Interface Hamiltonian Research Articles

Complete wetting of pits and grooves

For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the long range of substrate potentials is explicitly taken into account. Four types of geometrical patterns are considered: i) one-dimensional periodic arrays of rectangular or parabolic grooves and ii) two-dimensional lattices of cylindrical or parabolic pits. We present numerical evidence that at the centers of the cavity regions the thicknesses of the adsorbed films obey precisely the same geometrical covariance relation, which has been recently reported for complete cone and wedge filling. However, this covariance does not hold for the laterally averaged wetting film thicknesses. For sufficiently deep cavities with vertical walls and close to liquid-gas phase coexistence in the bulk, the film thicknesses exhibit an effective planar scaling regime, which as a function of undersaturation is characterized by a power law with the common critical exponent -1/3 as for a flat substrate, but with the amplitude depending on the geometrical features.

Electron transport in Nano‐Gold–Silicon interfaces

AbstractThe electron transport characteristics of gold–silicon interfaces are studied using a combined ab initio approach of the Green's function for electron transfer and quantum density functional theory (DFT) for finite and extended systems. The Kohn–Sham Hamiltonian of an extended cluster or molecule and the density of states (DOS) of bulk Si and Au are used to construct the interface Hamiltonian to obtain the DOS, electron transmission, and current–voltage characteristics of the interface. Diode behavior is observed with electron conduction when the gold side is positively biased with a threshold of 0.8 V. The presence of molecules trapped at the interface and the geometry of the metal atoms strongly affect the conductance, implying difficult or even impossible theory–experiment validations. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Local orientations of fluctuating fluid interfaces

Thermal fluctuations cause the local normal vectors of fluid interfaces to deviate from the vertical direction defined by the flat mean interface position. This leads to a nonzero mean value of the corresponding polar tilt angle which renders a characterization of the thermal state of an interface. Based on the concept of an effective interface Hamiltonian we determine the variances of the local interface position and of its lateral derivatives. This leads to the probability distribution functions for the metric of the interface and for the tilt angle which allows us to calculate its mean value and its mean-square deviation. We compare the temperature dependences of these quantities as predicted by the simple capillary-wave model, by an improved phenomenological model, and by the microscopic effective interface Hamiltonian derived from density-functional theory. The mean tilt angle discriminates clearly between these theoretical approaches and emphasizes the importance of the variation of the surface tension at small wavelengths. Also the tilt angle two-point correlation function is determined which renders an additional structural characterization of interfacial fluctuations. Various experimental accesses to measure the local orientational fluctuations are discussed.

Ising systems with pairwise competing surface fields

The magnetization distribution and phase behaviour of large but finite Ising simple cubicL × L × L lattices ind = 3 dimensionsand square L × L lattices in d = 2 dimensions are studied for the case where four free boundaries are present, at which surface fields+Hs act on one pair of opposite boundaries while surface fields−Hs act on theother pair (in d = 3, periodic boundary conditions are used for the remaining pair). Both the distributionPL(m) of the global magnetization and also the distribution of the local magnetizationm(x,z) are obtained by Monte Carlo simulations, wherex and z denote the coordinates when the boundaries are oriented along thex-axis andz-axis(in d = 2); oralong the xy-plane and zy-plane (in d = 3, where the periodic boundary condition applies in they-direction). Varyingthe temperature T and linear dimension L it is found that a single bulk rounded phase transition occurs, which converges to the bulk transitiontemperature Tcb as , unlike other geometric arrangements of competing boundary fields, where a secondtransition occurs in the bulk due to interface formation or delocalization, related to wedgeor corner filling or wetting transitions, respectively. In the present geometry, onlyprecursors of wetting layers form on those boundaries where the field is oppositely orientedto the magnetization in the bulk and the thickness of these layers is found to scale likeL1/2 (in d = 2) or lnL (in d = 3), respectively. These findings are explained in terms of a phenomenological theory basedon the effective interface Hamiltonian and scaling considerations.

Interfaces of semi-infinite smectic liquid crystals and equations of state of infinite smectic stacks of semiflexible manifolds.

