Electrostatic correlations at the Stern layer: Physics or chemistry?

Nonlinear Poisson-Boltzmann solutions for charged parallel plates: When opposite charges repel

I present an exact solution of the Poisson-Boltzmann equation for two parallel plates and discuss the solution properties. I discuss in more detail plates with opposite charges: In this case, there are two critical separations, Lc,1 < Lc,2. For separations less than Lc,1, the force between plates is repulsive. It switches to attractive at Lc,1, but with the electric potential having the same sign on both plates. For L > Lc,2, the force remains attractive, and the potential at the plates has the same sign as the charge on each plate. I also describe charge regulation, determined by pKa, and provide formulas for both the critical distance where oppositely charged plates repel and their charging process. The implications of these results for the nanoparticle assembly, as driven by electrostatic interactions, are also discussed.

Role of Sn(II) in Mediating the Formation and Organization of a Langmuir Monolayer

The influence of the Sn(II) ion on the formation and morphology of an arachidic acid (AA) monolayer was investigated using Langmuir film formation technology, pressure-area (Π-A) isotherm measurements, and Brewster angle microscopy (BAM). Our findings indicate that AA Langmuir monolayers exhibit organization that depends on subphase pH and Sn²⁺ concentration. There are multiple equilibria that are relevant to the complexation of AA monolayers, and the balance of Sn(OH)_n equilibria and Sn(AA)_n equilibria gives rise to unusual monolayer structural effects. With Sn²⁺ in the subphase, the AA monolayer exhibits an isotherm characterized by the absence of a collapse point and with a pH-dependent change in isotherm shape not consistent with the formation of an ordered solid phase. The amphiphile headgroup equilibrium mediates the absence of collapse seen experimentally and the ability of the monolayer to retain organization at a surface pressure of ca. 70 mN/m. BAM images show that the morphology of the monolayer depends on the Sn²⁺ concentration, consistent with several species of Sn(AA)_n, where n = 1, 2, or 3, contributing to the overall monolayer order.

A Cross-Scale Framework for Modelling Chloride Ions Diffusion in C-S-H: Combined Effects of Slip, Electric Double Layer and Ion Correlation

Water and chloride ions within pores of cementitious materials plays a crucial role in the damage processes of cement pastes, particularly in the binding material comprising calcium-silicate-hydrates (C-S-H). The migration mechanism of water and chloride ions restricted in C-S-H nanopores is complicated due to the presence of interfacial effects. The special mechanical properties of the solid-liquid interface determine the importance of boundary slip and Electric Double Layer (EDL) and ion diversity in pore solutions determines the difference of the EDL and the stability of water film slip. A cross-scale model covering slip effects, time-varying of EDL and ion correlation needs to be developed so that the interfacial effects concentrated at the pore scale can be extended to affect the overall diffusivity of C-S-H. The statistics of pore size distribution and fractal dimension were used to quantitatively compare the similarities between model and C-S-H structure, thus proving the reliability of cross-scale reconstructed C-S-H transmission model. The results show that the slip effect is the dominant factor affecting the diffusion ability of C-S-H, the contribution of the slip effect is up to 60% and the contribution rate of EDL time-varying only up to about 15%. Moreover, the slip effect is sensitive to both ion correlation and C-S-H inhomogeneity and EDL time-varying is almost insensitive to ion correlation changes. This quantification provides a necessary benchmark for understanding the destructiveness of cement-based materials in the salt rich environment and provides new insights into improving the durability of concrete by changing the solid-liquid interface on the micro-nanoscale.

Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions

The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters.

Quantitating the Binding Energy of Metal Ions to Langmuir-Blodgett Monolayers: The Copper(II)-Octadecylphosphonic Acid System

We report on the formation and organization of a Cu²⁺-complexed octadecylphosphonic acid (ODPA) monolayer formed by Langmuir-Blodgett deposition. The formation of the Cu-complexed monolayer is seen to depend sensitively on the subphase pH and Cu²⁺ concentration, and it is possible to form a monolayer containing the regions of complexed and free ODPA. From the pressure-area isotherm data for these monolayers, we determine the equilibrium constant and free energy of formation for the Cu²⁺-ODPA complex, ΔG = -22.5 kJ/mol.

