arXiv subjects

A. O. Parry

Publications and source records attributed to A. O. Parry.

At least 19 recordsLinked to original sources

arXiv2026

The exact solution of the Koga-Widom-Indekeu model and related models of wetting in fluid mixtures

We show how a broad class of two-component square-gradient models of wetting may be solved exactly for the surface tensions and density profile paths, and clarify how the presence or absence of critical point wetting, in binary and ternary mixtures, is related to universality and symmetry principles at critical end points. We begin by solving a model of fluid interfaces, first introduced by Koga and Widom, in ternary mixtures showing three phase coexistence. Numerical studies had revealed interesting wetting transitions, as well as curious geometrical properties of the profile paths in the density plane, and led these authors to conjecture expressions for the surface tensions. These conjectures were extended by Koga and Indekeu and predicted that partial wetting may persist up to the line of critical end points, i.e. critical point wetting was absent. Here, we obtain the exact density profiles and surface tensions for the Koga-Widom-Indekeu (KWI) model using complex analysis and drawing on the theory of algebraic curves. The exact solution determines the location and order of wetting transitions in the surface phase diagram, confirming that critical point wetting is absent. The model also displays the remarkable property that microscopic density profiles are mapped, by a conformal transform, onto the shape of a macroscopic drop near the contact line whose tensions satisfy the Neumann triangle. Two related models, which illustrate the role of the component isotropy, are also discussed. These models suggest that a universality principle governs wetting in fluid mixtures, resolving contradicting results from earlier studies: Critical point wetting is present if the order-parameter components of the mixture describe Ising-like criticality, but is absent if there is a local XY symmetry. Implications for wetting transitions in more microscopic models and in experiments are discussed.

cond-mat.soft↗

arXiv2022

Critical effects and scaling at meniscus osculation transitions

We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature $R_w$ in a confining parabolic geometry. We argue that the exponent $β_{\rm osc}$ characterising the scale of the interfacial height $\ell_0 \propto R_w^{β_{\rm osc}}$ at osculation, for large $R_w$, falls into two regimes representing fluctuation-dominated and mean-field like behaviour, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and which depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-ranged forces, the exponent is related to the value of the interfacial wandering exponent $ζ$ by $β_{\rm osc}=3ζ/(4-ζ)$. In contrast, in the mean-field regime, which has not been previously identified, and which occurs for systems with longer ranged forces (and higher dimensions), the exponent $β_{\rm osc}$ takes the same value as the exponent $β_s^{\rm co}$ for complete wetting which is determined directly by the intermolecular forces. The prediction $β_{\rm osc}=3/7$ in $d=2$ for systems with short-ranged forces (corresponding to $ζ=1/2$) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in $d=3$, based on a microscopic model Density Functional Theory, determines that $β_{\rm osc} \approx β_s^{\rm co}\approx 0.326$ close to the predicted value $1/3$ appropriate to the mean-field regime for dispersion forces.

cond-mat.soft↗

arXiv2020

Three-phase fluid coexistence in heterogenous slits

We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, where evaporated, locally condensed and globally condensed states all coexist are possible depending on the value of the aspect ratio $a=L/H$ where $H$ is the stripe width and $L$ the wall separation. In particular, for a capillary made from completely dry walls patterned with completely wet stripes the condition for the triple point occurs when the aspect ratio takes its maximum possible value $8/π$. These predictions are tested using a fully microscopic classical Density Functional Theory and shown to be remarkably accurate even for molecularly narrow slits. The qualitative differences with local and global condensation in heterogeneous cylindrical pores are also highlighted.

cond-mat.mes-hall↗

arXiv2019

Bridging of liquid drops at chemically structured walls

Using mesoscopic interfacial models and microscopic density functional theory we study fluid adsorption at a dry wall decorated with three completely wet stripes of width $L$ separated by distances $D_1$ and $D_2$. The stripes interact with the fluid with long-range forces inducing a large finite-size contribution to the surface free-energy. We show that this non-extensive free-energy contribution scales with $\ln L$ and drives different types of bridging transition corresponding to the merging of liquid drops adsorbed at neighbouring wetting stripes when the separation between them is molecularly small. We determine the surface phase diagram and show that this exhibits two triple points, where isolated drops, double drops and triple drops coexist. For the symmetric case, $D_1=D_2\equiv D$, our results also confirm that the equilbrium droplet configuration always has the symmetry of the substrate corresponding to either three isolated drops when $D$ is large or a single triple drop when $D$ is small; however, symmetry broken configurations do occur in a metastable part of the phase diagram which lies very close to the equilibrium bridging phase boundary. Implications for phase transitions on other types of patterned surface are considered.

