arXiv subjects

David Andelman

Publications and source records attributed to David Andelman.

At least 73 records · Page 4Linked to original sources

arXiv2014

Surface Tension of Electrolyte Solutions: A Self-consistent Theory

We study the surface tension of electrolyte solutions at the air/water and oil/water interfaces. Employing field-theoretical methods and considering short-range interactions of anions with the surface, we expand the Helmholtz free energy to first-order in a loop expansion and calculate the excess surface tension. Our approach is self-consistent and yields an analytical prediction that reunites the Onsager-Samaras pioneering result (which does not agree with experimental data), with the ionic specificity of the Hofmeister series. We obtain analytically the surface-tension dependence on the ionic strength, ionic size and ion-surface interaction, and show consequently that the Onsager-Samaras result is consistent with the one-loop correction beyond the mean-field result. Our theory fits well a wide range of concentrations for different salts using one fit parameter, reproducing the reverse Hofmeister series for anions at the air/water and oil/water interfaces.10.1029

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arXiv2013

Interfacial Phenomena of Solvent-diluted Block Copolymers

A phenomenological mean-field theory is used to investigate the properties of solvent-diluted di-block copolymers (BCP), in which the two BCP components (A and B) form a variety of phases that are diluted by a solvent (S). Using this approach, we model mixtures of di-block copolymers and a solvent and obtained the corresponding critical behavior. In the low solvent limit, we find how the critical point depends on the solvent density. Due to the non-linear nature of the coupling between the A/B and BCP/solvent concentrations, the A/B modulation induces modulations in the polymer-solvent relative concentration with a double wavenumber. The free boundary separating the polymer-rich phase from the solvent-rich one is studied in two situations. First, we show how the presence of a chemically patterned substrate leads to deformations of the BCP film/solvent interface, creation of terraces in lamellar BCP film and even formation of multi-domain droplets as induced by the patterned substrate. Our results are in agreement with previous self-consistent field theory calculations. Second, we compare the surface tension between parallel lamellae coexisting with a solvent phase with that of a perpendicular one, and show that the surface tension has a non-monotonic dependence on temperature. The anisotropic surface tension can lead to deformation of spherical BCP droplets into lens-shaped ones, together with re-orientation of the lamellae inside the droplet during the polymer/solvent phase separation process in agreement with experiment.

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arXiv2013

Physical aspects of heterogeneities in multi-component lipid membranes

Ever since the raft model for biomembranes has been proposed, the traditional view of biomembranes based on the fluid-mosaic model has been altered. In the raft model, dynamical heterogeneities in multi-component lipid bilayers play an essential role. Focusing on the lateral phase separation of biomembranes and vesicles, we review some of the most relevant research conducted over the last decade. We mainly refer to those experimental works that are based on physical chemistry approach, and to theoretical explanations given in terms of soft matter physics. In the first part, we describe the phase behavior and the conformation of multi-component lipid bilayers. After formulating the hydrodynamics of fluid membranes in presence of the surrounding solvent, we discuss the domain growth-law and decay rate of concentration fluctuations. Finally, we review several attempts to describe membrane rafts as two-dimensional microemulsion.

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arXiv2013

Revisiting the Poisson-Boltzmann theory: charge surfaces, multivalent ions and inter-plate forces

The Poisson-Boltzmann (PB) theory is extensively used to gain insight on charged colloids and biological systems as well as to elucidate fundamental properties of intermolecular forces. Many works were devoted in the past to study PB related features and to confirm them experimentally. In this work we explore the properties of inter-plate forces in terms of different boundary conditions. We treat the cases of constant surface charge, constant surface potential and mixed boundaries. The interplay between electrostatic interactions, attractive counter-ions release, and repulsive van 't Hoff contribution are discussed separately for each case. Finally, we discuss how the crossover between attractive and repulsive interactions for constant surface charge case is influenced by the presence of multivalent counter-ions, where it is shown that the range of the attractive interaction grows with the valency.

