Charge reversal seen in electrical double layer interaction of surfaces immersed in 2:1 calcium electrolyte

Cation valency in water-in-salt electrolytes alters the short- and long-range structure of the electrical double layer

Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI)2], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI)2], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.

Strong-coupling effective-field theory for asymmetrically charged plates with counterions only

We are interested in rationalizing the phenomenon of like-charge attraction between charged bodies, such as a pair of colloids, in the strong coupling regime. The two colloids are modelled as uniformly charged parallel plates, neutralized by mobile counterions. In an earlier work [Palaia et al., J. Phys. Chem. B 126, 3143 (2022)1520-610610.1021/acs.jpcb.2c00028], we developed an effective-field theory for symmetric plates, stemming from the ground-state description that holds at infinite couplings. Here, we generalize the approach to the asymmetric case, where the plates bear charges of the same sign, but of different values. In the symmetric situation, the mobile ions, which are localized in the vicinity of the two plates, share equally between both of them. Here, the sharing is nontrivial, depending both on the coupling parameter and the distance between the plates. We thus introduce a counterion occupation parameter that is determined variationally to ensure minimum of the free energy. The analytical results for the pressure as a function of the plate-plate distance d agree well with our Monte Carlo data, in a large interval of strong and intermediate coupling constants Ξ. We show in particular that within this description there exists a range of large distances at which the attractive pressure features a 1/d^{2} behavior.

Ion correlation-driven like-charge attraction in multivalent salt solutions

The electrostatic double layer force is key to determining the stability and self-assembly of charged colloids and many other soft matter systems. Fully understanding the attractive force between two like-charged surfaces remains a great challenge. Here, we apply the modified Gaussian renormalized fluctuation theory to study ion correlation-driven like-charge attraction in multivalent salt solutions. The effects of spatially varying ion correlations on the structure of overlapping double layers and their free energy are self-consistently accounted for. In the presence of multivalent salts, increasing surface charge or counterion valency leads to a short-range attraction. We demonstrate that although both overcharging and like-charge attraction are outcomes of ion correlation, there is no causal relationship between them. Our theory also captures the non-monotonic dependence of like-charge attraction on multivalent salt concentration. The reduction of attraction at high salt concentrations could be a contributing factor toward the reentrant stability of charged colloidal suspensions. Our theoretical predictions are consistent with the observations reported in experiments and simulations.

Neural network predicts ion concentration profiles under nanoconfinement

Modeling the ion concentration profile in nanochannel plays an important role in understanding the electrical double layer and electro-osmotic flow. Due to the non-negligible surface interaction and the effect of discrete solvent molecules, molecular dynamics (MD) simulation is often used as an essential tool to study the behavior of ions under nanoconfinement. Despite the accuracy of MD simulation in modeling nanoconfinement systems, it is computationally expensive. In this work, we propose neural network to predict ion concentration profiles in nanochannels with different configurations, including channel widths, ion molarity, and ion types. By modeling the ion concentration profile as a probability distribution, our neural network can serve as a much faster surrogate model for MD simulation with high accuracy. We further demonstrate the superior prediction accuracy of neural network over XGBoost. Finally, we demonstrated that neural network is flexible in predicting ion concentration profiles with different bin sizes. Overall, our deep learning model is a fast, flexible, and accurate surrogate model to predict ion concentration profiles in nanoconfinement.

Electrostatic Correlation Induced Ion Condensation and Charge Inversion in Multivalent Electrolytes