cond-mat.stat-mech↗

arXiv2015

The local structure factor near an interface; Beyond extended Capillary-Wave models

We investigate the local structure factor $S(z;q)$ at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of $S(z;q)$ known to occur for parallel wavevectors $q\to 0$. We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances $z$ far from the interface, where the profile decays exponentially, $S(z;q)$ splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, $σ_l(q)$ and $σ_g(q)$, which are determined solely by the $bulk$ two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of $S(z;q)$ within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for $σ_l(q)$ and $σ_g(q)$, and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended Capillary-Wave models which failed completely to describe the simulation results.

cond-mat.stat-mech↗

arXiv2015

Liquid-Gas Asymmetry and the Wavevector-Dependent Surface Tension

Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector ($q$) dependent surface tension $σ_\text{eff}(q)$, have encountered difficulties. There is no consensus as to even the shape of $σ_\text{eff}(q)$. By analysing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterised by a microscopic $q$-dependent length $ζ(q)$ not identified previously. The necessity of including the $q$ dependence of $ζ(q)$ is illustrated explicitly in our model and has wider implications, i.e. in typical experimental and simulation studies, an indeterminacy in $ζ(q)$ will always be present, reminiscent of the cut-off used in capillary-wave theory. This leads inevitably to a large uncertainty in the $q$ dependence of $σ_\text{eff}(q)$.

cond-mat.stat-mech↗

arXiv2014

Capillary Contact Angle in a Completely Wet Groove

We consider the phase equilibria of a fluid confined in a deep capillary groove of width $L$ with identical side walls and a bottom made of a different material. All walls are completely wet by the liquid. Using density functional theory and interfacial models, we show that the meniscus separating liquid and gas phases at two phase capillary-coexistence meets the bottom capped end of the groove at a capillary contact angle $θ^{\rm cap}(L)$ which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then $θ^{\rm cap}>0$ even though all the isolated walls are themselves completely wet. This alters the capillary condensation transition which is now first-order; this would be continuous in a capped capillary made wholly of either type of material. We show that the capillary contact angle $θ^{\rm cap}(L)$ vanishes in two limits, corresponding to different capillary wetting transitions. These occur as the width i) becomes macroscopically large, and ii) is reduced to a microscopic value determined by the difference in Hamaker constants. This second wetting transition is characterised by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions.

cond-mat.soft↗

arXiv2014

Pair correlation functions and the wavevector-dependent surface tension in a simple density functional treatment of the liquid-vapour interface

We study the density-density correlation function $G({\bf r},{\bf r}')$ in the interfacial region of a fluid (or Ising-like magnet) with short-ranged interactions using square gradient density functional theory. Adopting a simple double parabola approximation for the bulk free-energy density, we first show that the parallel Fourier transform $G(z,z';q)$ and local structure factor $S(z;q)$ separate into bulk and excess contributions. We attempt to account for both contributions by deriving an interfacial Hamiltonian, characterised by a wavevector dependent surface tension $σ(q)$, and then reconstructing density correlations from correlations in the interface position. We show that the standard crossing criterion identification of the interface, as a surface of fixed density (or magnetization), does not explain the separation of $G(z,z';q)$ and the form of the excess contribution. We propose an alternative definition of the interface position based on the properties of correlations between points that "float" with the surface and show that this describes the full $q$ and $z$ dependence of the excess contributions to both $G$ and $S$. However, neither the "crossing-criterion" nor the new "floating interface" definition of $σ(q)$ are quantities directly measurable from the total structure factor $S^{tot}(q)$ which contains additional $q$ dependence arising from the non-local relation between fluctuations in the interfacial position and local density. Since it is the total structure factor that is measured experimentally or in simulations, our results have repercussions for earlier attempts to extract and interpret $σ(q)$.

cond-mat.stat-mech↗

arXiv2013

Renormalization group calculations for wetting transitions of infinite order and continuously varying order. I. Local interface Hamiltonian approach

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group (RG) calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying $2-α_s = \infty$) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with $β_s = -1$) of the wetting layer thickness are not modified as long as $ω< 2$, with $ω$ the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with $ν_{\perp} = 1/2$). In contrast, the non-universal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate and strong fluctuation regimes.

cond-mat.stat-mech↗

arXiv2007

Derivation of a Non-Local Interfacial Hamiltonian for Short-Ranged Wetting II: General Diagrammatic Structure

In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zig-zag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.

