Related Experiment Video
Updated: Oct 16, 2025
10:23
Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
Published on: May 8, 2015
11.8K
Square-triangle tilings: an infinite playground for soft matter
Marianne Impéror-Clerc1, Anuradha Jagannathan1, Pavel Kalugin1
1LPS, Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, Orsay, France. marianne.imperor@universite-paris-saclay.fr.
Soft Matter
|October 21, 2021
Summary
This study introduces a 3D composition space to classify square-triangle tilings in soft matter. It reveals how tile area incommensurability drives diverse periodic and aperiodic tiling behaviors.
Area of Science:
- Soft Matter Physics
- Materials Science
- Geometric Crystallography
Background:
- Tiling phenomena are observed in various soft matter systems.
- Understanding the formation and properties of these tilings is crucial for materials design.
Purpose of the Study:
- To present a comprehensive framework for describing square-triangle tiling phases.
- To analyze the geometrical properties of specific tiling phases in soft matter.
- To elucidate the relationship between tile area ratios and tiling behavior.
Main Methods:
- Development of a three-dimensional composition space to parameterize tilings.
- Analysis of tile orientations and overall composition.
- Identification and description of special tiling phases (Archimedean, striped, 12-fold symmetric).
Main Results:
- A systematic method to describe all possible globally uniform square-triangle phases.
- Demonstration that the incommensurability of tile areas (ratio of 1:√3) dictates phase complexity.
- Characterization of geometric constraints at domain boundaries.
Conclusions:
- The 3D composition space effectively captures the rich behavior of square-triangle tilings.
- Inherent geometric properties, particularly area ratios, are key drivers of tiling patterns.
- The framework provides insights for experimental and numerical studies of soft matter systems.
Related Concept Videos
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
45.3K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
45.3K
01:16Surface Tension and Surface Energy
2.3K
When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason behind this effect is surface tension.
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
2.3K
01:18First Law: Particles in Two-dimensional Equilibrium
7.6K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
Newton's first law tells us about...
7.6K
01:34The Fluid Mosaic Model
165.0K
The fluid mosaic model was first proposed as a visual representation of research observations. The model comprises the composition and dynamics of membranes and serves as a foundation for future membrane-related studies. The model depicts the structure of the plasma membrane with a variety of components, which include phospholipids, proteins, and carbohydrates. These integral molecules are loosely bound, defining the cell’s border and providing fluidity for optimal function.
165.0K