CuAu structure in the restricted primitive model and oppositely charged colloids

Macroscopic photonic single crystals via seeded growth of DNA-coated colloids

Photonic crystals-a class of materials whose optical properties derive from their structure in addition to their composition-can be created by self-assembling particles whose sizes are comparable to the wavelengths of visible light. Proof-of-principle studies have shown that DNA can be used to guide the self-assembly of micrometer-sized colloidal particles into fully programmable crystal structures with photonic properties in the visible spectrum. However, the extremely temperature-sensitive kinetics of micrometer-sized DNA-functionalized particles has frustrated attempts to grow large, monodisperse crystals that are required for photonic metamaterial applications. Here we describe a robust two-step protocol for self-assembling single-domain crystals that contain millions of optical-scale DNA-functionalized particles: Monodisperse crystals are initially assembled in monodisperse droplets made by microfluidics, after which they are grown to macroscopic dimensions via seeded diffusion-limited growth. We demonstrate the generality of our approach by assembling different macroscopic single-domain photonic crystals with metamaterial properties, like structural coloration, that depend on the underlying crystal structure. By circumventing the fundamental kinetic traps intrinsic to crystallization of optical-scale DNA-coated colloids, we eliminate a key barrier to engineering photonic devices from DNA-programmed materials.

Anomalous Underscreening in the Restricted Primitive Model

Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.

Electrostatic Heteroaggregation: Fundamentals and Applications in Interfacial Engineering

The aggregation of oppositely charged soft materials (particles, surfactants, polyelectrolytes, etc.) that differ in one or more physical or chemical attributes, broadly referred to as electrostatic heteroaggregation, has been an active area of research for several decades now. While electrostatic heteroaggregation (EHA) is relevant to diverse fields such as environmental engineering, food technology, and pharmaceutical formulations, more recently there has been a resurgence to explore various aspects of this phenomenon in the context of interface stabilization and the development of functional materials. In this Feature Article, we provide an overview of the recent contributions of our group to this exciting field with particular emphasis on fundamental studies of electrostatic heteroaggregation between oppositely charged systems in the bulk, at interfaces, and across the bulk/interface. The influence of the size and shape of particles and the surface charge of heteroaggregates on the formation of Pickering emulsions and their utilization in the development of porous ceramics is discussed.

Controlled 3D assembly and stimuli responsive behavior of DNA and peptide functionalized gold nanoparticles in solutions

DNA mediated directed self assembly of gold nanoparticles (AuNPs) has garnered immense interest due to its ability to precisely control supramolecular assemblies. Most experimental works have relied on utilizing the...

Charge-Driven Self-Assembly of Polyelectrolyte-Grafted Nanoparticles in Solutions

Nanoparticle self-assembly in solution has gained immense interest due to the enhanced optical, chemical, magnetic, and electrical properties which manifest at the macroscale. Material properties in bulk are a direct consequence of the morphology of these nanoparticles in solutions. Precise control on the orientation, spatial arrangement, shape, size, composition, and control over the interactions of individual nanoparticles play a key role in enhancing their properties. While previous studies have used asymmetry in the nanoparticle and/or the use of linker grafts, nanoparticles grafted with polyelectrolyte grafts provide us a wide parameter space to control and tune their self-assembly in solutions. In this study, we have performed coarse-grained molecular dynamics simulations to understand the charge-driven self-assembly of spherical nanoparticles grafted with polyelectrolyte chains. Nanoparticles grafted with either positively or negatively charged polyelectrolyte chains self-assemble to different structures driven by both excluded volume and electrostatic interactions. Our study shows that by tuning the graft density, the chain length, and the charge density of the grafts, we could build and control a variety of self-assembled structures ranging from rings, dimers, strings, coil-like aggregates, and disordered-to-ordered aggregates.

