Chapter 3 - From classical to quantum dynamics of atomic and ionic species interacting with graphene and its analogue☆
Introduction
Understanding interactions and chemical activities of graphene and its two-dimensional layered analogues with small molecules or ions offers a broad range of opportunities for designing novel applications such as nanoscale (opto)-electronics, few-particle sensors, catalysis, membranes for efficient gas and liquid sieving, phase separation, energy conversion and storage, and quantum information devices [1]. The semiconducting properties of graphene nanoribbons and hexagonal boron nitride (hBN) nanoribbons are known to depend on their width and edge character [[2], [3], [4], [5]]. Further tailoring of their opto-electronic properties can be achieved by employing physicochemical processes and interactions that alter the number of π-conjugated electrons. Even a single vacancy deformation or interaction with a small number of molecules that chemically engage graphene's π-conjugated orbitals can have measurable effects [[6], [7], [8], [9]]. Toward engineering the properties of these materials for desired applications, techniques based on focused ion and electron beams have been demonstrated as effective tools for cleaning, cutting, etching, patterning, and controllable defect formation. Possible defects include Stone–Wales type transformation, lattice dislocations, formation of vacancies and nanopores, substitution of carbon with other atoms, as well as chemical functionalization that transforms sp2 hybridized carbon atoms into sp3 centers [1]. To gain fundamental understandings of beam–matter interactions, it is indispensable to conduct multiscale and multiphysics modeling of relevant physicochemical processes on realistic time scales and molecular system sizes.
In this chapter we survey the approaches for first-principles dynamics modeling of the interactions between graphene and its analogues with beams of atomic and ionic species. Methods for ab initio dynamics focusing on nuclear motion (classical and quantum) of graphene and beam species on the ground electronic state are discussed. We begin by sketching a theory of time-dependent field separation as a starting point for a multiscale and multiphysics decomposition of large molecular systems into fragments that are treatable with different theoretical approaches. A quantum trajectory method is then discussed as an approach for treating nuclear quantum effects (NQEs) for selected light nuclei. The density functional tight-binding (DFTB) theory, which is an inexpensive, approximate density functional theory (DFT) used in conjunction with a quantum trajectory, is also outlined. We do not include the effects of beam induced electronic excitation and dynamics on the excited states surfaces, which are addressed separately in chapter “From ground to excited electronic state dynamics of electron and ion irradiated graphene nanomaterials” by Lingerfelt et al. of this book. Following the review of theory we present a few examples of simulations that illustrate a range of physicochemical phenomena caused by interactions between beam and graphene and related computational aspects. We discuss reactivity, scattering, and transmission of atomic and ionic species including Ar cluster ion, H/D, and H+/D+ on graphene, focusing on the atomic-scale motion and energy dissipation pathways involved in forming and breaking covalent bonding, the NQEs for light species, and the isotopic substitution effects.
Section snippets
Theoretical methods
Today's fabrication and processing of advanced materials are increasingly complex with technological applications heading toward the quantum scale and involving simultaneous manipulation of atoms, electrons, and light (photons). The multiscale and multiphysics character of physics and chemistry behind processes related to fabrication and functioning of such materials often requires computational techniques and methods capable of spanning across several scales of time and space. Multiscale
Simulations
Depending on the type of particles and their energy, the beam irradiations can lead to different physical effects and therefore have different applications. Focused ion and electron beam techniques have been used to engineer defects, for patterning, surface functionalization, and nanopore fabrication [[57], [58], [59], [60], [61], [62]]. Ar atoms cluster beams, ionized for electrostatic acceleration, are an efficient sputterer of organic contamination from graphene surface [[63], [64], [65]].
Summary
There are significant experimental and theoretical interests in application of beams of atomic and ionic clusters and species for graphene engineering. In this chapter, we have presented techniques for direct dynamics modeling of irradiation of graphene with beams of atomic and ionic species. The discussed techniques include both classical and quantum trajectory methods in conjunction with DFTB. Nuclear quantum effects and isotopic substitution effects are also discussed. Depending on the type
Acknowledgments
This work was conducted at the Center for Nanophase Materials Sciences of the Oak Ridge National Laboratory, a U.S. Department of Energy Office of Science User Facility. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant No. ACI-1548562 (allocation TG-DMR110037) and resources of the Oak Ridge Leadership Computing Facility (OLCF) and of the Compute and Data Environment for Science (CADES) at the Oak Ridge
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