The study of the electrical double layer lies at the heart of colloidal and interfacial science. The standard mean-field Poisson-Boltzmann (PB) theory is incapable of modeling many phenomena originating from ion correlation. An important example is charge inversion or overcharging of electrical double layers in multivalent electrolyte solutions. Existing theories aiming to include correlations cannot capture the non-monotonic dependence of charge inversion on salt concentration because they have not systematically accounted for the inhomogeneous nature of correlations from surface to the bulk and the excluded volume effect of ions and solvent molecules. In this work, we modify the Gaussian renormalized fluctuation theory by including the excluded volume effect to study ion condensation and charge inversion. A boundary layer approach is developed to accurately model the giant difference in ion correlations between the condensed layer near the surface and the diffuse layer outside. The theory is used to study charge inversion in multivalent electrolytes and their mixtures. We predict a surface charge induced formation of a three-dimensional condensed layer, which is necessary but not sufficient for charge inversion. The value of the effective surface potential is found to depend non-monotonically on the bulk salt concentration. Our results also show a non-monotonic reduction in charge inversion in monovalent and multivalent electrolyte mixtures. Our work is the first to qualitatively reproduce experimental and simulation observations and explains the underlying physics.

Like-Charge Attraction at the Nanoscale: Ground-State Correlations and Water Destructuring

Like-charge attraction, driven by ionic correlations, challenges our understanding of electrostatics both in soft and hard matter. For two charged planar surfaces confining counterions and water, we prove that, even at relatively low correlation strength, the relevant physics is the ground-state one, oblivious of fluctuations. Based on this, we derive a simple and accurate interaction pressure that fulfills known exact requirements and can be used as an effective potential. We test this equation against implicit-solvent Monte Carlo simulations and against explicit-solvent simulations of cement and several types of clays. We argue that water destructuring under nanometric confinement drastically reduces dielectric screening, enhancing ionic correlations. Our equation of state at reduced permittivity therefore explains the exotic attractive regime reported for these materials, even in the absence of multivalent counterions.

Surface charge density measurement of a single protein molecule with a controlled orientation by AFM

The spatial distribution of functional groups causes a charge distribution that often has a close relationship with its biofunctions. To understand them of the protein molecules, measurements of the charge distribution under physiological conditions are desired. Atomic force microscopy (AFM) has been utilized to measure the surface charge density by measuring the electric double layer (EDL) force caused by the overlap of the EDLs on the surfaces of the AFM tip and the biomolecule. Here, we demonstrated the surface charge density measurement of a single streptavidin (SA) protein molecule by the three-dimensional force mapping method based on frequency modulation AFM (FM-AFM). The SA has a strong affinity to biotin because of the electrostatic interactions between the molecules. Therefore, the surface charge density measurements of the biotin-binding sites and other surface areas of the molecule have been anticipated. However, the surface charge density of the surfaces other than the biotin-binding side has never been measured. We demonstrate the surface charge density measurement of the top surface of the single SA molecule, which is perpendicular to the biotin-binding sides, with a controlled orientation using DNA origami as a template by FM-AFM in an electrolyte solution. The surface charge density of the top surface of the SA molecule was estimated by fitting the experimental force curves to the Derjaguin-Landau-Verwey-Overbeck theory. We found that the surface charge density of the top surface of the SA molecule is comparable to those reported earlier for the biotin-binding sides of the molecule. We expect that, by using the DNA origami technology, one can control the orientation of a biomolecule attached to the substrate and measure the surface charge density of the specific surface areas of the biomolecule to obtain information that will help us to understand the relationship between their structures and functions.

One-dimensional colloidal model with dielectric inhomogeneity

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.

Theory of cell membrane interaction with glass

There are three regimes of cell membrane interaction with glass: Tight and loose adhesion, separated by repulsion. Explicitly including hydration, this paper evaluates the pressure between the surfaces as functions of distance for ion correlation and ion-screened electrostatics and electromagnetic fluctuations. The results agree with data for tight adhesion energy (0.5-3 vs 0.4-4 mJ/m^{2}), detachment pressure (7.9 vs. 9 MPa), and peak repulsion (3.4-7.5 vs. 5-10 kPa), also matching the repulsion's distance dependence on renormalization by steric pressure mainly from undulations.

