Structural quantities of quasi-two-dimensional fluids

Abstract

Structural quantities of quasi-two-dimensional fluidsQuasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry. Taking the transversal degrees of freedom as a perturbation to an appropriate 2D reference fluid we provide a systematic expansion of the m-particle density for arbitrary m. To leading order in the slit width this density factorizes into the densities of the transversal and lateral degrees of freedom. Explicit expressions for the next-to-leading order terms are elaborated analytically quantifying the onset of inhomogeneity. The case m = 1 yields the density profile with a curvature given by an integral over the pair-distribution function of the corresponding 2D reference fluid, which reduces to its 2D contact value in the case of pure excluded-volume interactions. Interestingly, we find that the 2D limit is subtle and requires stringent conditions on the fluid-wall interactions. We quantify the rapidity of convergence for various structural quantities to their 2D counterparts.

Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory

“…52 The discrete version of the LJ potential is given by Eqs. (19) and (20) with λ p = λ c , where λ c is a cutoff distance for the LJ tail. It can be calculated by requiring |u LJ (r)/ε| < 10 −6 for r > λ c σ, which gives λ c ≃ 12.6.…”

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

“…However, analytical progress in this direction has been achieved only very recently [119,[132][133][134]. Within this theoretical study, the key observation was that in strong confinement the canonical ensemble for the fluid in a slit geometry decouples into a two-dimensional fluid in the lateral plane and an ideal gas in the transversal direction.…”

Strongly confined fluids: Diverging time scales and slowing down of equilibration

“…Decomposing x i = ( r i , z i ) into lateral and transversal coordinates r i = (x i , y i ) and z i , respectively, and following Refs. [13,14] one obtains for the pair interaction energy…”

“…In that case the fluid becomes quasi-two-(or quasi-one-) dimensional. Recently, it was shown that thermodynamic and structural properties of fluids strongly confined by two flat, parallel and hard walls can be calculated perturbatively, with n 0 L 2 as a smallness parameter [13,14]. L is the accessible width in transversal direction and n 0 = N/A is the 2D number density for N identical particles and a wall area A.…”