Freezing on a Sphere
December 7, 2016 -
3:00pm to 4:00pm
Molecular Science and Engineering Building, Room G011
New York University
Soft Matter Incubator Distinguished Lecture Series: Prof. Paul Chaikin, New York University
Melting in two dimensions is characterized by the thermal excitation and proliferation of free topological defects, disclinations and dislocations which destroy the rigidity of the crystal. This freezing/melting process has been well established for flat systems especially for dipolar, U(r) ~1/r3potentials, with control parameter, Γ = U(a)/kBT, where a is an interparticle spacing.
The flat spacing freezing occurs at Γ ~ 70. On a sphere topology requires that there must be a net 12 pentagons (1/2 disclinations) i.e. the 12 pentagons on a soccer ball, and energetically it is favorable to screen the pentagons with strings of dislocations (pentagon-heptagon pairs) known as “scars”.
Our system consists of charged colloidal particles in an oil droplet in water bound to the inner surface by image charges. We study particle mean square displacement, hexagonal order, defect structure, and scar-scar correlations by confocal microscopy for droplets of different Γ and number of particles.
Freezing on sphere proceeds by the formation of a single, encompassing, crystalline “continent” that forces the defects into 12 isolated “seas” with icosahedral symmetry at the flat space value of Γ ~ 70.