Bending elastic modulus of a polymer-doped lyotropic lamellar phase

The effect of inserting a neutral water-soluble adsorbing polymer on the flexibility of amphiphilic bilayers in a lamellar phase is investigated. The L_α system is a stack of charged undulating bilayers composed of sodium dodecyl sulfate (SDS) and octanol separated by aqueous solutions of polyethylene glycol (PEG). The mean bending elastic modulus κ is determined from the quadrupole splittings in the solid state NMR spectra of the perdeuterated octanol chains embedded in the membranes that undergo collective fluctuations. Parameters for describing the membrane behavior (bilayer thickness, elastic compressibility modulus, order parameter) are obtained by supplementing the NMR data with complementary experiments (x-ray scattering), NMR spectral simulations, and theoretical considerations. A fairly complete picture of the membrane rigidity emerges for any location in the lamellar phase thanks to a broad sweep of the lamellar domain by systematically varying the membrane fraction along dilution lines as well as the polymer composition. The most remarkable result is the difference between dilute and semi-dilute regimes. In the dilute PEG solution, no (or slight positive shift) polymer contribution to the rigidity curvature of the layered system is noted within the experimental resolution (≤0.3 k_BT) and κ remains around 2.7 k_BT. In contrast, the membrane rigidity increases steadily upon polymer addition once the crossover concentration c_p* is exceeded, amounting to a 60% increase in κ at polymer concentration 2.5 c_p* in the aqueous interlayers. These results are discussed with regard to the theoretical expectation of membrane rigidification upon irreversible polymer adsorption.

Nanoscale Forces between Basal Mica Surfaces in Dicarboxylic Acid Solutions: Implications for Clay Aggregation in the Presence of Soluble Organic Acids

The stability of organomineral aggregates in soils has a key influence on nutrient cycling, erosion, and soil productivity. Both clay minerals with distinct basal and edge surfaces and organic molecules with reactive functional groups offer rich bonding environments. While clay edges often promote strong inner-sphere bonding of -COOH-laden organics, we explore typically weaker, outer-sphere bonding of such molecules onto basal planes and its significance in organomineral interactions. In this surface force apparatus study, we probed face-specific interactions of negatively charged mica basal surfaces in solutions containing carboxyl-bearing, low-molecular-weight dicarboxylic acids (DAs). Our experiments provide distance-resolved, nanometer-range measurements of forces acting between two (001) mica surfaces and simultaneously probe DA adsorption. We show that background inorganic ions display crucial importance in nanoscale forces acting between basal mica surfaces and in DA adsorption: Na⁺ contributes to strong repulsion and little binding of dicarboxylic anions, while small amounts of Ca²⁺ are sufficient to screen the basal surface charge of mica, facilitate strong adhesion, and enhance dicarboxylic anion adsorption by acting as cationic bridges. Despite reversible and weak adsorption of DAs, we resolve their multilayer binding via assembly of hydrophobic chains in the presence of Ca²⁺, pointing the importance of abundant, less reactive basal clay surfaces in organomineral interactions.

Strong-coupling theory of counterions with hard cores between symmetrically charged walls

By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on pointlike counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two subpopulations, one for each plate, and integrates out one subpopulation to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard-sphere overlap are unavoidable, and thus rule out configurations.

Temperature-Induced Aggregation in Portlandite Suspensions

Temperature is well known to affect the aggregation behavior of colloidal suspensions. This paper elucidates the temperature dependence of the rheology of portlandite (calcium hydroxide: Ca(OH)₂) suspensions that feature a high ionic strength and a pH close to the particle's isoelectric point. In contrast to the viscosity of the suspending medium (saturated solution of Ca(OH)₂ in water), the viscosity of Ca(OH)₂ suspensions is found to increase with elevating temperature. This behavior is shown to arise from the temperature-induced aggregation of polydisperse Ca(OH)₂ particulates because of the diminution of electrostatic repulsive forces with increasing temperature. The temperature dependence of the suspension viscosity is further shown to diminish with increasing particle volume fraction as a result of volumetric crowding and the formation of denser fractal structures in the suspension. Significantly, the temperature-dependent rheological response of suspensions is shown to be strongly affected by the suspending medium's properties, including ionic strength and ion valence, which affect aggregation kinetics. These outcomes provide new insights into aggregation processes that affect the temperature-dependent rheology of portlandite-based and similar suspensions that feature strong charge screening behavior.