Underscreening and hidden ion structures in large scale simulations of concentrated electrolytes

The electrostatic screening length predicted by Debye-Hückel theory decreases with increasing ionic strength, but recent experiments have found that the screening length can instead increase in concentrated electrolytes. This phenomenon, referred to as underscreening, is believed to result from ion-ion correlations and short-range forces such as excluded volume interactions among ions. We use Brownian Dynamics to simulate a version of the Restrictive Primitive Model for electrolytes over a wide range of ion concentrations, ionic strengths, and ion excluded volume radii for binary electrolytes. We measure the decay of the charge-charge correlation among ions in the bulk and compare it against scaling trends found experimentally and determined in certain weak coupling theories of ion-ion correlation. Moreover, we find that additional large scale ion structures emerge at high concentrations. In this regime, the frequency of oscillations computed from the charge-charge correlation function is not dominated by electrostatic interactions but rather by excluded volume interactions and with oscillation periods on the order of the ion diameter. We also find the nearest neighbor correlation of ions sharing the same charge transitions from negative at small concentrations to positive at high concentrations, representing the formation of small, like-charge ion clusters. We conclude that the increase in local charge density due to the formation of these clusters and the topological constraints of macroscopic charged surfaces can help explain the degree of underscreening observed experimentally.

Reversible heat production during electric double layer buildup depends sensitively on the electrolyte and its reservoir

Several modern technologies for energy storage and conversion are based on the screening of electric charge on the surface of porous electrodes by ions in an adjacent electrolyte. This so-called electric double layer (EDL) exhibits an intricate interplay with the electrolyte's temperature that was the focus of several recent studies. In one of them, Janssen et al. [Phys. Rev. Lett. 119, 166002 (2017)] experimentally determined the ratio Q_rev/W_el of reversible heat flowing into a supercapacitor during an isothermal charging process and the electric work applied therein. To rationalize that data, here, we determine Q_rev/W_el within different models of the EDL using theoretical approaches such as density functional theory (DFT) as well as molecular dynamics simulations. Applying mainly the restricted primitive model, we find quantitative support for a speculation of Janssen et al. that steric ion interactions are key to the ratio Q_rev/W_el. Here, we identified the entropic contribution of certain DFT functionals, which grants direct access to the reversible heat. We further demonstrate how Q_rev/W_el changes when calculated in different thermodynamic ensembles and processes. We show that the experiments of Janssen et al. are explained best by a charging process at fixed bulk density or in a "semi-canonical" system. Finally, we find that Q_rev/W_el significantly depends on parameters such as pore and ion size, salt concentration, and valencies of the cations and anions of the electrolyte. Our findings can guide further heat production measurements and can be applied in studies on, for instance, nervous conduction, where reversible heat is a key element.

Parasitic crystallization of colloidal electrolytes: growing a metastable crystal from the nucleus of a stable phase

Colloidal particles have been extensively used to comprehend the main principles governing liquid-crystal nucleation. Multiple mechanisms and frameworks have been proposed, through either experiments or computational approaches, to rationalise the ubiquitous formation of colloidal crystals. In this work, we elucidate the nucleation scenario behind the crystallization of oppositely charged colloids. By performing molecular dynamics simulations of colloidal electrolytes in combination with the Seeding technique, we evaluate the fundamental factors, such as the nucleation rate, free energy barrier, surface tension and kinetic pre-factor, that determine the liquid-to-solid transition of several crystalline polymorphs. Our results show that at a high packing fraction, there is a cross-over between the nucleation of the CsCl structure and that of a substitutionally disordered fcc phase, despite the CuAu crystal being the most stable phase. We demonstrate that the crucial factor in determining which phase nucleates the fastest is the free energy cost of the cluster formation rather than their kinetic ability to grow from the liquid. While at a low packing fraction, the stable phase, CsCl, is the one that nucleates and subsequently grows, we show how at moderate and high packing fractions, a disordered fcc phase subsequently grows regardless of the nature of the nucleating phase, termed parasitic crystallization. Taken together, our results provide a panoramic perspective of the complex nucleation scenario of oppositely charged colloids at moderate temperature and rationalise the different thermodynamic and kinetic aspects behind it.

