Helium in polygonal nanopores at zero temperature: Density functional theory calculations

Abstract

We investigate adsorption of helium in nanoscopic polygonal pores at zero temperature using a finite-range density functional theory. The adsorption potential is computed by means of a technique denoted as the elementary source method. We analyze a rhombic pore with Cs walls, where we show the existence of multiple interfacial configurations at some linear densities, which correspond to metastable states. Shape transitions and hysterectic loops appear in patterns which are richer and more complex than in a cylindrical tube with the same transverse area. DOI: 10.1103/PhysRevB.77.195431 PACS number͑s͒: 68.08.Bc, 68.65.Ϫk, 68.35.Np A widely investigated topic in physics of quantum fluids is the wetting behavior of helium on substrates of different adsorbing powers. For flat surfaces, the latter is determined by the adatom-adsorber interaction; however, the geometrical structure of a matter exposed to the vapor modifies the adsorption strength and the growth of the film.1 A special concern is the filling of pores. Most reported research in this field addresses classical fluids at or close to bulk coexistence and resorts to Monte Carlo, molecular dynamics, and meanfield approaches.2-7 These systems display a rich variety of behaviors, and we expect that this is also true for liquid 4 He in extremely cold quantum regime. In addition to the competition between adhesive ͑fluid-wall͒ and cohesive ͑fluid-fluid͒ forces, which in wetting problems gives rise to phase changes governed by surface effects, pores make room to interplay among finite sizes, geometrical shape of the confinement, and varying dimensionality. Metastable fluid states show up in hysteresis loops in the sorption isotherms, traditionally associated with the onset of capillary condensation ͑CC͒.8 Furthermore, as pointed out in Ref. 3, among the complications arising from almost every model of condensation in pores, there are uncertainties in both the substratefluid and the fluid-fluid interactions. The latter is commonly selected as that in the bulk, while for the adhesive forces, the simplest reduction is the summation of Lennard-Jones pair interactions, 9 which ignores effects that are associated with the polarization and three-body forces.A simple matter unit out of which one may construct polygonal pores of various shapes is the infinite linear wedge. Recently, we presented the theoretical study of condensation of superfluid 4 He in wedges, 10 employing a zero-temperature, finite-range density functional ͑FRDF͒ that has proven helpful to understand a large variety of phenomena in finite systems of liquid helium isotopes and their mixtures.11 The summation employed there to construct the adsorption potential of two semi-infinite walls meeting at a corner can be improved by a newly reported method 12 that gives the potential of a substrate of arbitrary shape, provided that the ab initio adsorption field for the semi-infinite material with a planar surface is known. This method consists of solving an inverse problem to determine the elementary source ...

Fluid Helium in a Narrow Pore at Zero Temperature

“…[12]. In particular, Cs substrates of diverse shapes are excellent candidates to investigate nontrivial aspects of the physics of wetting, since the soft He-Cs potential, that prevents helium from condensing into a thick film on planar Cs surfaces at zero temperature, can be substantially enhanced by curving or folding the plane, giving rise, for example, to filling of linear wedges of intermediate openings [9], of infinite pores with polygonal section [10] as well as cavities on a nanostructured surface [5,11]. One additional advantage of carrying FRDF calculations with alkali metal surfaces is the substantial reduction in computing time with respect to the very strong graphite substrate, yielding results which are qualitative akin to those expected for very large adsorption strengths.…”

Helium on planar and nanostructured alkali-metal surfaces

“…In cases where the physical effects of such structure can be safely neglected, as for alkali-metal surfaces interacting with liquid helium, it provides a good adsorption potential for nonplanar geometries. 22 We have considered an alkali planar surface hosting a periodic array of parabolic nanocavities of height h =35 Å and outer radius R = 25 Å lying on the ͑x , y͒ plane. This geometry is inspired on substrates studied in Ref.…”

“…14 More recently, the existence of natural and manufactured nanopores 15,16 on the one side, and, on the other, the possibility of growing surfaces structured within the nanoscale, triggered experimental and theoretical lines of research, oriented toward pore filling and wetting of nanopatterned substrates by classical fluids. [16][17][18] The condensation of helium in nanopores at zero temperature has been analyzed using variational Jastrow-Feenberg, 19 variational Monte Carlo, 20 and mean field 21,22 techniques; in particular, we have proven that finite-range density-functional ͑FRDF͒ theory is a powerful instrument in detecting multiple equilibrium states and trace hysteretic loops in the road toward capillary condensation of helium in weakly adsorbing pores. 22 On the other hand, finite temperature FRDF is also adequate in examining aspects of wetting properties of helium on Cs, such as the contact angle 23,24 and the wetting temperature of the semi-infinite metal.…”

“…[16][17][18] The condensation of helium in nanopores at zero temperature has been analyzed using variational Jastrow-Feenberg, 19 variational Monte Carlo, 20 and mean field 21,22 techniques; in particular, we have proven that finite-range density-functional ͑FRDF͒ theory is a powerful instrument in detecting multiple equilibrium states and trace hysteretic loops in the road toward capillary condensation of helium in weakly adsorbing pores. 22 On the other hand, finite temperature FRDF is also adequate in examining aspects of wetting properties of helium on Cs, such as the contact angle 23,24 and the wetting temperature of the semi-infinite metal. 25 Other applications of T-dependent density functionals in describing liquid-gas coexistence, and interfacial properties of superfluid and normal 4 He validate this approach.…”

Hydrodynamical description of long-wavelength density fluctuations of helium in wedges

“…In particular, it has been shown that in addition to the well-known filling transition, which occurs as the liquidvapor interface becomes flat, an "emptying" transition preannouncing the formation of a bridge can take place for sufficiently narrow openings. Furthermore, the study of the adsorbed density profiles and their energetics has provided a reference frame for more involved analysis of the adsorption isotherms of helium in infinite pores 15 and on nanostructured surfaces. 16 Since these studies concentrate on the equilibrium properties of the confined fluid, it is natural to take one step forward and interrogate oneself about the low-energy collective excitations supported by such systems.…”