Previous Research

Carbon Nanocones

Carbon nanotubes are actually a special case of a more general structure, the carbon nanocones. Introducing pentagonal defects into a hexagonal graphene lattice causes the graphene sheet to take on a conical shape. Each additional pentagonal defect reduces the opening angle of the cone. Six pentagons reduce the opening angle to zero, producing a carbon nanotube. Graphene cones can have novel electronic and structural properties.

If pressed from the top, a graphene cone will buckle and transition from the traditional Hooke's Law behavior to acting as a constant force spring. When turned fully inside out, the cone becomes a perfect chiral invert of the original structure.

In my own research on carbon nanocones I use an empirical potential to calculate the binding energy of the nanocone molecules as a function of the atomic coordinates. The equilibrium structure is calculated using the conjugate gradient method under various external forcing conditions. This research was performed at Penn State in collaboration with Dr. Vincent Crespi. The software which I wrote for this project is freely available.

Critical Casimir Effect

Because helium-4 atoms have integer spin, they are bosons and therefore are not subject to the Pauli exclusion principle. As a result, at sufficiently low temperatures (approximately 2K), helium-4 Bose-condenses and becomes a superfluid. Superfluids exhibit many strange properties including zero viscosity.

The phase transition for helium-4 from conventional fluid to superfluid has no latent heat. As a result, it is possible for phase fluctuations of all length scales to exist at the critical point. In a superfluid helium film, the length scales of the fluctuations are restricted by the thickness in the film. This leads to a dependence of the energy of the fluctuations on the film thickness. The dependence of energy (E) on film thickness (x) leads to a force (F=-dE/dx) which acts to either thicken or thin the film. In the case of the a superfluid film, there is a thinning near the critical temperature.

I worked in a collaboration with Dr. Rafael Garcia (formerly of Penn State, now at WPI) and Dr. Moses Chan at Penn State to measure this film thinning using a quartz microbalance. The resonant frequency of vibration is inversely proportional to the square root of the oscillating mass. Thus the mass of the film, and hence its thickness, could be determined from the resonant frequency of vibration of the crystal onto which the film was adsorbed.

Relevant Publications

• Stephen P. Jordan and Vincent H. Crespi
  Mechanical manipulation of graphene nanocones: Chiral inversion of a micron-scale three-dimensional object. Phys. Rev. Lett. 93, 255504 (2004)
  
  
• R. Garcia, S. Jordan, J. Lazzaretti, and M. Chan
  Quartz microbalance study of thick He-4 film near the superfluid transition
  J. Low Temp. Phys. 134 (1-2): 527-533 Jan 2004