Antti-Pekka Hynninen

Ionic colloidal crystals of oppositely charged particles.

Colloidal suspensions are widely used to study processes such as melting, freezing and glass transitions. This is because they display the same phase behaviour as atoms or molecules, with the nano- to micrometre size of the colloidal particles making it possible to observe them directly in real space. Another attractive feature is that different types of colloidal interactions, such as long-range repulsive, short-range attractive, hard-sphere-like and dipolar, can be realized and give rise to equilibrium phases. However, spherically symmetric, long-range attractions (that is, ionic interactions) have so far always resulted in irreversible colloidal aggregation. Here we show that the electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with our theory and simulations confirming the stability of these structures. We find that in contrast to atomic systems, the stoichiometry of our colloidal crystals is not dictated by charge neutrality; this allows us to obtain a remarkable diversity of new binary structures. An external electric field melts the crystals, confirming that the constituent particles are indeed oppositely charged. Colloidal model systems can thus be used to study the phase behaviour of ionic species. We also expect that our approach to controlling opposite-charge interactions will facilitate the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications.

Re-entrant melting and freezing in a model-system of charged colloids

We studied the phase behavior of charged and sterically stabilized colloids using confocal microscopy in a low polarity solvent (dielectric constant 5.4). Upon increasing the colloid volume fraction we found a transition from a fluid to a body centered cubic crystal at 0.0415+/-0.0005, followed by reentrant melting at 0.1165+/-0.0015. A second crystal of different symmetry, random hexagonal close packed, was formed at a volume fraction around 0.5, similar to that of hard spheres. We attribute the intriguing phase behavior to the particle interactions that depend strongly on volume fraction, mainly due to the changes in the colloid charge. In this low polarity system the colloids acquire charge through ion adsorption. The low ionic strength leads to fewer ions per colloid at elevated volume fractions and consequently a density-dependent colloid charge.

Electrostatic Screening and Charge Correlation Effects in Micellization of Ionic Surfactants

We have used atomistic simulations to study the role of electrostatic screening and charge correlation effects in self-assembly processes of ionic surfactants into micelles. Specifically, we employed grand canonical Monte Carlo simulations to investigate the critical micelle concentration (cmc), aggregation number, and micellar shape in the presence of explicit sodium chloride (NaCl). The two systems investigated are cationic dodecyltrimethylammonium chloride (DTAC) and anionic sodium dodecyl sulfate (SDS) surfactants. Our explicit-salt results, obtained from a previously developed potential model with no further adjustment of its parameters, are in good agreement with experimental data for structural and thermodynamic micellar properties. We illustrate the importance of ion correlation effects by comparing these results with a Yukawa-type surfactant model that incorporates electrostatic screening implicitly. While the effect of salt on the cmc is well-reproduced even with the implicit Yukawa model, the aggregate size predictions deviate significantly from experimental observations at low salt concentrations. We attribute this discrepancy to the neglect of ion correlations in the implicit-salt model. At higher salt concentrations, we find reasonable agreement of the Yukawa model with experimental data. The crossover from low to high salt concentrations is reached when the electrostatic screening length becomes comparable to the headgroup size.

Implicit Solvent Models for Micellization of Ionic Surfactants

We propose a method for parametrization of implicit solvent models for the simulation of the self-assembly of ionic surfactants into micelles. The parametrization is carried out in two steps. The first step involves atomistic molecular dynamics simulations of headgroups and counterions with explicit solvent to determine structural properties. An implicit solvent model of the headgroup/counterion system is obtained by matching structural quantities between explicit solvent and implicit solvent systems. In the second step, we identify the solvophobic attractions between the tail beads. We determine the solvophobic parameters using grand canonical Monte Carlo simulations with histogram reweighting techniques. The matching objective for the identification of solvophobic attractions is the critical micelle concentration (cmc). We choose sodium dodecyl sulfate as the reference system. On the basis of hydrophobic parameters obtained from this particular model, we study specific ion effects (lithium and potassium instead of sodium) as well as the effect of cationic headgroups (dodecyltrimethylammonium bromide/chloride). Furthermore, the chain length dependence of micellization properties is investigated for sodium alkyl sulfate, with alkyl lengths between 6 and 14. All cases considered give results in broad agreement with experimental data, confirming the transferability of parameters and the generality of the approach.

