On the mechanics of 2-dimensional carbon allotropes

Abstract

This thesis reviews the progress leading to the modem picture of 2-dimensional carbon materials, while providing new contributions into the mechanics and failure of the graph-yne family of materials. A first original contribution involves a discussion of material failure across the graphyne family and discussion of a proposed spring abstraction for these materials under mechanical loading. A second contribution is the contrast of these behaviors with graphene and the implications for proposed applications. We apply the mathematical framework of category theory to articulate the precise relation between structure and mechanics of a microscopic system in a macroscopic model domain, by maintaining the chosen molecular properties across a multitude of length scales, from the nanoscale to the continuum scale. The process demonstrates how it becomes possible to 'protoype a model', as category theory enables us to maintain certain information across disparate fields of study, distinct scales, or physical realizations of an abstract system. This method can be thought of as a prototyped model in which a behavior is brought to a different realization as a case study, we use largescale multi-material printing to examine the scaling of the Young's modulus of a particular family 2-D carbon allotropes at the macroscale and validate the printed model using experimental testing. The resulting hand-held materials can be examined more readily and yield insights beyond those available in purely digital representations which is shown through a twisting analysis.