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Dielectric interfaces are crucial to the behavior of charged membranes, from graphene to synthetic and biological lipid bilayers. Understanding electrolyte behavior near these interfaces remains a challenge, especially in the case of rough dielectric surfaces. A lack of analytical solutions consigns this problem to numerical treatments. We report an analytic method for determining electrostatic potentials near curved dielectric membranes in a two-dimensional periodic "slab" geometry using a periodic summation of Green's functions. This method is amenable to simulating arbitrary groups of charges near surfaces with two-dimensional deformations. We concentrate on one-dimensional undulations. We show that increasing membrane undulation increases the asymmetry of interfacial charge distributions due to preferential ionic repulsion from troughs. In the limit of thick membranes, we recover results mimicking those for electrolytes near a single interface. Our work demonstrates that rough surfaces generate charge patterns in electrolytes of charged molecules or mixed-valence ions. [ABSTRACT FROM AUTHOR]

Understanding electrostatic interactions among dielectric bodies in the atmosphere and aerosols is central to controlling their aggregation. Polarization effects, which are frequently ignored, are crucial to determine interactions when geometrical anisotropies are present due to surface-induced charge segregation. Here, we adopt a direct integral formulation that accounts for the problem of charged dielectric bodies immersed in a continuum media to explore particle aggregation via geometrical tuning. We show that by breaking the structural symmetry and modifying the close-contact surface between particles of equal charge, it is possible to obtain attractive regimes at short and long distances. We evaluate the electrostatic forces and energy of a set of dimers and trimers composed of spheres, oblates, and prolates in a vacuum, where no counter-ions are present, to construct a phase diagram with the conditions required to form stable aggregates as a function of the geometrical anisotropy. We found that it is possible to direct the aggregation (or dispersion) of two and three positive dielectric particles by adjusting their geometry and controlling the contact surface among them. Our results give insight into a way to control the aggregation of dielectric systems and offer a prospect for directing the assembly of complex particle structures. [ABSTRACT FROM AUTHOR]

Mesoscopic clusters composed of oppositely charged particles are ubiquitous in synthetic and biological soft materials. The effective interaction between these clusters is influenced by their polarizability, that is, the ability of their constituent charges to re-arrange in response to an external electrical field. Here, using coarse-grained simulations, we show that the polarizability of electrically neutral ionic clusters decreases as the number of constituent charges increases and/or their Coulombic interaction strength increases for various ion valencies, ion densities, and degrees of cluster boundary hardness. For clusters of random ionomers and their counterions, their polarizability is shown to depend on the number of polymer chains. The variation of the cluster polarizability with the cluster size indicates that throughout the assembly, the induced-dipole interactions between the clusters may be reduced substantially as they acquire more charges while maintaining zero net charge. Under certain conditions, the induced-dipole interactions may become repulsive, as inferred from our simulations with a polarizable solvent. As a result, the dipole-induced related interactions can serve as a counterbalancing force that contributes to the self-limiting aggregation of charge-containing assemblies. [ABSTRACT FROM AUTHOR]

In solid–liquid, or liquid–liquid, interfaces with dielectric contrast, charged particles interact with the induced polarization charge of the interface. These interactions contribute to an effective self-energy of the bulk ions and mediate ion–ion interactions. For flat interfaces, the self-energy and the mediated interactions are neatly constructed by the image charge method. For other geometries, explicit results are scarce and the problem must be treated via approximations or direct computation. The case of interfaces with roughness is of great practical importance. This article provides analytical results, valid to first-order in perturbation theory, for the self-energy of particles near rough substrates. Explicit formulas are provided for the case of a sinusoidal deformation of a flat surface. Generic deformations can be treated by superposition. In addition to results for the self-energy, the surface polarization charge is presented as a quadrature. The interaction between an ion and the deformed surface is modified by the change in relative distance as well as by the local curvature of the surface. Solid walls, with a lower dielectric constant than the liquid, repel all ions. We show that the repulsion is reduced by local convexity and enhanced by concavity; dimples are more repulsive than pimples. [ABSTRACT FROM AUTHOR]