Crystal-to-Crystal Transitions in Binary Mixtures of Soft Colloids

In this article, we demonstrate a method for inducing reversible crystal-to-crystal transitions in binary mixtures of soft colloidal particles. Through a controlled decrease of salinity and increasingly dominating electrostatic interactions, a single sample is shown to reversibly organize into entropic crystals, electrostatic attraction-dominated crystals, or aggregated gels, which we quantify using microscopy and image analysis. We furthermore analyze crystalline structures with bond order analysis to discern between two crystal phases. We observe the different phases using a sample holder geometry that allows both in situ salinity control and imaging through confocal laser scanning microscopy and apply a synthesis method producing particles with high resolvability in microscopy with control over particle size. The particle softness provides for an enhanced crystallization speed, while altering the re-entrant melting behavior as compared to hard sphere systems. This work thus provides several tools for use in the reproducible manufacture and analysis of binary colloidal crystals.

Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites

Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.

Self-assembled multi-layer simple cubic photonic crystals of oppositely charged colloids in confinement

Designing and fabricating self-assembled open colloidal crystals have become one major direction in the soft matter community because of many promising applications associated with open colloidal crystals. However, most of the self-assembled crystals found in experiments are not open but close-packed. Here, by using computer simulation, we systematically investigate the self-assembly of oppositely charged colloidal hard spheres confined between two parallel hard walls, and we find that the confinement can stabilize multi-layer NaCl-like (simple cubic) open crystals. The maximal number of layers of stable NaCl-like crystals increases with decreasing inverse screening length. More interestingly, at finite low temperature, the large vibrational entropy can stabilize some multi-layer NaCl-like crystals against the most energetically favoured close-packed crystals. In the parameter range studied, we find up to 4-layer NaCl-like crystals to be stable in confinement. Our photonic calculation shows that the inverse 4-layer NaCl-like crystal can already reproduce the large photonic band gaps of the bulk simple cubic crystal, which open in the low frequency range with a low dielectric contrast. This suggests new possibilities of using confined colloidal systems to fabricate open crystalline materials with novel photonic properties.

Effect of size and charge asymmetry on aggregation kinetics of oppositely charged nanoparticles

We report a theoretical and experimental study of the aggregation kinetics of oppositely charged nanoparticles. Kinetic Monte Carlo simulations are performed for symmetric, charge-asymmetric and size-asymmetric systems of oppositely charged nanoparticles. Simulation results show that both the weight and number average aggregate size kinetics exhibit power law scaling with different exponents for small and intermediate time of evolution. The qualitative behavior of the symmetric and the size asymmetric system are the same, but the charge asymmetric system shows anomalous behavior for intermediate to high particle concentrations. We also observe a strong dependence of power law exponents on the particle concentration. Radius of gyration of the cluster that indicates how nanoparticles inside a cluster are distributed around the center of mass of the cluster shows a non-monotonic time evolution with pronounced peak at higher particle concentration. The dependence of particle concentration on aggregation kinetics as observed by predictive numerical simulation is further verified experimentally by monitoring the time evolution of aggregate size of nanoparticles assemblies of Poly (methacrylic acid) (PMMA) nanoparticles functionalized with oppositely charged ligands. These size and charge tunable asymmetric polymeric nanoparticles were synthesized by modified miniemulsion technique. The integrated approach for studying nanoparticles aggregation as described here renders new insights into super structure formation and morphology optimization which can be potentially useful in the design of new materials, such as organic photovoltaics.

Recent Advances in Multicomponent Particle Assembly

Particle assembly and co-assembly have been research frontiers in chemistry and material science in the past few decades. To achieve a large variety of intricate structures and functional materials, remarkable progress has been made in particle assembly principles and strategies. Essentially, particle assembly is driven by intrinsic interparticle interactions or the external control. In this article, we focus on binary or ternary particle co-assembly and review the principles and feasible strategies. These advances have led to new disciplines of microfabrication technology and material engineering. Although significant achievement on particle-based structures has been made, it is still challenging to fully develop general and facile strategies to precisely control the one-dimensional (1D) co-assembly. This article reviews the recent development on multicomponent particle co-assembly, which significantly increases structural complexity and functional diversity. In particular, we highlight the advances in the particle co-assembly of well-ordered 1D binary superstructures by liquid soft confinement. Finally, prospective outlook for future trends in this field is proposed.

