While the rest of my research group is invested in mentoring the PAYS student program at Pomona College, I have continued onto a different project concerning graphene lattices and electron transfer across carbon atoms along their covalent bonds. My previous research project was concerned with square lattices and the journey of reactants to different traps along the lattice (<n> walk length). Similarly, my current project is primarily concerned with the transfer of electrons across hexagonal lattices and calculating the probable walk lengths to a specific centrosymmetric site on the lattice. This would have applications in superconductors which graphite is known to have similar behaviors, as well as in the folding patterns of metalloproteins such as cytochromes and plastocyanin.
Based on previous literature, we decided to confine the hexagons that make up a graphene lattice onto triangular lattices made up of smaller triangles. The center of each triangle was made into a site (i.e. Carbon atom) which was then attached to the site directly adjacent to it that modeled the bonds (i.e. covalent bonds). This diagram made a neat pattern of quickly distinguishable hexagons across the triangle. Calculations were then done using a matrix system of equations and instituting different boundary conditions. It should also be mentioned that there were numerous different methods of triangular lattices that were experimented on, and we’re still looking at ways to connect the different models. For example, we did calculations using Sierpinski gaskets which had no triangles in the center surrounding the centrosymmetric site, and we did calculations on a “triangular lattice” which maximized the number of triangles and had 6 bonds connecting to the centrosymmetric site.
Recently, we have begun considering stacking layers of these lattices on top of each other to model graphite, which is a 3-dimensional structure composed of layers of graphene. 3D Paint has been a useful tool in creating the diagrams to model this, but we are still considering what would be reasonable boundary conditions to work with. We have also partnered with HPC to get access to more resources and programs that can aid in this component of our research. I will hopefully be included in this next venture which could open many new doors in our exploration of graphene.
By Ekeka Abazie