arXiv subjects

David Andelman

Publications and source records attributed to David Andelman.

At least 55 records · Page 3Linked to original sources

arXiv2018

Charge Regulation with Fixed and Mobile Charges

Uncompensated charges do not occur in Nature and any local charge should be a result of charge separation. Dissociable chemical groups at interfaces in contact with ions in solution, whose chemical equilibrium depends both on short-range non-electrostatic and long-range electrostatic interactions, are the physical basis of this charge separation, known as charge regulation phenomena. The charged groups can be either fixed and immobile, as in the case of solvent-exposed solid substrate and soft bounding surfaces, (e.g., molecularly smooth mica surfaces and soft phospholipid membranes), or free and mobile, as in the case of charged macro-ions, (e.g., protein or other biomolecules). Here, we review the mean-field formalism used to describe both cases, with a focus on recent advances in the modeling of mobile charge-regulated macro-ions in an ionic solution. The general form of the screening length in such a solution is derived, and is shown to combine the concept of intrinsic capacitance, introduced by Lund and Jönsson, and bulk capacitance, resulting from the mobility of small ions and macro-ions. The advantages and disadvantages of different formulations, such as the cell model vs. the collective approach, are discussed, along with several suggestions for future experiments and modeling.

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arXiv2018

Charge Regulating Macro-ions in Salt Solutions: Screening Properties and Electrostatic Interactions

We revisit the charge-regulation mechanism of macro-ions and apply it to mobile macro-ions in a bathing salt solution. In particular, we examine the effects of correlation between various adsorption/desorption sites and analyze the collective behavior in terms of the solution effective screening properties. We show that such a behavior can be quantified in terms of the charge {\em asymmetry} of the macro-ions, defined by their preference for a non-zero effective charge, and their {\em donor/acceptor} propensity for exchanging salt ions with the bathing solution. Asymmetric macro-ions tend to increase the screening, while symmetric macro-ions can in some cases decrease it. Macro-ions that are classified as donors display a rather regular behavior, while those that behave as acceptors exhibit an anomalous non-monotonic Debye length. The screening properties, in their turn, engender important modifications to the disjoining pressure between two charged surfaces. Our findings are in particular relevant for solutions of proteins, whose exposed amino acids can undergo charge dissociation/association processes to/from the bathing solution, and can be considered as a solution of charged regulated macro-ions, as analyzed here.

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arXiv2018

Complex Fluids with Mobile Charge-Regulated Macro-Ions

We generalize the concept of charge regulation of ionic solutions, and apply it to complex fluids with mobile macro-ions having internal non-electrostatic degrees of freedom. The suggested framework provides a convenient tool for investigating systems where mobile macro-ions can self-regulate their charge (e.g., proteins). We show that even within a simplified charge-regulation model, the charge dissociation equilibrium results in different and notable properties. Consequences of the charge regulation include a positional dependence of the effective charge of the macro-ions, a non-monotonic dependence of the effective Debye screening length on the concentration of the monovalent salt, a modification of the electric double-layer structure, and buffering by the macro-ions of the background electrolyte.

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arXiv2017

Permeation through a lamellar stack of lipid mixtures

We study material transport and permeation through a lamellar stack of multi-component lipid membranes by performing Monte Carlo simulations of a stacked two-dimensional Ising model in presence of permeants. In the model, permeants are transported through the stack via in-plane lipid clusters, which are inter-connected in the vertical direction. These clusters are formed transiently by concentration fluctuations of the lipid mixture, and the permeation process is affected, especially close to the critical temperature of the binary mixture. We show that the permeation rate decays exponentially as function of temperature and permeant lateral size, whereas the dependency on the characteristic waiting time obeys a stretched exponential function. The material transport through such lipid clusters can be significantly affected around physiological temperatures.

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arXiv2016

Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory

We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension, and the one-loop contribution gives a generalization of the Onsager-Samaras result. Our theory fits well a wide range of different acids and salts, and is in accord with the reverse Hofmeister series for acids.