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arXiv2013

Dipolar Poisson-Boltzmann Approach to Ionic Solutions: A Mean Field and Loop Expansion Analysis

We study the variation of the dielectric response of ionic aqueous solutions as function of their ionic strength. The effect of salt on the dielectric constant appears through the coupling between ions and dipolar water molecules. On a mean-field level, we account for any internal charge distribution of particles. The dipolar degrees of freedom are added to the ionic ones and result in a generalization of the Poisson-Boltzmann (PB) equation called the Dipolar PB (DPB). By looking at the DPB equation around a fixed point-like ion, a closed-form formula for the dielectric constant is obtained. We express the dielectric constant using the "hydration length" that characterizes the hydration shell of dipoles around ions, and thus the strength of the dielectric decrement. The DPB equation is then examined for three additional cases: mixture of solvents, polarizable medium and ions of finite size. Employing field-theoretical methods we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. For pure water, the dipolar fluctuations represent an important correction to the mean-field value and good agreement with the water dielectric constant is obtained. For ionic solutions we predict analytically the dielectric decrement that depends on the ionic strength in a non-linear way. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles. A linear dependence of the dielectric constant on the salt concentration is observed at low salinity, and a noticeable deviation from linearity can be seen for ionic strength above 1\,M, in agreement with experiments.

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arXiv2012

Interaction between Heterogeneously Charged Surfaces: Surface Patches and Charge Modulation

When solid surfaces are immersed in aqueous solutions, some of their charges can dissociate and leave behind charge patches on the surface. Although the charges are distributed heterogeneously on the surface, most of the theoretical models treat them as homogeneous. For overall non-neutral surfaces, the assumption of surface charge homogeneity is rather reasonable, since the leading terms of two such interacting surfaces depend on the non-zero average charge. However, for overall neutral surfaces, the nature of the surface charge distribution is crucial in determining the inter-surface interaction. In the present work we study the interaction between two charged surfaces across an aqueous solution for several charge distributions. The analysis is preformed within the framework of the linearized Poisson-Boltzmann theory. For periodic charge distributions the interaction is found to be repulsive at small separations, unless the two surface distributions are completely out-of-phase with respect to each other. For quenched random charge distributions we find that due to the presence of the ionic solution in between the surfaces, the inter-surface repulsion dominates over the attraction in the linear regime of the Poisson-Boltzmann theory. The effect of quenched charge heterogeneity is found to be particularly substantial in the case of large charge domains.

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arXiv2012

Tailoring Nanostructures Using Copolymer Nanoimprint Lithography

Finding affordable ways of generating high-density ordered nanostructures that can be transferred to a substrate is a major challenge for industrial applications like memories or optical devices with high resolution features. In this work, we report on a novel technique to direct self-assembled structures of block copolymers by NanoImprint Lithography. Surface energy of a reusable mold and nanorheology are used to organize the copolymers in defect-free structures over tens of micrometers in size. Versatile and controlled in-plane orientations of about 25 nm half-period lamellar nanostructures are achieved and, in particular, include applications to circular tracks of magnetic reading heads.

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arXiv2012

Block Copolymer at Nano-Patterned Surfaces

We present numerical calculations of lamellar phases of block copolymers at patterned surfaces. We model symmetric di-block copolymer films forming lamellar phases and the effect of geometrical and chemical surface patterning on the alignment and orientation of lamellar phases. The calculations are done within self-consistent field theory (SCFT), where the semi-implicit relaxation scheme is used to solve the diffusion equation. Two specific set-ups, motivated by recent experiments, are investigated. In the first, the film is placed on top of a surface imprinted with long chemical stripes. The stripes interact more favorably with one of the two blocks and induce a perpendicular orientation in a large range of system parameters. However, the system is found to be sensitive to its initial conditions, and sometimes gets trapped into a metastable mixed state composed of domains in parallel and perpendicular orientations. In a second set-up, we study the film structure and orientation when it is pressed against a hard grooved mold. The mold surface prefers one of the two components and this set-up is found to be superior for inducing a perfect perpendicular lamellar orientation for a wide range of system parameters.