Explicit characterization of counterion dynamics around a flexible polyelectrolyte

The article presents a comprehensive study of counterion dynamics around a generic linear polyelectrolyte chain with the help of coarse-grained computer simulations. The ion-chain coupling is discussed in the form of binding time, mean-square displacement (MSD) relative to the chain, local ion transport coefficient, and spatiotemporal correlations in the effective charge. We have shown that a counterion exhibits subdiffusive behavior 〈δR^{2}〉∼t^{δ}, δ≈0.9 w.r.t. chain's center of mass. The MSD of ions perpendicularly outward from the chain segment exhibits a smaller subdiffusive exponent compared to the one along the chain backbone. The effective diffusivity of ion is the lowest in chain's close proximity, extending up to the length-scale of radius of gyration R_{g}. Beyond R_{g} at larger distances, they attain diffusivity of free ion with a smooth cross-over from the adsorbed regime to the free ion regime. We have shown that the effective diffusivity drastically decreases for the multivalent ions, while the crossover length scale remains the same. Conversely, with increasing salt concentration the coupling-length scale reduces, while the diffusivity remains unaltered. The effective diffusivity of adsorbed-ion reveals an exponential reduction with electrostatic interaction strength. We further corroborate this from the binding time of ions on the chain, which also grows exponentially with the coupling strength of the ion-polymer duo. Moreover, the binding time of ions exhibits a weak dependence with salt concentration for the monovalent salt, while for multivalent salts the binding time decreases dramatically with concentration. Our work also elucidates fluctuations in the effective charge per site, where it exhibits strong negative correlations at short length-scales.

Multivalent ions and biomolecules: Attempting a comprehensive perspective

Ions are ubiquitous in nature. They play a key role for many biological processes on the molecular scale, from molecular interactions, to mechanical properties, to folding, to self-organisation and assembly, to reaction equilibria, to signalling, to energy and material transport, to recognition etc. Going beyond monovalent ions to multivalent ions, the effects of the ions are frequently not only stronger (due to the obviously higher charge), but qualitatively different. A typical example is the process of binding of multivalent ions, such as Ca2+ , to a macromolecule and the consequences of this ion binding such as compaction, collapse, potential charge inversion and precipitation of the macromolecule. Here we review these effects and phenomena induced by multivalent ions for biological (macro)molecules, from the "atomistic/molecular" local picture of (potentially specific) interactions to the more global picture of phase behaviour including, e. g., crystallisation, phase separation, oligomerisation etc. Rather than attempting an encyclopedic list of systems, we rather aim for an embracing discussion using typical case studies. We try to cover predominantly three main classes: proteins, nucleic acids, and amphiphilic molecules including interface effects. We do not cover in detail, but make some comparisons to, ion channels, colloidal systems, and synthetic polymers. While there are obvious differences in the behaviour of, and the relevance of multivalent ions for, the three main classes of systems, we also point out analogies. Our attempt of a comprehensive discussion is guided by the idea that there are not only important differences and specific phenomena with regard to the effects of multivalent ions on the main systems, but also important similarities. We hope to bridge physico-chemical mechanisms, concepts of soft matter, and biological observations and connect the different communities further.

Interaction between charged lipid vesicles and point- or rod-like trivalent ions

This work examines the influence of the charge distribution of trivalent cations on their interaction with soft anionic particles, using a combination of experimental measurements and theoretical modelling. In particular, we perform electrophoresis measurements to determine the zeta-potential of anionic liposomes in the presence of spermidine and lanthanum cations. We work in a range of electrolyte concentration where a reversal in the electrophoretic mobility of the liposomes is expected; however, unlike the case of lanthanum cations, spermidine does not induce mobility reversal of liposomes. As a result, the charge distribution within the counterion appears to be a key factor. This conclusion is supported by a theory that accounts for intra-ionic correlations, which has previously been successfully used to describe the colloidal electric double layer. It allows us to model spermidine as rod-like ions and lanthanum cations as point-like ions in order to test the importance of the ionic geometry in the interactions with soft particles such as lipid vesicles.