The transport of polyelectrolytes confined by oppositely charged surfaces and driven by a constant electric field is of interest in studies of DNA separation according to size. Using molecular dynamics simulations that include the surface polarization effect, we find that the mobilities of the polyelectrolytes and their counterions change non-monotonically with the confinement surface charge density. For an optimum value of the confinement charge density, efficient separation of polyelectrolytes can be achieved over a wide range of polyelectrolyte charge due to the differential friction imparted by oppositely charged confinement on the polyelectrolyte chains. Furthermore, by altering the placement of the charged confinement counterions, enhanced polyelectrolyte separation can be achieved by utilizing the surface polarization effect due to dielectric mismatch between the media inside and outside the confinement. [ABSTRACT FROM AUTHOR]

The ion distribution of electrolytes near interfaces with dielectric contrast has important consequences for electrochemical processes and many other applications. To date, most studies of such systems have focused on geometrically simple interfaces, for which dielectric effects are analytically solvable or computationally tractable. However, all real surfaces display nontrivial structure at the nanoscale and have, in particular, a nonuniform local curvature. Using a recently developed, highly efficient computational method, we investigate the effect of surface geometry on ion distribution and interface polarization. We consider an asymmetric 2:1 electrolyte bounded by a sinusoidally deformed solid surface. We demonstrate that even when the surface is neutral, the electrolyte acquires a nonuniform ion density profile near the surface. This profile is asymmetric and leads to an effective charging of the surface. We furthermore show that the induced charge is modulated by the local curvature. The effective charge is opposite in sign to the multivalent ions and is larger in concave regions of the surface. [ABSTRACT FROM AUTHOR]

In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it is important to take into account the spatial dependence of the permittivity of the medium. However, due to the ensuing theoretical and computational challenges, this inhomogeneous dielectric response of the medium is often ignored or excessively simplified. We develop a variational formulation of electrostatics to accurately investigate systems that exhibit this inhomogeneous dielectric response. Our formulation is based on a true energy functional of the polarization charge density. The defining characteristic of a true energy functional is that at its minimum it evaluates to the actual value of the energy; this is a feature not found in many commonly used electrostatic functionals. We explore in detail the charged systems that exhibit sharp discontinuous change in dielectric permittivity, and we show that for this case our functional reduces to a functional of only the surface polarization charge density. We apply this reduced functional to study model problems for which analytical solutions are well known. We demonstrate, in addition, that the functional has many properties that make it ideal for use in molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

By combining molecular dynamics simulations and analytical arguments, we investigate the elastic properties of charged lipid bilayers. We show that electrostatic interactions between the head groups can lead to solidification of the lipid bilayer that would otherwise be in a liquid state if the charges were absent. All elastic parameters of the bilayer such as the bending rigidity κ and the two-dimensional bulk modulus λ and Young's modulus Y are found to depend on the values of the charges assigned to the lipid head groups. To extract κ and λ, we fit the molecular dynamics data to a standard elastic model for lipid bilayers. Moreover, we analytically obtain the dependence of the Young modulus Y on the relative strengths of electrostatic and van der Waals interactions in the zero temperature limit. [ABSTRACT FROM AUTHOR]

Motivated by recent experimental findings, we present here a minimal analytical model illustrating that the steric interactions among the ionic components can provide a simple, generic mechanism for like-charge crystallization in prototypical nanoparticle systems with counterions in polar solvents. In particular, the underlying steric interactions among these ionic components arise from the structural organization of the polar solvent molecules surrounding these ions as molecular dipole moments that may cooperatively enhance or counteract existing entropic depletion and electrostatic forces. Phenomenologically capturing these steric effects, we assume only the existence of a short-range pairwise Gaussian interaction, which has already been employed usefully for nanoparticles with hydrophillic surfaces or grafted-polymer coatings, among these ionic components (nanoparticles and counterions). The corresponding Gaussian interaction parameters characterize tunable interaction strengths. Making use of an analytically obtained effective pairwise potential between two nanoparticles, upon the contraction of counterions, we derive phase diagrams for nanoparticle systems of varying charge- and size-ratios as a function of particle densities, and observe crystallization for a range of parameters. We further demonstrate that our minimal model is compatible with the phenomenon of charge asymmetry. [ABSTRACT FROM AUTHOR]