Monovalent - divalent cation competition at the muscovite mica surface: Experiment and theory

HYPOTHESIS

Ion adsorption on mineral surfaces depends on several factors, such as the mineral surface structure and the valency, size and hydration of the ion. In order to understand competitive adsorption at mineral surfaces, experimental techniques are required that can probe multiple ionic species at the same time. By comparing adsorption of two different cations, it should be possible to derive the factors governing ion adsorption. Divalent cations are expected to bind stronger to the negatively-charged muscovite surface than monovalent cations.

EXPERIMENTS

Here, the competition between the monovalent Cs⁺ and the divalent Ca²⁺ cation for adsorption at the muscovite mica basal plane was investigated using surface X-ray diffraction. Using an extended surface complexation model, we simultaneously fit the measured cation coverages and net surface charges reported in literature.

FINDINGS

In order to reproduce those complementary data sets, both cation adsorption and anion coadsorption were included in the surface complexation model. Moreover, the intrinsic muscovite surface charge and the maximum of available adsorption sites had to be reduced compared to existing literature values. Competition experiments revealed that the affinity of Cs⁺ for the muscovite surface is larger than the affinity of Ca²⁺, showing that hydration forces are more important than electrostatics.

Forces between solid surfaces in aqueous electrolyte solutions

This review addresses experimental findings obtained with direct force measurements between two similar or dissimilar solid surfaces in aqueous electrolyte solutions. Interpretation of these measurements is mainly put forward in terms of the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). This theory invokes a superposition of attractive van der Waals forces and repulsive double layer forces. DLVO theory is shown to be extremely reliable, even in the case of multivalent ions. However, such a description is only successful, when appropriate surface charge densities, charge regulation characteristics, and ion pairing or complexation equilibria in solution are considered. Deviations from DLVO theory only manifest themselves at distances of typically below few nm. More long-ranged non-DLVO forces can be observed in some situations, particularly, in concentrated electrolyte solutions, in the presence of strongly adsorbed layers, or for hydrophobic surfaces. The latter forces probably originate from patch-charge surface heterogeneities, which can be induced by ion-ion correlation effects, charge fluctuations, or other types of surface heterogeneities.

Attraction between Like-Charged Macroions Mediated by Specific Counterion Configurations

Attraction between like-charged macroions is fundamental to many processes in biology, chemistry, and physics. It also plays an important role in industrial applications such as ion-extraction processes or catalysis. In this work, we report a novel mechanism by which attraction can be realized between spherical macroions at high ionic strength. It consists of specific configurations of two, three, and more counterions that appear between macroions with high statistical probability. The attraction is manifested in a minimum in the potential of mean force between the macroions at short distances. Its depth increases with increasing charge of the macroion, demonstrating that the attraction is electrostatic in nature. It is shown that the implicit solvent model with a distance-dependent dielectric constant can capture both the geometry and thermodynamics of charge-stabilized macroion dimers on the qualitative level. The results obtained for a model colloid with a smooth surface are extrapolated to more realistic systems. Evidence is found that the reported mechanism can be observed in small chemical compounds with encapsulated ions such as fullerenes.

Attractive Interaction between Fully Charged Lipid Bilayers in a Strongly Confined Geometry

We investigate the interaction between highly charged lipid bilayers in the presence of monovalent counterions. Neutron and X-ray reflectivity experiments show that the water layer between like-charged bilayers is thinner than for zwitterionic lipids, demonstrating the existence of counterintuitive electrostatic attractive interaction between them. Such attraction can be explained by taking into account the correlations between counterions within the Strong Coupling limit, which falls beyond the classical Poisson-Boltzmann theory of electrostatics. Our results show the limit of the Strong Coupling continuous theory in a highly confined geometry and are in agreement with a decrease in the water dielectric constant due to a surface charge-induced orientation of water molecules.