Wettability of Amphoteric Surfaces: The Effect of pH and Ionic Strength on Surface Ionization and Wetting

We present a novel theory to predict the contact angle of water on amphoteric surfaces, as a function of pH and ionic strength. To validate our theory, experiments were performed on two commonly used amphoteric materials, alumina (Al₂O₃) and titania (TiO₂). We find good agreement at all pH values, and at different salt concentrations. With increasing salt concentration, the theory predicts the contact angle-pH curve to get steeper, while keeping the same contact angle at pH = PZC (point of zero charge), in agreement with data. Our model is based on the amphoteric 1-p K model and includes the electrostatic free energy of an aqueous system as well as the surface energy of a droplet in contact with the surface. In addition, we show how our theory suggests the possibility of a novel responsive membrane design, based on amphoteric groups. At pH ∼ PZC, this membrane resists flow of water but at slightly more acidic or basic conditions the wettability of the membrane pores may change sufficiently to allow passage of water and solutes. Moreover, these membranes could act as active sensors that only allow solutions of high ionic strength to flow through in wastewater treatment.

Silica sol as grouting material: a physio-chemical analysis

At present there is a pressing need to find an environmentally friendly grouting material for the construction of tunnels. Silica nanoparticles hold great potential of replacing the organic molecule based grouting materials currently used for this purpose. Chemically, silica nanoparticles are similar to natural silicates which are essential components of rocks and soil. Moreover, suspensions of silica nanoparticles of different sizes and desired reactivity are commercially available. However, the use of silica nanoparticles as grouting material is at an early stage of its technological development. There are some critical parameters such as long term stability and functionality of grouted silica that need to be investigated in detail before silica nanoparticles can be considered as a reliable grouting material. In this review article we present the state of the art regarding the chemical properties of silica nanoparticles commercially available, as well as experience gained from the use of silica as grouting material. We give a detailed description of the mechanisms underlying the gelling of silica by different salt solutions such as NaCl and KCl and how factors such as particle size, pH, and temperature affect the gelling and gel strength development. Our focus in this review is on linking the chemical properties of silica nanoparticles to the mechanical properties to better understand their functionality and stability as grouting material. Along the way we point out areas which need further research.

On the physics of both surface overcharging and charge reversal at heterophase interfaces

A series of Monte Carlo simulations are employed to reveal the physics of both surface overcharging and charge reversal at a negatively charged dielectric interface exposed to a bulk solution containing a +2:−1 electrolyte in the absence and presence of a monovalent salt.

Separation of the Stern and diffuse layer in coarse-grained models: the cases of phosphatidyl serine, phosphatidic acid, and PIP2 monolayers

We present here a method to separate the Stern and diffuse layer in general systems into two regions that can be analyzed separately. The Stern layer can be described in terms of Bjerrum pairing and the diffuse layer in terms of Poisson-Boltzmann theory (monovalent) or strong coupling theory plus a slowly decaying tail (divalent). We consider three anionic phospholipids: phosphatidyl serine, phosphatidic acid, and phosphatidylinositol(4,5)bisphosphate (PIP2), which we describe within a minimal coarse-grained model as a function of ionic concentration. The case of mixed lipid systems is also considered, which shows a high level of binding cooperativity as a function of PIP2 localization. Implications for existing experimental systems of lipid heterogeneities are also discussed.

Experimental observation of the ion-ion correlation effects on charge inversion and strong adhesion between mica surfaces in aqueous electrolyte solutions

Direct force measurements between two mica surfaces in aqueous electrolyte solutions over broad ranges of LaCl3 concentrations and pH values were carried out with a surface forces apparatus. Charge inversion on mica surfaces is detected once the LaCl3 concentration reaches a critical value. With the continual increase of LaCl3 concentrations, the mica surface will be overscreened by the counterions. It is demonstrated that the two mica surfaces may experience the jump-in contact even at high LaCl3 concentrations, which is seldom seen in monovalent salt solutions. The strong adhesion cannot be attributed to the van der Waals force alone, but should include the ion-ion correlation forces. Through adjusting the pH values in LaCl3 solutions, the ion-ion correlation force can be evaluated quantitatively. These results provide important insight into the fundamental understanding in the role of ion-ion correlations in ion screening mechanism and interactions between charged objects.

