Polymer confinement in undulated membrane boxes and tubes

We consider quantum particle or Gaussian polymer confinement between two surfaces and in cylinders with sinusoidal undulations. In terms of the variational method, we show that the quantum mechanical wave equations have lower ground state energy in these geometries under long wavelength undulations, where bulges are formed and waves are localized in the bulges. It turns out correspondingly that Gaussian polymer chains in undulated boxes or tubes acquire higher entropy than in exactly flat or straight ones. These phenomena are explained by the uncertainty principle for quantum particles, and by a "polymer confinement rule" for Gaussian polymers. If membrane boxes or tubes are flexible, polymer-induced undulation instability is suggested. We find that the wavelength of undulations at the threshold of instability for a membrane box is almost twice the distance between two walls of the box. Surprisingly we find that the instability for tubes begins with a shorter wavelength compared to the "Rayleigh" area-minimizing instability.Comment: 6 pages, 2 figures, submitted to Phys. Rev.

Rectangle--triangle soft-matter quasicrystals with hexagonal symmetry

Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from e.g. kites and darts, squares and equilateral triangles, rhombi or shield shaped tiles and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft-matter are of the dodecagonal type. Here, we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length-scales that form aperiodic stable states with two different examples of rectangle--triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft-matter.Comment: 15 pages, 13 figures. Submitted to Physical Review E. The data associated with this paper are openly available from the University of Leeds Data Repository at https://doi.org/10.5518/118

Archimedean Tiling Phases from ABC Starpolymers : The Road to Polymeric Quasicrystals

この論文は国立情報学研究所の電子図書館事業により電子化されました。研究会報告ABC星型ブロック共重合体のミクロ相分離によって,テキスタイルのような2次元タイル3色塗り分け紋様ができることが明らかになってきた.最近,分子周りの環境の複雑なアルキメデスタイリング(3^2.4.3.4)構造が実験的に発見されたが,これは複雑な合金相として知られるFrank-Kasper相(σ相)と類似な構造で,12回対称準結晶の近似結晶になっている.われわれのABC星型高分子の格子モンテカルロシミュレーションは12回対称高分子準結晶の可能性を示唆している

2. Polymeric Quasicrystals : Dodecagonal quasicrystal in ABC star block copolymers(poster presentation,Soft Matter as Structured Materials)

この論文は国立情報学研究所の電子図書館事業により電子化されました。ABC星型ブロック共重合体の格子高分子モデルのモンテカルロ・シミュレーションによって,12回対称準結晶(近似結晶)の形成に成功した。以下の特徴が観察された。(1)フーリエ変換(構造関数)はほぼ12回対称性を示す。(2)Stampfli変換による自己相似性が観察される。(3)ランダムに形態変化や合体分離を繰り返しながらもグローバルな12回対称性は保存する。(4)(3)はタイリングの入れ替えに対応する準結晶特有のフェイブン.ダイナミクスとみなせる。(5)よく知られた12回対称性正三角形-正方形タイリングよりもランダウ理論から導かれる密度彼の構造と一致する。最近,合金のFrank-Kasper相(σ相)に関連した80nmの辺の長さを待つ正三角形,正方形からなる3^2434アルキメデスタイリング構造が実験的に発見されているが,この構造は常に準結晶相に隣接して現れる構造である。このことと合わせ,高分子準結晶の発見が期待される

Bronze-mean hexagonal quasicrystal

The most striking feature of conventional quasicrystals is their nontraditional symmetry characterised by icosahedral, dodecagonal, decagonal, or octagonal axes. The symmetry and the aperiodicity of these materials stem from an irrational ratio of two or more length scales controlling their structure, the best-known examples being the Penrose and the Ammann-Beenker tiling as two-dimensional models related to the golden and the silver mean, respectively. Surprisingly, no other metallic-mean tilings have been discovered so far. Here we propose a self-similar bronze-mean hexagonal pattern, which may be viewed as a projection of a higher-dimensional periodic lattice with a Koch-like snowflake projection window. We use numerical simulations to demonstrate that a disordered variant of this quasicrystal can be materialised in soft polymeric colloidal particles with a core-shell architecture. Moreover, by varying the geometry of the pattern we generate a continuous sequence of structures, which provide an alternative interpretation of quasicrystalline approximants observed in several metal- silicon alloys