Ginzburg-Landau theory of oil-water-surfactant mixtures

Prediction of Micellar Thermodynamics of Nonionic Surfactants Based on the Square Gradient Theory

A geometry-dependent contribution based on the square gradient theory of van der Waals is proposed as a predictive modification of the interfacial energy contribution for the micellar thermodynamic theory. The model has an analytic prediction for the spherical and cylindrical geometries. For ellipsoidal geometry, a simple yet physically meaningful approximation is proposed. The critical micelle concentration (CMC) and the surface tension isotherm under the new contribution are compared with the classical theory. The modified model describes qualitatively the available experimental data and the surface isotherm, showing an improvement in the predictions of the CMC.

Elastic properties of self-assembled bilayer membranes: Analytic expressions via asymptotic expansion

Bilayer membranes self-assembled from amphiphilic molecules are ubiquitous in biological and soft matter systems. The elastic properties of bilayer membranes are essential in determining the shape and structure of bilayers. A novel method to calculate the elastic moduli of the self-assembled bilayers within the framework of the self-consistent field theory is developed based on an asymptotic expansion of the order parameters in terms of the bilayer curvature. In particular, the asymptotic expansion method is used to derive analytic expressions of the elastic moduli, which allows us to design more efficient numerical schemes. The efficiency of the proposed method is illustrated by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents.

Generalization of the swelling method to measure the intrinsic curvature of lipids

Via computer simulation of a coarse-grained model of two-component lipid bilayers, we compare two methods of measuring the intrinsic curvatures of the constituting monolayers. The first one is a generalization of the swelling method that, in addition to the assumption that the spontaneous curvature linearly depends on the composition of the lipid mixture, incorporates contributions from its elastic energy. The second method measures the effective curvature-composition coupling between the apposing leaflets of bilayer structures (planar bilayers or cylindrical tethers) to extract the spontaneous curvature. Our findings demonstrate that both methods yield consistent results. However, we highlight that the two-leaflet structure inherent to the latter method has the advantage of allowing measurements for mixed lipid systems up to their critical point of demixing as well as in the regime of high concentration (of either species).

Elastic and dynamic properties of membrane phase-field models

Phase-field models have been extensively used to study interfacial phenomena, from solidification to vesicle dynamics. In this article, we analyze a phase-field model that captures the relevant physical features that characterize biological membranes. We show that the Helfrich theory of elasticity of membranes can be applied to phase-field models, allowing to derive the expressions of the stress tensor, lateral stress profile and elastic moduli. We discuss the relevance and interpretations of these magnitudes from a phase-field perspective. Taking the sharp-interface limit we show that the membrane macroscopic equilibrium equation can be derived from the equilibrium condition of the phase-field interface. We also study two dynamic models that describe the behaviour of a membrane. From the study of the relaxational behaviour of the membrane we characterize the relevant dynamics of each model, and discuss their applications.

Membrane stress profiles from self-consistent field theory

Using self-consistent field theory (SCFT), we develop an accurate, local expression for the stress profiles in membranes and soft matter interfaces, in general. The bond stresses are expressed in terms of pre-computed chain propagators, which are used to describe the statistical weight of the molecules and therefore require minimal additional calculations. In addition, we overcome the resolution limit of the molecular bond length by including the Irving and Kirkwood bond assignment and recover a constant normal stress profile across an interface. Using this theory, we find that the membrane lateral stress profile contains repulsive (positive) stresses in the regions of the head and tail groups, and attractive (negative) stresses near the hydrophobic/hydrophilic interface. We also verify that the zeroth and first moments of the stress profile correspond to the thermodynamic tension and product of the bending modulus and the spontaneous curvature, respectively.