Monovalent ion adsorption at the muscovite (001)-solution interface: relationships among ion coverage and speciation, interfacial water structure, and substrate relaxation

The interfacial structure between the muscovite (001) surface and aqueous solutions containing monovalent cations (3 × 10(-3) m Li(+), Na(+), H(3)O(+), K(+), Rb(+), or Cs(+), or 3 × 10(-2) m Li(+) or Na(+)) was measured using in situ specular X-ray reflectivity. The element-specific distribution of Rb(+) was also obtained with resonant anomalous X-ray reflectivity. The results demonstrate complex interdependencies among adsorbed cation coverage and speciation, interfacial hydration structure, and muscovite surface relaxation. Electron-density profiles of the solution near the surface varied systematically and distinctly with each adsorbed cation. Observations include a broad profile for H(3)O(+), a more structured profile for Li(+) and Na(+), and increasing electron density near the surface because of the inner-sphere adsorption of K(+), Rb(+), and Cs(+) at 1.91 ± 0.12, 1.97 ± 0.01, and 2.26 ± 0.01 Å, respectively. Estimated inner-sphere coverages increased from ~0.6 to 0.78 ± 0.01 to ~0.9 per unit cell area with decreasing cation hydration strength for K(+), Rb(+), and Cs(+), respectively. Between 7 and 12% of the Rb(+) coverage occurred as an outer-sphere species. Systematic trends in the vertical displacement of the muscovite lattice were observed within ~40 Å of the surface. These include a <0.1 Å shift of the interlayer K(+) toward the interface that decays into the crystal and an expansion of the tetrahedral-octahedral-tetrahedral layers except for the top layer in contact with solution. The distortion of the top tetrahedral sheet depends on the adsorbed cation, ranging from an expansion (by ~0.05 Å vertically) in 3 × 10(-3)m H(3)O(+) to a contraction (by ~0.1 Å) in 3 × 10(-3) m Cs(+). The tetrahedral tilting angle in the top sheet increases by 1 to 4° in 3 × 10(-3) m Li(+) or Na(+), which is similar to that in deionized water where the adsorbed cation coverages are insufficient for full charge compensation.

Regulation of the electric charge in phosphatidic acid domains

Although a minor component of the lipidome, phosphatidic acid (PA) plays a crucial role in nearly all signaling pathways involving cell membranes, in part because of its variable electrical charge in response to environmental conditions. To investigate how charge is regulated in domains of PA, we applied surface-sensitive X-ray reflectivity and fluorescence near-total-reflection techniques to determine the binding of divalent ions (Ca(2+) at various pH values) to 1,2-dimyristoyl-sn-glycero-3-phosphate (DMPA) and to the simpler lipid dihexadecyl phosphate (DHDP) spread as monolayers at the air/water interface. We found that the protonation state of PA is controlled not only by the pK(a) and local pH but also by the strong affinity to PA driven by electrostatic correlations from divalent ions and the cooperative effect of the two dissociable protons, which dramatically enhance the surface charge. A precise theoretical model is presented providing a general framework to predict the protonation state of PA. Implications for recent experiments on charge regulation by hydrogen bonding and the role of pH in PA signaling are discussed in detail.

Lateral dynamics of charged lipids and peripheral proteins in spatially heterogeneous membranes: comparison of continuous and Monte Carlo approaches

Biological membranes are complex environments whose physico-chemical properties are of utmost importance for the understanding of many crucial biological processes. Much attention has been given in the literature to the description of membranes along the z-axis perpendicular to the membrane. Here, we instead consider the lateral dynamics of lipids and peripheral proteins due to their electrostatic interaction. Previously, we constructed a Monte Carlo automaton capable of simulating mutual diffusive dynamics of charged lipids and associated positively charged peptides. Here, we derive and numerically analyze a system of Poisson-Boltzmann-Nernst-Planck (PBNP) equations that provide a mean-field approximation compatible with our Monte Carlo model. The thorough comparison between the mean-field PBNP equations and Monte Carlo simulations demonstrates that both the approaches are in a good qualitative agreement in all tested scenarios. We find that the two methods quantitatively deviate when the local charge density is high, presumably because the Poisson-Boltzmann formalism is applicable in the so-called weak coupling limit, whose validity is restricted to low charge densities. Nevertheless, we conclude that the mean-field PBNP approach provides a good approximation for the considerably more detailed Monte Carlo model at only a fraction of the associated computational cost and allows simulation of the membrane lateral dynamics on the space and time scales relevant for the realistic biological problems.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: theory versus experiment