Theory of Surface Forces in Multivalent Electrolytes

Aqueous electrolyte solutions containing multivalent ions exhibit various intriguing properties, including attraction between like-charged colloidal particles, which results from strong ion-ion correlations. In contrast, the classical Derjaguin-Landau-Verwey-Overbeek theory of colloidal stability, based on the Poisson-Boltzmann mean-field theory, always predicts a repulsive electrostatic contribution to the disjoining pressure. Here, we formulate a general theory of surface forces, which predicts that the contribution to the disjoining pressure resulting from ion-ion correlations is always attractive and can readily dominate over entropic-induced repulsions for solutions containing multivalent ions, leading to the phenomenon of like-charge attraction. Ion-specific short-range hydration interactions, as well as surface charge regulation, are shown to play an important role at smaller separation distances but do not fundamentally change these trends. The theory is able to predict the experimentally observed strong cohesive forces reported in cement pastes, which result from strong ion-ion correlations involving the divalent calcium ion.

The long-range attraction between hydrophobic macroscopic surfaces

Direct measurements of the long-range strongly attractive force observed between macroscopic hydrophobic surfaces across aqueous solutions are reexamined in light of recent experiments and theoretical developments. The focus is on systems in the absence of submicroscopic bubbles (preexistent or induced) to avoid capillary bridging forces. Other possible interferences to the measurements are also eliminated. The force-distance profiles are obtained directly (no contributions from electrical double layer or hydrodynamics) between symmetric identical hydrophobic surfaces, overall charge-neutral, at the thermodynamic equilibrium and in a quenched state. Therefore in the well-defined geometry of crossed-cylinders, sphere-flat, or sphere-sphere, there is no additional interaction to be considered except the ever-present dispersion forces, negligible at large separations. For the three main categories of substrates rendered hydrophobic, namely surfaces obtained with surfactant monolayers physically adsorbed from solution to deposited ones, and substrates coated with a hydrophobizing agent bonded chemically onto the surface, the interaction energy scales as A exp (-2κD)/2κD at large separations, with measured decay lengths in accord with theoretical predictions, simply being half the Debye screening length, κ^-1/2, at least in non vanishing electrolyte. Taken together with the prefactor A scaling as the ionic strength, the interaction energy is demonstrated to have an electrostatic origin in all the systems. Thanks to our recent SFAX coupling force measurements with x-ray solution scattering under controlled nano-confinement, the microstructuration of the adsorbed film emerges as an essential feature in the molecular mechanism for explaining the observed attraction of larger magnitude than dispersion forces. The adsorption of pairs of positive and negative ions on small islands along the interface, the fluctuation of the surface charge density around a zero mean-value with desorption into or adsorption from the electrolyte solution, the correlations in the local surface ion concentrations along the surfaces, the redistribution of counterions upon intersurface variation, all contribute and are tuned finely by the inhomogeneities and defects present in the hydrophobic layers. It appears that the magnitude of the interacting energy can be described by a single master curve encompassing all the systems.

Cationic Hofmeister Series of Wettability Alteration in Mica-Water-Alkane Systems

The specific interaction of ions with macromolecules and solid-liquid interfaces is of crucial importance to many processes in biochemistry, colloid science, and engineering, as first pointed out by Hofmeister in the context of (de)stabilization of protein solutions. Here, we use contact angle goniometry to demonstrate that the macroscopic contact angle of aqueous chloride salt solutions on mica immersed in ambient alkane increases from near-zero to values exceeding 10°, depending on the type and concentration of cations and pH. Our observations result in a series of increasing ability of cations to induce partial wetting in the order Na⁺, K⁺ < Li⁺ < Rb⁺ < Cs⁺ < Ca²⁺ < Mg²⁺ < Ba²⁺. Complementary atomic force microscopy measurements show that the transition to partial wetting is accompanied by cation adsorption to the mica-electrolyte interface, which leads to charge reversal in the case of divalent cations. In addition to electrostatics, hydration forces seem to play an important role, in particular for the monovalent cations.

