voronoi space division. We find that the volume of a Voronoi polyhedron for a chain end is larger than that for an internal or junction atom, and that it is the most sensitive to temperature, both of which suggest higher mobility of chain ends. Moreover, chain ends dominantly localize at the surface of the globule: The striking evidence is that while the ratio of surface atoms is only 24% of all atoms, the ratio of ends at the surface is 91% out of all ends. The shape of Voronoi polyhedra for internal atoms is prolate even in the bulk, and near the surface it becomes more prolate. We propose the concept of bonding faces, which play a significant role in the Voronoi space division of covalently bonding polymers. Two bonding faces occupy 38% of the total surface area of a Voronoi polyhedron and determine the prolate shape.

Mean-field theory of Archimedean and quasicrystalline tilings

A simple Landau theory of three-component alloy systems under incompressible condition is investigated, which appears to give regions of the phase diagram in which Archimedean tiling phases are stable in two dimensions. Moreover, we find regions where dodecagonal and decagonal quasicrystals appear to be stable. The Alexander–MacTague and Mermin–Troian theories of weak crystallization are revisited.

Curvature Entropy Trapping of Long DNA under Hydrodynamic Flows in Microfluidic Devices

We investigated the curvature effect on the dynamics of long DNA using microfluidic devices. Long DNA has larger configurational entropy in a curved channel than in a straight channel. Under weak hydrodynamic flows, long DNA exhibited a curvature entropy trapping effect. The effect disappeared as the hydrodynamic flow was increased.

Electrophoresis of long deoxyribonucleic acid in curved channels: The effect of channel width on migration dynamics

We investigated the dynamics of long deoxyribonucleic acid (DNA) migrating through curved channels under electric fields. Long DNA exhibits large conformational changes in the curved channels because of the inhomogeneity of the electric fields around curves. Two kinds of channel shapes were used for the examination. One (type I) has the same width in the curved region as in the straight region. The other (type II) is wider in the curved region than in the straight region. The difference in migration rates between long DNA and short DNA was larger in type II than in type I chips. We discuss the separation mechanism of the type II chip.

High temperature expansion for the Ising model on the dual penrose lattice

High temperature expansion for ln Z ( Z : the partition function in the absence of magnetic field) of the Ising model on the Penrose lattice is discussed. The terms up to the order of w 8 are derived. To illustrate an extrapolation procedure employed here, the critical compressibility factor Z c and the correlation function C at T c for the neighboring spin pair are first treated in the case of two-dimensional square lattice. It turns out that the terms up to w 8 for ln Z lead to the results within the error of 0.2∼0.3% as compared to exact values. Along the same line, Z c and \bar C (average correlation function) are calculated for the Penrose lattice. The final results are Z c =0.138±0.002 and \bar C =0.673±0.003.

Hard spheres on the gyroid surface

We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Eschers Circle Limit IV.