Thermal capillary waves relaxing on atomically thin liquid films

Atomistic simulations are used to investigate the relaxation dynamics of thermal capillary waves on thin flat liquid films. Short Lennard-Jones polymers (n=2, 4, and 8) model the liquid in films of thickness 6σ to 96σ, where σ is the Lennard-Jones atomic length-scale parameter. Assuming no-slip boundary conditions on the solid wall and constant surface tension and viscosity, the standard continuum model predicts that capillary waves decay with rates ω that scale with wavenumber q as ω∼q4 for long wavelengths and ω∼q for short wavelengths. The atomistic simulations do indeed show these scalings for ranges of q, and, of course, this model must fail for large q as wavelengths approach atomic scales. However, before a complete breakdown of the continuum description, an unexpected intermediate regime is found. Here the decay rates follow an apparent ω∼q2 power law. The behavior in this range collapses for all the cases simulated when q is scaled with the radius of gyration of the polymers, indicating that a molecular-scale effect underlies the relaxation mechanics of these short waves.