Entropy Stabilizes Floppy Crystals of Mobile DNA-Coated Colloids

Grafting linkers with open ends of complementary single-stranded DNA makes a flexible tool to tune interactions between colloids, which facilitates the design of complex self-assembly structures. Recently, it has been proposed to coat colloids with mobile DNA linkers, which alleviates kinetic barriers without high-density grafting, and also allows the design of valency without patches. However, the self-assembly mechanism of this novel system is poorly understood. Using a combination of theory and simulation, we obtain phase diagrams for the system in both two and three dimensional spaces, and find stable floppy square and CsCl crystals when the binding strength is strong, even in the infinite binding strength limit. We demonstrate that these floppy phases are stabilized by vibrational entropy, and "floppy" modes play an important role in stabilizing the floppy phases for the infinite binding strength limit. This special entropic effect in the self-assembly of mobile DNA-coated colloids is very different from conventional molecular self-assembly, and it offers a new axis to help design novel functional materials using mobile DNA-coated colloids.

Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it

Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.

Self-consistent theory for systems with mesoscopic fluctuations

We have developed a theory for inhomogeneous systems that allows for the incorporation of the effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess [Formula: see text] of the volume fraction of particles ζ has been obtained, and an approximation leading to a closed set of equations for the two-point functions has been introduced for the disordered inhomogeneous phase. We have numerically solved the self-consistent equations for one-dimensional (1D) and three-dimensional (3D) models with short-range attraction and long-range repulsion. Predictions for all of the qualitative properties of the 1D model agree with the exact results, but only semi-quantitative agreement is obtained in the simplest version of the theory. The effects of fluctuations in the two 3D models considered are significantly different, despite the very similar properties of these models in the mean-field approximation. In both cases we obtain the sequence of large-small-large compressibility for increasing ζ. The very small compressibility is accompanied by the oscillatory decay of correlations with correlation lengths that are orders of magnitude larger than the size of particles. In one of the two models considered, the small compressibility becomes very small and the large compressibility becomes very large with decreasing temperature, and eventually van der Waals loops appear. Further studies are necessary in order to determine the nature of the strongly inhomogeneous phase present for intermediate volume fractions in 3D.

Generic phase diagram of binary superlattices

Emergence of a large variety of self-assembled superlattices is a dramatic recent trend in the fields of nanoparticle and colloidal sciences. Motivated by this development, we propose a model that combines simplicity with a remarkably rich phase behavior applicable to a wide range of such self-assembled systems. Those systems include nanoparticle and colloidal assemblies driven by DNA-mediated interactions, electrostatics, and possibly, controlled drying. In our model, a binary system of large and small hard spheres (L and S, respectively) interacts via selective short-range ("sticky") attraction. In its simplest version, this binary sticky sphere model features attraction only between S and L particles. We show that, in the limit when this attraction is sufficiently strong compared with [Formula: see text], the problem becomes purely geometrical: the thermodynamically preferred state should maximize the number of [Formula: see text] contacts. A general procedure for constructing the phase diagram as a function of system composition f and particle size ratio r is outlined. In this way, the global phase behavior can be calculated very efficiently for a given set of plausible candidate phases. Furthermore, the geometric nature of the problem enables us to generate those candidate phases through a well-defined and intuitive construction. We calculate the phase diagrams for both 2D and 3D systems and compare the results with existing experiments. Most of the 3D superlattices observed to date are featured in our phase diagram, whereas several more are predicted for future discovery.

