Enumerating Stable Nanopores in Graphene and their Geometrical Properties Using the Combinatorics of Hexagonal Lattices

Nanopores in two-dimensional (2D) materials, including graphene, can be used for a variety of applications, such as gas separations, water desalination, and DNA sequencing. So far, however, all plausible isomeric shapes of graphene nanopores have not been enumerated. Instead, a probabilistic approach has been followed to predict nanopore shapes in 2D materials, due to the exponential increase in the number of nanopores as the size of the vacancy increases. For example, there are 12 possible isomers when N=6 atoms are removed, a number that theoretically increases to 11.7 million when N=20 atoms are removed from the graphene lattice. The development of a smaller, exhaustive dataset of stable nanopore shapes can help future experimental and theoretical studies focused on using nanoporous 2D materials in various applications. In this work, we use the theory of 2D triangular "lattice animals" to create a library of all stable graphene nanopore shapes based on a modification of a well-known algorithm in the mathematical combinatorics of polyforms known as Redelmeier's algorithm. We show that there exists a correspondence between graphene nanopores and triangular polyforms (called polyiamonds) as well as hexagonal polyforms (called polyhexes). We develop the concept of a polyiamond ID to identify unique nanopore isomers. We also use concepts from polyiamond and polyhex geometry to eliminate unstable nanopores containing dangling atoms, bonds, and moieties. The exclusion of such unstable nanopores leads to a remarkable reduction in the possible nanopores from 11.7 million for N=20 to only 0.184 million nanopores, thereby indicating that the number of stable nanopores is almost two orders of magnitude lower and is much more tractable. Not only that, by extracting the polyhex outline, our algorithm allows searching for nanopores with dimensions and shape factors in a specified range.Comment: 27 pages and 12 figures in the main text, 6 pages and 5 figures in the supporting informatio

Multi-scale approach for modeling stability, aggregation, and network formation of nanoparticles suspended in aqueous solutions

Multi-scale computational framework to investigate interactions between bare and surfactant-coated nanoparticles in aqueous solutions beyond classical DLVO and aggregation theories

Atomistic modeling and simulations of 2D materials : chemical vapor deposition, nanoporous defects, force-field development, wetting, and friction

This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemical Engineering, 2019Cataloged from student-submitted PDF version of thesis.Includes bibliographical references.Two-dimensional (2D) materials, such as, graphene, transition metal dichalcogenides (TMDs) (e.g., molybdenum disulfide (MoS₂)), and hexagonal boron nitride (hBN), have recently received considerable attention, due to their layer-number-dependent optoelectronic, mechanical, and barrier properties. However, physical understanding of the controlled synthesis and interfacial behavior of 2D materials is still lacking. In this thesis: First, I construct a generalized mechanistic model for the growth of TMD monolayers using chemical vapor deposition (CVD). Combining kinetic Monte Carlo (KMC) simulations and a chemical engineering transport model, I am able to predict the experimentally-observed shape and size evolution of the MoS₂ morphology inside a CVD reactor. Second, I address the challenge of solving the Isomer Cataloging Problem (ICP) for lattice nanopores in 2D materials.Combining electronic structure density functional theory (DFT) calculations, KMC simulations, and chemical graph theory, I generate a catalog of unique, most-probable isomers of 2D lattice nanopores, demonstrating remarkable agreement with experimental microscopy data for nanopores in graphene and hBN. Third, I study the photoluminescent properties of nanoporous defects in hBN by combining my solution to the ICP with extensive hybrid DFT calculations of electronic bandgaps. Doing so, I map the experimentally-observed emission energies to one or more defect shapes in hBN, thereby demonstrating structure-property relationships for defects in hBN, with implications for single-photon emission from hBN devices. Fourth, using molecular dynamics (MD) simulations, I show that electrostatic interactions play a negligible role in determining the contact angle and the friction coefficient of water on the MoS₂ basal plane.I show that other planes (e.g., the zigzag plane) are polar with respect to interactions with water, thereby illustrating the role of edge effects in MoS₂. Fifth, I combine lattice dynamics calculations with DFT-based MD simulations to develop a force field for hBN for use in mechanical and interfacial applications. The force field predicts the crystal structure, elastic constants, and phonon dispersion relation of hBN with good accuracy, and demonstrates remarkable agreement with the interlayer and water-hBN binding energies predicted by advanced ab initio calculations. Finally, using MD simulations, I study the wetting and frictional properties of hBN by three different liquids of varying degrees of polarity. I infer that electrostatic interactions affect the frictional properties of various liquids in contact with hBN to different extents, and propose the mean-squared total lateral force as a physical metric to rationalize this observation.This finding implies that liquids with lower wettability can exhibit higher friction on hBN surfaces. In conclusion, the theoretical and simulation methods developed and applied in this thesis should inform the synthesis of 2D materials, and their use in various applications, such as, optoelectronic devices, mechanical composites, and membranes for gas separation and water desalination.by Ananth Govind Rajan.Ph. D.Ph.D. Massachusetts Institute of Technology, Department of Chemical Engineerin

