  We study in this paper the possible existence of Roskilde-simple liquids and
their isomorphs in a rough-wall nanoconfinement. Isomorphs are curves in the
thermodynamic phase diagram along which structure and dynamics are invariant in
suitable nondimensionalized units. Two model liquids using molecular dynamics
computer simulations are considered: the single-component Lennard-Jones (LJ)
liquid and the Kob-Andersen binary LJ mixture, both of which in the bulk phases
are known to have isomorphs. Nanoconfinement is implemented by adopting a
slit-pore geometry with fcc crystalline walls; this implies inhomogenous
density profiles both parallel and perpendicular to the confining walls.
Despite this fact and consistent with an earlier study [Ingebrigtsen et. al,
Phys. Rev. Lett. 111, 235901 (2013)] we find that these nanoconfined liquids
have isomorphs to a good approximation. More specifically, we show good scaling
of inhomogenous density profiles, mean-square displacements, and higher-order
structures probed using the topological cluster classification algorithm along
the isomorphs. From this study, we conjecture that in experiments,
Roskilde-simple liquids may exhibit isomorphs if confined in a suitable manner,
for example with carbon nanotubes. Our study thus provides an alternative
framework for understanding nanoconfined liquids.
