Wetting at nonplanar substrates: Unbending and unbinding

Abstract

We consider fluid wetting on a corrugated substrate using effective interfacial Hamiltonian theory and show that breaking the translational invariance along the wall can induce an unbending phase transition in addition to unbinding.Both first order and second order unbending transitions can occur at and out of coexistence. Results for systems with short-ranged and long-ranged forces establish that the unbending critical point is characterised by hyperuniversal scaling behaviour. We show that, at bulk coexistence, the adsorption at the unbending critical point is a universal multiple of the adsorption for the correspondent planar system.

Surface phase diagrams for wetting on heterogenous substrates

“…3). This phenomenology is identical to that described for a homogeneous but corrugated substrate [24], showing that the physics involved is essentially the same: the transition takes place due to a balance between the free-energy associated with the direct intemolecular interaction with the substrate and the energetic cost of increasing the area of the liquid-vapour interface. For this particular model, Eq.…”

“…Notice that Eq. (24) implies that the thickness at the unbending critical point ℓ 1 C must be lower than the pre-wetting critical thickness ℓ pw for any finite value of L 1 . This allows us to sharpen our upper bound for the finite stripe width critical temperature to T C < T pw for all widths L 1 .…”

“…For smaller values of L 1 , however, this energetic contribution becomes comparable to that arising from the second term of (2) and the interface adopts distinct configurations in order to minimise the free-energy of the system. This gives rise to certain surface phase transitions, denoted surface condensation or unbending transitions, in which different liquid interfacial configurations coexist [20][21][22]24]. In order to calculate the loci of these transitions in the T -µ diagram, the free-energy functional (2) must be minimised for different values of the temperature T and the chemical potential µ.…”

Classical density functional study of wetting transitions on nanopatterned surfaces

“…This phase transition corresponds to a local condensation of liquid driven by the competition between attractive substrate-fluid forces and the effect of the liquid-gas surface tension. This phenomenon was first described for a corrugated wall, in which the troughs discontinuously fill with liquid below the wetting temperature, thereby flattening the liquid-gas interface (hence, the name unbending) [25]. Similar phenomena were studied on chemically patterned substrates, including stripes and arrays of stripes [24].…”

“…Earlier studies based mainly on phenomenological interfacial models have shown that the stripe may induce a first-order unbending transition, where the local adsorption near the stripe jumps between two microscopic values [21][22][23][24]. Heuristically, this transition is associated with the flattening of the local height of the liquid-gas interface pinned to the wall, which also occurs on homogeneous but non-planar substrates [25], and is closely related to the change from Wenzel to Cassie-Baxter states on rough surfaces. What was not appreciated in these earlier studies was how the pre-wetting transition is modified on patterned surfaces.…”