Sugar Surfactant Based Microemulsions at Solid Surfaces: Influence of the Oil Type and Surface Polarity

The structure of sugar-surfactant-based bicontinuous microemulsions in the bulk and at hydrophilic and hydrophobic solid planar surfaces was studied by means of neutron scattering techniques (SANS, NR, and GISANS). In particular, the influence of the type of oil (tetradecane and methyl oleate) on the structural properties in the vicinity of surfaces was investigated at different oil-to-water ratios. In the case of hydrophilic surfaces, the analysis of the scattering length density profiles reveals an induced ordering of the oil and water domains perpendicular to the solid-liquid interface in both sets of microemulsions. At hydrophobic surfaces, differences in the near-surface ordering between microemulsions containing polar and nonpolar oils are observed.

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models-a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.

Phase inversion emulsification: Current understanding and applications

This review is addressed to the phase inversion process, which is not only a common, low-energy route to make stable emulsions for a variety of industrial products spanning from food to pharmaceuticals, but can also be an undesired effect in some applications, such as crude oil transportation in pipelines. Two main ways to induce phase inversion are described in the literature, i.e., phase inversion composition (PIC or catastrophic) and phase inversion temperature (PIT or transitional). In the former, starting from one phase (oil or water) with surfactants, the other phase is more or less gradually added until it reverts to the continuous phase. In PIT, phase inversion is driven by a temperature change without varying system composition. Given its industrial relevance and scientific challenge, phase inversion has been the subject of a number of papers in the literature, including extensive reviews. Due to the variety of applications and the complexity of the problem, most of the publications have been focused either on the phase behavior or the interfacial properties or the mixing process of the two phases. Although all these aspects are quite important in studying phase inversion and much progress has been done on this topic, a comprehensive picture is still lacking. In particular, the general mechanisms governing the inversion phenomenon have not been completely elucidated and quantitative predictions of the phase inversion point are limited to specific systems and experimental conditions. Here, we review the different approaches on phase inversion and highlight some related applications, including future and emerging perspectives.

Analysis of Ginzburg-Landau-type models of surfactant-assisted liquid phase separation

In this paper diffuse interface models of surfactant-assisted liquid-liquid phase separation are addressed. We start from the generalized version of the Ginzburg-Landau free-energy-functional-based model of van der Sman and van der Graaf. First, we analyze the model in the constant surfactant approximation and show the presence of a critical point at which the interfacial tension vanishes. Then we determine the adsorption isotherms and investigate the validity range of previous results. As a key point of the work, we propose a new model of the van der Sman/van der Graaf type designed for avoiding both unwanted unphysical effects and numerical difficulties present in previous models. In order to make the model suitable for describing real systems, we determine the interfacial tension analytically more precisely and analyze it over the entire accessible surfactant load range. Emerging formulas are then validated by calculating the interfacial tension from the numerical solution of the Euler-Lagrange equations. Time-dependent simulations are also performed to illustrate the slowdown of the phase separation near the critical point and to prove that the dynamics of the phase separation is driven by the interfacial tension.

Phase field modelling of spinodal decomposition in the oil/water/asphaltene system

In this paper the quantitative applicability of van der Sman/van der Graaf type Ginzburg–Landau theories of surfactant assisted phase separation [van der Smanet al.,Rheol. Acta, 2006,46, 3] is studied for real systems displaying high surfactant concentrations at the liquid–liquid interface.

Rheology of red blood cells under flow in highly confined microchannels: I. effect of elasticity

We analyze the rheology of dilute red blood cell suspensions in pressure driven flows at low Reynolds number, in terms of the morphologies and elasticity of the cells. We focus on narrow channels of width similar to the cell diameter, when the interactions with the walls dominate the cell dynamics. The suspension presents a shear-thinning behaviour, with a Newtonian-behaviour at low shear rates, an intermediate region of strong decay of the suspension viscosity, and an asymptotic regime at high shear rates in which the effective viscosity converges to that of the solvent. We identify the relevant aspects of cell elasticity that contribute to the rheological response of blood at high confinement. In a second paper, we will explore the focusing of red blood cells while flowing at high shear rates and how this effect is controlled by the geometry of the channel.

