  Using ab initio thermodynamics, the stability of a wide range of hydrocarbon
adsorbates under various chemical vapor deposition (CVD) conditions
(temperature, methane and hydrogen pressures) used in experimental graphene
growth protocols at solid and liquid Cu surfaces has been explored. At the
employed high growth temperatures around the melting point of Cu, we find that
commonly used thermodynamic models such as the harmonic oscillator model may no
longer be accurate. Instead, we account for the translational and rotational
mobility of adsorbates using a recently developed hindered translator and
rotator model or a two-dimensional ideal gas model. The thermodynamic
considerations turn out to be crucial for explaining experimental results and
allow us to improve and extend the findings of earlier theoretical studies
regarding the role of hydrogen and hydrocarbon species in CVD. In particular,
we find that smaller hydrocarbons will completely dehydrogenate under most CVD
conditions. For larger clusters our results show that metal-terminated and
hydrogen-terminated edges have very similar stabilities. While both cluster
types might thus form during the experiment, we show that the low binding
strength of clusters with hydrogen-terminated edges could result in instability
towards desorption.