We investigate the equilibrium properties and the underlying dynamics of emulsions formed in asymmetric A-B copolymers in matrices of immiscible B and C molecular fluids using coarse-grained molecular dynamics simulations. The emulsions are generated by introducing net attractions among the A units of the copolymers and the C molecules. They coexist with an absorbed copolymer monolayer. We determine the interfacial properties as the emulsions are forming. In general, highly asymmetric copolymers self-assemble within the B-matrix phase into swollen micelles; the cores of which are composed of C-component material. Less asymmetric copolymers, however, after initially budding and eventually fissioning from the interfacial copolymer monolayer, generate emulsified “inverse swollen micelles” within the C-matrix phase. These stable inverse (crew-cut) swollen micelles, which form under the inward bending of the saturated or oversaturated interfaces toward the longer B-block due to the attraction between the A and C units, can encapsulate large amounts of B-matrix component in their cores. This monolayer collapse mechanism can be exploited to generate nanoreactors or containers that enhance the delivery of molecular components into immiscible molecular fluid environments. [ABSTRACT FROM AUTHOR]

The swelling of polyelectrolyte (PE) gels by 1:1 and 2:1 salts is studied via osmotic ensemble Monte Carlo simulations at constant osmotic pressure and electrolyte chemical potential of a reservoir phase in equilibrium with a model PE network. Large molecular weight gels exhibit a remarkable swelling response to small changes in 2:1 salt concentration. Gel collapse is accompanied by the formation of a previously unknown heterogeneous nanostructure, predicted by theory and observed in simulations, consisting of regions dense in monomers coexisting with regions rich in mono- and divalent ions. [ABSTRACT FROM AUTHOR]

We study the equilibrium thermodynamics between two ternary ionic systems in immiscible solvents characterized by different dielectric constants. We consider system geometries wherein the two phases of immiscible solvents occupy, respectively, semi-infinite regions of space separated by neutral and charged planar interfaces. Specifically we analyze the case where the ternary system is composed of a pair of symmetric ions plus a minority charged component of high valence. We describe the system by means of a nonlinear mean-field theory. We first obtain exact analytical solutions for the electrostatic potentials, as well as density profiles for a symmetric binary system, and then extend these results to the ternary case using the perturbation theory. We show that the corresponding adsorption and depletion of multivalent macroions at the interface are highly enhanced when compared with the monovalent case. [ABSTRACT FROM AUTHOR]

The structure of soft matter systems at interfaces is of utmost importance in the fields of nanopatterning and self-assembly. It has been shown that lamellar and hexagonal patterns can form on interfaces, for a wide variety of systems. The asphericity of charged domains is considered here for different strengths of the electrostatics, determined by the interface media, relative to the short range van der Waals interactions between the molecular components. The phase behavior of the surface structure is explored by using molecular dynamics simulations, including some dynamical aspects of the interaction between neighboring domains, using the Lindemann criterion [F. Lindemann, Z. Phys. 11, 609 (1910)]. The charge ratio of the electrostatic components influences the shape of the domains, as well as the degree of local order in the interdomain structure. [ABSTRACT FROM AUTHOR]

The microphase separation transition for asymmetric triblock and (A–B)m star copolymer melts is investigated following a mean-field approach proposed by Leibler for diblock copolymer melts. Continuous transitions are found in all triblock architectures and in stars for any m at some composition fc. The phase diagram for the equilibrium morphologies is notably altered by varying the architecture of triblock copolymers. [ABSTRACT FROM AUTHOR]

Surface  energy is a fundamental material property that determines important functions such as catalytic, sensing, and imaging properties. Over the past century, various experimental studies and models including the broken bond theory and Wulff construction have been developed to analyze surface  free energies. However, it remains a challenge to measure or predict thermal fluctuation effects on surface  energies. In particular, crystals of functionalized building blocks, such as self-assembling proteins and DNA-functionalized nanoparticles, assembled via the specific surface interactions of the building blocks, are highly sensitive to thermal fluctuations. In the case of DNA-functionalized nanoparticles, it has been shown that the crystals are formed as a result of thermally active hybridizations. We show here that the surface  energy along different planes can be obtained from the ratio of hybridization events. The surface  energy fluctuations in these systems are shown to bear a nearly linear correlation with the fluctuations in DNA hybridization events in the bulk. We further demonstrate that short DNA chains and high DNA loading increase the volume density of the DNA sticky ends. The relationship between thermally active hybridizations and surface  energy found here can be used to aid the design of single crystals of functionalized colloids with active surface groups.