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arXiv2016

Defect-free Perpendicular Diblock Copolymer Films: The Synergistic Effect of Surface Topography and Chemistry

We propose a direct self-assembly mechanism towards obtaining defect-free perpendicular lamellar phases of diblock copolymer (BCP) thin films. In our numerical study, a thin BCP film having a flat top surface is casted on a uni-directional corrugated solid substrate. The substrate is treated chemically and has a weak preference toward one of the two BCP components. Employing self-consistent field theory (SCFT), we find that there is an enhanced synergy between two substrate characteristics: its topography (geometrical roughness) combined with a weak surface preference. This synergy produces the desired perpendicular lamellar phase with perfect inplane ordering. Defect-free BCP lamellar phases are reproducible for several random initial states, and are obtained for a range of substrate roughness and chemical characteristics, even for a uni-directional multi-mode substrate roughness. Our theoretical study suggests possible experiments that will explore the interplay between uni-directional substrate corrugation and chemical surface treatment. It may lead to viable and economical ways of obtaining BCP films with defect-free lateral alignment.

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arXiv2016

Budding Transition of Asymmetric Two-component Lipid Domains

We propose a model that accounts for the budding transition of asymmetric two-component lipid domains, where the two monolayers (leaflets) have different average compositions controlled by independent chemical potentials. Assuming a coupling between the local curvature and local lipid composition in each of the leaflets, we discuss the morphology and thermodynamic behavior of asymmetric lipid domains. The membrane free-energy contains three contributions: the bending energy, the line tension, and a Landau free-energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams containing fully budded, dimpled, and flat states as a function of the two leaflet compositions. The global phase behavior is analyzed, and depending on system parameters, the phase diagrams include one-phase, two-phase and three-phase regions. In particular, we predict various phase coexistence regions between different morphologies of domains, which may be observed in multi-component membranes or vesicles.

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arXiv2016

Electrostatic Attraction between Overall Neutral Surfaces

Two overall neutral surfaces with positive and negative charged domains ("patches") have been shown in recent experiments to exhibit long-range attraction when immersed in an ionic solution. Motivated by the experiments, we calculate analytically the osmotic pressure between such surfaces within the Poisson-Boltzmann framework, using a variational principle for the surface-averaged free energy. The electrostatic potential, calculated beyond the linear Debye-Hückel theory, yields an {\it overall attraction} at large inter-surface separations, over a wide range of the system's controlled length scales. In particular, the attraction is stronger and occurs at smaller separations for surface patches of larger size and charge density. In this large patch limit, we find that the attraction-repulsion crossover separation is inversely proportional to the square of the patch charge-density and to the Debye screening length.

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arXiv2016

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions

We study, by incorporating short-range ion-surface interactions, ionic profiles of electrolyte solutions close to a non-charged interface between two dielectric media. In order to account for important correlation effects close to the interface, the ionic profiles are calculated beyond mean-field theory, using the loop expansion of the free energy. We show how it is possible to overcome the well-known deficiency of the regular loop expansion close to the dielectric jump, and treat the non-linear boundary conditions within the framework of field theory. The ionic profiles are obtained analytically to one-loop order in the free energy, and their dependence on different ion-surface interactions is investigated. The Gibbs adsorption isotherm, as well as the ionic profiles are used to calculate the surface tension, in agreement with the reverse Hofmeister series. Consequently, from the experimentally-measured surface tension, one can extract a single adhesivity parameter, which can be used within our model to quantitatively predict hard to measure ionic profiles.

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arXiv2016

Phase diagrams and ordering in charged membranes: Binary mixtures of charged and neutral lipids

We propose a model describing the phase behavior of two-component membranes consisting of binary mixtures of electrically charged and neutral lipids. We take into account the structural phase transition (main-transition) of the hydrocarbon chains, and investigate the interplay between this phase transition and the lateral phase separation. The presence of charged lipids significantly affects the phase behavior of the multi-component membrane. Due to the conservation of lipid molecular volume, the main-transition temperature of charged lipids is lower than that of neutral ones. Furthermore, as compared with binary mixtures of neutral lipids, the membrane phase separation in binary mixtures of charged lipids is suppressed, in accord with recent experiments. We distinguish between two types of charged membranes: mixtures of charged saturated lipid/neutral unsaturated lipid and a second case of mixtures of neutral saturated lipid/charged unsaturated lipid. The corresponding phase behavior is calculated and shown to be very different. Finally, we discuss the effect of added salt on the phase separation and the temperature dependence of the lipid molecular area.