The role of water in fault lubrication

The friction between two adjacent tectonic plates under shear loading may dictate seismic activities. To advance the understanding of mechanisms underlying fault strength, we investigate the frictional characteristics of calcite in an aqueous environment. By conducting single-asperity friction experiments using an atomic force microscope, here we show three pathways of energy dissipation with increasing contact stresses: viscous shear of a lubricious solution film at low normal stresses; shear-promoted thermally activated slip, similar to dry friction but influenced by the hydrated ions localized at the interface; and pressure-solution facilitated slip at sufficiently high stresses and slow sliding velocities, which leads to a prominent decrease in friction. It is also shown that the composition of the aqueous solution affects the frictional response. We use this nanoscale evidence to scrutinize the role of brines on fault behavior and argue that pressure solution provides a weakening mechanism of the fault strength at the level of single-asperity contacts.

Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance d. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner strong-coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of d comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

Observation of Dynamic Surfactant Adsorption Facilitated by Divalent Cation Bridging

Dynamic evidence of the mechanism for surfactant adsorption to surfaces of like charge has been observed. Additionally, removal and retention of surfactant molecules on the surface were observed as a function of time. A decrease in surface charge is observed when metal counterions are introduced and is dependent on charge density as well as valency of the metal ion. When surfactant species are also present with the metals, a dramatic increase in surface charge arises. We observed that the rate and quantity of surfactant adsorption can be controlled by the presence of divalent Ca²⁺. Under isotonic conditions the introduction of Ca²⁺ is also easily distinguishable from that of monovalent Na⁺ and provides dynamic evidence of the divalent "cation bridging" phenomenon. Dynamic changes to surface charge are experimentally determined by utilizing current monitoring to quantify the zeta potential in a microfluidic device.

Complex Formations between Surfactants and Polyelectrolytes of the Same Charge on a Water Surface

The mechanism of complex formation between surfactants and polyelectrolytes with the same charge on the water surface was investigated using molecular dynamics simulations and phase-sensitive sum-frequency generation vibrational spectroscopy. Although complex formation between highly charged surfactants and polyelectrolytes of the same charge is generally expected to be prohibited by the electrostatic repulsive force, our study shows that it is possible to form thermodynamically stable complexes when excess ions are present in the solution. We found that anionic partially hydrolyzed polyacrylamide (HPAM) could interact with anionic sodium dodecyl sulfate (SDS) on a water surface in the presence of salts. With excess Na⁺ ions in the solution, the charge screening effect allows HPAM to weakly interact with SDS via hydrogen bonds. In the presence of divalent Ca²⁺ ions, the surfactant and the polymer are strongly coupled by forming Ca²⁺ ion bridges and hydrogen bonds. Our calculation shows that the presence of Ca²⁺ ions creates a steep binding energy of ∼30 kJ/mol near the water surface. These results were qualitatively verified using phase-sensitive sum-frequency generation vibrational spectroscopy.

Bundling in semiflexible polymers: A theoretical overview

Supramolecular assemblies of polymers are key modules to sustain the structure of cells and their function. The main elements of these assemblies are charged semiflexible polymers (polyelectrolytes) generally interacting via a long(er)-range repulsion and a short(er)-range attraction. The most common supramolecular structure formed by these polymers is the bundle. In the present paper, we critically review some recent theoretical and computational advances on the problem of bundle formation, and point a few promising directions for future work.

The effect of multivalent cations and Tau on paclitaxel-stabilized microtubule assembly, disassembly, and structure