The behavior of ions in liquids confined between macromolecules determines the outcome of many nanoscale assembly processes in synthetic and biological materials such as colloidal dispersions, emulsions, hydrogels, DNA, cell membranes, and proteins. Theoretically, the macromolecule-liquid boundary is often modeled as a dielectric interface and an important quantity of interest is the ionic structure in a liquid confined between two such interfaces. The knowledge gleaned from the study of ionic structure in such models can be useful in several industrial applications, such as in the design of double-layer supercapacitors for energy storage and in the extraction of metal ions from wastewater. In this article, we compute the ionic structure in a model system of electrolyte confined by two planar dielectric interfaces using molecular dynamics simulations and liquid state theory. We explore the effects of high electrolyte concentrations, multivalent ions, dielectric contrasts, and external electric field on the ionic distributions. We observe the presence of non-monotonic ionic density profiles leading to a layered structure in the fluid which is attributed to the competition between electrostatic and steric (entropic) interactions. We find that thermal forces that arise from symmetry breaking at the interfaces can have a profound effect on the ionic structure and can oftentimes overwhelm the influence of the dielectric discontinuity. The combined effect of ionic correlations and inhomogeneous dielectric permittivity significantly changes the character of the effective interaction between the two interfaces.

Polymer mixtures such as blends or block copolymers are of great interest in energy applications and functional materials, and often, one or more of these species contain charges. The traditional fashion in which such materials are studied uses Self-Consistent Field Theory (SCFT) methods that incorporate electrostatics using Poisson-Boltzmann (PB) theory. We adapt a new and rigorous approach that does not rely on the mean-field assumptions inherent in the PB theory and instead uses Liquid State (LS) integral equation theory to articulate charge correlations that are completely neglected in PB. We use this theory to calculate phase diagrams for both blends and block copolyelectrolytes using SCFT-LS and demonstrate how their phase behavior is highly dependent on chain length, charge fraction, charge size, and the strength of Coulombic interactions. Beyond providing phase behavior of blends and block copolyelectrolytes, we can use this theory to investigate the interfacial properties such as surface tension and block copolyelectrolyte lamellar spacing. Lamellar spacing provides a way to directly compare the SCFT-LS theory to the results of experiments. SCFT-LS will provide conceptual and mathematical clarification of the role of charge correlations in these systems and aid in the design of materials based on charge polymers.

A closure for the Ornstein-Zernike equation is presented, applicable for fluids of charged, hard spheres. From an exact, but intractable closure, we derive the radial distribution function of nonlinearized Debye-Hückel theory by subsequent approximations, and use the information to formulate a new closure by an extension of the mean spherical approximation. The radial distribution functions of the new closure, coined Debye-Hückel-extended mean spherical approximation, are in excellent agreement with those resulting from the hyper-netted chain approximation and molecular dynamics simulations, in the regime where the latter are applicable, except for moderately dilute systems at low temperatures where the structure agrees at most qualitatively. The method is numerically more efficient, and more important, convergent in the entire temperature-density plane. We demonstrate that the method is accurate under many conditions for the determination of the structural and thermodynamic properties of homogeneous, symmetric hard-sphere Coulomb systems, and estimate it to be a valuable basis for the formulation of density functional theories for inhomogeneous or highly asymmetric systems.

We investigate the equilibrium properties and the underlying dynamics of emulsions formed in asymmetric A-B copolymers in matrices of immiscible B and C molecular fluids using coarse-grained molecular dynamics simulations. The emulsions are generated by introducing net attractions among the A units of the copolymers and the C molecules. They coexist with an absorbed copolymer monolayer. We determine the interfacial properties as the emulsions are forming. In general, highly asymmetric copolymers self-assemble within the B-matrix phase into swollen micelles; the cores of which are composed of C-component material. Less asymmetric copolymers, however, after initially budding and eventually fissioning from the interfacial copolymer monolayer, generate emulsified "inverse swollen micelles" within the C-matrix phase. These stable inverse (crew-cut) swollen micelles, which form under the inward bending of the saturated or oversaturated interfaces toward the longer B-block due to the attraction between the A and C units, can encapsulate large amounts of B-matrix component in their cores. This monolayer collapse mechanism can be exploited to generate nanoreactors or containers that enhance the delivery of molecular components into immiscible molecular fluid environments.

