arXiv subjects

A. O. Parry

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

At least 37 records · Page 2Linked to original sources

arXiv2003

Interfacial structure at a two-dimensional wedge filling transition: exact results and a renormalization group study

Interfacial structure and correlation functions near a two-dimensional (2D) wedge filling transition are studied using effective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzer binding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decay of the interfacial profile relative to the substrate and the correlations between interfacial positions above different positions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is related geometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior is consistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functional renormalization group scheme that keeps the geometry invariant.

cond-mat.stat-mech↗

arXiv2002

Fluid adsorption near an apex: Covariance between complete and critical wetting

Critical wetting is an elusive phenomenon for solid-fluid interfaces. Using interfacial models we show that the diverging length scales, which characterize complete wetting at an apex, precisely mimic critical wetting with the apex angle behaving as the contact angle. Transfer matrix, renormalization group (RG) and mean field analysis (MF) shows this covariance is obeyed in 2D, 3D and for long and short ranged forces. This connection should be experimentally accesible and provides a means of checking theoretical predictions for critical wetting.

cond-mat.stat-mech↗

arXiv2002

Critical wetting in power-law wedge geometries

We investigate critical wetting transitions for fluids adsorbed in wedge-like geometries where the substrate height varies as a power-law, $z(x,y) \sim |x| ^γ$, in one direction. As $γ$ is increased from 0 to 1, the substrate shape is smoothly changed from a planar-wall to a linear wedge. The continuous wetting and filling transitions pertinent to these limiting geometries are known to have distinct phase boundaries and critical singularities. We predict that the intermediate critical wetting behaviour occurring for $0<γ< 1$ falls into one of {\it{three}} possible regimes depending on the values of $γ$, p and q. The unbinding behaviour is characterised by a high degree of non-universality, strongly anisotropic correlations and enhanced interfacial roughness. The shift in phase boundary and emergence of universal critical behaviour in the linear wedge limit is discussed in detail.

cond-mat.soft↗

arXiv2001

Universal phase boundary shifts for corner wetting and filling

The phase boundaries for corner wetting (filling) in square and diagonal lattice Ising models are exactly determined and show a universal shift relative to wetting near the bulk criticality. More generally, scaling theory predicts that the filling phase boundary shift for wedges and cones is determined by a universal scaling function $R_d(ψ)$ depending only on the opening angle $2ψ$. $R_d(ψ)$ is determined exactly in $d=2$ and approximately in higher dimensions using non-classical local functional and mean-field theory. Detailed numerical transfer matrix studies of the the magnetisation profile in finite-size Ising squares support the conjectured connection between filling and the strong-fluctuation regime of wetting.

cond-mat.stat-mech↗

arXiv2001

Wedge covariance for 2D filling and wetting

A comprehensive theory of interfacial fluctuation effects occurring at 2D wedge (corner) filling transitions in pure (thermal disorder) and impure (random bond-disorder) 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 fluctuation-dominated, 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.

cond-mat.soft↗

arXiv2001

Surface Phase Diagrams for Wetting on Heterogenous Substrates

We propose a simplified description of fluid adsorption on heterogenenous micropatterned substrates. Using this approach, we are able to rederive results obtained earlier using effective interfacial Hamiltonian methods and predict a number of new examples of surface phase behaviour for both singly and periodically striped substrates. In particular, we show that, for a singly striped system, the manner in which the locus of surface unbending phase transitions approaches the pre-wetting line of the infinite pure system, in the limit of large stripe widths, is non-trivial and sensitive to several characteristic lengthscales and competing free-energies. For periodic substrates, we investigate finite-size deviations from Cassie's law for the wetting temperature of the heterogeneous system when the domain sizes are mesoscopic.

cond-mat↗

arXiv2000

Geometry dominated fluid adsorption on sculptured substrates

Experimental methods allow the shape and chemical composition of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption characteristics compared to that occuring for planar systems, which may well play an important role in developing technologies such as super-repellent surfaces or micro-fluidics. Recent studies have concentrated on adsorption of liquids at rough and heterogeneous substrates and the characterisation of nanoscopic liquid films. However, the fundamental effect of geometry has hardly been addressed. Here we show that varying the shape of the substrate can exert a profound influence on the adsorption isotherms allowing us to smoothly connect wetting and capillary condensation through a number of novel and distinct examples of fluid interfacial phenomena. This opens the possibility of tailoring the adsorption properties of solid substrates by sculpturing their surface shape.

cond-mat↗

arXiv2000

Wedge filling, cone filling and the strong fluctuation regime

Interfacial fluctuation effects occuring at wedge and cone filling transitions are investigated and shown to exhibit very different characteristics. For both geometries we show how the conditions for observing critical (continuous) filling are much less restrictive than for critical wetting, which is known to require fine tuning of the Hamaker constants. Wedge filling is critical if the wetting binding potential does not exhibit a local maximum, whilst conic filling is critical if the integrated strength of the potential is attractive. This latter scenario is particularly encouraging for future experimental studies. Using mean-field and effective Hamiltonian approaches, which allow for breather-mode fluctuations which translate the interface up and down the sides of the confining geometry, we are able to completely classify the possible critical behaviour (for purely thermal disorder). For the three dimensional wedge, the interfacial fluctuations are very strong and characterised by a universal roughness critical exponent $ν_{\perp} =1/4$ independent of the range of the forces. For the physical dimensions d=2 and d=3, we show that the influence of the cone geometry on the fluctuations at critical filling is to mimic the analogous interfacial behaviour occuring at critical wetting in the strong-fluctuation regime. In particular, for d=3 and for quite arbitary choices of intermolecular potential, the filling height and roughness show the same critical properties as those predicted for three dimensional critical wetting with short-ranged forces in the large wetting parameter ($ω>2$) regime.