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arXiv2012

Block Copolymer Films with Free Interfaces: Ordering by Nano-Patterned Substrates

We study block copolymers (BCP) on patterned substrates, where the top polymer film surface is not constrained but is a free interface that adapts its shape self-consistently. In particular, we investigate the combined effect of the free interface undulations with the wetting of the BCP film as induced by nano-patterned substrates. For a finite volume of BCP material, we find equilibrium droplets composed of coexisting perpendicular and parallel lamellar domains. The self-assembly of BCP on topographic patterned substrates was also investigated and it was found that the free interface induces mixed morphologies of parallel and perpendicular domains coupled with a non-flat free interface. In both cases, the free interface relaxes the strong constraints that would otherwise be imposed by a fixed top boundary (which is commonly used in simulations), and affects strongly the BCP ordering. Our study has some interesting consequences for experimental setups of graphoepitaxy and nanoimprint lithography.

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arXiv2012

Concentration fluctuations and phase transitions in coupled modulated bilayers

We consider the formation of finite-size domains in lipid bilayers consisting of saturated and hybrid lipids. First, we describe a monolayer model that includes a coupling between a compositional scalar field and a two-dimensional vectorial order-parameter. Such a coupling yields an effective two-dimensional microemulsion free-energy for the lipid monolayer, and its characteristic length of compositional modulations can be considered as the origin of finite-size domains in biological membranes. Next, we consider a coupled bilayer composed of two modulated monolayers, and discuss the static and dynamic properties of concentration fluctuations above the transition temperature. We also investigate the micro-phase separation below the transition temperature, and compare the micro-phase separated structures with statics and dynamics of concentration fluctuations above the transition.

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arXiv2012

The Dielectric Constant of Ionic Solutions: A Field-Theory Approach

We study the variation of the dielectric response of a dielectric liquid (e.g. water) when a salt is added to the solution. Employing field-theoretical methods we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. We predict analytically the dielectric decrement which depends on the ionic strength in a complex way. Furthermore, a qualitative description of the hydration shell is found and is characterized by a single length scale. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles.

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arXiv2011

A Model of Electrowetting, Reversed Electrowetting and Contact Angle Saturation

While electrowetting has many applications, it is limited at large voltages by contact angle saturation - a phenomenon that is still not well understood. We propose a generalized approach for electrowetting that, among other results, can shed new light on contact angle saturation. The model assumes the existence of a minimum (with respect to the contact angle) in the electric energy and accounts for a quadratic voltage dependence ~U^2 in the low-voltage limit, compatible with the Young-Lippmann formula, and a ~1/U^2 saturation at the high-voltage limit. Another prediction is the surprising possibility of a reversed electrowetting regime, in which the contact angle increases with applied voltage. By explicitly taking into account the effect of the counter-electrode, our model is shown to be applicable to several AC and DC experimental electrowetting-on-dielectric (EWOD) setups. Several features seen in experiments compare favorably with our results. Furthermore, the AC frequency dependence of EWOD agrees quantitatively with our predictions. Our numerical results are complemented with simple analytical expressions for the saturation angle in two practical limits.

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arXiv2011

Ion-Specific Hydration Effects: Extending the Poisson-Boltzmann Theory

In aqueous solutions, dissolved ions interact strongly with the surrounding water, thereby modifying the solution properties in an ion-specific manner. These ion-hydration interactions can be accounted for theoretically on a mean-field level by including phenomenological terms in the free energy that correspond to the most dominant ion-specific interactions. Minimizing this free energy leads to modified Poisson-Boltzmann equations with appropriate boundary conditions. Here, we review how this strategy has been used to predict some of the ways ion-specific effects can modify the forces acting within and between charged interfaces immersed in salt solutions.

