Relaxation of Thermal Capillary Waves for Nanoscale Liquid Films on Anisotropic-Slip Substrates

Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction

Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.

Thermal capillary waves on bounded nanoscale thin films

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.