Divergence of the point tension at wetting

We initially simplify a three-phase contact line to a 'primitive' star-shaped structure formed by three planar interfaces meeting at a common line of intersection, and calculate the line tension associated with this primitive picture. Next, we consider the well-known more refined picture of the contact line that includes a 'core structure' consisting of interface deviations away from the planar interface picture. The corresponding contact line properties were calculated earlier, within mean-field theory, using an interface displacement model or a more microscopic density-functional theory. The question we ask is to what extent the thermodynamic line tension of the contact line near a wetting phase transition can be attributed to the core structure. To answer it we compare our result for the line tension contribution associated with the primitive structure to the known line tension of the full structure (within mean-field theory). While our primitive structure calculation provides a surprisingly useful upper bound to the known line tension near a critical wetting transition, the nontrivial core structure of the contact line near first-order wetting is found to be responsible for an important difference between the known line tension and the upper bound provided by the primitive picture calculation. This accounts also for the discrepancy between the line tensions calculated by two different methods in an earlier mean-field density-functional model of a first-order wetting transition.

Section: Multicritical Wettingsupporting

confidence: 85%

How much does the core structure of a three-phase contact line contribute to the line tension near a wetting transition?

Indekeu

Koga

Widom

2011

“…We will also use the covariance relations to derive new results for the point tension and position dependence of the local compressibility. Indeed for the point tension we will be able to derive a conjectured critical exponent relation due to Indekeu and Robledo [19,20] and also explain why, for pure systems, the point tension shows a logarithmic singularity as θ → 0 [21].…”

Section: Introductionmentioning

confidence: 67%

“…The one ingredient missing in our review of fluctuation effects at 2D wetting is the nature of the point tension τ measuring the excess free-energy associated with the point of threephase contact between wall-vapour and wall-liquid interfaces [19,20,21,31,32]. The reason for this, as first pointed out by Abraham, Latrémolière and Upton (ALU) [21], is that beyond mean-field level, fluctuation effects make the definition of τ a rather subtle issue. The purpose of this long section is to identify a method of defining τ within continuum effective interfacial Hamiltonian theory that we can apply to the case of wetting with random-bond disorder.…”

Section: The Indekeu-robledo Conjecturementioning

confidence: 99%

Wedge covariance for two-dimensional filling and wetting

Parry¹,

Greenall²,

Wood³

2002

A comprehensive theory of interfacial fluctuation effects occurring at 2D wedge (corner) filling transitions in pure (thermal disorder) and impure (random bonddisorder) systems is presented. Scaling theory and the explicit results of transfer matrix and replica trick studies of interfacial Hamiltonian models reveal that, for almost all examples of intermolecular forces, the critical behaviour at filling is fluctuationdominated, characterised by universal critical exponents and scaling functions that depend only on the wandering exponent ζ. Within this filling fluctuation (FFL) regime, the critical behaviour of the mid-point interfacial height, probability distribution function, local compressibility and wedge free energy are identical to corresponding quantities predicted for the strong-fluctuation (SFL) regime for critical wetting transitions at planar walls. In particular the wedge free energy is related to the SFL regime point tension which is calculated for systems with random-bond disorder using the replica trick. The connection with the SFL regime for all these quantities can be expressed precisely in terms of special wedge covariance relations which complement standard scaling theory and restrict the allowed values of the critical exponents for both FFL filling and SFL critical wetting. The predictions for the values of the exponents in the SFL regime recover earlier results based on random-walk arguments. The covariance of the wedge free energy leads to a new, general relation for the SFL regime point tension which derives the conjectured Indekeu-Robledo critical exponent relation and also explains the origin of the logarithmic singularity for pure systems known from exact Ising studies due to Abraham and co-workers. Wedge covariance is also used to predict the numerical values of critical exponents and position dependence of universal one-point functions for pure systems.

“…As noted above the generalised breather-mode result smoothly recovers the correct numerical result β w = 1 in this limit. There is however something remarkable about this since equating the two expressions (20) and (68) implies ζ(2) = ζ(1)/2 yielding information about the allowed value of the wandering exponent. Noting that the lower critical dimension for pure systems is d L = 1 and that at this dimension ζ = 1 we may conclude that equality of the breather-mode and wedge-covariant results for the critical exponents necessitates that for thermal fluctuations…”

Section: Discussionmentioning

confidence: 99%

Three-dimensional wedge filling in ordered and disordered systems

Greenall

Parry

Romero-Enrique

2004

We investigate interfacial structural and fluctuation effects occurring at continuous filling transitions in 3D wedge geometries.We show that fluctuation-induced wedge covariance relations that have been reported recently for 2D filling and wetting have mean-field or classical analogues that apply to higher-dimensional systems. Classical wedge covariance emerges from analysis of filling in shallow wedges based on a simple interfacial Hamiltonian model and is supported by detailed numerical investigations of filling within a more microscopic Landau-like density functional theory. Evidence is presented that classical wedge covariance is also obeyed for filling in more acute wedges in the asymptotic critical regime. For sufficiently short-ranged forces mean-field predictions for the filling critical exponents and covariance are destroyed by pseudo-one-dimensional interfacial fluctuations. In this filling fluctuation regime we argue that the critical exponents describing the divergence of lengthscales are related to values of the interfacial wandering exponent ζ(d) defined for planar interfaces in (bulk) twodimensional (d = 2) and three-dimensional (d = 3) systems. For the interfacial height lw ∼ (θ − α) −βw , with θ the contact angle and α the wedge tilt angle, we find βw = ζ(2)/2(1 − ζ(3)). For pure systems (thermal disorder) we recover the known result βw = 1/4 predicted by interfacial Hamiltonian studies whilst for random-bond disorder we predict the universal critical exponent β ≈ 0.59 even in the presence of dispersion forces. We revisit the transfer matrix theory of three-dimensional filling based on an effective interfacial Hamiltonian model and discuss the interplay between breather, tilt and torsional interfacial fluctuations. We show that the coupling of the modes allows the problem to be mapped onto a quantum mechanical problem as conjectured by previous authors. The form of the interfacial height probability distribution function predicted by the transfer matrix approach is shown to be consistent with scaling and thermodynamic requirements for distances close to and far from the wedge bottom respectively.