Aqueous dispersions of phosphatidylglycerol (PG) lipids may present an anomalous chain-melting transition at low ionic strengths, as seen by different experimental techniques such as calorimetry or light scattering. The anomaly disappears at high ionic strengths or for longer acyl-chain lengths. In this article, we use a statistical model for the bilayer that distinguishes both lipid chain and headgroup states in order to compare model and experimental thermotropic and electrical properties. The effective van der Waals interactions among hydrophobic chains compete with the electrostatic repulsions between polar headgroups, which may be ionized (counterion dissociated) or electrically neutral (associated with counterions). Electric degrees of freedom introduce new thermotropic charge-ordered phases in which headgroup charges may be spatially ordered, depending on the electrolyte ionic strength, introducing a new rationale for experimental data on PGs. The thermal phases presented by the model for different chain lengths, at fixed ionic strength, compare well with an experimental phase diagram constructed on the basis of differential scanning calorimetry profiles. In the case of dispersions of DMPG (dimyristoyl phosphatidylglycerol) with added monovalent salt, the model properties reproduce the main features displayed by data from differential scanning calorimetry as well as the characteristic profile for the degree of ionization of the bilayer surface across the anomalous transition region, obtained from the theoretical interpretation of electrokinetic (conductivity and electrophoretic mobility) measurements.

Divalent cation-dependent formation of electrostatic PIP2 clusters in lipid monolayers

Polyphosphoinositides are among the most highly charged molecules in the cell membrane, and the most common polyphosphoinositide, phosphatidylinositol-4,5-bisphosphate (PIP(2)), is involved in many mechanical and biochemical processes in the cell membrane. Divalent cations such as calcium can cause clustering of the polyanionic PIP(2), but the origin and strength of the effective attractions leading to clustering has been unclear. In addition, the question of whether the ion-mediated attractions could be strong enough to alter the mechanical properties of the membrane, to our knowledge, has not been addressed. We study phase separation in mixed monolayers of neutral and highly negatively charged lipids, induced by the addition of divalent positively charged counterions, both experimentally and numerically. We find good agreement between experiments on mixtures of PIP(2) and 1-stearoyl-2-oleoyl phosphatidylcholine and simulations of a simplified model in which only the essential electrostatic interactions are retained. In addition, we find numerically that under certain conditions the effective attractions can rigidify the resulting clusters. Our results support an interpretation of PIP(2) clustering as governed primarily by electrostatic interactions. At physiological pH, the simulations suggest that the effective attractions are strong enough to give nearly pure clusters of PIP(2) even at small overall concentrations of PIP(2).

Ionic specificity in pH regulated charged interfaces: Fe3+ versus La3+

We determine the distribution of two trivalent ions Fe(3+) and La(3+) next to two different amphiphilic charged interfaces as ions or complexes, consisting of the phosphate lipid dihexadecyl phosphate (DHDP) and the fatty acid arachidic acid (AA). These amphiphiles provide a wide range of pK(a) values, from 2.1 (DHDP) to 5.1 (AA), thus allowing manipulation of the surface charge over extremely low pH (pH ∼1 or larger), and the two ions provide two limiting cases of specificity for the amphiphiles. We find that La(3+) distribution is mostly sensitive to the surface charge, whereas the Fe(3+) binding depends on its character in the solution and is highly specific, as indicated by the crucial role played by iron complexes (Fe(OH)(3) or Fe(OH)(2+)) forming covalent bonds even for an uncharged interface. The implications of the results to other ions and/or amphiphilic interfaces are also discussed.