In this paper, we first elucidate the classical problem of the elastic free energy of a semi-infinite smectic-A liquid crystals, that fills the semispace above an interface (a boundary smectic layer) of a given shape. For the free energy of this interface, we obtain an effective interface Hamiltonian that takes into account the system discreteness introduced by the layered character of smectic-A liquid crystals. It is thus applicable to both short and long wavelength fluctuations of the interface shape. Next, we use our interface Hamiltonian to develop an efficient approach to the statistical mechanics of stacks of N semiflexible manifolds, such as two-dimensional smectic phases of long semiflexible polymers and three-dimensional lamellar fluid membrane phases. Within our approach, doing the practically interesting thermodynamic limit N--> infinity is reduced to considering a small stack, with just a few interacting manifolds, representing a subsystem of an infinite smectic. This dramatic reduction in the number of degrees of freedom is achieved by treating the first (the last) manifold of the small stack as an interface with the semi-infinite smectic medium below (above) the small stack. We illustrate our approach by considering in detail two-dimensional sterically stabilized smectic liquid crystals of long semiflexible polymers with hard-core repulsion. Smectic bulk (N= infinity ) equation of state and the universal constant characterizing entropic repulsion in these phases are obtained with a high accuracy from numerical simulations of small subsystems with just a few semiflexible polymers.

Effective interface Hamiltonians for unbinding transitions in ternary amphiphilic mixtures

We outline an analytic method for deriving effective interfacial models, suitable for describing unbinding behaviour in ternary amphiphilic mixtures, from underlying non-critical bulk models. Herein we concentrate on deriving interfacial properties (the surface tension and rigidity coefficients) for the simple case of a free oil-phase/microemulsion interface. This calculation allows us to explicitly demonstrate the difference between the interfacial tension, which is a uniquely defined quantity, and the rigidities which are highly sensitive to the choice of interface location definition. We conclude by describing how the model derivation may be extended to include the effect of an external surface, which is appropriate for the study of wetting in a confined ternary mixture. We briefly summarize the results of a recent study of wetting at such a surface for which a rich phase diagram is predicted.

Fluctuation-induced constraints on the observation of unbinding in a confined complex fluid.

An extensive study of the effect of fluctuations on the unbinding of an interface from a wall in a ternary system is presented. The framework upon which the analysis is based is a linear functional renormalization group scheme of the appropriate effective interface Hamiltonian. The interface model includes position-dependent gradient coefficients, and their presence is shown to be equivalent to modifications of the bare interface potential that are highly relevant in determining the renormalized critical behavior. We analyze the modified interface potential in a mean-field-like way for both bare critical and first-order unbinding transitions in order to highlight the key effects. We further perform a detailed study of the linearized renormalization group equations identifying three fluctuation regimes and recovering earlier predictions for nonuniversal critical exponents. The surface phase diagram changes dramatically under renormalization with, most notably, fluctuation-induced reentrant behavior. We show that in the revised phase diagram the unbound region is limited in extent indicating that the opportunity for observing an unbinding transition in a confined complex fluid is highly restricted.

Interface structures and Hamiltonians : Exact results

There have been many recent applications of interface models and Hamiltonians to problems in the theory of wetting. These models help to understand more abstract calculations on the type of problem which can be treated on the one hand, and on the other, to extend the type of problem which can be treated. A very recent example of this is corner wetting, also known as filling. This contribution discusses the validity of such concepts from first principles using exactly calculated interface structures and phase diagrams. The planar Ising model, with boundary conditions and surface fields imposed to bring in wetting, is used. The well-known Jordan–Wigner transformation to lattice fermions is composed of a product of spin reversals to one side (on a strip) of the point at which the lattice Fermi operator acts. Such spin reversals introduce a domain wall in a natural way which can be exploited to bring in interface Hamiltonians in a natural and precise way. The perennial problem of intrinsic structure is discussed. The findings do not support the notion of such a structure attached to capillary waves by convolution. In a sense to be made precise, kinks have to be taken into account.