Fundamental scaling laws for the direct-write chemical vapor deposition of nanoscale features: modeling mass transport around a translating nanonozzle

© 2019 The Royal Society of Chemistry. The nanometer placement of nanomaterials, such as nanoribbons and nanotubes, at a specific pitch and orientation on a surface, remains an unsolved fundamental problem in nanotechnology. In this work, we introduce and analyze the concept of a direct-write chemical vapor deposition (CVD) system that enables the in-place synthesis of such structures with control over orientation and characteristic features. A nanometer scale pore or conduit, called the nanonozzle, delivers precursor gases for CVD locally on a substrate, with spatial translation of either the nozzle or the substrate to enable a novel direct write (DW) tool. We analyze the nozzle under conditions where it delivers reactants to a substrate while translating at a constant velocity over the surface at a fixed reaction temperature. We formulate and solve a multi-phase three-dimensional reaction and diffusion model of the direct-write operation, and evaluate specific analytically-solvable limits to determine the allowable operating conditions, including pore dimensions, reactant flow rates, and nozzle translation speed. A Buckingham Π analysis identifies six dimensionless quantities crucial for the design and operation of the direct-write synthesis process. Importantly, we derive and validate what we call the ribbon extension inequality that brackets the allowable nozzle velocity relative to the CVD growth rate-a key constraint to enabling direct-write operation. Lastly, we include a practical analysis using attainable values towards the experimental design of such a system, building the nozzle around a commercially available near-field scanning optical microscopy (NSOM) tip as a feasible example

Dominance of dispersion interactions and entropy over electrostatics in determining the wettability and friction of two-dimensional MoS2 surfaces.

International audienceThe existence of partially ionic bonds in molybdenum disulfide (MoS2), as opposed to covalent bonds in graphene, suggests that polar (electrostatic) interactions should influence the interfacial behavior of two-dimensional MoS2 surfaces. In this work, using molecular dynamics simulations, we show that electrostatic interactions play a negligible role in determining not only the equilibrium contact angle on the MoS2 basal plane, which depends solely on the total interaction energy between the surface and the liquid, but also the friction coefficient and the slip length, which depend on the spatial variations in the interaction energy. While the former is found to result from the exponential decay of the electric potential above the MoS2 surface, the latter results from the trilayered sandwich structure of the MoS2 monolayer, which causes the spatial variations in dispersion interactions in the lateral direction to dominate over those in electrostatic interactions in the lateral direction. Further, we show that the nonpolarity of MoS2 is specific to the two-dimensional basal plane of MoS2 and that other planes (e.g., the zigzag plane) in MoS2 are polar with respect to interactions with water, thereby illustrating the role of edge effects, which could be important in systems involving vacancies or nanopores in MoS2. Finally, we simulate the temperature dependence of the water contact angle on MoS2 to show that the inclusion of entropy, which has been neglected in recent mean-field theories, is essential in determining the wettability of MoS2. Our findings reveal that the basal planes in graphene and MoS2 are unexpectedly similar in terms of their interfacial behavior