Growth, Characterization, and Properties of Hybrid Graphene-Carbon Nanotube Films and Related Carbon Nanostructures

Graphene, first isolated in 2004 and the subject of the 2010 Nobel Prize in physics, has generated a tremendous amount of research interest in recent years due to its incredible mechanical and electrical properties. However, difficulties in large-scale production and low as-prepared surface area have hindered commercial applications. In this dissertation, a new material is described incorporating the superior electrical properties of graphene edge planes into the high surface area framework of carbon nanotube forests using a scalable and reproducible technology.

The objectives of this research were to investigate the growth parameters and mechanisms of a graphene-carbon nanotube hybrid nanomaterial termed “graphenated carbon nanotubes” (g-CNTs), examine the applicability of g-CNT materials for applications in electrochemical capacitors (supercapacitors) and cold-cathode field emission sources, and determine materials characteristics responsible for the superior performance of g-CNTs in these applications. The growth kinetics of multi-walled carbon nanotubes (MWNTs), grown by plasma-enhanced chemical vapor deposition (PECVD), was studied in order to understand the fundamental mechanisms governing the PECVD reaction process. Activation energies and diffusivities were determined for key reaction steps and a growth model was developed in response to these findings. Differences in the reaction kinetics between CNTs grown on single-crystal silicon and polysilicon were studied to aid in the incorporation of CNTs into microelectromechanical systems (MEMS) devices. To understand processing-property relationships for g-CNT materials, a Design of Experiments (DOE) analysis was performed for the purpose of determining the importance of various input parameters on the growth of g-CNTs, finding that varying temperature alone allows the resultant material to transition from CNTs to g-CNTs and finally carbon nanosheets (CNSs): vertically oriented sheets of few-layered graphene. In addition, a phenomenological model was developed for g-CNTs. By studying variations of graphene-CNT hybrid nanomaterials by Raman spectroscopy, a linear trend was discovered between their mean crystallite size and electrochemical capacitance. Finally, a new method for the calculation of nanomaterial surface area, more accurate than the standard BET technique, was created based on atomic layer deposition (ALD) of titanium oxide (TiO2).

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.