Shape of the nematic-isotropic interface in conditions of partial wetting

A nematic liquid crystal in contact with a solid substrate is studied in the partial wetting regime. Both a mesoscopic Landau-de Gennes theory and a macroscopic effective interface Hamiltonian approach are considered. A generalized Young equation for the balance of forces at the three-phase contact line is derived, which takes into account corrections due to distortions of the nematic director field. It is also shown that the asymptotic form of the separation of the nematic-isotropic interface from the substrate has a logarithmic correction to the usual linear behaviour. The characteristic length scale of this correction is given by the ratio K/(2σNI), where K and σNI are the average elastic constant and the nematic-isotropic surface tension, respectively, and is of the order of a few hundred angstroms. Then, a simple form of an effective interface Hamiltonian is proposed, and results consistent with the predictions of the Landau-de Gennes theory are obtained. It is shown, in the framework of this macroscopic approach, that the line tension associated with the contact line remains finite, when the thermodynamic limit is taken, if the anchoring at both the nematic-substrate and the nematic-isotropic interfaces is homeotropic. However, in the case of different anchoring directions, the line tension diverges logarithmically with the system size.

Capillary-wave effects at critical wetting in type-I superconductors

We discuss the effect of fluctuations of the superconductor-normal (SC/N) interface on the (short-range) critical wetting transition in type-I superconductors. Functional renormalization of a standard effective interface Hamiltonian shows that the fluctuation regimes found for short-range critical wetting in conventional fluid systems appear in superconductors with slight modifications. Because the fluctuation parameter omega approximately 1/(1-sqrt[2]kappa) depends on the Ginzburg-Landau parameter kappa, strong fluctuation effects would be expected in the limit kappa-->1/sqrt[2]. However, the capillary-wave spectrum of the SC/N interface has an unusual form due to a relevant magnetic field contribution which suppresses long wavelength fluctuations, invalidating conclusions drawn from the standard effective interface Hamiltonian, and validating the results of mean-field theory.

Surface-induced disorder in body-centered-cubic alloys

We present Monte Carlo simulations of surface-induced disordering in a model of a binary alloy on a bcc lattice which undergoes a first-order bulk transition from the ordered DO3 phase to the disordered A2 phase. The data are analyzed in terms of an effective interface Hamiltonian for a system with several order parameters in the framework of the linear renormalization approach due to Br\'ezin, Halperin, and Leibler. We show that the model provides a good description of the system in the vicinity of the interface. In particular, we recover the logarithmic divergence of the thickness of the disordered layer as the bulk transition is approached, we calculate the critical behavior of the maxima of the layer susceptibilities, and demonstrate that it is in reasonable agreement with the simulation data. Directly at the (110) surface, the theory predicts that all order parameters vanish continuously at the surface with a nonuniversal, but common critical exponent ${\ensuremath{\beta}}_{1}.$ However, we find different exponents ${\ensuremath{\beta}}_{1}$ for the order parameter $({\ensuremath{\psi}}_{2},{\ensuremath{\psi}}_{3})$ of the DO3 phase and the order parameter ${\ensuremath{\psi}}_{1}$ of the B2 phase. Using the effective interface model, we derive the finite size scaling function for the surface order parameter and show that the theory accounts well for the finite size behavior of $({\ensuremath{\psi}}_{2},{\ensuremath{\psi}}_{3}),$ but not for that of ${\ensuremath{\psi}}_{1}.$ The situation is even more complicated in the neighborhood of the (100) surface, due to the presence of an ordering field which couples to ${\ensuremath{\psi}}_{1}.$

Interface Hamiltonian with a position-dependent stiffness: A nonlinear functional renormalization group study

A detailed study of the wetting behavior predicted from an effective interfacial Hamiltonian approach which allows for a position-dependent stiffness coefficient is given. A nonlinear functional renormalization group scheme is introduced enabling earlier studies to be extended into general dimensions $1<d<~3$ while permitting a semiquantitative numerical analysis. We find that the prediction of Fisher and Jin of a bare critical wetting transition being driven fluctuation-induced first order can occur for dimensions $d>{d}_{c}\ensuremath{\approx}2.41$ while at lower $d$ the transition remains critical. For $d>{d}_{c}$ first-order wetting is found if the wetting parameter $\ensuremath{\omega}(T)$ is less than a tricritical value ${\ensuremath{\omega}}_{t}(T).$ Importantly in three dimensions numerical analysis reveals ${\ensuremath{\omega}}_{t}>\ensuremath{\omega}$ thus clearly supporting the premise that the wetting transition in this case is indeed first order. We focus especially on demonstrating the robustness of this result under variation of the stiffness strength and renormalization group rescaling parameter.

