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The water-graphite interaction potential proposed recently (Gonz\'alez etal.\emph{J. Phys. Chem. C} \textbf{2007}, \emph{111}, 14862), the three TIP$N$P($N=3,\:4,\:5$) water-water interaction models, and basin-hopping globaloptimization are used to find the likely candidates for the global potentialenergy minima of (H$_{2}$O)$_{n}$ clusters with $n\leq21$ on the (0001)-surfaceof graphite and to perform a comparative study of these minima. We show that,except for the smaller clusters ($n<6$), for which ab-initio results areavailable, the three water-water potential models provide mostly inequivalentconformations. While TIP3P seems to favor monolayer water structures for$n<18$, TIP4P and TIP5P favor bilayer or volume structures for $n>6$. These $n$values determine the threshold of dominance of the hydrophobic nature of thewater-graphite interaction at the nanoscopic scale for these potential models.

Global Potential Energy Minima of $(H_2O)_n$ Clusters on Graphite: A Comparative Study of the TIP$N$P ($N=3,4,5$) Family