Phase-field theories for mathematical modeling of biological membranes

Biological membranes are complex structures whose mechanics are usually described at a mesoscopic level, such as the Helfrich bending theory. In this article, we present the phase-field methods, a useful tool for studying complex membrane problems which can be applied to very different phenomena. We start with an overview of the general theory of elasticity, paying special attention to its derivation from a molecular scale. We then study the particular case of membrane elasticity, explicitly obtaining the Helfrich bending energy. Within the framework of this theory, we derive a phase-field model for biological membranes and explore its physical basis and interpretation in terms of membrane elasticity. We finally explain three examples of applications of these methods to membrane related problems. First, the case of vesicle pearling and tubulation, when lipidic vesicles are exposed to the presence of hydrophobic polymers that anchor to the membrane, inducing a shape instability. Finally, we study the behavior of red blood cells while flowing in narrow microchannels, focusing on the importance of membrane elasticity to the cell flow capabilities.

Mesoscale models of dispersions stabilized by surfactants and colloids

In this paper we discuss and give an outlook on numerical models describing dispersions, stabilized by surfactants and colloidal particles. Examples of these dispersions are foams and emulsions. In particular, we focus on the potential of the diffuse interface models based on a free energy approach, which describe dispersions with the surface-active agent soluble in one of the bulk phases. The free energy approach renders thermodynamic consistent models with realistic sorption isotherms and adsorption kinetics. The free energy approach is attractive because of its ability to describe highly complex dispersions, such as emulsions stabilized by ionic surfactants, or surfactant mixtures and dispersions with surfactant micelles. We have classified existing numerical methods into classes, using either a Eulerian or a Lagrangian representation for fluid and for the surfactant/colloid. A Eulerian representation gives a more coarse-grained, mean field description of the surface-active agent, while a Lagrangian representation can deal with steric effects and larger complexity concerning geometry and (amphiphilic) wetting properties of colloids and surfactants. However, the similarity between the description of wetting properties of both Eulerian and Lagrangian models allows for the development of hybrid Eulerian/Lagrangian models having advantages of both representations.

Bending rigidities of surfactant bilayers using self-consistent field theory

Self-consistent field (SCF) theory is used to find bending moduli of surfactant and lipid bilayers. Recently, we successfully applied low-memory search methods to solve the SCF equations. Using these we are now able to directly evaluate the Gaussian bending modulus for molecularly detailed models of bilayers by evaluating the excess Helmholtz energy of tensionless bilayers in a (part of the) Im3m cubic phase. The result prompted us to reconsider the protocol that has been used thus far to find the mean bending modulus kc and Gaussian bending modulus k[overline]. With respect to previous predictions, the value of kc is reduced by a factor of two and the Gaussian bending modulus is less negative and much closer to zero. In line with experimental data we now find that k[overline] can also become positive. In this paper we use the non-ionic surfactants series of the type CnEm for illustration.

Method of evaluating curvature-dependent elastic parameters for small unilamellar vesicles using molecular dynamics trajectory

A numerical method is proposed for evaluating the curvature dependency of elastic parameters of a spherical vesicle based on a calculation of the pressure profile across the membrane. The proposed method is particularly useful for small unilamellar vesicles (SUVs), in which the internal structure of the membrane is asymmetric owing to the high curvature. In this case, the elastic energy is insufficiently described as a perturbation from a planar membrane. The calculated saddle-splay curvature modulus of SUVs, which is about 16 nm in diameter, is found to be much higher than that of a planar membrane. A comparison of the free energy change in the initial stage of vesicle-to-bicelle transformation with the Fromherz theory demonstrates that the elastic parameters estimated for SUVs provide better estimation of the free energy than those estimated for a planar membrane.

Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model

We calculate the Gaussian curvature modulus kappa of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value kappa/kappa = -1.04 +/- 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce kappa(m)/kappa(m) = -0.98 +/- 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z0 of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K(0m). By also analyzing the lateral stress profile sigma0(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K(0m) and kappa through the first and second moment of sigma0(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.

Description of hard-sphere crystals and crystal-fluid interfaces: a comparison between density functional approaches and a phase-field crystal model

In materials science the phase-field crystal approach has become popular to model crystallization processes. Phase-field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase-field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three-dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions, and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase-field crystal model. Thereby it turns out that the order parameter of the phase-field crystal model is more consistent with a smeared density field (shifted and rescaled) than with the shifted and rescaled density itself. In brief, we conclude that fundamental measure theory is very accurate and can serve as a benchmark for the other theories. Taylor expansion strongly affects free energies, surface tensions, and vacancy concentrations. Furthermore it is phenomenologically misleading to interpret the phase-field crystal model as stemming directly from Taylor-expanded density functional theory.

Heterogeneous diffuse interfaces: a new mechanism for arrested coarsening in binary mixtures. Heterogeneous diffuse interfaces

We discuss the dynamics of binary fluid mixtures in which surface tension density is allowed to become locally negative within the interface, while still preserving positivity of the overall surface tension (heterogeneous diffuse interface). Numerical simulations of two-dimensional Ginzburg-Landau phase field equations implementing such mechanism and including hydrodynamic motion, show evidence of dynamically arrested domain coarsening. Under specific conditions on the functional form of the surface tension density, dynamical arrest can be interpreted in terms of the collective dynamics of metastable, non-linear excitations of the density field, named compactons, as they are localized to finite-size regions of configuration space and strictly zero elsewhere. Aside from compactons, the heterogeneous diffuse interface scenario appears to provide a robust mechanism for the interpretation of many aspects of soft-glassy behaviour in binary fluid mixtures.

Phase-field model of long-time glasslike relaxation in binary fluid mixtures

We present a new phase-field model for binary fluids, exhibiting typical signatures of soft-glassy behavior, such as long-time relaxation, aging, and long-term dynamical arrest. The present model allows the cost of building an interface to vanish locally within the interface, while preserving positivity of the overall surface tension. A crucial consequence of this property, which we prove analytically, is the emergence of free-energy minimizing density configurations, hereafter named "compactons," to denote their property of being localized to a finite-size region of space and strictly zero elsewhere (no tails). Thanks to compactness, any arbitrary superposition of compactons still is a free-energy minimizer, which provides a direct link between the complexity of the free-energy landscape and the morphological complexity of configurational space.

Near-surface structure of a bicontinuous microemulsion with a transition region

The lamellar ordering of bicontinuous microemulsions adjacent to a planar hydrophilic wall is investigated experimentally by grazing-incidence small-angle neutron scattering and theoretically by computer simulations. It is shown that precise depth information in neutron scattering can be obtained by tuning the scattering length density of the overall microemulsion. Neutron reflectometry completes the characterization. The nucleation of a lamellar phase at the wall is observed, and a perforated lamellar transition region is identified at the lamellar-microemulsion interface. The thickness of the lamellar region is about 400 Å, which corresponds to two bilayers.

The self-interaction of a fluid interface, the wavevector dependent surface tension and wedge filling

We argue that whenever an interface, separating bulk fluid phases, adopts a non-planar configuration (induced by a confining geometry or thermal fluctuations, say), the energy cost of it will contain a non-local self-interaction term. For systems with short-ranged forces and Ising symmetry, we determine the self-interaction by integrating out bulk-like degrees of freedom from a more microscopic Landau-Ginzburg-Wilson model. The self-interaction can be written in a simple diagrammatic form involving integrals over effective two-body forces acting at the interface and consistently accounts for a number of known features of the microscopic model, including the wavevector dependence of the surface tension describing the fluctuations of a near planar interface. When applied to wedge filling transitions, the self-interaction describes the attraction between the wetting films on either side of the wedge. We show that, for sufficiently acute wedges, this can alter the order of the filling phase transition.

