Correlation between structural and interfacial properties of amphiphilic systems

Wetting Behavior of a Three-Phase System in Contact with a Surface

We extend the Cahn-Landau-de Gennes mean field theory of wetting in binary mixtures to understand the wetting thermodynamics of a three phase system (e.g., polymer dispersed liquid crystals or polymer-colloid mixtures) that is in contact with an external surface, which prefers one of the phases. Using a model free-energy, which has three minima in its landscape, we show that as the central minimum becomes more stable compared to the remaining ones, the bulk phase diagram encounters a triple point and then bifurcates and we observe a novel non-monotonic dependence of the surface tension as a function of the stability of the central minimum. We show that this non-monotonicity in surface tension is associated with a complete to partial wetting transition. We obtain the complete wetting phase behavior as a function of phase stability and the surface interaction parameters when the system is close to the bulk triple point. The model free-energy that we use is qualitatively similar to that of a renormalized free energy, which arises in the context of polymer-liquid crystal mixtures. Finally, we study the thermodynamics of wetting for an explicit polymer-liquid crystal mixture and show that its thermodynamics is similar to that of our model free-energy.

Using Microemulsions: Formulation Based on Knowledge of Their Mesostructure

Microemulsions, as thermodynamically stable mixtures of oil, water, and surfactant, are known and have been studied for more than 70 years. However, even today there are still quite a number of unclear aspects, and more recent research work has modified and extended our picture. This review gives a short overview of how the understanding of microemulsions has developed, the current view on their properties and structural features, and in particular, how they are related to applications. We also discuss more recent developments regarding nonclassical microemulsions such as surfactant-free (ultraflexible) microemulsions or ones containing uncommon solvents or amphiphiles (like antagonistic salts). These new findings challenge to some extent our previous understanding of microemulsions, which therefore has to be extended to look at the different types of microemulsions in a unified way. In particular, the flexibility of the amphiphilic film is the key property to classify different microemulsion types and their properties in this review. Such a classification of microemulsions requires a thorough determination of their structural properties, and therefore, the experimental methods to determine microemulsion structure and dynamics are reviewed briefly, with a particular emphasis on recent developments in the field of direct imaging by means of electron microscopy. Based on this classification of microemulsions, we then discuss their applications, where the application demands have to be met by the properties of the microemulsion, which in turn are controlled by the flexibility of their amphiphilic interface. Another frequently important aspect for applications is the control of the rheological properties. Normally, microemulsions are low viscous and therefore enhancing viscosity has to be achieved by either having high concentrations (often not wished for) or additives, which do not significantly interfere with the microemulsion. Accordingly, this review gives a comprehensive account of the properties of microemulsions, including most recent developments and bringing them together from a united viewpoint, with an emphasis on how this affects the way of formulating microemulsions for a given application with desired properties.

The physics of microemulsions extracted from modeling balanced tensionless surfactant-loaded liquid-liquid interfaces

Microemulsions are explored using the self-consistent field approach. We consider a balanced model that features two solvents of similar size and a symmetric surfactant. Interaction parameter χ and surfactant concentration φ_s ^b complement the model definition. The phase diagram in χ-φ_s ^b coordinates is known to feature two lines of critical points, the Scott and Leibler lines. Only upon imposing a finite distance between the interfaces, we observe that the Scott line meets the Leibler line. We refer to this as a Lifshitz point (LP) for real systems. We add regions that are relevant for microemulsions to this phase diagram by considering the saturation line, which connects (χ, φ_s ^b)-points for which the interface becomes tensionless. Crossing this line implies a first-order phase transition as internal interfaces develop, characteristic for one-phase microemulsions. The saturation line ends at the so-called microemulsion point (MP). The MP is shown to connect with the LP by a line of MP-like critical points, found by searching for a "MP" while the distance between interfaces is fixed. A pair of binodal lines that envelop the three-phase (Winsor III) microemulsion region is shown to connect to the MP. The cohesiveness of the middle phase in Winsor III is related to non-monotonic, inverse DLVO-type interaction curves between the surfactant-loaded tensionless interfaces. The mean and Gaussian bending modulus, relevant for the shape fluctuations and the topology of interfaces, respectively, are evaluated along the saturation line. Near the MP, both rigidities are positive and vanish in a power-law fashion with coefficient unity at the MP. Overseeing these results proves that the MP has a pivoting role in the physics of microemulsions.

