Vacancy and dislocation dynamics in colloidal dimer crystals

with Sharon Gerbode and Itai Cohen, and in collaboration with Chekesha Liddell-Watson, Umang Argawal, and Fernando Escobedo.
August 2008 -- August 2010
Department of Physics, Cornell University

With then-graduate student Sharon Gerbode (now a faculty member at Harvey-Mudd) and Professor Itai Cohen, I was studying defect dynamics in non-spherical colloidal systems for 2 years as an undergraduate research assistant.

Using fluorescent confocal microscopy, I examined how adding geometric restrictions to a crystal of spheres, in the form of "bonds" between the spheres (i.e. having dimers instead of monomer spheres), changes the dynamics of both dislocations and vacancies.

Left: An example of one of the beautiful dimer crystals that we studied. Our colleagues in Materials Science grew the dimer particles (If one looks closely, one would notice that there is a small proportion of "mutant" particles, that do not have symmetric lobes), and then we crystallized the particles using a ramp-cell (details below).
Right: We can model the symmetric dimer as two spherical particles that are joined and have their relative motions constrained (see the visualization above). If the aspect ratio (i.e. the separation of the two lobes) is tuned perfectly to the distance between two spheres in a crystal, then we can see that the dimer crystal would assemble into the same crystalline structure (hexagonal close-packing in 2D) as dimers. Informally we refer to these dimer particles as "peanuts".

We built a model of the dimer crystal as an extenion of a crystal of spheres (see above for an illustration and an example of a dimer crystal). We can see that if the aspect ratio of the dimer is tuned right (i.e. the separation of the lobes of the dimer is "just right"), then the dimers would crystallize in a similar fashion to spheres. The lobes of the dimers would fall onto a hexagonal lattice.

However, the structural properties of such a dimer crystal is radically different. The connections between the lobes serve as constraints to how the crystal can be sheared or dislocated. See below for an illustration. What this means is that dislocations in a crystal of dimers have much less mobility as compared to a crystal of spheres. This results in a stronger crystal that resists shearing.

An illustration of how the bonds in a dimer crystal restrict dislocations. Left: Imagine that the crystal was to be sheared along the axis shown. The dimers in green would just slide along with the shear, and the dimers in blue would "rotate"; however the bonds of the dimers in red would have to be broken. This is shown in the Middle image. Right: However, in a crystal of spheres, dislocation happens easily along any of the axes of the crystal.

We measured this experimentally using home-built "rampcells" (see diagram below). The rampcell allowed us to assemble monolayer crystals -- particles that crystallize only in 2D -- where the gap between the microscope slides became on the order of 1 particle diameter. We injected the colloidal suspension (particles suspended in liquid) from the top, and allowed them to slowly settle and self-organize into crystals. In order to experimentally induce dislocations and study the relaxation response of the crystal, we added small spherical "intruder" particles into the colloidal suspension. These spherical intruders which were the same size as the lobes of the dimers, but were of a different optical density. This allows them to be manipulated by optical tweezers. We used a Holographic Optical Tweezer setup to drag these intruder particle through the crystals, and observed the relaxation response.

An example of the "rampcell" that we designed and used. The cell consists of two microscope slides that are bonded at one end (the right end), and are separated by cured UV glue spacers on the left. The left-most row of spacers are have larger than the middle row. This creates a cell whose depth (spacing between the slides) decreases as one goes from left to right. Thus, as we move from left to right, we would reach a region where only one layer of particles can fit. We perform our analyses on this monolayer region.

An example of dragging a particle through a crystal of spheres (left) and a crystal of dimers (right).

We found a new type of "glassy" dislocation dynamics where the dislocations in pure dimer crystals exhibit glassy behavior while the colloidal particles are crystalline (Gerbode et al., PRL 2010, link below).

As an extension to this work, we next studied mixed crystals of spheres and dimers. On one extreme (100% spheres), we get high defect mobility (earlier, we focused on studying dislocations). At low concentrations, the distribution of dimer bonds would not be enough to reduce the mobility of defects within the crystal. However, at really high dimer concentrations (up to 100% as studied above), we see a heavily restricted defect mobility. The aim of this extension was to study defects: specifically vacancies and vacancy-mediation dislocation dynamics, as a function of dimer concentration in these mixed crystals.

Two examples of mixed sphere-dimer crystals. The bright spheres are intruder particles.

An example of an experiment in a low-dimer concentration region. Watch how the intruder is dragged through the crystal, and how the crystal relaxes.

We uncovered a novel mechanism by which vacancies enhance dislocation mobility by allowing them to "cage-hop" (Gerbode et al., PRE 2010, link below).

More information can be found on my old lab website, here. Or check out our 2010 publications in Physical Review Letters and Physical Review E, links below.

Relevant Publications

Gerbode, S. J., Ong, D. C., Liddell, C. M., & Cohen, I. (2010). Dislocations and vacancies in two-dimensional mixed crystals of spheres and dimers. Phys. Rev. E 82, 041404 [pdf]

Gerbode, S. J., Agarwal, U., Ong, D. C., Liddell, C. M., Escobedo, F., & Cohen, I. (2010). Glassy Dislocation Dynamics in 2-D Colloidal Dimer Crystals. Phys. Rev. Lett. 105, 078301 [pdf]