  Thermal motions of molecules can generate nanowaves on the free surface of a
liquid film. As nanofilms are susceptible to the contamination of surfactants,
this work investigates the effects of surfactants on dynamics of nanowaves on a
bounded film with a finite depth, using both molecular dynamics simulations and
analytical theories. In molecular simulations, a bead-spring model is adopted
to simulate surfactants, where beads are connected by the finite extensive
nonlinear elastic potentials. Fourier transforms of the film surface profiles
$h(x,t)$ extracted from molecular simulations are performed to obtain the
static spectrum $|h_q|_{\mathrm{rms}}$ and temporal correlations of surface
modes $<h_q(0)h_q^*(t)>$. It is shown that the spectral amplitude is increased
for the contaminated liquid surface compared to the clean surface because
surfactants can decrease surface tension. A higher concentration of surfactants
on the surface not only decreases the surface tension but also causes elastic
energy to the free surface, as the scaling of spectral amplitude with
wavenumbers changes from $|h_q|_{\mathrm{rms}}\sim q^{-1}$ to
$|h_q|_{\mathrm{rms}}\sim q^{-2}$ for modes with large wavenumbers. Regarding
the temporal correlations of surface modes, it is observed that the presence of
surfactants leads to a slower decay, which, however, cannot be predicted by
only considering the decreased surface tension. Based on the Boussinesq Scriven
model for surface viscosity, a linear stability analysis of Stokes flow for
films with arbitrary depth is conducted and the obtained dispersion relation
considering surface viscosity can justify the simulation results.