Coarse-Grained Simulations of Rapid Assembly Kinetics for Polystyrene-b-poly(ethylene oxide) Copolymers in Aqueous Solutions

We present a coarse-grained, implicit solvent model for polystyrene-b-poly(ethylene oxide) in aqueous solution and study its assembly kinetics using Brownian dynamics simulations. The polymer is modeled as a chain of freely jointed beads interacting through effective potentials. Coarse-grained force field parameters are determined by matching experimental thermodynamic quantities including radius of gyration, second virial coefficient, aggregation number, and critical micelle concentration. We investigate the influence of cooling rate (analogous to the rate of solvent quality change in rapid precipitations), polymer concentration, and friction coefficient on the assembly kinetics and compare simulation results to flash nanoprecipitation experiments. We find that assembly kinetics show a linear scaling relation with inverse friction coefficient when the friction coefficient is larger than 1. When the cooling time is less than the characteristic micellization time, stable kinetically arrested clusters are obtained; otherwise, close-to-equilibrium micelles are formed. The characteristic micellization time is estimated to be only 3-6 ms, in contrast to 30-40 ms previously determined in experiments. We suggest that previous experiments probed the formation of micellar clusters while simulations in this work studied the kinetics of a single micelle assembled from free polymer chains.

Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres

We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76 < or = q < or = 0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases.

Simulations of phase transitions and free energies for ionic systems

A review of simulation studies of phase equilibria and free energies for systems dominated by coulombic interactions is presented. Phase transitions occur for ionic systems in the strong-coupling limit realized in low-dielectric constant solvents, at low temperatures, or for high charge valences. The majority of simulation results to date are for primitive models that treat the solvent as a uniform dielectric continuum. Transitions involving fluid and solid phases for such models have been studied extensively in the past decade. There is now strong evidence that the vapour–liquid transition is in the Ising universality class. For highly charged colloids the vapour–liquid transition becomes metastable with respect to the fluid–solid transition and the behaviour matches that of charged hard plates. Phase transitions of charged chains illustrate sensitivity of the phase behaviour to the charge pattern. Studies of salt solubilities using models with explicit solvent suggest that reasonable agreement with experiment can be achieved with existing force fields, but there is considerable room for improvement. Areas of future research needs are briefly discussed.

Gas-liquid phase separation in oppositely charged colloids: Stability and interfacial tension

We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma<or=4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In addition, we determine the gas-liquid interfacial tension using grand-canonical Monte Carlo simulations. The interfacial tension decreases upon increasing the range of the interaction. In particular, we find that simple scaling can be used to relate the interfacial tension of the YRPM to that of the restricted primitive model, where particles interact with bare Coulomb interactions.

Phase diagram of hard-core repulsive Yukawa particles with a density-dependent truncation: a simple model for charged colloids

Using computer simulations we study the phase behaviour of hard spheres with repulsive Yukawa interactions and with the repulsion set to zero at distances larger than a density-dependent cut-off distance. Earlier studies based on experiments and computer simulations in colloidal suspensions have shown that the effective colloid–colloid pair interaction that takes into account many-body effects resembles closely this truncated Yukawa potential. We present a phase diagram for the truncated Yukawa system by combining Helmholtz free energy calculations and the Kofke integration method. Compared to the non-truncated Yukawa system we observe (i) a radical reduction of the stability of the body centred cubic (BCC) phase, (ii) a wider fluid region due to instability of the face centred cubic (FCC) phase and due to a re-entrant fluid phase and (iii) hardly any shift of the (FCC) melting line when compared with the (BCC) melting line for the full Yukawa potential for sufficiently high salt concentrations, i.e. truncation of the potential does not affect the location of the solid–fluid line but replaces onl yt he BCC phase with the FCC at the melting line. We compare our results with earlier results on the truncated Yukawa potential and with results from simulations where the full many-body Poisson–Boltzmann problem is solved. (Some figures in this article are in colour only in the electronic version)

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).