  We investigate the impact of the substrate on the structural properties and
the morphology of alkanethiol self-assembled monolayers (SAMs) on gold, using
first principles calculations and atomistic molecular dynamics simulations. We
consider hexadecanethiols on Au(211), Au(221) and Au(311) surfaces which
contain few-atom wide terraces separated by monoatomic steps similar to the
complex Au surfaces used in experiments. The structure of the SAMs is probed
via several structural properties including tilt angles, mean C atom heights
from the surface, precession angles, gauche defects, gyration tensors and
relative shape anisotropy. Comparing these properties to those of the
well-studied SAMs on Au(111), we observe similarities but also striking
differences. A clear order to disorder transition is observed by changing the
substrate: well-ordered SAMs on (111) and (211) surfaces become mixed
ordered-disordered structures on (311) and fully disordered on (221). The
presence of steps on the Au surfaces also results in preferential tilt
orientations with long-range order. Our results show that in addition to the
expected grafting density dependence, the transition from order to disorder
crucially depends on substrate morphology. The onset of ordering behavior is
related to the atomic structure of the surface. The key parameter that affects
long-range order is the energy for changing the dihedral angle between
Au-S-$\mathrm{C^{(1)}-C^{(2)}}$ of the adsorbed alkanethiol.
