Equivalence between condensation and boiling in a Lennard-Jones fluid

Condensation and boiling are phase transitions highly relevant to industry, geology, and atmospheric science. These phase transitions are initiated by the nucleation of a drop in a supersaturated vapor and of a bubble in an overstretched liquid, respectively. The surface tension between both phases, liquid and vapor, is a key parameter in the development of such nucleation stage. Whereas the surface tension can be readily measured for a flat interface, there are technical and conceptual limitations to obtain it for the curved interface of the nucleus. On the technical side, it is quite difficult to observe a critical nucleus in experiments. From a conceptual point of view, the interfacial free energy depends on the choice of the dividing surface, being the surface of tension the one relevant for nucleation. We bypass the technical limitation by performing simulations of a Lennard-Jones fluid where we equilibrate critical nuclei (both drops and bubbles). Regarding the conceptual hurdle, we find the relevant cluster size by searching the radius that correctly predicts nucleation rates and nucleation free energy barriers when combined with Classical Nucleation Theory. With such definition of the cluster size we find the same value of the surface tension for drops and bubbles of a given radius. Thus, condensation and boiling can be viewed as two sides of the same coin. Finally, we combine the data coming from drops and bubbles to obtain, via two different routes, estimates of the Tolman length, a parameter that allows describing the curvature dependence of the surface tension in a theoretical framework.

Inverse design of self-assembling colloidal crystals with omnidirectional photonic bandgaps

Open colloidal lattices possessing omnidirectional photonic bandgaps in the visible or near-visible regime are attractive optical materials the realization of which has remained elusive. We report the use of an inverse design strategy termed landscape engineering that rationally sculpts the free energy self-assembly landscape using evolutionary algorithms to discover anisotropic patchy colloids capable of spontaneously assembling pyrochlore and cubic diamond lattices possessing complete photonic bandgaps. We validate the designs in computer simulations to demonstrate the defect-free formation of these lattices via a two-stage hierarchical assembly mechanism. Our approach demonstrates a principled strategy for the inverse design of self-assembling colloids for the bottom-up fabrication of desired crystal lattices.

Active acoustic switches using two-dimensional granular crystals

We employ numerical simulations to study active transistor-like switches made from two-dimensional (2D) granular crystals containing two types of grains with the same size but different masses. We tune the mass contrast and arrangement of the grains to maximize the width of the frequency band gap in the device. The input signal is applied to a single grain on one side of the device, and the output signal is measured from another grain on the other side of the device. Changing the size of one or many grains tunes the pressure, which controls the vibrational response of the device. Switching between the on and off states is achieved using two mechanisms: (1) pressure-induced switching where the interparticle contact network is the same in the on and off states and (2) switching through contact breaking. In general, the performance of the acoustic switch, as captured by the gain ratio and switching time between the on and off states, is better for pressure-induced switching. We show that in these acoustic switches the gain ratio between the on and off states can be larger than 10^{4} and the switching time (multiplied by the driving frequency) is comparable to that obtained recently for sonic crystals and less than that for photonic transistor-like switches. Since the self-assembly of grains with different masses into 2D granular crystals is challenging, we describe simulations of circular grains with small circular knobs placed symmetrically around the perimeter mixed with circular grains without knobs. Using umbrella sampling techniques, we show that grains with six knobs most efficiently form the hexagonal crystals that yield the largest frequency band gap. Using the simulation results, we estimate the time required for vibration experiments to generate granular crystals of millimeter-sized steel beads with maximal band gaps.

Hybrid Monte Carlo with LAMMPS

We describe a strategy for performing canonical and isothermal-isobaric ensemble hybrid Monte Carlo (HMC) simulations with the widely-used Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) molecular dynamics (MD) software package. The overall workflow for the HMC simulations is handled using an external Python driver script, which invokes LAMMPS’ library interface to perform numerically intensive tasks such as MD integration. We document several rigorous consistency checks that have been used to validate our HMC implementation. We also demonstrate that our approach can be readily extended to implement biased HMC sampling schemes for computing free energies. Codes and input files from the documented examples are available on the web.

Colloidal Cluster Assembly into Ordered Superstructures via Engineered Directional Binding

Recent experimental studies have demonstrated a facile route for fabricating large numbers of geometrically uniform colloidal clusters out of submicron DNA-functionalized spheres. These clusters are ideally suited for use as anisotropic building blocks for hierarchical assembly of superstructures with symmetries that are otherwise inaccessible with simple spherical particles. We study computationally the self-assembly of cubic, tetrahedral, and octahedral clusters mediated by "bond spheres" that dock with the clusters at specific preferential sites, providing robust and well-defined directional bonding. We analyze the assembly process with a combination of direct molecular dynamics simulations of superstructure growth and state-of-the-art umbrella sampling techniques to compute nucleation free energy profiles. The simulations confirm the versatility and robustness of hierarchical cluster assembly but also reveal potential obstacles in the form of energetically accessible defect states. We find and study solutions for bypassing these defects that rely on appropriate selection of particle size and interparticle interaction as a function of building block shape and, therefore, provide operational guidelines for future experimental demonstrations.

Lattice mold technique for the calculation of crystal nucleation rates

We present a new simulation method for the calculation of crystal nucleation rates by computer simulation. The method is based on the use of molds to induce crystallization in state points where nucleation is a rare event. The mold is a cluster of potential energy wells placed in the lattice positions of the solid. The method has two distinct steps. In the first one the probability per unit volume of forming a sub-critical crystal cluster in the fluid is computed by means of thermodynamic integration. The thermodynamic route consists in gradually switching on an attractive interaction between the wells and the fluid particles. In the second step, the frequency with which such cluster becomes post-critical is computed in Molecular Dynamics simulations with the mold switched on. We validate our method with a continuous version of the hard sphere potential and with the sodium chloride Tosi–Fumi model. In all studied state points we obtain a good agreement with literature data obtained from other rare event simulation techniques. Our method is quite suitable for the study of both crystal nucleation of arbitrarily complex structures and the competition between different polymorphs in the nucleation stage.