Dynamical behavior of graphene models
Master Thesis
2017
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University of Cape Town
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Since the discovery of a method to obtain graphene in 2004, there has been intensive research on this material by several researchers ranging from investigations of its physical and chemical properties to some novel applications of graphene. The discovery of graphene came about despite the fact that some leading researchers such as Landau and Peierls had predicted that twodimensional (2D) crystals were thermodynamically unstable. Andre Geim and Konstantin Novoselov managed to obtain graphene using a rather surprising technique called the scotch tape method. The scotch tape method involves carefully peeling off layer after layer in graphite which is a three-dimensional (3D) material without making any distortions to the subsequent layers. Due to the many applications of graphene, understanding the dynamical behavior of the material is a very important problem. In order to investigate the chaoticity in graphene, empirical force fields appropriate for modeling its dynamics are required. In this study we use such models which have been established to accurately describe bond stretching and bond deformation in graphene. Based on the corresponding Hamiltonian formalism we derive the system's Hamilton equations of motion, whose numerical solution determine the dynamical behavior of graphene, as well as the so-called variational equations needed for the numerical computation of several chaos indicators like the maximum Lyapunov Characteristic Exponent.
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Ngapasare, A. 2017. Dynamical behavior of graphene models. University of Cape Town.