Controlling the structure and mixing properties of anisotropic active particles with the direction of self-propulsion.

In the search for advanced materials active particles could offer unique structural and functional properties, with tunable time-dependent characteristics. We demonstrate here that the direction of self-propulsion, relative to the particle orientation, may be as influential for the phase behavior as the pair interactions are for passive particles, and enable dynamic properties that are not available to passive systems. We perform simulations on ensembles of self-propelled squares, and find that squares that self-propel in the direction perpendicular to a side rapidly reach a steady state with a characteristic cluster distribution, positional order, and well-defined diffusion constant. After tuning the direction towards a corner, the particles form large and dense clusters that show a transient collective motion, and display remarkable fluctuations over long time scales, with a distinct periodicity. Clusters of these particles appear unstable beyond a critical size, and susceptible to a catastrophic disintegration. Directionality is found to effect equally sharp transitions in the mixing properties of active squares and passive squares, and the behavior of the passive ensemble. We relate directionality to the collision dynamics and the resulting reaction network of clusters, evolved by a Kinetic Monte Carlo algorithm, to correlate propulsion direction to the observed phase behavior. Understanding this behavior could offer new design rules for programmable materials, and grant further insights in the dynamic processes that nature employs for self-assembly.

Solubility and interfacial segregation of salts in ternary polyelectrolyte blends.

Solid Polymer Electrolytes (SPEs) consisting of ternary blends of charged polymer, neutral polymer, and plasticizer or salt have received much interest for their low volatility and high flexibility of polymers with ion-selective conductivity of the charge-carrying backbone. It has been shown that in these polyelectrolyte blends, where the dielectric constant is relatively low, ionic correlations can significantly influence the miscibility, inducing phase separation even at negative values of χN. Here we present a comprehensive study of phase behavior and interfacial segregation upon the addition of a tertiary component in blends of charged and neutral homopolymers. Using a hybrid of self-consistent field and liquid state theories (SCFT-LS), we investigate the bulk miscibility and the distribution of ions across the interface, looking at interfacial adsorption and selectivity of the minority component. We demonstrate that the competition between ionic correlations and ion entropy induces complex charge-dependent selectivity that can be tuned by the value of Γ, the ionic correlation strength. We show that charge interactions can have a pronounced effect on the interfacial width and tension, especially at low χN.

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.

Electrostatic control of block copolymer morphology.

Energy storage is at present one of the foremost issues society faces. However, material challenges now serve as bottlenecks in technological progress. Lithium-ion batteries are the current gold standard to meet energy storage needs; however, they are limited owing to the inherent instability of liquid electrolytes. Block copolymers can self-assemble into nanostructures that simultaneously facilitate ion transport and provide mechanical stability. The ions themselves have a profound, yet previously unpredictable, effect on how these nanostructures assemble and thus the efficiency of ion transport. Here we demonstrate that varying the charge of a block copolymer is a powerful mechanism to predictably tune nanostructures. In particular, we demonstrate that highly asymmetric charge cohesion effects can induce the formation of nanostructures that are inaccessible to conventional uncharged block copolymers, including percolated phases desired for ion transport. This vastly expands the design space for block copolymer materials and is informative for the versatile design of battery electrolyte materials.

Ionic structure in liquids confined by dielectric interfaces.

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.

Theory of melt polyelectrolyte blends and block copolymers: phase behavior, surface tension, and microphase periodicity.

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.

Interfacial behavior in polyelectrolyte blends: hybrid liquid-state integral equation and self-consistent field theory study.

Polyelectrolytes and electrolyte solutions are known to demonstrate a rich array of phase behaviors due to the effects of long-ranged interactions inherent in Coulombic attractions and repulsions. While there is a wealth of literature examining these materials to provide some physical insight into their thermodynamics, all of these methods make strong approximations with regards to the nature of the ionic component. In this investigation we develop a hybrid liquid-state integral equation and self-consistent field theory numerical theory, and systematically demonstrate the ramifications on local ion structure on the overall thermodynamics of segregated polymer blends. We show effects on phase separation such as suppression due to hard sphere interactions and enhancement due to ion cohesion that are not described using traditional Poisson-Boltzmann mean-field theory.

A practical integral equation for the structure and thermodynamics of hard sphere Coulomb fluids.

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.

Before the breach: Interactions between colloidal particles and liquid interfaces at nanoscale separations.

Particles bound to fluid-fluid interfaces are widely used to study self-assembly and to make materials such as Pickering emulsions. In both contexts, the lateral interactions between such particles have been studied extensively. However, much less is known about the normal interactions between a particle and the interface prior to contact. We use digital holographic microscopy to measure the dynamics of individual micrometer-size colloidal particles as they approach an interface between an aqueous phase and oil. Our measurements show that the interaction between the particle and interface changes nonmonotonically as a function of salt concentration, from repulsive at 1 mM to attractive at tens of mM to negligible at 100 mM and attractive again above 200 mM. In the attractive regimes, the particles can bind to the interface at nanometer-scale separation without breaching it. Classical Derjaguin-Landau-Verwey-Overbeek theory does not explain these observations. However, a theory that accounts for nonlinear screening and correlations between the ions does predict the nonmonotonic dependence on salt concentration and produces trajectories that agree with experimental data. We further show that the normal interactions determine the lateral interactions between particles that are bound to the interface. Because the interactions we observe occur at salt concentrations used to make Pickering emulsions and other particle-laden interfaces, our results suggest that particle arrangements at the interface are likely out of equilibrium on experimental timescales.

