Alex Malins

Identification of long-lived clusters and their link to slow dynamics in a model glass former

We study the relationship between local structural ordering and dynamical heterogeneities in a model glass-forming liquid, the Wahnström mixture. A novel cluster-based approach is used to detect local energy minimum polyhedral clusters and local crystalline environments. A structure-specific time correlation function is then devised to determine their temporal stability. For our system, the lifetime correlation function for icosahedral clusters decays far slower than for those of similarly sized but topologically distinct clusters. Upon cooling, the icosahedra form domains of increasing size and their lifetime increases with the size of the domains. Furthermore, these long-lived domains lower the mobility of neighboring particles. These structured domains show correlations with the slow regions of the dynamical heterogeneities that form on cooling towards the glass transition. Although icosahedral clusters with a particular composition and arrangement of large and small particles are structural elements of the crystal, we find that most icosahedral clusters lack such order in composition and arrangement and thus local crystalline ordering makes only a limited contribution to this process. Finally, we characterize the spatial correlation of the domains of icosahedra by two structural correlation lengths and compare them with the four-point dynamic correlation length. All the length scales increase upon cooling, but in different ways.

Identification of structure in condensed matter with the topological cluster classification

We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids with m ≤ 13 particles. We detail a modified Voronoi bond detection method that optimizes the cluster detection. The method to identify each cluster is outlined, and a test example of Lennard-Jones liquid and crystal phases is considered and critically examined.

Geometric frustration in small colloidal clusters

We study the structure of clusters in a model colloidal system with competing interactions using Brownian dynamics simulations. A short-ranged attraction drives clustering, while a weak, long-ranged repulsion is used to model electrostatic charging in experimental systems. The former is treated with a short-ranged Morse attractive interaction, the latter with a repulsive Yukawa interaction. We consider the yield of clusters of specific structure as a function of the strength of the interactions, for clusters with m = 3,4,5,6,7,10 and 13 colloids. At sufficient strengths of the attractive interaction (around 10k(B)T), the average bond lifetime approaches the simulation timescale and the system becomes nonergodic. For small clusters, m≤5, where geometric frustration is not relevant, despite nonergodicity, for sufficient strengths of the attractive interaction the yield of clusters which maximize the number of bonds approaches 100%. However for m = 7 and higher, in the nonergodic regime we find a lower yield of these structures where we argue geometric frustration plays a significant role. m = 6 is a special case, where two structures, of octahedral and C(2v) symmetry, compete, with the latter being favoured by entropic contributions in the ergodic regime and by kinetic trapping in the nonergodic regime. We believe that our results should be valid as long as the one-component description of the interaction potential is valid. A system with competing electrostatic repulsions and van der Waals attractions may be such an example. However, in some cases, the one-component description of the interaction potential may not be appropriate.

Novel kinetic trapping in charged colloidal clusters due to self-induced surface charge organization

We study metastable clusters in a colloidal system with competing interactions. A short-ranged polymer-induced attraction drives clustering, while a weak, long-ranged electrostatic repulsion prevents extensive aggregation. We compare experimental yields of cluster structures expected from theory, which assumes simple addition of the competing isotropic interactions. For clusters of size

A structural comparison of models of colloid―polymer mixtures

4leq mleq6

Strong geometric frustration in model glassformers

, the yield is significantly less than that expected. We attribute this to an anisotropic self-organized surface charge distribution linked to the cluster symmetry: non-additivity of electrostatic repulsion and polymer-induced attraction. 7-membered clusters have a clear optimal yield of the expected pentagonal bipyramid structure as a function of strength of the attractive interaction.Colloidal clusters are an unusual state of matter where tunable interactions enable a sufficient reduction in their degrees of freedom that their energy landscapes can become tractable — they form a playground for statistical mechanics and promise unprecedented control of structure on the submicron lengthscale. We study colloidal clusters in a system where a short-ranged polymer-induced attraction drives clustering, while a weak, long-ranged electrostatic repulsion prevents extensive aggregation. We compare experimental yields of cluster structures with theory which assumes simple addition of competing isotropic interactions between the colloids. Here we show that for clusters of size 4 ≤ m ≤ 7, the yield of minimum energy clusters is much less than expected. We attribute this to an anisotropic self-organized surface charge distribution which leads to unexpected kinetic trapping. We introduce a model for the coupling between counterions and binding sites on the colloid surface with which we interpret our findings.

Investigating isomorphs with the topological cluster classification.

We study the structure of colloidal fluids with reference to colloid-polymer mixtures. We compare the one-component description of the Asakura-Oosawa (AO) idealization of colloid-polymer mixtures with the full two-component model. We also consider the Morse potential, a variable range interaction, for which the ground state clusters are known. Mapping the state points between these systems, we find that the pair structure of the full AO model is equally well described by the Morse potential and the one-component AO approach. We employ a recently developed method to identify in the bulk fluid the ground state clusters relevant to the Morse potential. Surprisingly, when we measure the cluster populations, we find that the Morse fluid is significantly closer the full AO fluid than the one-component AO description.

The effect of inter-cluster interactions on the structure of colloidal clusters

Abstract We consider three popular model glassformers, the Kob–Andersen and Wahnstrom binary Lennard–Jones models and weakly polydisperse hard spheres. Although these systems exhibit a range of fragilities, all feature a rather similar behaviour in their local structure approaching dynamic arrest. In particular we use the dynamic topological cluster classification to extract a locally favoured structure which is particular to each system. These structures form percolating networks, however in all cases there is a strong decoupling between structural and dynamic lengthscales. We suggest that the lack of growth of the structural lengthscale may be related to strong geometric frustration.

The effect of attractions on the local structure of liquids and colloidal fluids

Isomorphs are lines in the density-temperature plane of certain strongly correlating or Roskilde simple liquids where two-point structure and dynamics have been shown to be close to identical up to a scale transformation. Here we consider such a liquid, a Lennard-Jones glass former, and investigate the behavior along isomorphs of higher-order structural and dynamical correlations. We then consider an inverse power law reference system mapped to the Lennard-Jones system [Pedersen et al., Phys. Rev. Lett. 105, 157801 (2010)]. Using the topological cluster classification to identify higher-order structures, in both systems we find bicapped square antiprisms, which are known to be a locally favored structure in the Lennard-Jones glass former. The population of these locally favored structures is up to 80% higher in the Lennard-Jones system than the equivalent inverse power law system. The structural relaxation time of the two systems, on the other hand, is almost identical, and the four-point dynamical susceptibility is marginally higher in the inverse power law system. Upon cooling, the lifetime of the locally favored structures in the Lennard-Jones system is up to 40% higher relative to the reference system.

Local structure of liquid–vapour interfaces

Colloidal systems present exciting opportunities to study clusters. Unlike atomic clusters, which are frequently produced at extremely low density, colloidal clusters may interact with one another. Here we consider the effect of such interactions on the intra-cluster structure in simulations of colloidal cluster fluids. A sufficient increase in density leads to a higher population of clusters in the ground state. In other words, inter-cluster interactions perturb the intra-cluster behaviour, such that each cluster may no longer be considered as an isolated system. Conversely, for dilute, weakly interacting cluster fluids little dependence on colloid concentration is observed, and we thus argue that it is reasonable to treat each cluster as an isolated system.