Computer models for the study of graphene

Abstract

Graphene can now be found in many different technologies, with new and innovative products expected to reach the market during this decade. There are still important issues with the production of this remarkable two-dimensional material and structural defects are still common. Defects affect the material at long-range, and can significantly alter its properties. Computer simulations are an appropriate tool for the study of the complex behaviour of defected graphene, but speed is critical and can be a limiting factor in the analysis of larger samples. We introduce and discuss two techniques and a tool for generating large realistic random samples of defected graphene; on such a sample we examine how graphene behaves under a stretching force. Tiny increases of the magnitude of the force can lead to significant displacements, similar to avalanches. These behaviours open up another direction in studying the elasticity of quasi-two-dimensional systems. We then study the problem of sampling an outcome from a list of items with a given rate that can be updated at runtime. We introduce different data structures as solutions and examine whether they are computationally efficient in a realistic setting. We finally discuss an Event-Based approach to simulating the evolution of defected graphene in well-relaxed samples. Instead of randomly trying different structural changes before accepting one, we compute the probability of each possible change and select one of the previously introduced data structures, and discuss the consequences of this approach to future work.