Theoretical prediction of morphological selection in amphiphilic systems

Biological and synthetic amphiphilic systems exhibit a wide range of morphologies. A density functional model for amphiphilic polymer phase mixtures is utilized to quantify localized equilibria and their stability, and ultimately predict and explain morphological preference. This is done by utilizing matched asymptotic expansions, which produces explicit connections between model parameters and macroscopic properties of equilibrium structures. Bilayers, cylindrical, and spherical micelle and vesicle configurations are found, and formulas which connect their geometry to ambient chemical potential are derived. Dynamics are studied in the context of a free boundary problem which describes the evolution of the hydrophobic-solvent domain interface. Linearization of this problem is used to explicitly determine growth rates and parameter regions of stability. All equilibria are found to have two branches of solutions terminating at a fold in the bifurcation diagram which signals the crossover from competitive stability to instability leading to ripening behavior. Ideally flat bilayers are determined to always possess a long wavelength buckling instability, suggesting that curved structures should be generically preferred. Spherical micelles exhibit morphological instabilities which are suppressed by large enough surface tension. Cylindrical micelles may have short-wavelength pearling and long-wavelength Rayleigh-Plateau-type instabilities. In addition, ideally infinite cylinders have an undulatory instability, suggesting that only finite length structures should be observed. A morphological phase diagram can be assembled which takes into account both existence and stability of different geometries. Consistent with experimental evidence, a bifurcation sequence from spheres to cylinders to vesicles is found as either surface tension or polymer composition increases. Coexistence of different stable morphologies is also observed.

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.

Existence, bifurcation, and geometric evolution of quasi-bilayers in the multicomponent functionalized Cahn-Hilliard equation

Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery, and emulsion stabilization within the context of synthetic chemistry. We present the multicomponent functionalized Cahn-Hilliard (mFCH) free energy as a model which allows competition between bilayers with distinct composition and between bilayers and higher codimensional structures, such as co-dimension two filaments and co-dimension three micelles. We construct symmetric and asymmetric homoclinic bilayer profiles via a billiard limit potential and show that co-dimensional bifurcation is driven by the experimentally observed layer-by-layer pearling mechanism. We investigate the stability and slow geometric evolution of multicomponent bilayer interfaces within the context of an [Formula: see text] gradient flow of the mFCH, addressing the impact of aspect ratio of the amphiphile (lipid or copolymer unit) on the intrinsic curvature and the codimensional bifurcation. In particular we derive a Canham-Helfrich sharp interface energy whose intrinsic curvature arises through a Melnikov parameter associated to amphiphile aspect ratio.

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.

Formation Kinetics of Oil-Rich, Nonionic Microemulsions

The formation kinetics of oil-rich, nonionic microemulsions were investigated along different mixing pathways using a fast stopped-flow device in combination with the new high-flux small-angle neutron spectrometer D33 (ILL, Grenoble, France). While the kinetics along most pathways were too fast to be resolved, two processes could be detected mixing brine and the binary cyclohexane/C10E5 solution. Here, too, the formation of large water-in-oil droplets was found to be faster than 20 ms and therewith faster than the accessible dead time. However, subsequently, both the disintegration of the large water-in-oil droplets (600 Å) and the uptake of water by swollen micelles (50-60 Å) could be resolved. Both processes occur on the time scale of a second. Strikingly, the total internal interface forms faster than 20 ms and does not change over time.