cond-mat.stat-mech↗

arXiv2007

Controlling the order of wedge filling transitions: the role of line tension

We study filling phenomena in 3D wedge geometries paying particular attention to the role played by a line tension associated with the wedge bottom. Our study is based on transfer matrix analysis of an effective one dimensional model of 3D filling which accounts for the breather-mode excitations of the interfacial height. The transition may be first-order or continuous (critical) depending on the strength of the line tension associated with the wedge bottom. Exact results are reported for the interfacial properties near filling with both short-ranged (contact) forces and also van der Waals interactions. For sufficiently short-ranged forces we show the lines of critical and first-order filling meet at a tricritical point. This contrasts with the case of dispersion forces for which the lines meet at a critical end-point. Our transfer matrix analysis is compared with generalized random-walk arguments based on a necklace model and is shown to be a thermodynamically consistent description of fluctuation effects at filling. Connections with the predictions of conformal invariance for droplet shapes in wedges is also made.

cond-mat.soft↗

arXiv2007

Continuous Capillary Condensation

We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions (3d), the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively and are equivalent to 2d-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In 2d we establish precise connection, or covariance, with 2d critical-wetting and wedge-filling transitions, i.e. we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in 2d and 3d.

cond-mat.stat-mech↗

arXiv2006

Point tension in adsorption at a chemically inhomogeneous substrate in two dimensions

We study adsorption of liquid at a one-dimensional substrate composed of a single chemical inhomogeneity of width $2L$ placed on an otherwise homogeneous, planar, solid surface. The excess point free energy $η(L,T)$ associated with the adsorbed layer's inhomogeneity induced by the substrate's chemical structure is calculated within exact continuum transfer-matrix approach. It is shown that the way $η(L,T)$ varies with $L$ depends sensitively on the temperature regime. It exhibits logarithmic divergence as a function of $L$ in the limit $L\to\infty$ for temperatures such that the chemical inhomogeneity is completely wetted by the liquid. In the opposite case $η(L,T)$ converges for large $L$ to $2η_0$, where $η_0$ is the corresponding point tension, and the dominant $L$-dependent correction to $2η_0$ decays exponentially. The interaction between the liquid layer inhomogeneities at $-L$ and $L$ for the two temperature regimes is discussed and compared to earlier mean-field theory predictions.

cond-mat.stat-mech↗

arXiv2005

Tricritical wedge filling transitions with short-ranged forces

We show that the 3D wedge filling transition in the presence of short-ranged interactions can be first-order or second order depending on the strength of the line tension associated with to the wedge bottom. This fact implies the existence of a tricritical point characterized by a short-distance expansion which differs from the usual continuous filling transition. Our analysis is based on an effective one-dimensional model for the 3D wedge filling which arises from the identification of the breather modes as the only relevant interfacial fluctuations. From such analysis we find a correspondence between continuous 3D filling at bulk coexistence and 2D wetting transitions with random-bond disorder.

cond-mat.stat-mech↗

arXiv2005

3D wedge filling and 2D random-bond wetting

Fluids adsorbed in 3D wedges are shown to exhibit two types of continuous interfacial unbinding corresponding to critical and tricritical filling respectively. Analytic solution of an effective interfacial model based on the transfer-matrix formalism allows us to obtain the asymptotic probability distribution functions for the interfacial height when criticality and tricriticality are approached. Generalised random walk arguments show that, for systems with short-ranged forces, the critical singularities at these transitions are related to 2D complete and critical wetting with random bond disorder respectively.

cond-mat.stat-mech↗

arXiv2004

Covariance for Conic and Wedge Complete Filling

Interfacial phenomena associated with fluid adsorption in two dimensional systems has recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We show that covariance also occurs in three dimensional systems and is likely to be verifiable experimentally and in Ising model simulations studies. Specifically, we study complete wetting in wedge (W) and cone (C) geometries as bulk coexistence is approached and show that the equilibrium mid-point heights satisfy $l_c (h,α)=l_w(\frac{h}{2} ,α),$ where $h$ measures the partial pressure and $α$ is the tilt angle. This covariance is valid for both short-ranged and long-ranged intermolecular forces and identifies both leading and next-to-leading order critical exponents and amplitudes in the confining geometries. Connection with capillary condensation-like phenomena is also made.

cond-mat.stat-mech↗

arXiv2004

Non-locality and short-range wetting phenomena

We propose a non-local interfacial model for 3D short-range wetting at planar and non-planar walls. The model is characterized by a binding potential \emph{functional} depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tube-like fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories, and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong non-perturbative influence of non-locality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.

cond-mat.stat-mech↗

arXiv2004

Three-dimensional wedge filling in ordered and disordered systems

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. 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) two-dimensional ($d=2$) and three-dimensional ($d=3$) systems, recovering the known results for pure (thermal disorder) systems and predicting universal critical exponents for the case of random-bond disorder. Finally 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.

cond-mat.stat-mech↗