  The interfacial behaviour of water remains a central question to fields as
diverse as protein folding, friction and ice formation[1,2]. While the
structural and dynamical properties of water at interfaces differ strongly from
those in the bulk, major gaps in our knowledge at the molecular level still
prevent us from understanding these ubiquitous chemical processes. Information
concerning the microscopic motion of water comes mostly from computational
simulation[3,4] but the dynamics of molecules, on the atomic scale, is largely
unexplored by experiment. Here we present experimental results combined with ab
initio calculations to provide a detailed insight into the behaviour of water
monomers on a graphene surface. We show that motion occurs by activated hopping
on the graphene lattice. The dynamics of water diffusion displays remarkably
strong signatures of cooperative behaviour due to repulsive forces between the
monomers. The repulsive forces enhance the monomer lifetime ($t_m \approx 3$ s
at $T_S = 125$ K) in a $\textit{free-gas}$ phase that precedes the nucleation
of ice islands and, in turn, provides the opportunity for our experiments to be
performed. Our results give a unique molecular perspective of barriers to ice
nucleation on material surfaces, providing new routes to understand and
potentially control the more general process of ice formation.