Splitting instability of cellular structures in the Ginzburg-Landau model under feedback control

We study numerically a Ginzburg-Landau-type equation for micelles in two dimensions. The domain size and the interface length of a cellular structure are controlled by two feedback terms. The deformation and the successive splitting of the cellular structure are observed when the controlled interface length is increased. The splitting instability is further investigated using coupled mode equations to understand the bifurcation structure.

Transformation from spots to waves in a model of actin pattern formation

Actin networks in certain single-celled organisms exhibit a complex pattern-forming dynamics that starts with the appearance of static spots of actin on the cell cortex. Spots soon become mobile, executing persistent random walks, and eventually give rise to traveling waves of actin. Here we describe a possible physical mechanism for this distinctive set of dynamic transformations, by equipping an excitable reaction-diffusion model with a field describing the spatial orientation of its chief constituent (which we consider to be actin). The interplay of anisotropic actin growth and spatial inhibition drives a transformation at fixed parameter values from static spots to moving spots to waves.

Correspondence between curvature, packing parameter, and hydrophilic-lipophilic deviation scales around the phase-inversion temperature

We show in this paper that three ways of characterizing "spontaneous" lateral packing of amphiphiles are equivalent: the spontaneous curvature, the molecular packing parameter, and the refined hydrophilic-lipophilic balance known as HLD (hydrophilic-lipophilic deviation). Recognition of this equivalence, with its underlying hypothesis of incompressible fluid with lowest surface energy, reinforces the single parameter bending energy expression implicit in the classical papers by Ninham and Israelachvili, as well as all the predictive models of solubilization developed as yet.

Quasiwetting on spherical solid surfaces by oil-water-amphiphile mixtures

We study the wetting behavior on spherical walls by ternary mixtures of oil, water, and an amphiphile. We use the Ginzburg-Landau free energy with a single order parameter and find that there are different stable structures of the interface and that a quasiwetting transition is the mechanism involved in the transition among them. We calculate these wetting transitions for two sets of parameters in the bulk free energy which are known to show microemulsion behavior. The surface transitions are thin-thick first-order transitions (continuous transitions are absent), and the phase diagram in surface parameter space is constructed. For the first set of bulk parameters water, oil, and a microemulsion coexist, and we study the first-order transition where the oil phase wets the wall-microemulsion interface and its behavior as the radius of the wall becomes large. Therefore, we recover the known wetting transitions on a planar wall. In the second set of bulk parameters only water and oil coexist, and for some sizes of the solid wall, the oil phase wets the wall-water interface, and the phase behavior is extremely rich. We obtain a coexistence of four surface phases or two triple points followed by three lines of first-order transitions which end at three critical points depending on the radius of the surface. When there are micellar metastable solutions in bulk, the behavior of the thickness of the wetting layer of the oil phase as the radius of the spherical wall gets larger is nonmonotonic. We associate this behavior with the intrinsic micelle structure due to the spontaneous curvature of the model.

Signatures of non locality for short-ranged wetting at curved substrates

The binding potential for wetting near planes, spheres, and cylinders in systems with short-ranged forces is shown to have a universal geometrical structure. This arises from the nonlocal nature of the interfacial interactions and is exactly described by a recently proposed binding potential functional, which provides a systematic framework for studying wetting at arbitrarily shaped substrates. The corrections to the equilibrium wetting layer thickness induced by nonlocality are comparable to those arising from a Tolman length and lead to diverging terms in the total mass adsorption.

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.

Casimir effect in fluids above the isotropic-lamellar transition

We study fluctuation-induced interaction in confined fluids above the isotropic-lamellar transition. At an ideally continuous transition, the disjoining pressure has the asymptotic form Pi(d-->infinity) approximately -Ck(B)Tq(2)(0)/d, where d is the interwall distance, q(0) is the wave number of the scattering peak, and C = 1/4pi in the strong anchoring limit. The long-rangedness is enhanced due to continuous distribution of soft modes in the q space. An unconventionally strong Casimir force with a range of several lamella thicknesses is realistic above the transition. We also find an oscillatory force profile near a surface-induced transition.

