A model for characterizing anisotropic diffusion in confined molecular fluids exemplified on water in slit pores and thin ionic liquid films

Diffusion in confined geometries of porous structures of thin films is an important problem from the fundamental and applied points of view. However, accurately resolving the spatial dependence of the diffusion coefficients, particularly in the direction perpendicular to the interfaces, has been a standing problem. Naturally, the issue is the interface-induced broken symmetry. Furthermore, molecules have a finite size, and their shape fluctuates on a similar time scale as diffusion occurs, while deformation behavior is additionally spatially dependent. Accounting for these properties of interfaces and the molecular constituents of the fluid was hitherto not possible. Here we propose a new approach to deriving the spatially dependent diffusion coefficients of extended flexible molecules based on a 2-dimensional Fokker Plank equation and systematic coarse-graining of the internal molecular degrees of freedom. Our technique does not make assumptions on the separation of time scales. For small molecules, it reduces to an analytic expression with the prefactor adapted to different types of interfaces. To demonstrate our method, we choose water and a family of ILs with increasing cation sizes as paradigmatic examples of a systems where internal degrees of freedom have little to major effects. After validating our model on the bulk liquids, we clearly demonstrate the anisotropic nature of diffusion coefficients and provide quantitative profiles for the mobility perpendicular to the interfaces. We find that spatial variations in the diffusivities strongly correlate with interface-induced structuring of the liquid. Notably, the diffusivity of strongly confined ILs scales with the density at the solid-liquid interface, but with a molecular size at the liquid vapor interface.