It is easy to perfectly tile a flat surface with hexagons, as in parks and playgrounds and bathroom floors. But when you try to tile a curved surface, the hexagonal tiling is frustrated and the defects, for example pentagons, are essential for relieving the stresses and strains. Witness the 12 pentagons required to close an otherwise hexagonally tiled geodesic dome, or a soccer ball or a C60 molecule. The present study introduces a unique system whereby particles bound to a surface of arbitrary curvature solve the geometric problem and create a relaxed structure with defects arranged optimally. The study involves colloidal particles, thirty times smaller than a human hair, which arrange themselves on different shaped water droplets a tenth of a millimeter in diameter. The particles are imaged microscopically and added or moved with focused light, optical tweezers. Students working on this project are trained in the latest optical techniques. The video imaging of defects and their dynamics in crystals is a great pedagogical tool for instructing students and researchers at all levels as to the basic properties of liquids and solids. Since geometry is important for structures at all length scales these results will be important for designing new molecules, for assembling nano and colloidal particles and for engineering new architectural structures.

Technical Abstract

Topology plays a crucial role in the geometry and order of materials and topological defects, disclinations and dislocations, determine many of the mechanical properties of crystals. Curvature tends to frustrate periodic order, and here topological defects play an important role in relieving the resulting stresses and strains. Witness the 12 pentagons required to close an otherwise hexagonally tiled geodesic dome, or a soccer ball or a C60 molecule, curvature requires the introduction of topological defects, pentagons - disclinations, which force reorientation. But within the past several years it has been realized that although topology constrains the net number of defects it is energetics that dictates the actual arrangements. The present study introduces a system and a number of techniques to experimentally observe and manipulate mobile colloidal particles which are bound to an arbitrarily curved surface oil-water interface. Students involved will be trained in the latest soft matter and optical techniques. The video images are great pedagogically for students and researchers at all levels. These topological results will be important for designing new molecules, for assembling nano and colloidal particles and for engineering new architectural structures.

Agency
National Science Foundation (NSF)
Institute
Division of Materials Research (DMR)
Type
Standard Grant (Standard)
Application #
1105417
Program Officer
Guebre X. Tessema
Project Start
Project End
Budget Start
2011-07-01
Budget End
2014-06-30
Support Year
Fiscal Year
2011
Total Cost
$435,000
Indirect Cost
Name
New York University
Department
Type
DUNS #
City
New York
State
NY
Country
United States
Zip Code
10012