cond-mat.soft↗

arXiv2000

Droplet shapes on structured substrates and conformal invariance

We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase co-existence) on heterogeneous substrates and also in wedge geometries in which only a finite domain $Λ_{A}$ of the substrate is completely wet. For three-dimensional systems with short-ranged forces we use renormalization group ideas to establish that both the shape of the droplet height and the height-height correlations can be understood from the conformal invariance of an appropriate operator. This allows us to predict the explicit scaling form of the droplet height for a number of different domain shapes. For systems with long-ranged forces, conformal invariance is not obeyed but the droplet shape is still shown to exhibit strong scaling behaviour. We argue that droplet formation in heterogeneous wedge geometries also shows a number of different scaling regimes depending on the range of the forces. The conformal invariance of the wedge droplet shape for short-ranged forces is shown explicitly.

cond-mat↗

arXiv2000

Local functional models of critical correlations in thin-films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin-films with symmetric surface fields in arbitrary dimension d. In d=2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths as well as the detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin-film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.

cond-mat↗

arXiv1999

Universality for 2D Wedge Wetting

We study 2D wedge wetting using a continuum interfacial Hamiltonian model which is solved by transfer-matrix methods. For arbitrary binding potentials, we are able to exactly calculate the wedge free-energy and interface height distribution function and, thus, can completely classify all types of critical behaviour. We show that critical filling is characterized by strongly universal fluctuation dominated critical exponents, whilst complete filling is determined by the geometry rather than fluctuation effects. Related phenomena for interface depinning from defect lines in the bulk are also considered.

cond-mat↗

arXiv1999

Critical Effects at 3D Wedge-Wetting

We show that continuous filling or wedge-wetting transitions are possible in 3D wedge-geometries made from (angled) substrates exhibiting first-order wetting transitions and develop a comprehensive fluctuation theory yielding a complete classification of the critical behaviour. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also an exact transfer-matrix analysis of a novel effective Hamiltonian which we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is shown to be very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness $ξ_{\perp}\sim (T_F-T)^{-1/4}$ on approaching the filling temperature $T_F$, valid for all possible types of intermolecular forces.

cond-mat↗

arXiv1999

Morphological phase transitions of thin fluid films on chemically structured substrates

Using an interface displacement model derived from a microscopic density functional theory we investigate thin liquidlike wetting layers adsorbed on flat substrates with an embedded chemical heterogeneity forming a stripe. For a wide range of effective interface potentials we find first-order phase transitions as well as continuous changes between lateral interfacial configurations bound to and repelled from the stripe area. We determine phase diagrams and discuss the conditions under which these morphological changes arise.

cond-mat.soft↗

arXiv1999

Wetting at Non-Planar Substrates: Unbending & Unbinding

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.

cond-mat.soft↗

arXiv1998

Interfacial Structural Changes and Singularities in Non-Planar Geometries

We consider phase coexistence and criticality in a thin-film Ising magnet with opposing surface fields and non-planar (corrugated) walls. We show that the loss of translational invariance has a strong and unexpected non-linear influence on the interface structure and phase diagram. We identify 4 non-thermodynamic singularities where there is a qualitative change in the interface shape. In addition, we establish that at the finite-size critical point, the singularity in the interface shape is characterized by two distint critical exponents in contrast to the planar case (which is characterised by one). Similar effects should be observed for prewetting at a corrugated substrate. Analogy is made with the behaviour of a non-linear forced oscillator showing chaotic dynamics.

cond-mat↗

arXiv1998

Corrugation-Induced First-Order Wetting: An Effective Hamiltonian Study

We consider an effective Hamiltonian description of critical wetting transitions in systems with short-range forces at a corrugated (periodic) wall. We are able to recover the results obtained previously from a `microscopic' density-functional approach in which the system wets in a discontinuous manner when the amplitude of the corrugations reaches a critical size A*. Using the functional renormalization group, we find that A* becomes dependent on the wetting parameter ωin such a way as to decrease the extent of the first-order regime. Nevertheless, we still expect wetting in the Ising model to proceed in a discontinuous manner for small deviations of the wall from the plane.

cond-mat.soft↗

arXiv1997

Coupled Hamiltonians and Three Dimensional Short-Range Wetting Transitions

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate \ell representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d=3 at critical and complete wetting respectively which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. We investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates X_i we show that arbitrary two-field models H[X_1,X_2] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set of Hamiltonians based on proper collective coordinates s near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,\ell] in which the degree of coupling is controlled by an angle-like variable, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility χ_1 is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalized critical amplitude θin good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects.

cond-mat.soft↗

arXiv1997

An exact solution for two dimensional wetting with a corrugated wall

An exact solution of a two dimensional RSOS model of wetting at a corrugated (periodic) wall is found using transfer matrix techniques. In contrast to mean-field analysis of the same problem the wetting transition remains second-order and occurs at a lower temperature than that of the planar system. Comparison with numerical studies and other analytical approaches is made.

cond-mat.soft↗