Wigner-crystal formulation of strong-coupling theory for counterions near planar charged interfaces

We present a new analytical approach to the strong electrostatic coupling regime (SC) that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity, etc. Two geometries are analyzed in detail: one charged wall first, and then two parallel walls at small distances that can be likely or oppositely charged. In all cases, only one type of mobile counterions is present, and ensures electroneutrality (salt-free case). The method is based on a systematic expansion around the ground state formed by the two-dimensional Wigner crystal(s) of counterions at the plate(s). The leading SC order stems from a single-particle theory, and coincides with the virial SC approach that has been much studied in the last 10 years. The first correction has the functional form of the virial SC prediction, but the prefactor is different. The present theory is free of divergences and the obtained results, both for symmetrically and asymmetrically charged plates, are in excellent agreement with available data of Monte Carlo simulations under strong and intermediate Coulombic couplings. All results obtained represent relevant improvements over the virial SC estimates. The present SC theory starting from the Wigner crystal and therefore coined Wigner SC, sheds light on anomalous phenomena like the counterion mediated like-charge attraction, and the opposite-charge repulsion.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: a statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types--each one associated, respectively, with the polar-headgroup and the acyl-chain states--which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Interactions between charged surfaces with ionizable sites

A key factor controlling the interactions between surfaces in aqueous solutions is the surface charge density. Surfaces typically become charged though a titration process where surface groups can become ionized based on their dissociation constant and the pH of the solution. In this work, we use a Monte Carlo method to treat this process in a system with two planar surfaces with explicitly described ionizable sites in a salt solution. We focus on a system with a surface density of ionizable sites set to 4.8 nm(-2), corresponding to silica. We find that the surface charge density changes as the surfaces come close to contact due to interactions between the ionizable groups on each surface. In addition, we observe an attraction between the surfaces above a threshold surface charge, in good agreement with previous theoretical predictions based on uniformly charged surfaces. However, close to contact we find the force is significantly different than for the uniformly charged case.

Thermodynamics of monolayers formed by mixtures of phosphatidylcholine/phosphatidylserine

In this work we obtain the thermodynamic properties of mixed (1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine) PC and (1-stearoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (sodium salt)) PS monolayers. Measurements of compressibility (isotherms, bulk modulus, and excess area per molecule) and surface potential show that the properties of monolayers at the air-water interface depend on the concentration of ions (Na(+) and K(+)) and the proportion of PS in the mixture. The dependence on PS arises because the molecule is originally bound to a Na(+) counterion; by increasing the concentration of ions the entropy changes, creating a favorable system for the bound counterions of PS to join the bulk, leaving a negatively charged molecule. This change leads to an increase in electrostatic repulsions which is reflected by the increase in area per molecule versus surface pressure and a higher surface potential. The results lead to the conclusion that this mixture of phospholipids follows a non ideal behavior and can help to understand the thermodynamic behavior of membranes made of binary mixtures of a zwitterionic and an anionic phospholipid with a bound counterion.

Electrostatics at the nanoscale

Electrostatic forces are amongst the most versatile interactions to mediate the assembly of nanostructured materials. Depending on experimental conditions, these forces can be long- or short-ranged, can be either attractive or repulsive, and their directionality can be controlled by the shapes of the charged nano-objects. This Review is intended to serve as a primer for experimentalists curious about the fundamentals of nanoscale electrostatics and for theorists wishing to learn about recent experimental advances in the field. Accordingly, the first portion introduces the theoretical models of electrostatic double layers and derives electrostatic interaction potentials applicable to particles of different sizes and/or shapes and under different experimental conditions. This discussion is followed by the review of the key experimental systems in which electrostatic interactions are operative. Examples include electroactive and "switchable" nanoparticles, mixtures of charged nanoparticles, nanoparticle chains, sheets, coatings, crystals, and crystals-within-crystals. Applications of these and other structures in chemical sensing and amplification are also illustrated.

Ion-specific induced charges at aqueous soft interfaces

Ionic specificity effects, i.e., ions of the same valence leading to different macroscopic effects, are studied by considering a Langmuir monolayer of arachidic acid over a solution containing either Fe(3+) or La(3+). We systematically vary pH levels as a way to control the interfacial surface charge and characterize the system by surface-sensitive x-ray scattering and spectroscopic techniques. We show that the critical surface pressure at the tilted (L2) to untilted (LS) transition is ionic specific and varies with pH. While the maximum density of surface bound La(3+) per head group of arachidic acid is ∼0.3, the amount necessary to neutralize the surface charge, for Fe(3+) it is nearly 0.6 and it is accompanied with a significant accumulation of the coions Cl(-) as revealed by surface x-ray spectroscopy. We account for the experimental observations by a statistical mechanical model including ion specificity.

