A simple and accurate method to determine fluid-crystal phase boundaries from direct coexistence simulations.

One method for computationally determining phase boundaries is to explicitly simulate a direct coexistence between the two phases of interest. Although this approach works very well for fluid-fluid coexistences, it is often considered to be less useful for fluid-crystal transitions, as additional care must be taken to prevent the simulation boundaries from imposing unwanted strains on the crystal phase. Here, we present a simple adaptation to the direct coexistence method that nonetheless allows us to obtain highly accurate predictions of fluid-crystal coexistence conditions, assuming that a fluid-crystal interface can be readily simulated. We test our approach on hard spheres, the screened Coulomb potential, and a 2D patchy-particle model. In all cases, we find excellent agreement between the direct coexistence approach and (much more cumbersome) free-energy calculation methods. Moreover, the method is sufficiently accurate to resolve the (tiny) free-energy difference between the face-centered cubic and hexagonally close-packed crystal of hard spheres in the thermodynamic limit. The simplicity of this method also ensures that it can be trivially implemented in essentially any simulation method or package. Hence, this approach provides an excellent alternative to free-energy based methods for the precise determination of phase boundaries.

In search of a precursor for crystal nucleation of hard and charged colloids.

The interplay between crystal nucleation and the structure of the metastable fluid has been a topic of significant debate over recent years. In particular, it has been suggested that even in simple model systems such as hard or charged colloids, crystal nucleation might be foreshadowed by significant fluctuations in local structure around the location where the nucleus first arises. We investigate this using computer simulations of spontaneous nucleation events in both hard and charged colloidal systems. To detect local structural variations, we use both standard and unsupervised machine learning methods capable of finding hidden structures in the metastable fluid phase. We track numerous nucleation events for the face-centered cubic and body-centered cubic crystals on a local level and demonstrate that all signs of crystallinity emerge simultaneously from the very start of the nucleation process. We thus conclude that we observe no precursor for the crystal nucleation of hard and charged colloids.

Crystal nucleation of highly screened charged colloids.

We study the nucleation of nearly hard charged colloidal particles. We use Monte Carlo simulations in combination with free-energy calculations to accurately predict the phase diagrams of these particles and map them via the freezing density to hard spheres, then we use umbrella sampling to explore the nucleation process. Surprisingly, we find that even very small amounts of charge repulsion can have a significant effect on the phase behavior. Specifically, we find that phase boundaries and nucleation barriers are mostly dependent on the Debye screening length and that even screening lengths as small as 2% of the particle diameter are sufficient to show marked differences in both. This work demonstrates clearly that even mildly charged colloids are not effectively hard spheres.

Defects in crystals of soft colloidal particles.

In this paper we use computer simulations to examine point defects in systems of "soft" colloidal particles including Hertzian spheres, and star polymers. We use Monte Carlo simulations to determine the deformation of the different crystals associated with vacancies and interstitials and use thermodynamic integration to predict the equilibrium concentrations of such defects. We find that the nature of the lattice distortion is mainly determined by the crystal structure and not by the specifics of the interaction potential. We can distinguish one-, two-, and three-dimensional lattice distortions and find that the range of the distortion generally depends on the dimensionality. We find that in both model systems the deformation of the body-centered cubic (BCC) crystal caused by an interstitial is one-dimensional and we show that its structure is well described as a crowdion. Similarly, we show that the one-dimensional deformation of the hexagonal (H) crystal of Hertzian spheres caused by a vacancy can be characterized as a voidion. Interestingly, with the exception of the FCC crystal in the Hertzian sphere model, in all cases we find that the interstitial concentration is higher than the vacancy concentration. Most noteworthy, the concentration of interstitials in the BCC crystals can reach up to 1%.

Point defects in crystals of charged colloids.

Charged colloidal particles-on both the nano and micron scales-have been instrumental in enhancing our understanding of both atomic and colloidal crystals. These systems can be straightforwardly realized in the lab and tuned to self-assemble into body-centered-cubic (BCC) and face-centered-cubic (FCC) crystals. While these crystals will always exhibit a finite number of point defects, including vacancies and interstitials-which can dramatically impact their material properties-their existence is usually ignored in scientific studies. Here, we use computer simulations and free-energy calculations to characterize vacancies and interstitials in FCC and BCC crystals of point-Yukawa particles. We show that, in the BCC phase, defects are surprisingly more common than in the FCC phase, and the interstitials manifest as so-called crowdions: an exotic one-dimensional defect proposed to exist in atomic BCC crystals. Our results open the door to directly observe these elusive defects in the lab.

Ratchet-induced variations in bulk states of an active ideal gas.

We study the distribution of active, noninteracting particles over two bulk states separated by a ratchet potential. By solving the steady-state Smoluchowski equations in a flux-free setting, we show that the ratchet potential affects the distribution of particles over the bulks and thus exerts an influence of infinitely long range. As we show, an external potential that is nonlinear is crucial for having such a long-range influence. We characterize how the difference in bulk densities depends on activity and on the ratchet potential, and we identify power law dependencies on system parameters in several limiting cases. While weakly active systems are often understood in terms of an effective temperature, we present an analytical solution that explicitly shows that this is not possible in the current setting. Instead, we rationalize our results by a simple transition state model that presumes particles to cross the potential barrier by Arrhenius rates modified for activity. While this model does not quantitatively describe the difference in bulk densities for feasible parameter values, it does reproduce-in its regime of applicability-the complete power law behavior correctly.