Swetlana Jungblut

Crystallization of a binary Lennard-Jones mixture

Transition interface path sampling combined with straightforward molecular dynamics simulation was applied to study the mechanism and kinetics of the crystallization of an undercooled 3:1 binary Lennard-Jones mixture with diameter ratio 0.85 and equal interaction strengths. We find that this mixture freezes via the formation of crystalline clusters consisting of a fcc-rich core and a bcc-rich surface layer, with an excess of large particles and particle species distributed randomly. A detailed comparison reveals that the transition mechanism is similar to that of the pure fluid but occurs with much smaller nucleation rates even at comparable degrees of undercooling. Also, the growth of the crystalline cluster in the mixture proceeds at a pace about 1 order of magnitude slower than in the pure system. Possibly, this slow dynamics of the mixture is related to the occurrence and subsequent relaxation of icosahedral structures in the growing crystal as well as in the liquid surrounding it.

Optimising reaction coordinates for crystallisation by tuning the crystallinity definition

We apply maximum likelihood analysis to optimise crystallisation measures based on Steinhardt bond order parameters. Assuming that the size of the largest cluster of crystalline particles serves as a good reaction coordinate for the freezing transition, we write down the likelihood to observe the committor values computed for a large number of configurations. We then maximise the likelihood function by varying the parameters that enter the definition of crystallinity. For the crystallinity definition considered here this parameter set consists of the thresholds for the next-neighbour distance, the strength of the crystalline bonds and the number of crystalline connections. The optimum parameter set found by the likelihood maximisation differs considerably from the parameters that are commonly used, but leads only to a marginal improvement of the quality of the reaction coordinate.

Heterogeneous crystallization on tiny clusters

The crystallization transition of an undercooled monodisperse Lennard-Jones fluid in the presence of small pre-structured seeds is studied with transition interface path sampling combined with molecular dynamics simulations. Compared to the homogeneous crystallization, clusters of 13 particles arranged into a face-centered cubic structure enhance the crystallization rate by one order of magnitude, while icosahedrally ordered seeds do not change the reaction rate at all. We identify two distinct nucleation regimes —close to the seed and in the bulk. Crystallites formed close to the seed attach to it, if it has face-centered cubic structure, and grow around the seed, if its structure is icosahedral.

Pathways to self-organization: Crystallization via nucleation and growth

Abstract.Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In this article, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.Graphical abstract

Dynamic phases of colloidal monolayers sliding on commensurate substrates

We report on numerical simulations of a monolayer of charge-stabilized colloids driven over a substrate potential by an external dc force acting along a symmetry axis of the monolayer. Using overdamped Langevin dynamics, we studied the sliding transition for various inter-particle interaction strengths as a function of the driving force. For weak interactions, the diffusion of individual defects is responsible for the motion of the monolayer. As the interaction strength is increased, sliding is induced by distinct density compression and decompression zones. For very strong interactions, a type of stick-slip mechanism emerges, in which the sliding of the monolayer is mediated by the propagation of collective distortion waves. Our predictions can be tested experimentally with two-dimensional arrangements of colloidal particles exposed to periodic light fields and our work shows that the inter-particle interaction strength tunes the degree of correlation in the sliding mechanism adopted by a monolayer driven over a commensurate substrate.

Caveats of mean first-passage time methods applied to the crystallization transition: Effects of non-Markovianity

Using the crystallization transition in a Lennard-Jones fluid as example, we show that mean first-passage time based methods may underestimate the reaction rates. We trace the reason of this deficiency back to the non-Markovian character of the dynamics caused by the projection to a poorly chosen reaction coordinate. The non-Markovianity of the dynamics becomes apparent in the behavior of the recurrence times.

On the reaction coordinate for seeded crystallisation

Small pre-structured seeds introduced into an undercooled fluid are known to increase the crystal nucleation rate by some orders of magnitude, if the structure of the seeds is commensurate with the bulk crystalline phase. The presence of such seeds also alters the crystallisation mechanism by favouring particular structures at the early stages of the nucleation process. Here, we study with computer simulations the effect of small face-centred cubic and body-centred cubic seeds on the crystallisation of a Lennard-Jones liquid in the strongly undercooled regime. We find that seeds with body-centred cubic structure lead to a larger enhancement of the crystallisation rate than face-centred cubic seeds. An analysis of recurrence times reveals that the size of the largest crystalline cluster used as reaction coordinate is affected by pronounced memory effects, which depend on the particular seed structure and point to the importance of structural information in the definition of a good reaction coordinate for crystallisation.

Crystallization and flow in active patch systems

Based upon recent experiments in which Janus particles are made into active swimmers by illuminating them with laser light, we explore the effect of applying a light pattern on the sample, thereby creating activity inducing zones or active patches. We simulate a system of interacting Brownian diffusers that become active swimmers when moving inside an active patch and analyze the structure and dynamics of the ensuing stationary state. We find that, in some respects, the effect of spatially inhomogeneous activity is qualitatively similar to a temperature gradient. For asymmetric patches, however, this analogy breaks down because the ensuing stationary state is specific to partial active motion.

Heterogeneous Crystallization on Pairs of Pre-Structured Seeds

Studying the effects of small pre-structured seeds on the crystallization transition in an undercooled monodisperse Lennard-Jones fluid with transition interface path sampling combined with molecular dynamics simulations, we analyze the impact of the simultaneous presence of two seeds with various structures. In the presence of seeds with face- and body-centered cubic structures, we find that decreasing the seed-to-seed distance enhances the probability of the crystalline clusters formed on one of the seeds to grow beyond the critical size, thus, increasing the crystal nucleation rates. In contrast, when seeds have an icosahedral structure, the crystalline clusters form mostly in the bulk. The crystal nucleation rate, however, is also determined by the distance between the seeds with regular structure in which the lattice spacing is equal to the bulk lattice constant, pointing to a heterogeneous crystal nucleation that occurs away from the icosahedrally structured seeds. For slightly squeezed seeds, the effects of the presence of seeds with face- and body-centered cubic structures are reduced in comparison to the regular seeds, and we do not see any effect of the presence of the second seed for seeds with squeezed icosahedral structure.

Dynamical phases of attractive particles sliding on a structured surface.

Inspired by experiments on quartz crystal microbalance setups, we study the mobility of a monolayer of Lennard-Jones particles driven over a hexagonal external potential. We pay special attention to the changes in the dynamical phases that arise when the lattice constant of the external substrate potential and the Lennard-Jones interaction are mismatched. We find that if the average particle separation is such that the particles repel each other, or interact harmonically, the qualitative behavior of the system is akin to that of a monolayer of purely repulsive Yukawa particles. On the other hand, if the particles typically attract each other, the ensuing dynamical states are determined entirely by the relative strength of the Lennard-Jones interaction with respect to that of the external potential.