We study ion condensation on a patterned surface with stripes of alternating charge. The competition between adsorbed ion-ion and adsorbed ion-surface interactions leads to the formation of different strongly correlated structures of condensed ions in the low-temperature limit (LTL). We consider two types of arrangements which have lowest energy in the LTL: (1) ions adsorbed onto the stripe center lines and (2) arrays of dipoles at the interfaces between charged domains. We determine the preferred arrangement as a function of surface charge density, the chemical potential of the ions in the surrounding medium, and the geometric parameters of the system. We determine the conditions for the appearance of more complex ionic patterns by considering simple perturbations of the stripe-centered and dipolar array structures.

We propose a mean-field analytical model to account for the observed asymmetry in the ability to form long-range attraction by the negatively charged colloidal particles and not their equivalently charged positive counterpart. We conjecture that this asymmetry is due to solvation effects, and we phenomenologically capture its physics by considering the relative strength of this water-induced short-range repulsion between the different charge species. We then apply our model to the colloidal system of negatively charged disks that are neutralized by a sea of counterions and strongly absorbed to an interface in a compressible binary system. We demonstrate the resulting coexistence between a dilute isotropic ionic phase and a condensed hexagonal lattice phase as a function of density and interaction strength.

A binary mixture of oppositely charged components confined to a plane such as cationic and anionic lipid bilayers may exhibit local segregation. The relative strengths of the net short range interactions, which favors macroscopic segregation, and the long range electrostatic interactions, which favors mixing, determine the length scale of the finite size or microphase segregation. The free energy of the system can be examined analytically in two separate regimes, when considering small density fluctuations at high temperatures and when considering the periodic ordering of the system at low temperatures [F. J. Solis, S. I. Stupp, and M. Olvera de la Cruz, J. Chem. Phys. 122, 054905 (2005)]. A simple molecular dynamics simulation of oppositely charged monomers, interacting with a short range Lennard-Jones potential and confined to a two dimensional plane, is examined at different strengths of short and long range interactions. The system exhibits well-defined domains that can be characterized by their periodic length scale as well as the orientational ordering of their interfaces. By adding salt, the ordering of the domains disappears and the mixture macroscopically phase segregates in agreement with analytical predictions.

The bulk and interfacial properties of ternary mixtures with asymmetric amphiphiles (A2B8) in A2 and B2 matrices and in A2 and B10 matrices are investigated by the dissipative particle dynamics type of molecular-dynamics simulations. The monomer concentrations of A2B8(phiA2B8) studied are below the critical micelle concentration (phiA2B8(cmc)) for the formation of micelles in the presence of an adsorbed amphiphilic monolayer at the interface. Macrophase separation from the mixed phase to the segregated state with A-rich and B-rich coexisting phases and the segregation of A2B8 at the interface are thermodynamically gradual but are accompanied by a pronounced stretching and orientation of the constituent chains. The segregation of A2B8 at the interface broadens the interfacial region and reduces the interfacial tension. The chain conformation of the asymmetric amphiphilic molecules and the interfacial properties are dominated by the majority block in the amphiphilic chain and dependent on the composition of the matrix in contact with the majority block. In the A2 and B2 matrices, the B8 blocks in A2B8 chains at the interface resemble a wet brush swollen by short B2 chains. Swelling is responsible for the pronounced stretching and orienting of the amphiphilic chains and the reduced interfacial amphiphile enrichment. At the same interfacial amphiphile excess, however, swollen amphiphiles are more efficient in reducing the interfacial tension than nonswollen amphiphiles.

We study phase separation in symmetric solutions of weakly charged flexible chains of opposite sign. Precipitation is caused by effective attractions due to charge fluctuations and by short-range attractions between monomers. The contribution from charge fluctuations is computed within the random phase approximation (RPA), which takes into account the connectivity of charges in the polyions. The impenetrability of the ions is accounted for by using a modified Coulomb potential in the RPA. In good solvent conditions the precipitate monotonically swells and eventually dissolves upon addition of salt. However, near the theta-solvent condition, but still in the good solvent, the precipitate can be stable at any salt concentration. Moreover, the density of the precipitate after initial decrease can increase with addition of salt. This effect is a result of redistribution of salt between the precipitate and the supernatant, which is due to an interplay of electrostatic and hardcore interactions. For not too weakly charged polyions the precipitate properties become strongly dependent on temperature even in good solvent conditions., ((c) 2004 American Institute of Physics)