Angelo Cacciuto

Onset of heterogeneous crystal nucleation in colloidal suspensions

The addition of small ‘seed’ particles to a supersaturated solution can greatly increase the rate at which crystals nucleate. This process is understood, at least qualitatively, when the seed has the same structure as the crystal that it spawns. However, the microscopic mechanism of seeding by a ‘foreign’ substance is not well understood. Here we report numerical simulations of colloidal crystallization seeded by foreign objects. We perform Monte Carlo simulations to study how smooth spherical seeds of various sizes affect crystallization in a suspension of hard colloidal particles. We compute the free-energy barrier associated with crystal nucleation. A low barrier implies that nucleation is easy. We find that to be effective crystallization promoters, the seed particles need to exceed a well-defined minimum size. Just above this size, seed particles act as crystallization ‘catalysts’ as newly formed crystallites detach from the seed. In contrast, larger seed particles remain covered by the crystallites that they spawn. This phenomenon should be experimentally observable and can have important consequences for the control of the resulting crystal size distribution.

Grain Boundary Scars and Spherical Crystallography

We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the minimum-energy configurations of particles with arbitrary repulsive interactions on curved surfaces. Above a critical system size we find that crystals develop distinctive high-angle grain boundaries, or scars, not found in planar crystals. The number of excess defects in a scar is shown to grow linearly with the dimensionless system size. The observed slope is expected to be universal, independent of the microscopic potential.

Clusters of Amphiphilic Colloidal Spheres

Orientation-dependent interactions can drive unusual self-assembly of colloidal particles. This study, based on combined epifluorescence microscopy and Monte Carlo simulations, shows that amphiphilic colloidal spheres, hydrophobic on one hemisphere and charged on the other, assemble in water into extended structures not formed by spheres of uniform surface chemical makeup. Small, compact clusters each comprised of less than 10 of these Janus spheres link up, as increasing salt concentration enhances electrostatic screening, into wormlike strings.

Crystalline order on a sphere and the generalized Thomson problem

We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy E(core) of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0<gamma<2) to four significant figures. The generality of our approach is illustrated by a study of grain boundary proliferation for tilted crystalline order and square lattices on the sphere.

Fluid membranes can drive linear aggregation of adsorbed spherical nanoparticles.

Using computer simulations, we show that lipid membranes can mediate linear aggregation of spherical nanoparticles binding to it for a wide range of biologically relevant bending rigidities. This result is in net contrast with the isotropic aggregation of nanoparticles on fluid interfaces or the expected clustering of isotropic insertions in biological membranes. We present a phase diagram indicating where linear aggregation is expected and compute explicitly the free-energy barriers associated with linear and isotropic aggregation. Finally, we provide simple scaling arguments to explain this phenomenology.

Phase diagram of Hertzian spheres.

We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of weakly deformable bodies and, therefore, it is a reliable physical model of soft macromolecules, like star polymers and globular micelles. Using thermodynamic integration and extensive Monte Carlo simulations, we computed accurate free energies of the fluid phase and a large number of crystal structures. For this, we defined a general primitive unit cell that allows for the simulation of any lattice. We found multiple re-entrant melting and first-order transitions between crystals with cubic, trigonal, tetragonal, and hexagonal symmetries.

Confinement-driven translocation of a flexible polymer

We consider the escape of a flexible, self-avoiding polymer chain out of a confined geometry. By means of simulations, we demonstrate that the translocation time can be described by a simple scaling law that exhibits a nonlinear dependence on the degree of polymerization and that is sensitive to the nature of the confining geometry. These results contradict earlier predictions but are in agreement with recently confirmed geometry-dependent expressions for the free energy of confinement.

Universal negative poisson ratio of self-avoiding fixed-connectivity membranes.

We determine the Poisson ratio of self-avoiding fixed-connectivity membranes, modeled as impenetrable plaquettes, to be sigma = -0.37(6), in statistical agreement with the Poisson ratio of phantom fixed-connectivity membranes sigma = -0.32(4). Together with the equality of critical exponents, this result implies a unique universality class for fixed-connectivity membranes. Our findings thus establish that physical fixed-connectivity membranes provide a wide class of auxetic (negative Poisson ratio) materials with significant potential applications in materials science.

Mechanism of Membrane Tube Formation Induced by Adhesive Nanocomponents

We report numerical simulations of membrane tubulation driven by large colloidal particles. Using Monte Carlo simulations we study how the process depends on particle size and binding strength, and present accurate free energy calculations to sort out how tube formation compares with the competing budding process. We find that tube formation is a result of the collective behavior of the particles adhering on the surface, and it occurs for binding strengths that are smaller than those required for budding. We also find that long linear aggregates of particles forming on the membrane surface act as nucleation seeds for tubulation by lowering the free energy barrier associated to the process.

Hierarchical self-assembly of asymmetric amphiphatic spherical colloidal particles.

From dumbbells to fcc crystals, we study the self-assembly pathway of amphiphatic spherical colloidal particles as a function of the size of the hydrophobic region using molecular-dynamics simulations. Specifically, we analyze how local interparticle interactions correlate to the final self-assembled aggregate and how they affect the dynamical pathway of structure formation. We present a detailed diagram separating the many phases that we find for different sizes of the hydrophobic area and uncover a narrow region where particles self-assemble into hollow faceted cages that could potentially find interesting engineering applications.