1
|
Yu T, Mason TG. Heptatic liquid quasi-crystals by colloidal lithographic pre-assembly. J Colloid Interface Sci 2024; 665:535-544. [PMID: 38538483 DOI: 10.1016/j.jcis.2023.12.157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 12/06/2023] [Accepted: 12/27/2023] [Indexed: 04/17/2024]
Abstract
HYPOTHESIS We hypothesize that pre-assembled lithographic Brownian seven-fold quasi-crystals (QCs) of colloidal tiles at high densities can exhibit a heptatic liquid quasi-crystal (LQC) phase upon release; such heptatic LQCs can undergo heterogeneous dynamics at different length scales, reflecting the underlying symmetry, corrugation, and hierarchy of local sets of tiles. EXPERIMENTS We design, fabricate, and release a seven-fold QC composed of three differently shaped rhombic tiles using the method of lithographically pre-assembled monolayers (litho-PAMs). High resolution optical microscopy enables spatio-temporal particle tracking of Brownian fluctuations of many tiles in a large area over a long time. We develop an edge-proximity tessellation method for analyzing nearest neighboring particles that can be applied to assemblies and dense systems of complex shapes. FINDINGS A fluctuating heptatic LQC phase is identified at high tile area fractions. Heterogenous dynamics and order at different length scales indicate diverse, hierarchical motif structures. We show that certain motifs can collectively rotate without any cage breaking, leading to alterations of the local tile-structure reminiscent of phason-flips in atomic QCs; this rotation causes a slow decline in the system's spatial order. We anticipate that edge-proximity tessellation will help elucidate phase transitions of other systems made of diverse building blocks having significant geometrical complexity at multiple length scales.
Collapse
Affiliation(s)
- Tianren Yu
- Department of Chemistry and Biochemistry, University of California-Los Angeles, Los Angeles, CA 90095, USA
| | - Thomas G Mason
- Department of Chemistry and Biochemistry, University of California-Los Angeles, Los Angeles, CA 90095, USA; Department of Physics and Astronomy, University of California-Los Angeles, Los Angeles, CA 90095, USA; California NanoSystems Institute, University of California-Los Angeles, Los Angeles, CA 90095, USA.
| |
Collapse
|
2
|
Sarkar T, Chaudhuri P, Sain A. Poiseuille Flow of Soft Polycrystals in 2D Rough Channels. PHYSICAL REVIEW LETTERS 2020; 124:158003. [PMID: 32357064 DOI: 10.1103/physrevlett.124.158003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Revised: 07/10/2019] [Accepted: 03/16/2020] [Indexed: 06/11/2023]
Abstract
Polycrystals are partially ordered solids where crystalline order extends over mesoscopic length scales, namely, the grain size. We study the Poisuielle flow of such materials in a rough channel. In general, similar to yield stress fluids, three distinct dynamical states, namely, flowing, stick-slip, and jammed can be observed, with a yield threshold dependent on channel width. Importantly, the interplay between the finite channel width, and the intrinsic ordering scale (the grain size) leads to a new type of spatiotemporal heterogeneity. In wide channels, although the average flow profile remains pluglike, at the underlying granular level, there is vigorous grain remodeling activity resulting from the velocity heterogeneity among the grains. As the channel width approaches typical grain size, the flowing polycrystalline state breaks up into a spatially heterogeneous mixture of flowing liquid like patches and chunks of nearly static grains. Despite these static grains, the average velocity still shows a parabolic profile, dominated by the moving liquidlike patches. However, the solid-liquid front moves at nearly constant speed in the opposite direction of the external drive.
Collapse
Affiliation(s)
- Tanmoy Sarkar
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| | - Pinaki Chaudhuri
- Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
| | - Anirban Sain
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| |
Collapse
|
3
|
Nielsen BF, Linga G, Christensen A, Mathiesen J. Substrate curvature governs texture orientation in thin films of smectic block copolymers. SOFT MATTER 2020; 16:3395-3406. [PMID: 32159549 DOI: 10.1039/c9sm02389e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering of extrinsic as well as intrinsic substrate geometry may provide such a controllable ordering mechanism for block copolymers films. We develop an effective two-dimensional model of thin films of striped-phase diblock copolymers on general curved substrates. The model is obtained as an expansion in the film thickness and thus takes the third dimension into account, which crucially allows us to predict the preferred orientations even in the absence of intrinsic curvature. We determine the minimum-energy textures on several curved surfaces and arrive at a general principle for using substrate curvature as an ordering field, namely that the stripes will tend to align along directions of maximal curvature.