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arXiv2010

Dielectric decrement as a source of ion specific effects

Many theoretical studies were devoted in the past to ion-specific effects, trying to interpret a large body of experimental evidence, such as surface tension at air/water interfaces and force measurements between charged objects. Although several mechanisms were suggested to explain the results, such as dispersion forces and specific surface-ion interactions, we would like to suggest another source of ion-specificity, originating from the local variations of the dielectric constant due to the presence of ions in the solution. We present a mean-field model to account for the heterogeneity of the dielectric constant caused by the ions. In particular, for ions that decrease the dielectric constant we find a depletion of ions from the vicinity of charged surfaces. For a two-plate system, the same effect leads to an increase of the pressure in between two surfaces. Our results suggest that the effect of ions on the local dielectric constant should be taken into account when interpreting experiments that address ion-specific effects.

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arXiv2010

Kinetics of Surfactant Micellization: a Free Energy Approach

We present a new theoretical approach to the kinetics of micelle formation in surfactant solutions, in which the various stages of aggregation are treated as constrained paths on a single free-energy landscape. Three stages of well-separated time scales are distinguished. The first and longest stage involves homogeneous nucleation of micelles, for which we derive the size of the critical nuclei, their concentration, and the nucleation rate. Subsequently, a much faster growth stage takes place, which is found to be diffusion-limited for surfactant concentrations slightly above the critical micellar concentration ({\it cmc}), and either diffusion-limited or kinetically limited for higher concentrations. The time evolution of the growth is derived for both cases. At the end of the growth stage the micelle size may be either larger or smaller than its equilibrium value, depending on concentration. A final stage of equilibration follows, during which the micelles relax to their equilibrium size through fission or fusion. Both cases of fixed surfactant concentration (closed system) and contact with a reservoir of surfactant monomers (open system) are addressed and found to exhibit very different kinetics. In particular, we find that micelle formation in an open system should be kinetically suppressed over macroscopic times and involve two stages of micelle nucleation rather than one.

cond-mat.soft↗

arXiv2010

Dynamic Surface Tension of Aqueous Solutions of Ionic Surfactants: Role of Electrostatics

The adsorption kinetics of the cationic surfactant dodecyltrimethylammonium bromide at the air-water interface has been studied by the maximum bubble pressure method at concentrations below the critical micellar concentration. At short times, the adsorption is diffusion-limited. At longer times, the surface tension shows an intermediate plateau and can no longer be accounted for by a diffusion limited process. Instead, adsorption appears kinetically controlled and slowed down by an adsorption barrier. A Poisson-Boltzmann theory for the electrostatic repulsion from the surface does not fully account for the observed potential barrier. The possibility of a surface phase transition is expected from the fitted isotherms but has not been observed by Brewster angle microscopy.

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arXiv2010

Ionic effects on the electric field needed to orient dielectric lamellae

We consider the effect of mobile ions on the applied potential needed to reorient a lamellar system of two different materials placed between two planar electrodes. The reorientation occurs from a configuration parallel to the electrodes favored by surface interactions to an orientation perpendicular to the electrodes favored by the electric field. The system consists of alternating A and B layers with different dielectric constants. The mobile ions are assumed to be insoluble in the B layers and hence confined to the A layers. We find that the ions reduce the needed voltage most strongly when they are constrained such that each A lamella is electrically neutral. In this case, a macroscopic separation of charge and its concomitant lowering of free energy, is attained only in the perpendicular orientation. When the ions are free to move between different A layers, such that charge neutrality is only required globally, their effect is smaller and depends upon the preferred surface interaction of the two materials. Under some conditions, the addition of ions can actually stabilize the parallel configuration. Our predictions are relevant to recent experiments conducted on lamellar phases of diblock copolymer films with ionic selective impurities.

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arXiv2009

Coupled Modulated Bilayers

We propose a model addressing the coupling mechanism between two spatially modulated monolayers. We obtain the mean-field phase diagrams of coupled bilayers when the two monolayers have the same preferred modulation wavelength. Various combinations of the monolayer modulated phases are obtained and their relative stability is calculated. Due to the coupling, a spatial modulation in one of the monolayers induces a similar periodic structure in the second one. We have also performed numerical simulations for the case when the two monolayers have different modulation wavelengths. Complex patterns may arise from the frustration between the two incommensurate but annealed structures.

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