Casimir Contribution to the Interfacial Hamiltonian for 3D Wetting

Critical Casimir forces in soft matter

We review recent advances in the theoretical, numerical, and experimental studies of critical Casimir forces in soft matter, with particular emphasis on their relevance for the structures of colloidal suspensions and on their dynamics. Distinct from other interactions which act in soft matter, such as electrostatic and van der Waals forces, critical Casimir forces are effective interactions characterised by the possibility to control reversibly their strength via minute temperature changes, while their attractive or repulsive character is conveniently determined via surface treatments or by structuring the involved surfaces. These features make critical Casimir forces excellent candidates for controlling the equilibrium and dynamical properties of individual colloids or colloidal dispersions as well as for possible applications in micro-mechanical systems. In the past 25 years a number of theoretical and experimental studies have been devoted to investigating these forces primarily under thermal equilibrium conditions, while their dynamical and non-equilibrium behaviour is a largely unexplored subject open for future investigations.

Critical-point wedge filling and critical-point wetting

For simple fluids adsorbed at a planar solid substrate (modeled as an inert wall) it is known that critical-point wetting, that is, the vanishing of the contact angle θ at a temperature T_{w} lying below that of the critical point T_{c}, need not occur. While critical-point wetting necessarily happens when the wall-fluid and fluid-fluid forces have the same range (e.g., both are long ranged or both short ranged) nonwetting gaps appear in the surface phase diagram when there is an imbalance between the ranges of these forces. Here we show that despite this, the convergence of the lines of constant contact angle, 0<θ<π, to an ordinary surface phase transition at T_{c}, means that fluids adsorbed in wedges (and cones) always exhibit critical-point filling (wedge wetting or wedge drying) regardless of the range and imbalance of the forces. We illustrate the necessity of critical-point filling, even in the absence of critical-point wetting, using a microscopic model density functional theory of fluid adsorption in a right angle wedge, with dispersion and also retarded dispersionlike wall-fluid forces. The location and order of the filling phase boundaries are determined and shown to be in excellent agreement with exact thermodynamic requirements and also predictions for critical singularities based on interfacial models.

Critical behaviour of the contact angle within nonwetting gaps

Recent density functional theory and simulation studies of fluid adsorption near planar walls in systems where the wall-fluid and fluid-fluid interactions have different ranges, have shown that critical point wetting may not occur and instead nonwetting gaps appear in the surface phase diagram, separating lines of wetting and drying transitions, that extend up to the critical temperatureTc. Here we clarify the features of the surface phase diagrams that are common, regardless of the range and balance of the forces, showing, in particular, that the lines of temperature driven wetting and drying transitions, as well as lines of constant contact angleπ>θ>0, always converge to an ordinary surface phase transition atTc. When nonwetting gaps appear the contact angle either vanishes or tends toπast≡(Tc-T)/Tc→0. More specifically, when the wall-fluid interaction is long-ranged (dispersion-like) and the fluid-fluid short-ranged we estimateπ-θ∝t0.16, compared withθ∝t0.77when the wall-fluid interaction is short-ranged and the fluid-fluid dispersion-like, allowing for the effects of bulk critical fluctuations. The universal convergence of the lines of constant contact angle implies that critical point filling always occurs for fluids adsorbed in wedges.

Surface Phase Diagrams for Wetting with Long-Ranged Forces

Recent density functional theory and simulation studies of wetting and drying transitions in systems with long-ranged, dispersionlike forces, away from the near vicinity of the bulk critical temperature T_{c}, have questioned the generality of the global surface phase diagrams for wetting, due to Nakanishi and Fisher, pertinent to systems with short-ranged forces. We extend these studies deriving fully analytic results which determine the surface phase diagrams over the whole temperature range up to T_{c}. The phase boundaries, order of, and asymmetry between the lines of wetting and drying transitions are determined exactly showing that they always converge to an ordinary surface critical point. We highlight the importance of lines of maximally multicritical wetting and drying transitions, for which we determine the exact critical singularities.

Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces

Surfaces between 3D solids and fluids exhibit a wide variety of phenomena both at equilibrium, such as roughening transitions, interfacial fluctuations and wetting, and also out-of-equilibrium, such as the surface growth of driven interfaces. These phenomena are described very successfully using lower dimensional (2D) effective models which focus on the physics associated with emergent mesoscopic lengths scales, parallel to the interface, where the 2D-like behaviour is physically transparent. However, the precise conditions under which this dimensional reduction is justifiable have remained unclear. Here we show that, for a wall-fluid interface, a dimensional reduction from 3D-like to 2D-like behaviour - identified via the decay of density correlations - occurs abruptly at a specific value of the contact angle, and indicates the beginning of interfacial-like 2D behaviour and the spontaneous onset of the capillary-wave spectrum. The reduction from 3D to 2D is characterised by the divergence of a correlation length perpendicular to the interface revealing a morphological change in the nature of density correlations. Counter-intuitive effects occur, including that 3D behaviour can persist up to the wetting temperature and also that 2D behaviour can begin when no wetting layer is present and the adsorption is negative.

Noether-Constrained Correlations in Equilibrium Liquids

Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field Noether's theorem yields the local force balance. Three distinct two-body correlation functions emerge at second order, namely the standard two-body density, the localized force-force correlation function, and the localized force gradient. An exact Noether sum rule interrelates these correlators. Simulations of Lennard-Jones, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate the fundamental role in the characterization of spatial structure.

Fluctuation-induced dispersion forces on thin DNA films

In this work, the calculation of Casimir forces across thin DNA films is carried out based on the Lifshitz theory. The variations of Casimir forces due to the DNA thicknesses, volume fractions of containing water, covering media, and substrates are investigated. For a DNA film suspended in air or water, the Casimir force is attractive, and its magnitude increases with decreasing thickness of DNA films and the water volume fraction. For DNA films deposited on a dielectric (silica) substrate, the Casimir force is attractive for the air environment. However, the Casimir force shows unusual features in a water environment. Under specific conditions, switching sign of the Casimir force from attractive to repulsive can be achieved by increasing the DNA-film thickness. Finally, the Casimir force for DNA films deposited on a metallic substrate is investigated. The Casimir force is dominated by the repulsive interactions at a small DNA-film thickness for both the air and water environments. In a water environment, the Casimir force turns out to be attractive for a large DNA-film thickness, and a stable Casimir equilibrium can be found. The influences of electrolyte screening on the Casimir pressure of DNA films are also discussed at the end. In addition to the adhesion stability, our finding could be applicable to the problems of condensation and decondensation of DNA, due to fluctuation-induced dispersion forces.

Classical nucleation of vapor between hydrophobic plates

In this work, an extended classical nucleation theory (CNT), including line tension, is used to disentangle classical and non-classical effects in the nucleation of vapor from a liquid confined between two hydrophobic plates at a nanometer distance. The proposed approach allowed us to gauge, from the available simulation work, the importance of elusive nanoscale effects, such as line tension and non-classical modifications of the nucleation mechanism. Surprisingly, the purely macroscopic theory is found to be in quantitative accord with the microscopic data, even for plate distances as small as 2 nm, whereas in extreme confinement ([Formula: see text] nm), the CNT approximations proved to be unsatisfactory. These results suggest how classical nucleation theory still offers a computationally inexpensive and predictive tool useful in all domains where nanoconfined evaporation occurs—including nanotechnology, surface science, and biology.