Electrolyte-Mediated Assembly of Charged Nanoparticles.

Solutions at high salt concentrations are used to crystallize or segregate charged colloids, including proteins and polyelectrolytes via a complex mechanism referred to as "salting-out". Here, we combine small-angle X-ray scattering (SAXS), molecular dynamics (MD) simulations, and liquid-state theory to show that salting-out is a long-range interaction, which is controlled by electrolyte concentration and colloid charge density. As a model system, we analyze Au nanoparticles coated with noncomplementary DNA designed to prevent interparticle assembly via Watson-Crick hybridization. SAXS shows that these highly charged nanoparticles undergo "gas" to face-centered cubic (FCC) to "glass-like" transitions with increasing NaCl or CaCl2 concentration. MD simulations reveal that the crystallization is concomitant with interparticle interactions changing from purely repulsive to a "long-range potential well" condition. Liquid-state theory explains this attraction as a sum of cohesive and depletion forces that originate from the interelectrolyte ion and electrolyte-ion-nanoparticle positional correlations. Our work provides fundamental insights into the effect of ionic correlations in the salting-out mechanism and suggests new routes for the crystallization of colloids and proteins using concentrated salts.

Ion Correlation-Induced Phase Separation in Polyelectrolyte Blends.

Inhomogeneous polyelectrolyte materials have been of both longstanding and recent interest; polymer blends exhibit technologically advantageous properties for adhesives and fuel cell membranes and serve as an ideal model system to study more complicated behaviors in polyelectrolyte materials. However, the physics governing the phase behavior of polyelectrolyte blends remains poorly understood. Traditional self-consistent field theory (SCFT) can include Coulombic interactions that arise in polyelectrolytes but can only reproduce Poisson-Boltzmann behavior or perturbations thereof due to the mean-field nature of the SCFT calculation. Recently, tools have been developed to couple SCFT with liquid state (LS) integral equation theory, which can calculate ion correlations in a quantitative fashion. This permits the articulation of ion effects in very low dielectric εr constant regimes that are relevant to polymer blends in nonaqueous conditions. We show that the inclusion of local ion correlations can give rise to marked enhancement of phase separation, contrary to theories invoking the Poisson-Boltzmann approximation, even to the extent of driving phase separation when two polymers are fully miscible (χN = 0). We provide both a demonstration of this effect as well as a conceptual explanation.

Counterion distribution surrounding spherical nucleic acid-Au nanoparticle conjugates probed by small-angle x-ray scattering.

The radial distribution of monovalent cations surrounding spherical nucleic acid-Au nanoparticle conjugates (SNA-AuNPs) is determined by in situ small-angle x-ray scattering (SAXS) and classical density functional theory (DFT) calculations. Small differences in SAXS intensity profiles from SNA-AuNPs dispersed in a series of solutions containing different monovalent ions (Na(+), K(+), Rb(+), or Cs(+)) are measured. Using the "heavy ion replacement" SAXS (HIRSAXS) approach, we extract the cation-distribution-dependent contribution to the SAXS intensity and show that it agrees with DFT predictions. The experiment-theory comparisons reveal the radial distribution of cations as well as the conformation of the DNA in the SNA shell. The analysis shows an enhancement to the average cation concentration in the SNA shell that can be up to 15-fold, depending on the bulk solution ionic concentration. The study demonstrates the feasibility of HIRSAXS in probing the distribution of monovalent cations surrounding nanoparticles with an electron dense core (e.g., metals).

Correlated electrolyte solutions and ion-induced attractions between nanoparticles.

Simple expressions are presented for the equations of state of a correlated electrolyte solution, calculated straightforwardly within a full nonlinear Debye-Hückel approach in terms of the mean potential at contact, that predict quantitatively different phase behavior from the popular Debye-Hückel limiting law. The theory includes pair correlations accurately and may provide a basis for a quantitative theoretical study of organic or multivalent ionic solutions. As an example, cohesive effects are addressed of strong couplings between ions on the effective interactions between nanoparticles.

Computer simulations of the restricted primitive model at very low temperature and density.

The problem of successfully simulating ionic fluids at low temperature and low density states is well known in the simulation literature: using conventional methods, the system is not able to equilibrate rapidly due to the presence of strongly associated cation-anion pairs. In this paper we present a numerical method for speeding up computer simulations of the restricted primitive model (RPM) at low temperatures (around the critical temperature) and at very low densities (down to 10(-10)σ(-3), where σ is the ion diameter). Experimentally, this regime corresponds to typical concentrations of electrolytes in nonaqueous solvents. As far as we are aware, this is the first time that the RPM has been equilibrated at such extremely low concentrations. More generally, this method could be used to equilibrate other systems that form aggregates at low concentrations.