In this review we describe recent studies directed at understanding the formation of novel nanoscale assemblies in biological materials systems. In particular, we focus on the effects of multivalent cations, and separately, of microtubule-associated protein (MAP) Tau, on microtubule (MT) ordering (bundling), MT disassembly, and MT structure. Counter-ion directed bundling of paclitaxel-stabilized MTs is a model electrostatic system, which parallels efforts to understand MT bundling by intrinsically disordered proteins (typically biological polyampholytes) expressed in neurons. We describe studies, which reveal an unexpected transition from tightly spaced MT bundles to loose bundles consisting of strings of MTs as the valence of the cationic counter-ion decreases from Z=3 to Z=2. This transition is not predicted by any current theories of polyelectrolytes. Notably, studies of a larger series of divalent counter-ions reveal strong ion specific effects. Divalent counter-ions may either bundle or depolymerize paclitaxel-stabilized MTs. The ion concentration required for depolymerization decreases with increasing atomic number. In a more biologically related system we review synchrotron small angle x-ray scattering (SAXS) studies on the effect of the Tau on the structure of paclitaxel-stabilized MTs. The electrostatic binding of MAP Tau isoforms leads to an increase in the average radius of microtubules with increasing Tau coverage (i.e. a re-distribution of protofilament numbers in MTs). Finally, inspired by MTs as model nanotubes, we briefly describe other more robust lipid-based cylindrical nanostructures, which may have technological applications, for example, in drug encapsulation and delivery.

Ionic Behavior in Highly Concentrated Aqueous Solutions Nanoconfined between Discretely Charged Silicon Surfaces

Through molecular dynamics simulations considering thermal vibration of surface atoms, ionic behaviors in concentrated NaCl solutions confined between discretely charged silicon surfaces have been investigated. The electric double layer structure was found to be sensitive to the density and distribution of surface charges. Due to the discreteness of the surface charge, a slight charge inversion appeared which depended on the surface charge density, bulk concentration, and confinement. In the nanoconfined NaCl solutions concentrated from 0.2 to 4.0 M, the locations of accumulation layers for Na(+) and Cl(-) ions remained stable, but their peak values increased. The higher the concentration was, the more obvious the charge inversion appeared. In 4.0 M NaCl solution, Na(+) and Cl(-) ions show obvious alternating layered distributions which may correspond to the solidification found in experiments. By changing surface separation, the confinement had a large effect on the ionic distribution. As both surfaces approached each other, many ions and water molecules were squeezed out of the confined space. Two adjacent layers in ion or water distribution profiles can be forced closer to each other and merge together. From ionic hydration analysis, the coordination number of Na(+) ions in highly confined space was much lower than that in the bulk.

Strong-coupling electrostatic theory of polymer counterions close to planar charges

Strong-coupling phenomena, such as like-charge macroion attraction, opposite-charged macroion repulsion, charge renormalization, and charge inversion, are known to be mediated by multivalent counterions. Most theories treat the counterions as point charges and describe the system by a single coupling parameter that measures the strength of the Coulomb interactions. In many biological systems, the counterions are highly charged and have finite sizes and can be well-described by polyelectrolytes. The shapes and orientations of these polymer counterions play a major role in the thermodynamics of these systems. In this work we apply a field-theoretic description in the strong-coupling regime to the polymer counterions in the presence of a fixed charge distribution. We work out the special cases of rodlike polymer counterions confined by one, and two charged walls, respectively. The effects of the geometry of the rodlike counterions and the excluded volume of the walls on the density, pressure, and free energy of the rodlike counterions are discussed.

Ion adsorption-induced wetting transition in oil-water-mineral systems

The relative wettability of oil and water on solid surfaces is generally governed by a complex competition of molecular interaction forces acting in such three-phase systems. Herein, we experimentally demonstrate how the adsorption of in nature abundant divalent Ca(2+) cations to solid-liquid interfaces induces a macroscopic wetting transition from finite contact angles (≈ 10°) with to near-zero contact angles without divalent cations. We developed a quantitative model based on DLVO theory to demonstrate that this transition, which is observed on model clay surfaces, mica, but not on silica surfaces nor for monovalent K(+) and Na(+) cations is driven by charge reversal of the solid-liquid interface. Small amounts of a polar hydrocarbon, stearic acid, added to the ambient decane synergistically enhance the effect and lead to water contact angles up to 70° in the presence of Ca(2+). Our results imply that it is the removal of divalent cations that makes reservoir rocks more hydrophilic, suggesting a generalizable strategy to control wettability and an explanation for the success of so-called low salinity water flooding, a recent enhanced oil recovery technology.