Collapse
Affiliation(s)
| | - Gaute Linga
- PoreLab, The Njord Centre, Department of Physics, University of Oslo, P. O. Box 1048, 0316 Oslo, Norway.
| | - Amalie Christensen
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark. and Danmarks Nationalbank, DK-1093 Copenhagen K, Denmark
| | - Joachim Mathiesen
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark.
| |
Collapse
|
4
|
Baggio R, Arbib E, Biscari P, Conti S, Truskinovsky L, Zanzotto G, Salman OU. Landau-Type Theory of Planar Crystal Plasticity. PHYSICAL REVIEW LETTERS 2019; 123:205501. [PMID: 31809089 DOI: 10.1103/physrevlett.123.205501] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2019] [Revised: 09/28/2019] [Indexed: 06/10/2023]
Abstract
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as a Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group GL(2,Z). Quasistatic loading can be then handled by athermal dynamics, while lattice-based discretization can play the role of regularization. As a proof of principle, we study dislocation nucleation in a homogeneously sheared 2D crystal and show that the global tensorial invariance of the elastic energy foments the development of complexity in the configuration of collectively nucleating defects. A crucial role in this process is played by the unstable higher symmetry crystallographic phases, typically thought to be unrelated to plastic flow.
Collapse
Affiliation(s)
- R Baggio
- CNRS, LSPM, Université Paris 13, 93430 Villetaneuse, France
- PMMH, ESPCI, F-75005 Paris, France
| | - E Arbib
- Department of Physics, Politecnico di Milano, 20133 Milano, Italy
| | - P Biscari
- Department of Physics, Politecnico di Milano, 20133 Milano, Italy
| | - S Conti
- Institut für Angewandte Mathematik, Universität Bonn, 53115 Bonn, Germany
| | | | - G Zanzotto
- DPG, Università di Padova, 35131 Padova, Italy
| | - O U Salman
- CNRS, LSPM, Université Paris 13, 93430 Villetaneuse, France
| |
Collapse
|
5
|
Skaugen A, Angheluta L, Viñals J. Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model. PHYSICAL REVIEW LETTERS 2018; 121:255501. [PMID: 30608801 DOI: 10.1103/physrevlett.121.255501] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2018] [Revised: 10/15/2018] [Indexed: 06/09/2023]
Abstract
A consistent small-scale description of plasticity and dislocation motion in a crystalline solid is presented based on the phase field crystal description. By allowing for independent mass motion and lattice distortion, the crystal can maintain elastic equilibrium on the timescale of plastic motion. We show that the singular (incompatible) strains are determined by the phase field crystal density, while the smooth distortions are constrained to satisfy elastic equilibrium. A numerical implementation of the model is presented and used to study a benchmark problem: the motion of an edge dislocation dipole in a triangular lattice. The time dependence of the dipole separation agrees with continuum elasticity with no adjustable parameters.
Collapse
Affiliation(s)
- Audun Skaugen
- Njord Center, Department of Physics, University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo, Norway
| | - Luiza Angheluta
- Njord Center, Department of Physics, University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo, Norway
| | - Jorge Viñals
- School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis, Minnesota 55455, USA
| |
Collapse
|
6
|
A Study of Strain-Driven Nucleation and Extension of Deformed Grain: Phase Field Crystal and Continuum Modeling. MATERIALS 2018; 11:ma11101805. [PMID: 30249056 PMCID: PMC6213540 DOI: 10.3390/ma11101805] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Revised: 09/15/2018] [Accepted: 09/20/2018] [Indexed: 12/03/2022]
Abstract
The phase-field-crystal (PFC) method is used to investigate migration of grain boundary dislocation and dynamic of strain-driven nucleation and growth of deformed grain in two dimensions. The simulated results show that the deformed grain nucleates through forming a gap with higher strain energy between the two sub-grain boundaries (SGB) which is split from grain boundary (GB) under applied biaxial strain, and results in the formation of high-density ensembles of cooperative dislocation movement (CDM) that is capable of plastic flow localization (deformed band), which is related to the change of the crystal lattice orientation due to instability of the orientation. The deformed grain stores the strain energy through collective climbing of the dislocation, as well as changing the orientation of the original grain. The deformed grain growth (DGG) is such that the higher strain energy region extends to the lower strain energy region, and its area increase is proportional to the time square. The rule of the time square of the DGG can also be deduced by establishing the dynamic equation of the dislocation of the strain-driven SGB. The copper metal is taken as an example of the calculation, and the obtained result is a good agreement with that of the experiment.
Collapse
|
7
|
Tarp JM, Mathiesen J. Rotation-limited growth of three-dimensional body-centered-cubic crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012409. [PMID: 26274188 DOI: 10.1103/physreve.92.012409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2015] [Indexed: 06/04/2023]
Abstract
According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered-cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe, as a function of the quenching depth, a crossover between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescence through rotation and alignment of the lattices of neighboring grains. We show that the grain rotation per volume change of a grain follows a power law with an exponent of -1.25. The scaling exponent is consistent with theoretical considerations based on the conservation of dislocations.
Collapse
Affiliation(s)
- Jens M Tarp
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Joachim Mathiesen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| |
Collapse
|