Dense ionic fluids confined in planar capacitors: in- and out-of-plane structure from classical density functional theory

The ongoing scientific interest in the properties and structure of electric double layers (EDLs) stems from their pivotal role in (super)capacitive energy storage, energy harvesting, and water treatment technologies. Classical density functional theory (DFT) is a promising framework for the study of the in- and out-of-plane structural properties of double layers. Supported by molecular dynamics simulations, we demonstrate the adequate performance of DFT for analyzing charge layering in the EDL perpendicular to the electrodes. We discuss charge storage and capacitance of the EDL and the impact of screening due to dielectric solvents. We further calculate, for the first time, the in-plane structure of the EDL within the framework of DFT. While our out-of-plane results already hint at structural in-plane transitions inside the EDL, which have been observed recently in simulations and experiments, our DFT approach performs poorly in predicting in-plane structure in comparison to simulations. However, our findings isolate fundamental issues in the theoretical description of the EDL within the primitive model and point towards limitations in the performance of DFT in describing the out-of-plane structure of the EDL at high concentrations and potentials.

Gas-liquid phase coexistence and crossover behavior of binary ionic fluids with screened Coulomb interactions

We study the effects of an interaction range on the gas-liquid phase diagram and the crossover behavior of a simple model of ionic fluids: an equimolar binary mixture of equisized hard spheres interacting through screened Coulomb potentials which are repulsive between particles of the same species and attractive between particles of different species. Using the collective variables theory, we find explicit expressions for the relevant coefficients of the effective φ{4} Ginzburg-Landau Hamiltonian in a one-loop approximation. Within the framework of this approximation, we calculate the critical parameters and gas-liquid phase diagrams for varying inverse screening length z. Both the critical temperature scaled by the Yukawa potential contact value and the critical density rapidly decrease with an increase of the interaction range (a decrease of z) and then for z<0.05 they slowly approach the values found for a restricted primitive model (RPM). We find that gas-liquid coexistence region reduces with an increase of z and completely vanishes at z≃2.78. Our results clearly show that an increase in the interaction range leads to a decrease of the crossover temperature. For z≃0.01, the crossover temperature is the same as for the RPM.

Free energy calculations for molecular solids using GROMACS

In this work, we describe a procedure to evaluate the free energy of molecular solids with the GROMACS molecular dynamics package. The free energy is calculated using the Einstein molecule method that can be regarded as a small modification of the Einstein crystal method. Here, the position and orientation of the molecules is fixed by using an Einstein field that binds with harmonic springs at least three non-collinear atoms (or points of the molecule) to their reference positions. The validity of the Einstein field is tested by performing free-energy calculations of methanol, water (ice), and patchy colloids molecular solids. The free energies calculated with GROMACS show a very good agreement with those obtained using Monte Carlo and with previously published results.

Study of the B1-B2 transition in colloidal clusters

The possible mechanisms for the B1 (NaCl-type) to B2 (CsCl-type) transition in crystalline colloidal clusters of equally sized particles are studied by means of two computational techniques: metadynamics and nudged elastic band calculations. The system is modelled by a screened Coulomb potential. Different interaction ranges are considered. The transition from a perfect NaCl cubic cluster to a full CsCl cluster is forced by metadynamics, revealing a transition path with intermediate metastable configurations in which planes are shifted one by one. The presence of metastable configurations in the transition path, corresponding to a certain number of NaCl planes turned into CsCl, has clear analogies with the known Hyde and O'Keeffe mechanism for ionic crystals, with some important differences due to finite-size effects. These comprise the fact that the transition starts by shifting a surface plane by means of a row-by-row mechanism that has no analog in bulk crystals. The energy barriers between the local minima in the transition path are calculated, showing that the barriers strongly depend on the screening length, in such a way that the B1 metastable phase can have very long lifetimes when the interaction is sufficiently long-ranged.

Liquid-vapor phase diagram and surface properties in oppositely charged colloids represented by a mixture of attractive and repulsive Yukawa potentials

The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.

Kinetically driven ordered phase formation in binary colloidal crystals

The aggregation of binary colloids of the same size and balanced charges is studied by Brownian dynamics simulations for dilute suspensions. It is shown that, under appropriate conditions, the formation of colloidal crystals is dominated by kinetic effects leading to the growth of well-ordered crystallites of the sodium-chloride (NaCl) bulk phase. These crystallites form with very high probability even when the cesium-chloride (CsCl) phase is more stable thermodynamically. Global optimization searches show that this result is not related to the most favorable structures of small clusters, which are either amorphous or of the CsCl structure. The formation of the NaCl phase is related to the specific kinetics of the crystallization process, which takes place by a two-step mechanism. In this mechanism, dense fluid aggregates form at first and then crystallization follows. It is shown that the type of short-range order in these dense fluid aggregates determines which phase is finally formed in the crystallites. The role of hydrodynamic effects in the aggregation process is analyzed by stochastic rotation dynamics - molecular dynamics simulations, and we find that these effects do not play a major role in the formation of the crystallites.