Density functional models of the interfacial tensions near the critical endpoints and tricritical point of three-phase equilibria

We treat two different density-functional models of the structures and tensions of the interfaces between phases on approach to the tricritical point of three-phase equilibrium. The major objective is to account for some of the results of earlier experimental measurements of these tensions. The thermodynamic background is first reviewed, including representations of the properties near the critical endpoints and tricritical point and of the wetting transitions that may occur on approach to those critical points. The first of the models treated is analytically soluble. Its properties are illuminating but at the price of some artificiality paid for its analytical solubility. The second model, called model T, is in a class of those treated in the past and analyzed numerically. Some of its properties are obtained with sufficient precision to allow one to conclude with near certainty what the analytically exact results would be. This model, too, illuminates the experimental measurements. It is noted where its properties are in accord with those of the analytically soluble model and where the two differ.

Phase Behavior of Nonionic Microemulsions with Multi-end-capped Polymers and Its Relation to the Mesoscopic Structure

The polymer architecture of telechelic or associative polymers has a large impact on the bridging of self-assembled structures. This work presents the phase behavior, small angle neutron scattering (SANS), dynamic light scattering (DLS), and fluorescence correlation spectroscopy (FCS) of a nonionic oil-in-water (O/W) microemulsion with hydrophobically end-capped multiarm polymers with functionalities f = 2, 3, and 4. For high polymer concentrations and large average interdroplet distance relative to the end-to-end distance of the polymer, d/R(ee), the system phase separates into a dense, highly connected droplet network phase, in equilibrium with a dilute phase. The extent of the two-phase region is larger for polymers with similar length but higher f. The interaction potential between the droplets in the presence of polymer has both a repulsive and an attractive contribution as a result of the counterbalancing effects of the exclusion by polymer chains and bridging between droplets. This study experimentally demonstrates that higher polymer functionalities induce a stronger attractive force between droplets, which is responsible for a more extended phase separation region, and correlate with lower collective droplet diffusivities and higher amplitude of the second relaxation time in DLS. The viscosity and the droplet self-diffusion obtained from FCS, however, are dominated by the end-capped chain concentration.

Oil-in-water microemulsion droplets of TDMAO/decane interconnected by the telechelic C18-EO150-C18: clustering and network formation

The effect of a doubly hydrophobically end-capped water soluble polymer (C18-PEO150-C18) on the properties of an oil-in-water (O/W) droplet microemulsion (R ∼ 2.85 nm) has been studied as a function of the amount of added telechelic polymer. Macroscopically one observes a substantial increase of viscosity once a concentration of ∼5 hydrophobic stickers per droplet is surpassed and effective cross-linking of the droplets takes place. SANS measurements show that the size of the individual droplets is not affected by the polymer addition but it induces attractive interactions at low concentration and repulsive ones at high polymer content. Measurements of the diffusion coefficient by DLS and FCS show increasing sizes at low polymer addition that can be attributed to the formation of clusters of microemulsion droplets interconnected by the polymer. At higher polymer content the network formation leads to an additional slow relaxation mode in DLS that can be related to the rheological behaviour, while the self-diffusion observed in FCS attains a lower plateau value, i.e., the microemulsion droplets remain effectively fixed within the network. The combination of SANS, DLS, and FCS allows us to derive a self-consistent picture of the evolution of structure and dynamics of the mixed system microemulsion/telechelic polymer as a function of the polymer content, which is not only relevant for controlling the macroscopic rheological properties but also with respect to the internal dynamics as it is, for instance, relevant for the release and transport of active agents.

Hybrid lipids increase nanoscale fluctuation lifetimes in mixed membranes

A recently proposed ternary mixture model is used to predict fluctuation domain lifetimes in the one phase region. The membrane is made of saturated, unsaturated, and hybrid lipids that have one saturated and one unsaturated hydrocarbon chain. The hybrid lipid is a natural linactant which can reduce the packing incompatibility between saturated and unsaturated lipids. The fluctuation lifetimes are predicted as a function of the hybrid lipid fraction and the fluctuation domain size. These lifetimes can be increased by up to three orders of magnitude compared to the case of no hybrids. With hybrid, small length scale fluctuations have sizable amplitudes even close to the critical temperature and, hence, benefit from enhanced critical slowing down. The increase in lifetime is particularly important for nanometer scale fluctuation domains where the hybrid orientation and the other lipids composition are highly coupled.