Systematic smoothing of constrained interface profiles

We introduce a family of crossing constraints for defining an interface Hamiltonian that yield order-parameter profiles of any desired smoothness. The usual local crossing criterion is generalized to include integral constraints. Application to short-range critical wetting allows us to demonstrate that fundamental predictions from the local crossing criterion are robust under a change of constraint. Further, interface Hamiltonians derived from any member of the family are shown to reproduce exact results for order-parameter correlation functions.

Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach

The phase diagram of the 2D Ising model confined between two infinite walls and subject to opposing surface fields and to a bulk "gravitational" field is calculated by means of density matrix renormalization methods. In absence of gravity two phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores the two phase coexistence up to the bulk critical temperature, in agreement with previous mean-field predictions. We calculate the exponents governing the finite size scaling in the temperature and in the gravitational field directions. The former is the exponent which describes the shift of the critical temperature in capillary condensation. The latter agrees, for large surface fields, with a scaling assumption of Van Leeuwen and Sengers. Magnetization profiles in the two phase and in the single phase region are calculated. The profiles in the single phase region, where an interface is present, agree well with magnetization profiles calculated from a simple solid-on-solid interface hamiltonian.

Surface Order Parameter Interface Hamiltonian: Renormalization of the Capillary Parameter at Complete Wetting.

Surface Order Parameter Interface Hamiltonian: Renormalization of the Capillary Parameter at Complete Wetting.

Dynamics of first-order wetting transitions

Abstract For first-order wetting transitions we discuss the nucleation process on the wall of a system and the late-stage growth properties of supercritical droplets. The properties of the critical droplets are determined by an effective interface Hamiltonian. For the dynamic properties we adopt the simplest Langevin model obeying detailed balance with a non-conserved order parameter. Within this approach we derive geometrical and stability properties of the critical droplets, the nucleation rate and Lifshitz-type asymptotic growth laws. Finally we discuss the crossover behaviour of critical droplets from the wetting to the partial wetting and prewetting regimes.

Effective interface Hamiltonians for short-range critical wetting

The derivation of effective interface Hamiltonians on the basis of an underlying noncritical bulk order-parameter theory is critically examined for use in studying critical wetting transitions in (d=3)-dimensional systems with short-range forces. A crossing constraint on the interfacial profile is used to define the fluctuating interface location l(y) and exact general expressions are obtained for the effective wall-interface potential W[l(y)] and for the wall-modified interfacial stiffness Σ[l(y)] in terms of a constrained planar order-parameter profile. Previous discussions in the literature are shown to be inadequate

Structure of the effective Hamiltonian for liquid-vapor interfaces.

Using the microscopic density-functional theory for inhomogeneous simple fluids, we derive a nonlocal and non-Gaussian expression for the effective Hamiltonian of a fluctuating liquid-vapor interface. If a gradient expansion is applied to this Hamiltonian, one obtains\char22{}after a partial resummation\char22{}as the leading term the standard effective interface Hamiltonian which is proportional to the increase of the area of the interface relative to that of the flat configuration. The next to leading terms are proportional to the Gaussian and to the mean curvature of the interface, respectively. Microscopic expressions for the coefficients in this expansion are derived. If the interparticle interactions in the fluid decay according to power laws, the gradient expansion breaks down. This is reflected in the nonanalytic behavior of the wave-vector-dependent surface tension which can be expressed in terms of the Fourier transform of the interaction potential between the fluid particles. Various approximations of the nonlocal Hamiltonian are compared quantitatively. The relevance of this Hamiltonian for interpreting scattering experiments is discussed.

Sum rules for interface Hamiltonians

We derive exact identities for a general class of interface Hamiltonians describing wetting transitions that relate force fluctuations to interface fluctuations and the surface tension. These sum rules are analogous to the Triezenberg, Zwanzig and Wertheim formulas for the surface tension derived using the theory of inhomogeneous fluids. Relations between these two approaches are discussed. Our sum rules are consistent with the scaling theory of wetting transitions.

Microscopic derivation of the effective interface Hamiltonian for liquid-vapor interfaces

Based on a microscopic theory of inhomogeneous fluids we derive a non-local expression for the effective interface Hamiltonian of a fluctuating liquid-vapor interface. For smooth interface configurations the leading term of this expression takes on the familiar form being proportional to the total area spanned by the interface.