Spatial inhomogeneities in ionic liquids, charged proteins, and charge stabilized colloids from collective variables theory

Effects of size and charge asymmetry between oppositely charged ions or particles on spatial inhomogeneities are studied for a large range of charge and size ratios. We perform a stability analysis of the primitive model of ionic systems with respect to periodic ordering using the collective variables-based theory. We extend previous studies [Ciach et al., Phys. Rev. E 75, 051505 (2007)] in several ways. First, we employ a nonlocal approximation for the reference hard-sphere fluid which leads to the Percus-Yevick pair direct correlation functions for the uniform case. Second, we use the Weeks-Chandler-Anderson regularization scheme for the Coulomb potential inside the hard core. We determine the relevant order parameter connected with the periodic ordering and analyze the character of the dominant fluctuations along the λ lines. We show that the above-mentioned modifications produce large quantitative and partly qualitative changes in the phase diagrams obtained previously. We discuss possible scenarios of the periodic ordering for the whole range of size and charge ratios of the two ionic species, covering electrolytes, ionic liquids, charged globular proteins or nanoparticles in aqueous solutions, and charge-stabilized colloids.

Modeling the structure of liquids and crystals using one- and two-component modified phase-field crystal models

A modified phase-field crystal model in which the free energy may be minimized by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where modulated and uniform phases are formed and also regions where localized states are formed. We investigate the effectiveness of the phase-field crystal model for describing fluids and crystals with defects. We further consider a two-component model and elucidate how the structure transforms from hexagonal crystalline ordering to square ordering as the concentration changes. Our conclusion contains a discussion of possible interpretations of the order parameter field.

Micro-rheology on (polymer-grafted) colloids using optical tweezers

Optical tweezers are experimental tools with extraordinary resolution in positioning (± 1 nm) a micron-sized colloid and in the measurement of forces (± 50 fN) acting on it-without any mechanical contact. This enables one to carry out a multitude of novel experiments in nano- and microfluidics, of which the following will be presented in this review: (i) forces within single pairs of colloids in media of varying concentration and valency of the surrounding ionic solution, (ii) measurements of the electrophoretic mobility of single colloids in different solvents (concentration, valency of the ionic solution and pH), (iii) similar experiments as in (i) with DNA-grafted colloids, (iv) the nonlinear response of single DNA-grafted colloids in shear flow and (v) the drag force on single colloids pulled through a polymer solution. The experiments will be described in detail and their analysis discussed.

Charge ordering induces a smectic phase in oblate ionic liquid crystals

We report a computer simulation study of an electroneutral mixture of oppositely charged oblate ellipsoids of revolution with aspect ratio A=1/3. In contrast with hard or soft repulsive ellipsoids, which are purely nematic, this system exhibits a smectic-A phase in which charges of equal sign are counterintuitively packed in layers perpendicular to the nematic director.

Self-assembled structures of Gaussian nematic particles

We investigate the stable crystalline configurations of a nematic liquid crystal made of soft parallel ellipsoidal particles interacting via a repulsive, anisotropic Gaussian potential. For this purpose, we use genetic algorithms (GA) in order to predict all relevant and possible solid phase candidates into which this fluid can freeze. Subsequently we present and discuss the emerging novel structures and the resulting zero-temperature phase diagram of this system. The latter features a variety of crystalline arrangements, in which the elongated Gaussian particles in general do not align with any one of the high-symmetry crystallographic directions, a compromise arising from the interplay and competition between anisotropic repulsions and crystal ordering. Only at very strong degrees of elongation does a tendency of the Gaussian nematics to align with the longest axis of the elementary unit cell emerge.

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.