Hydrated cation speciation at the muscovite (001)-water interface

Charged materials in aqueous systems interact according to their interfacial properties, typically described by the electrical double layer (EDL). Distributions of divalent metal cations at the muscovite (001)-solution interface observed using resonant anomalous X-ray reflectivity demonstrate an unexpected complexity with respect to the EDL structure. Three forms of adsorbed cations can coexist: the classical inner-sphere and outer-sphere complexes and a third "extended" outer-sphere complex located farther from the surface. Their relative proportions are controlled by the energy balance among cation hydration, interface hydration, and electrostatic attraction. Systematic trends in coverage and position establish the defining role of cation hydration in stabilizing the multiple coexisting species.

Electrostatic bending of lipid membranes: how are lipid and electrostatic properties interrelated?

Electrostatic modification of lipid headgroups and its effect on membrane curvature are not only relevant in a variety of contexts such as cell shape transformation and membrane tubulation but also are intriguingly implicated in membrane functions. For instance, the gating (open vs closed) properties of mechanosensitive channels can be influenced by membrane curvature and ion valence. However, a full theoretical description of membrane electrostatics is still lacking; in the past, membrane bending has often been considered under a few assumptions about how bending modifies lipid arrangements and surface charges. Here, we present a unified theoretical approach to spontaneous membrane curvature, C(0), in which lipid properties (e.g., packing shape) and electrostatic effects are self-consistently integrated. For the description of electrostatic interactions, especially between a lipid charge and a divalent counterion, we implement the Poisson-Boltzmann (PB) approach by incorporation of finite ionic sizes, so as to capture both lateral and transverse charge correlations on the membrane surface. Our results show that C(0) is sensitive to the way lipid rearrangements and divalent counterions are modeled. Interestingly, it can change its sign in the presence of divalent counterions, thus stabilizing reverse hexagonal (H(II)) phases. Our results show how electrostatic modification of headgroups influences the preferred structure of lipid aggregates (inverted micelles vs bilayers).

Microscopic approach to the kinetics of pattern formation of charged molecules on surfaces

A microscopic formalism based on computing many-particle densities is applied to the analysis of the diffusion-controlled kinetics of pattern formation in oppositely charged molecules on surfaces or adsorbed at interfaces with competing long-range Coulomb and short-range Lennard-Jones interactions. Particular attention is paid to the proper molecular treatment of energetic interactions driving pattern formation in inhomogeneous systems. The reverse Monte Carlo method is used to visualize the spatial molecular distribution based on the calculated radial distribution functions (joint correlation functions). We show the formation of charge domains for certain combinations of temperature and dynamical interaction parameters. The charge segregation evolves into quasicrystalline clusters of charges, due to the competing long- and short-range interactions. The clusters initially co-exist with a gas phase of charges that eventually add to the clusters, generating "fingers" or line of charges of the same sign, very different than the nanopatterns expected by molecular dynamics in systems with competing interactions in two dimensions, such as strain or dipolar versus van der Waals interactions.

The interaction between electrolyte and surfaces decorated with charged groups: A molecular dynamics simulation study

In this paper, we perform molecular dynamics simulations of an interface containing charged functional groups of different valences in contact with 2:1 ionic solution. We take into account both the finite sizes of the ions in solution and the functional groups but we neglect the structural details of the solvent (primitive model). We show that the distribution of ions and the electrostatic properties of the system depend strongly on the valence of the interfacial charged groups. In the case of surfaces containing well-separated charged interfacial groups, we observe counterion binding at these groups induced by electrostatic interactions. A detailed analysis of the potential of mean force between interfacial charged groups and ions reveals significant features not anticipated by present theories of electrolytes near interfaces. Overall, our results show that, in primitive models of the ion-interface interaction, not only the ionic size and valence are important but the size and valence of the interfacial charged groups also have a significant impact.