Cluster Crystals Stabilized by Hydrophobic and Electrostatic Interactions

Cluster crystals are crystalline materials in which each site is occupied by multiple identical particles, atoms, colloids, or polymers. There are two classes of systems that make cluster crystals. One is composed of particles that interact via potentials that are bound at the origin and thus are able to penetrate each other. The other consists of non-interpenetrating particles whose interaction potential diverges at the origin. The goal of this work is to find which systems of the second class can make cluster crystals that are stable at room temperature. First, the general properties of the required potentials are established using an analytical model and Monte Carlo simulations. Next, we ask how such potentials can be constructed by combining hydrophobic attraction and electrostatic repulsion. A colloid model with a hard-sphere core and a repulsive wall is introduced to mimic the hydrophobic interaction. Charge is added to create long-range repulsion. A search in the parameter space of the colloid size, counterion type, and charge configuration uncovers several models for which effective colloid-colloid interaction, determined in explicit solvent as a potential of mean force, has the necessary shape. For the effective potential, cluster crystals are confirmed as low free-energy configurations in replica-exchange molecular dynamics simulations, which also generate the respective transition temperature. The model that exhibits a transition above room temperature is further studied in explicit solvent. Simulations on a 10 ns time scale show that crystalline conformations are stable below the target temperature but disintegrate rapidly above it, supporting the idea that hydrophobic and electrostatic interactions are sufficient to induce an assembly of cluster crystals. Finally, we discuss which physical systems are good candidates for experimental observations of cluster crystals.