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.

Thermodynamics and mechanics of bilayer membranes

A mean-field lattice model is applied to chain molecules for the study of surfactant systems. As an example, C12E5 surfactants, modeled as C12O(C2O)(5) chains, are forced into cylindrical and spherical shaped vesicles in a monomer solvent. These aggregates are used to obtain the rigidity constants of the bilayers as a function of the hydrophilicity of the surfactant's headgroup from both a thermodynamic and a mechanical route. Within the numerical accuracy, both routes are fully consistent. The magnitude and sign of the rigidity constants are interpreted to gain insight into features of the experimentally well-established phase diagram. It is concluded that the lattice model is a potentially valuable tool to help understand the generic phase behavior of surfactant systems.

Lattice model results for lamellar phases in slits

A mixture of oil, water, and surfactant confined between parallel hydrophilic walls is studied close to phase boundaries between lamellar and uniform phases within a vector lattice model in a mean-field approximation. Relations between energy and force-distance profiles, and the structure of the confined fluid (given by density profiles) are found and discussed. For large wall separations L elastic response to compression or decompression, accompanied by shrinking or swelling of the period lambda of the lamellar phase, is found for lamellar and induced (by capillary condensation) lamellar phases. Very good agreement with recent experiments is obtained. For L<4 lambda the system responds to decompression by swelling of the central, either oil- or water-rich layer, with the layers adsorbed at the surfaces remaining unaffected. The solvation force is very weak and independent of L when the central layer is swollen, and jumps to much larger values when new layers are introduced into the slit.

Adsorption phenomena in amphiphilic systems

The wetting behavior of a ternary mixture of oil, water, and amphiphile in the presence of a surface is studied. An interface model carefully derived from an underlying Ginzburg-Landau theory is introduced, which contains position dependent rigidity and stiffness coefficients. Using this model we predict a rich surface phase diagram containing thin-thick, first-order, and continuous wetting transitions. Application of the model to other interface behavior in these mixtures is also addressed.

Effective Hamiltonian for liquid-vapor interfaces

Starting from a density functional theory for inhomogeneous fluids we derive an effective Hamiltonian for liquid-vapor interfaces of simple fluids which goes beyond the common phenomenological capillary-wave description. In contrast to other approaches we take into account the long-ranged power-law decay of the dispersion forces between the fluid particles which changes the functional form of the wave-vector-dependent surface tension qualitatively. In particular, we find two different forms of the bending rigidity for the capillary waves, a negative one for small wave vectors determined by the long-ranged dispersion forces and a positive rigidity for large wave vectors due to the distortions of the intrinsic density profile in the vicinity of the locally curved interface. The differences to the standard capillary-wave theory and the relevance of these results for the interpretation of scattering experiments are discussed.

Systematic approach to bicontinuous cubic phases in ternary amphiphilic systems

The Fourier approach and theories of space groups and color symmetries are used to systematically generate and compare bicontinuous cubic structures in the framework of a Ginzburg-Landau model for ternary amphiphilic systems. Both single and double structures are investigated; they correspond to systems with one or two monolayers in a unit cell, respectively. We show how and why single structures can be made to approach triply periodic minimal surfaces very closely, and give improved nodal approximations for G, D, I-WP, and P surfaces. We demonstrate that the relative stability of the single structures can be calculated from the geometrical properties of their interfaces only. The single gyroid G turns out to be the most stable bicontinuous cubic phase since it has the smallest porosity. The representations are used to calculate distributions of the Gaussian curvature and 2H-nuclear-magnetic-resonance band shapes for C(P), C(D), S, C(Y), and F-RD surfaces.