2D or Not To Be: The Story and Science of Graphene

abstract: The story of graphene truly began in what was simply a stub in the journal Physical Review not two years after the end of World War II. In 1947, McGill University physicist P.R. Wallace authored “The Band Theory of Graphite” and attempted to develop a foundation on which the structure-property relationship of graphite could be explored; he calculates the number of free electrons and conductivity of what he describes as “a single hexagonal layer” and “suppos[es] that conduction takes place only in layers” in bulk graphite to predict wave functions, energies at specific atomic sites in the hexagonal lattice, and energy contours using a tight binding approximation for a hypothesized version of what we now call ‘armchair-style’ graphene. While Wallace was the first to explore the band structure and Brillouin Zones of single-layer graphite, the concept of two-dimensional materials was not new. In fact, for years, it was dismissed as a thermodynamic impossibility. \n\nEverything seemed poised against any proposed physical and experimental stability of a structure like graphene. “Thermodynamically impossible”– a not uncommon shutdown to proposed novel physical or chemical concepts– was once used to describe the entire field of proposed two-dimensional crystals functioning separately from a three-dimensional base or crystalline structure. Rudolf Peierls and Lev Davoidovich Landau, both very accomplished physicists respectively known for the Manhattan Project and for developing a mathematical theory of helium superfluidity, rejected the possibility of isolated monolayer to few-layered crystal lattices. Their reasoning was that diverging thermodynamic-based crystal lattice fluctuations would render the material unstable regardless of controlled temperature. This logic is flawed, but not necessarily inaccurate– diamond, for instance, is thermodynamically metastable at room temperature and pressure in that there exists a slow (i.e. slow on the scale of millions of years) but continuous transformation to graphite. However, this logic was used to support an explanation of thermodynamic impossibility that was provided for graphene’s lack of isolation as late as 1979 by Cornell solid-state physicist Nathaniel David Mermin. These physicists’ claims had clear and consistent grounding in experimental data: as thin films become thinner, there exists a trend of a decreasing melting temperature and increasing instability that renders the films into islands at somewhere around ten to twenty atomic layers. This is driven by the thermodynamically-favorable minimization of surface energy.

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