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arXiv2016

Free energy approach to micellization and aggregation: Equilibrium, metastability, and kinetics

We review a recently developed micellization theory, which is based on a free-energy approach and offers several advantages over the conventional one, based on mass action and rate equations. As all the results are derived from a single free-energy expression, one can adapt the theory to different scenarios by merely modifying the initial expression. We present results concerning various features of micellization out of equilibrium, such as the existence of metastable aggregates (premicelles), micellar nucleation and growth, transient aggregates, and final relaxation toward equilibrium. Several predictions that await experimental investigation are discussed.

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arXiv2016

Charged Membranes: Poisson-Boltzmann theory, DLVO paradigm and beyond

In this chapter we review the electrostatic properties of charged membranes in aqueous solutions, with or without added salt, employing simple physical models. The equilibrium ionic profiles close to the membrane are governed by the well-known Poisson-Boltzmann (PB) equation. We analyze the effect of different boundary conditions, imposed by the membrane, on the ionic profiles and the corresponding osmotic pressure. The discussion is separated into the single membrane case and that of two interacting membranes. For one membrane setup, we show the different solutions of the PB equation and discuss the interplay between constant-charge and constant-potential boundary conditions. A modification of the PB theory is presented to treat the extremely high counter-ion concentration in the vicinity of a charge membrane. For two equally-charged membranes, we analyze the different pressure regimes for the constant-charge boundary condition, and discuss the difference in the osmotic pressure for various boundary conditions. The non-equal charged membranes is reviewed as well, and the crossover from repulsion to attraction is calculated analytically. We then examine the charge-regulation boundary condition and discuss its effects on the ionic profiles and the osmotic pressure for two equally-charged membranes. In the last section, we briefly review the van der Waals (vdW) interactions and their effect on the free energy between two planar membranes. We explain the simple Hamaker pair-wise summation procedure, and introduce the more rigorous Lifshitz theory. The latter is a key ingredient in the DLVO theory, which combines repulsive electrostatic with attractive vdW interactions, and offers a simple explanation for colloidal or membrane stability. Finally, the chapter ends by a short account of the limitations of the approximations inherent in the PB theory.

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arXiv2016

Charge regulation: a generalized boundary condition?

The three most commonly-used boundary conditions for charged colloidal systems are constant charge (insulator), constant potential (conducting electrode) and charge regulation (ionizable groups at the surface). It is usually believed that the charge regulation is a generalized boundary condition that reduces in some specific limits to either constant charge or constant potential boundary conditions. By computing the disjoining pressure between two symmetric planes for these three boundary conditions, both numerically (for all inter-plate separations) and analytically (for small inter-plate separations), we show that this is not, in general, the case. In fact, the limit of charge regulation is a separate boundary condition, yielding a disjoining pressure with a different characteristic separation-scaling. Our findings are supported by several examples demonstrating that the disjoining pressure at small separations for the charge regulation boundary-condition depends on the details of the dissociation/association process.

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arXiv2015

Contact angle saturation in electrowetting: Injection of ions into the surrounding media

We use the Poisson-Boltzmann theory to predict contact angle saturation of aqueous droplets in electrowetting. Our theory predicts that injection of ions from the droplet into its surrounding medium is responsible for the deviation of the apparent contact angle from the Young-Lippmann equation for large applied voltages. The ion injection substantially decreases the Maxwell stress and increases the osmotic pressure at the interface between the two media, leading to saturation of the apparent contact angle. Moreover, we find that the contact angle does not saturate, but only has a broad minimum that increases again upon further increase of the applied voltage, in agreement with experiments.

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arXiv2015

Lamellar Diblock Copolymers on Rough Substrates: Self-consistent Field Theory Studies

