Vibrational properties of long linear carbon chains and hyperbolic graphene

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Siegel, Ross
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Carbon nanostructures exhibit important physical, chemical, and mechanical properties, however, not all of these have been fully explored. In this thesis I focus on two carbon morphologies, linear carbon chains and hyperbolic graphene, known as Schwarzites.
I also investigate zeolite templated carbons (ZTC), microporous aluminosilicates that leave an imprint of their pore network on carbon structures, as a potential route to the experimental realization of Schwarzites, crystalline hyperbolic sp\textsuperscript{2} carbon surfaces. The energetic, electronic, mechanical, and vibrational properties of the ZTC Schwarzites generated by Braun, et al, with simulated carbon impregnation of zeolites, and the know cubic Schwarzites were compared. The ZTC Schwarzites were found to be energetically and dynamically stable, with energy per atom comparable to C\textsubscript{60} and the smallest cubic Schwarzites. They also span the range of metallic, semimetallic, and semiconducting, with the largest electronic gap being \mbox{0.073 eV}. The ZTC Schwarzites are also elastically stable, with bulk moduli within the known ranges of cubic Schwarzites, but two orders of magnitude larger than the experimental value. The phonon density of states of the ZTC Schwarzites was found to be graphenic in nature and the cubic Schwarzites to posses substructure unique to each Schwarzite family. Low frequency Raman active modes in the cubic Schwarzites were identified that possess an inverse relationship between frequency and lattice constant. In an effort to build our own ZTC Schwarzite structure, I found it unlikely that a Schwarzite could form inside the micropres of a zeolite because they are too small, but identified some promising larger porous structures.
Long sp hybridized linear carbon chains are highly reactive, but, the environment inside carbon nanotubes allows them to grow thousands of atoms, hundreds of nanometers, in length. These linear carbon chains encapsulated in carbon nanotubes produce a resonant Raman signal in the range of 1770-\mbox{1880 cm\textsuperscript{-1}}, known as the C-mode. The longitudinal optical (LO) mode of these chains was investigated as the origin of this signal because it produces a large change in the polarizability, making it the most intense Raman active mode. The asymptotic limit, with respect to chain length, of the LO mode was calculated to examine the vibrational response of an infinitely long chain. Only hybrid density functional theory (DFT) predicts an LO mode within the known range of the C-mode. This method predicts that the difference in LO mode between a \mbox{25 nm} chain and an infinite one will be less than \mbox{1 cm\textsuperscript{-1}}, explaining why no length dependence is experimentally found. Rather, the effects of charged states of the chain were examined, modeling the charge transfer between the host nanotube and the encapsulated chain, and identify a softening effect entirely capable of producing the \mbox{$\sim$100 cm\textsuperscript{-1}} range of the C-mode.
May 2020
School of Science
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Rensselaer Polytechnic Institute, Troy, NY
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