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C. Rascon

Publications and source records attributed to C. Rascon.

18 recordsLinked to original sources
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

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↗
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↗
arXiv2002

Landau Expansion for the Critical Point of a Polydisperse System

The effect of polydispersity on the phase diagram of a simple binary mixture is to split the binodal curve into cloud and shadow curves that cross at the critical point (which, in general, is not at the maximum of either curve). Recent theories of polydispersity have shown, in favorable cases, how to project the (infinite-dimensional) free energy of the polydisperse system into a low dimensional space of `moment densities'. We address here the issue of how to construct a Landau expansion from the projected free energy. For the simplest case where the excess free energy depends on one moment density $ρ_1$ (this includes Flory Huggins theory for length-polydisperse chains) we show that the minimal expansion remains quartic in $ρ_1$ but nonetheless has seven independent coefficients, not two. When this expansion is handled correctly all the peculiar qualitative features of the polydisperse phase diagram are recovered, as are the slopes of the cloud and shadow curves, and the curvature of the cloud. However, to correctly predict the curvature of the shadow, certain fifth order terms must be retained. We also consider the phase diagram on the temperature-pressure plane, where the coexistence line broadens into a region. In general, the critical point lies between the point of maximum temperature and the point of maximum pressure on the perimeter of this region. This behaviour is again captured by the Landau expansion.

cond-mat.stat-mech↗
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

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↗
arXiv1996

Perturbation Theory for Classical Solids

The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional difficulties of all previous approaches are overcome. The perturbation is a first order term in an expansion of the Helmholtz free energy functional instead of an additive {\it ad hoc} term and the proper solid reference structure is used instead of some kind of mapping into the fluid structure at some effective density. As the theory reduces to the usual liquid perturbation theory in the uniform limit, it can describe consistently the complete phase diagram. Excellent results are obtained when applied to different model systems.

cond-mat↗
arXiv1996

Theoretical Approach to the Correlations of a Hard-Sphere Crystal

We present the first theoretical approach to the angular-average of the two-body correlation function $\tilde g(r)$ for simple solids. It is based on three sum rules for $\tilde g(r)$: the compressibility and virial equations and the normalization. We apply the theory to determine this correlation function for the case of the FCC solid phase of hard spheres. The agreement with simulation data is excellent over all the density range. The application to other simple systems is discussed. The approach opens a new route to perturbation theories for simple solids.

cond-mat↗
arXiv1996

Equation of State of the Hard-Sphere Crystal

A new approach to the averaged two-particle distribution function of a crystalline phase is presented. It includes an indirect check of the merit of the Gaussian approximation for the local density and a new way to inferring values of the thermodynamic variables from simulation data. The equation of state and the compressibility of the hard-sphere FCC crystal is computed from Tarazona free energy density functional [Phys. Rev. A {\bf 31}, 2672 (1985)]. They are in excellent agreement with simulation results over the physical range of densities up to almost close packing. We also include the comparison with the results obtained by two other functional approaches which are also excellent.

cond-mat↗
arXiv1995

Solid-to-solid isostructural transition in the hard sphere/attractive Yukawa system

A thermodynamically consistent density functional-perturbation theory is used to study the isostructural solid-to-solid transition which takes place in the hard sphere/attractive Yukawa system when the Yukawa tail is sufficiently short-ranged. A comparison with results for the square well potential allows us to study the effect of the attractive potential form on the solid-solid transition. Reasonable agreement with simulations is found for the main transition properties as well as for the phase diagram evolution with the the range of the attractive potential.

cond-mat↗