We present numerical calculations of lamellar phases of di-block copolymers (BCP) confined between two surfaces, where the top surface is flat and the bottom one is corrugated. The corrugated substrate is assumed to have a single $q$-mode of lateral undulations with a wavenumber q_s and amplitude R. We focus on the effects of substrate roughness, parameterized by the dimensionless quantity, q_sR, on the relative stability between parallel and perpendicular orientations of the lamellar phase. The competition between film confinement, energy cost of elastic deformation and gain in surface energy induces a parallel-to-perpendicular transition of the BCP lamellae. Employing self-consistent field theory (SCFT), we study the critical substrate roughness value corresponding to this transition. The critical value increases as function of the surface preference towards one of the two BCP components, and as function of film thickness. But, it decreases with increasing values of the Flory-Huggins parameter. Our findings are equivalent to stating that the critical value decreases as the BCP molecular weight or the natural BCP periodicity increases. We further show that the rough substrate can overcome the formation of parallel lamellae in cases where the top surface has a preference towards one of the two BCP components. Our results are in good agreement with previous experiments, and highlight the physical conditions behind the perpendicular orientation of lamellar phases, as is desired in nanolithography and other industrial applications.

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arXiv2015

Differential capacitance of the electric double layer: The interplay between ion finite size and dielectric decrement

We study the electric double layer by combining the effects of ion finite size and dielectric decrement. At high surface potential, both mechanisms can cause saturation of the counter-ion concentration near a charged surface. The modified Grahame equation and differential capacitance are derived analytically for a general expression of a permittivity epsilon(n) that depends on the local ion concentration, n, and under the assumption that the co-ions are fully depleted from the surface. The concentration at counter-ion saturation is found for any epsilon(n), and a criterion predicting which of the two mechanisms (steric vs. dielectric decrement) is the dominant one is obtained. At low salinity, the differential capacitance as function of surface potential has two peaks (so-called camel-shape). Each of these two peaks is connected to a saturation of counter-ion concentration caused either by dielectric decrement or by their finite size. Because these effects depend mainly on the counter-ion concentration at the surface proximity, for opposite surface-potential polarity either the cations or anions play the role of counter-ions, resulting in an asymmetric camel-shape. At high salinity, we obtain and analyze the crossover in the differential capacitance from a double-peak shape to a uni-modal one. Finally, several nonlinear models of the permittivity decrement are considered, and we predict that the concentration at dielectrophoretic saturation shifts to higher concentration than those obtained by the linear decrement model.

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arXiv2015

Budding of domains in mixed bilayer membranes

We propose a model that accounts for budding behavior of domains in lipid bilayers, where each of the bilayer leaflets has a coupling between its local curvature and local lipid composition. The compositional asymmetry between the two monolayers leads to an overall spontaneous curvature. The membrane free-energy contains three contributions: bending energy, line tension, and a Landau free-energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams which contain fully-budded, dimpled and flat states. In particular, for some range of membrane parameters, the phase diagrams exhibit a tricritical behavior as well as three-phase coexistence region. The global phase diagrams can be divided into three types and are analyzed in terms of the curvature-composition coupling parameter and domain size.

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arXiv2014

Charge-induced phase separation in lipid membranes

The phase separation in lipid bilayers that include negatively charged lipids is examined experimentally. We observed phase-separated structures and determined the membrane miscibility temperatures in several binary and ternary lipid mixtures of unsaturated neutral lipid, dioleoylphosphatidylcholine (DOPC), saturated neutral lipid, dipalmitoylphosphatidylcholine (DPPC), unsaturated charged lipid, dioleoylphosphatidylglycerol (DOPG$^{\scriptsize{(-)}}$), saturated charged lipid, dipalmitoylphosphatidylglycerol (DPPG$^{\scriptsize{(-)}}$), and cholesterol. In binary mixtures of saturated and unsaturated charged lipids, the combination of the charged head with the saturation of hydrocarbon tail is a dominant factor for the stability of membrane phase separation. DPPG$^{\scriptsize{(-)}}$ enhances phase separation, while DOPG$^{\scriptsize{(-)}}$ suppresses it. Furthermore, the addition of DPPG$^{\scriptsize{(-)}}$ to a binary mixture of DPPC/cholesterol induces phase separation between DPPG$^{\scriptsize{(-)}}$-rich and cholesterol-rich phases. This indicates that cholesterol localization depends strongly on the electric charge on the hydrophilic head group rather than on the ordering of the hydrocarbon tails. Finally, when DPPG$^{\scriptsize{(-)}}$ was added to a neutral ternary system of DOPC/DPPC/Cholesterol (a conventional model of membrane rafts), a three-phase coexistence was produced. We conclude by discussing some qualitative features of the phase behaviour in charged membranes using a free energy approach.

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