Thermodynamic stability and structural properties of cluster crystals formed by amphiphilic dendrimers

Self assembling cluster crystals from DNA based dendritic nanostructures

Cluster crystals are periodic structures with lattice sites occupied by several, overlapping building blocks, featuring fluctuating site occupancy, whose expectation value depends on thermodynamic conditions. Their assembly from atomic or mesoscopic units is long-sought-after, but its experimental realization still remains elusive. Here, we show the existence of well-controlled soft matter cluster crystals. We fabricate dendritic-linear-dendritic triblock composed of a thermosensitive water-soluble polymer and nanometer-scale all-DNA dendrons of the first and second generation. Conclusive small-angle X-ray scattering (SAXS) evidence reveals that solutions of these triblock at sufficiently high concentrations undergo a reversible phase transition from a cluster fluid to a body-centered cubic (BCC) cluster crystal with density-independent lattice spacing, through alteration of temperature. Moreover, a rich concentration-temperature phase diagram demonstrates the emergence of various ordered nanostructures, including BCC cluster crystals, birefringent cluster crystals, as well as hexagonal phases and cluster glass-like kinetically arrested states at high densities.

Experimental realization of cluster crystals- periodic structures with lattice sites occupied by several, overlapping building blocks, has been elusive. Here, the authors show the existence of well-controlled soft matter cluster crystals composed of a thermosensitive water-soluble polymer and nanometer-scale all-DNA dendrons.

Structure and stimuli-responsiveness of all-DNA dendrimers: theory and experiment

We present a comprehensive theoretical and experimental study of the solution phase properties of a DNA-based family of nanoparticles - dendrimer-like DNA molecules (DL-DNA). These charged DNA dendrimers are novel macromolecular aggregates, which hold high promise in targeted self-assembly of soft matter systems in the bulk and at interfaces. To describe the behaviour of this family of dendrimers (with generations ranging from G1 to G7), we use a theoretical model in which base-pairs of a single DL-DNA molecule are modeled by charged monomers, whose interactions are chosen to mimic the equilibrium properties of DNA correctly. Experimental results on the sizes and conformations of DL-DNA are based on static and dynamic light scattering; and molecular dynamics simulations are employed to model the equilibrium properties of DL-DNA, which compare favorably to the findings from experiments while at the same time providing a host of additional information and insight into the molecular structure of the nanostructures. We also examine the salt-responsiveness of these macromolecules, finding that despite the strong screening of electrostatic interactions brought about by the added salt, the macromolecules shrink only slightly, their size robustness stemming from the high bending rigidity of the DNA-segments. The study of these charged dendrimer systems is an important field of research in the area of soft matter due to their potential role for various interdisciplinary applications, ranging from molecular cages and carriers for drug delivery in a living organism to the development of dendrimer- and dendron-based ultra-thin films in the area of nanotechnology. These findings are essential to determine if DL-DNA is a viable candidate for the experimental realization of cluster crystals in the bulk, a novel form of solid with multiple site occupancy.

Formation of cluster crystals in an ultra-soft potential model on a spherical surface

We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to clustering: we generalize the criterion devised in C. N. Likos et al., Phys. Rev. E, 2001, 63, 031206 to spherical systems in order to distinguish between cluster-forming systems and fluids which display reentrant melting. We use both DFT and Monte Carlo simulations to characterize the behavior of the system, and obtain semi-quantitative agreement between the two. We find that the number of clusters is determined by the ratio between the size σ of the ultra-soft particles and the radius R of the sphere in such a way that each stable configuration spans a certain interval of σ/R. Furthermore, we study the effect of topological frustration on the system due to the sphere curvature by comparing the properties of disclinations, i.e., clusters with fewer than six neighbors, and non-defective clusters. Disclinations are shown to be less stable, contain fewer particles, and be closer to their neighbors than other lattice points: these properties are explained on the basis of geometric and energetic considerations.

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.