Geometric evolution of bilayers under the functionalized Cahn–Hilliard equation

We use a multi-scale analysis to derive a sharp interface limit for the dynamics of bilayer structures of the functionalized Cahn–Hilliard equation. In contrast to analysis based on single-layer interfaces, we show that the Stefan and Mullins–Sekerka problems derived for the evolution of single-layer interfaces for the Cahn–Hilliard equation are trivial in this context, and the sharp interface limit yields a quenched mean-curvature-driven normal velocity at O ( ε −1 ), whereas on the longer O ( ε −2 ) time scale, it leads to a total surface area preserving Willmore flow. In particular, for space dimension n =2, the constrained Willmore flow drives collections of spherically symmetric vesicles to a common radius, whereas for n =3, the radii are constant, and for n ≥4 the largest vesicle dominates.

Hybrid lipids increase the probability of fluctuating nanodomains in mixed membranes

A ternary mixture model is proposed to describe composition fluctuations in mixed membranes composed of saturated, unsaturated, and hybrid lipids (with one saturated and one unsaturated hydrocarbon chain). The hybrids are line-active and can reduce the packing incompatibility between the saturated and unsaturated lipids. We introduce a lattice model that extends previous studies by taking into account the dependence of the interactions of the hybrid lipids on their orientations in a simple way. A methodology to recast the free energy of the lattice model in terms of a continuous, isotropic field theory is proposed and used to analyze composition fluctuations in the one-phase region (above the critical temperature). The effect of hybrid lipids on fluctuation domains rich in saturated/unsaturated lipids is predicted. The correlation length of such fluctuations decreases significantly with increasing amounts of hybrids; this implies that nanoscale fluctuation domains are more probable compared to the case with no hybrids. Smaller correlated fluctuation domains arise even when the temperature is close to a critical point, where very large correlation lengths are normally expected. This decrease in the correlation length is largest as the hybrid composition tends toward a crossover value above which stripelike fluctuations are predicted. This crossover value defines the Lifshitz line. The characteristic wavelength of the stripelike fluctuations is large close to the Lifshitz point but decreases toward a molecular size in a membrane that contains only hybrids. Micrometer size, stripelike domains have recently been observed experimentally in giant unilamelar vesicles (GUVs) made of saturated, unsaturated, and hybrid lipids. These results suggest that the line activity of hybrid lipids in such mixtures may be significant only at large hybrid fractions; in that regime, the interface between domains can be diffuse and several hybrid molecules with correlated orientations can separate saturated and unsaturated lipid regions.

Branching mechanisms in surfactant micellar growth

We present a phase-field model to study the morphological transitions of surfactant micelles in supersaturated dilute solution. Simulations reveal that multiply connected micellar structure can be produced by interface branching instability of a growing micelle at relatively large supersaturation and intermediate spontaneous curvatures. Two branching mechanisms, i.e., a disk-to-cylinder shape transition and a tip bifurcation process, are identified for disklike and cylindrical micelles, respectively. We propose that dynamic branching at the micelle growth front provides an important kinetic pathway for the formation of branched wormlike micelles that are observed in many surfactant systems.

Scattering intensity of bicontinuous microemulsions and sponge phases

Monte Carlo simulations of dynamically triangulated surfaces of variable topology are used to investigate the scattering intensities of bicontinuous microemulsions. The bulk scattering intensity is shown to follow the Teubner-Strey expression. The domain size and the correlation length are extracted from the scattering peaks as a function of the bending rigidity, saddle-splay modulus, and surfactant density. The results are compared to earlier theories based on Ginzburg-Landau and Gaussian random field models. The ratio of the two length scales is shown to be well described by a linear combination of logarithmically renormalized bending rigidity and saddle-splay modulus with universal prefactors. This is in contrast to earlier theoretical predictions in which the scattering intensity is independent of the saddle-splay modulus. The equation of state, and the asymptotics of the bulk and film scattering intensities for high and low wave vectors are determined from simulations and compared with theoretical results.