On the theoretical description of weakly charged surfaces

It is widely accepted that the Poisson-Boltzmann (PB) theory provides a valid description for charged surfaces in the so-called weak coupling limit. Here, we show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. In the presence of dielectric discontinuity, there is no limiting condition for which the PB theory is valid.

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.

Effects of image charges on double layer structure and forces

The study of the electrical double layer lies at the heart of soft matter physics and biophysics. Here, we address the effects of the image charges on the double layer structure and forces. For electrolyte solutions between two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. In comparison to a 1:1 electrolyte solution, both the attractive and the repulsive parts of the interaction are stronger for the 2:1 electrolyte solution. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like-charge attraction and charge inversion. These results are in stark contrast with predictions from the Poisson-Boltzmann theory.

Salt dependent stability of stearic acid Langmuir-Blodgett films exposed to aqueous electrolytes

We use contact angle goniometry, imaging ellipsometry, and atomic force microscopy to study the stability and wettability of Langmuir-Blodgett (LB) monolayers of stearic acid on silica substrates, upon drying and exposure to aqueous solutions of varying salinity. The influences of Ca(2+) and Na(+) ions are compared by varying their concentrations, both in the subphase before the LB transfer, and in the droplets to which the dried LB layers are exposed. Ca(2+) ions in the subphase are found to enhance the stability, leading to contact angles up to 100°, as compared to less than 5° for Na(+). Consistent with the macroscopic wettability, AFM images show almost intact films with few holes exposing bare substrate when prepared in the presence of Ca(2+), while subphases containing Na(+) result in large areas of bare substrate after exposure to aqueous drops. The observations on varying the composition of the droplets corroborate the stabilizing effect of Ca(2+). We attribute these findings to the cation-bridging ability of Ca(2+) ions, which can bind the negatively charged stearate groups to the negatively charged substrates. We discuss the relevance of our findings in the context of enhanced oil recovery.

Tunable soft structure in charged fluids confined by dielectric interfaces

Fluids of charged particles act as the supporting medium for chemical reactions and physical, dynamical, and biological processes. The local structure in an electrolytic background is deformed by micro- and nanoscopic polarizable objects. Vice versa, the forces between the objects are regulated by the cohesive properties of the background. We study here the range and strength of these forces and the microscopic origin from which they emerge. We find the forces to be sensitively dependent on the material properties of the charged fluid and the immersed solutes. The induced interactions can be varied over decades, offering high tunability and aided by accurate theory, control in experiments and applications. To distinguish correlational effects from simple ionic screening, we describe electrolyte-induced forces between neutral objects. The interplay of thermal motion, short-range repulsions, and electrostatic forces is responsible for a soft structure in the fluid. This structure changes near polarizable interfaces and causes diverse attractions between confining walls that seem well-exploited by microbiological systems. For parameters that correspond to monovalent electrolytes in biologically and technologically relevant aqueous environments, we find induced forces between nanoscopic areas of the order of piconewtons over a few nanometers.

Inversion of membrane surface charge by trivalent cations probed with a cation-selective channel

We demonstrate that the cation-selective channel formed by gramicidin A can be used as a reliable sensor for studying the multivalent ion accumulation at the surfaces of charged lipid membranes and the "charge inversion" phenomenon. In asymmetrically charged membranes with the individual leaflets formed from pure negative and positive lipids bathed by 0.1 M CsCl solutions the channel exhibits current rectification, which is comparable to that of a typical n/p semiconductor diode. We show that even at these highly asymmetrical conditions the channel conductance can be satisfactorily described by the electrodiffusion equation in the constant field approximation but, due to predictable limitations, only when the applied voltages do not exceed 50 mV. Analysis of the changes in the voltage-dependent channel conductance upon addition of trivalent cations allows us to gauge their interactions with the membrane surface. The inversion of the sign of the effective surface charge takes place at the concentrations, which correlate with the cation size. Specifically, these concentrations are close to 0.05 mM for lanthanum, 0.25 mM for hexaamminecobalt, and 4 mM for spermidine.