Prediction and Observation of Crystal Structures of Oppositely Charged Colloids

Abstract

We studied crystal structures in mixtures of large and small oppositely charged spherical colloids with size ratio 0.31 using Monte Carlo simulations and confocal microscopy. We developed an interactive method based on simulated annealing to predict new binary crystal structures with stoichiometries from 1 to 8. Employing these structures in Madelung energy calculations using a screened Coulomb potential, we constructed a ground-state phase diagram, which shows a remarkably rich variety of crystals. Our phase diagram displays colloidal analogs of simple-salt structures and of the doped fullerene C 60 structures, but also novel structures that do not have an atomic or molecular analog. We found three of the predicted structures experimentally, which provides confidence that our method yields reliable results. DOI: 10.1103/PhysRevLett.96.138308 PACS numbers: 82.70.Dd, 61.50.Ah Colloidal dispersions consist of nanometer to micrometer sized particles suspended in a solvent. Colloids are important model systems for atoms and molecules, as they exhibit the same phase behavior, but are easier to investigate and to manipulate. The possibility to tune colloidal interactions chemically or by an external field has led to a great variety of model systems. Recently, our group and others presented a new model system, consisting of oppositely charged colloids that form equilibrium crystals [1,2]. A profound difference with atomic systems is that ionic colloidal crystal structures are not dictated by charge neutrality as the charge balance is covered by the presence of counterions. This severs the link between charge ratio and stoichiometry and enlarges the number of possible crystal structures. Predicting these is a computational challenge, not only because of the overwhelming number of possible structures and system parameters (charge, size, solvent, salinity, composition, etc.) but also because of the intricate interplay between attractive and repulsive interactions, entropy, and packing effects. In this Letter, we develop a novel interactive simulation method to predict binary crystal structures of oppositely charged colloids, based on simulated annealing [3]. Employing this method, we are able to predict a whole variety of new binary crystal structures with different stoichiometries, which we used in Madelung energy calculations to map out the ground-state phase diagram. Results are presented for binary mixtures of small and large oppositely charged colloids with size ratio 0.31, corresponding to one of our experimental systems that triggered our theoretical interest [1]. The calculated phase diagram exhibits a plethora of different crystal structures, some of which have atomic and molecular analogs, while others do not. Using the theoretical predictions, we experimentally confirmed the stability of three of the crystal structures.Our experimental system consists of spherical, sterically stabilized polymethylmethacrylate (PMMA) particles [4], dispersed in a less polar solvent mixture. The negatively charged larger part...

Confined colloidal crystals in and out of equilibrium

“…There are three basic equimolar structures whose stability depends on the ratio of the ion radii involving the cesium-chloride, sodium-chloride, and zincblende structures. These (and some more) structures are not only realized for molecular salts but also for mesoscopic colloids [49][50][51].…”

Nonadditivity in the effective interactions of binary charged colloidal suspensions

“…Even if this interaction is pairwise additive, the full calculation of structure and phase behaviour has only been done for selected cases. Among those are hard spheres [4][5][6][7], oppositely charged colloids [8,9], twodimensional dipolar mixtures [10,11] and two-dimensional Yukawa mixtures [12].…”

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

“…11(a) and 11(b). We observe a tendency for bumps in φ a and in φ b to sit pairwise next to each other resembling configurations occurring in mixtures of oppositely charged colloidal particles [34][35][36]. Whenφ a ≈φ b , the arrangement of the bumps also resembles snapshots of monovalent salts.…”