Soft matter approaches to food structuring

We give an overview of the many opportunities that arise from approaching food structuring from the perspective of soft matter physics. This branch of physics employs concepts that build upon the seminal work of van der Waals, such as free volume, the mean field, and effective temperatures. All these concepts aid scientists in understanding and controlling the thermodynamics and (slow) dynamics of structured foods. We discuss the use of these concepts in four topics, which will also be addressed in a forthcoming Faraday Discussion on food structuring.

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.

Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics

Polar liquids like water carry a characteristic nanometric length scale, the correlation length of orientation polarizations. Continuum theories that can capture this feature commonly run under the name of "nonlocal" electrostatics since their dielectric response is characterized by a scale-dependent dielectric function ε(q), where q is the wave vector; the Poisson(-Boltzmann) equation then turns into an integro-differential equation. Recently, "local" formulations have been put forward for these theories and applied to water, solvated ions, and proteins. We review the local formalism and show how it can be applied to a structured liquid in slit and plate geometries, and solve the Poisson-Boltzmann theory for a charged plate in a structured solvent with counterions. Our results establish a coherent picture of the local version of nonlocal electrostatics and show its ease of use when compared to the original formulation.

Chirality and domain growth in the gyroid mesophase

We describe the first dynamical simulations of domain growth during the self-assembly of the gyroid mesophase from a ternary amphiphilic mixture, using the lattice Boltzmann method. The gyroid is a chiral structure; we demonstrate that, for a symmetric amphiphile with no innate preference for left- or right-handed morphologies, the self-assembly process may give rise to a racemic mixture of domains. We use measurements of the averaged mean curvature to analyse the behaviour of domain walls, and suggest that diffusive domain growth may be present in this system.

Dynamic model and stationary shapes of fluid vesicles

A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find stationary shapes of vesicles with different topologies and the dynamic evolution towards them. The results are in agreement with those found by minimization of the Canham-Helfrich free energy. This fact shows that our phase-field model could be applied to more complex problems of instabilities.

Preferential solubilization of dodecanol from dodecanol–limonene binary oil mixture in sodium dihexyl sulfosuccinate microemulsions: Effect on optimum salinity and oil solubilization capacity

Solubilization of dodecanol-limonene binary oil mixtures has been studied in saturated Winsor type I and III sodium dihexyl sulfosuccinate microemulsions. The systems showed different oil solubilization behavior below and above dodecanol volume fraction 0.2. Below 0.2 dodecanol volume fraction regular Winsor type microemulsions formed. The oil solubilization was characterized in this concentration range by the optimum salinity and the maximum characteristic length. Dodecanol showed Langmuirian-type surface excess adsorption at the vicinity of the surfactant layer. Variation of the optimum salinity and middle phase characteristic length with increasing dodecanol concentration could be linked to changes in the dodecanol surface excess. These relationships were used to develop new mathematical models for the optimum salinity and characteristic length as a function of oil phase composition. Both models yield excellent agreement with the data. Above dodecanol volume fraction 0.2 regular Winsor type III microemulsions are not formed. Therefore our new models are not applicable in this concentration range.

Formation and structure of the microemulsion phase in two-dimensional ternary AB+A+B polymeric emulsions

We present an analysis of the structure of the fluctuation-induced microemulsion phase in a ternary blend of balanced AB diblock copolymers with equal amounts of A and B homopolymers. To this end, graphical analysis methods are employed to characterize two-dimensional configuration snapshots obtained with the recently introduced field-theoretic Monte Carlo method. We find that a microemulsion forms when the mean curvature diameter of the lamellar phase coincides roughly with the periodicity of the lamellar phase. Further, we provide evidence to the effect of a subclassification of the microemulsion into a genuine and a defect-driven region.

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.

Steady state of microemulsions in shear flow

Steady-state properties of microemulsions in shear flow are studied in the context of a Ginzburg-Landau free-energy approach. Explicit expressions are given for the structure factor and the time correlation function at the one-loop level of approximation. Our results predict a four-peak pattern for the structure factor, implying the simultaneous presence of interfaces aligned with two different orientations. Due to the peculiar interface structure a nonmonotonous relaxation of the time correlator is also found.