Two features at the two-dimensional freezing transitions

Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: phase behavior and structural properties

Competing short-range attractive (SA) and long range repulsive (LR) particle interactions can be used to describe three-dimensional charge-stabilized colloid or protein dispersions at low added salt concentrations, as well as membrane proteins with interaction contributions mediated by lipid molecules. Using Langevin dynamics (LD) simulations, we determine the generalized phase diagram, cluster shapes and size distributions of a generic quasi-two-dimensional (Q2D) dispersion of spherical SALR particles confined to in-plane motion inside a bulk fluid. The SA and LR interaction parts are modelled by a generalized Lennard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the detected equilibrium and non-equilibrium Q2D phases are distinctly different from those observed in three-dimensional (3D) SALR systems, by exhibiting different levels of hexagonal ordering. We discuss a thermodynamic perturbation theory prediction for the metastable binodal line of a reference system of particles with SA interactions only, which in the explored Q2D-SALR phase diagram region separates cluster from non-clustered phases. The transition from the high-temperature (small SA) dispersed fluid (DF) phase to the lower-temperature equilibrium cluster (EC) fluid phase is characterised by a low-wavenumber peak height of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller value (≈1.4) than in 3D SALR systems. With decreasing temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster segments formed in a cluster-percolated (CP) gel-like phase. This transition can be quantified by a hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the CP phase are insensitive to changes in the attraction strength.

Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.

Ordering and Dynamics of Interacting Colloidal Particles under Soft Confinement

Confinement can induce substantial changes in the physical properties of macromolecules in suspension. Soft confinement is a particular class of restriction where the boundaries that constraint the particles in a region of the space are not well-defined. This scenario leads to a broader structural and dynamical behavior than observed in systems enclosed between rigid walls. In this contribution, we study the ordering and diffusive properties of a two-dimensional colloidal model system subjected to a one-dimensional parabolic trap. Increasing the trap strength makes it possible to go through weak to strong confinement, allowing a dimensional transition from two- to one-dimension. The non-monotonic response of the static and dynamical properties to the gradual dimensionality change affects the system phase behavior. We find that the particle dynamics are connected to the structural transitions induced by the parabolic trap. In particular, at low and intermediate confinement regimes, complex structural and dynamical scenarios arise, where the softness of the external potential induces melting and freezing, resulting in faster and slower particle diffusion, respectively. Besides, at strong confinements, colloids move basically along one direction, and the whole system behaves structurally and dynamically similar to a one-dimensional colloidal system.

Bond-orientational order and Frank's constant in two-dimensional colloidal hard spheres

Recently, the full phase behaviour of 2D colloidal hard spheres was experimentally established, and found to involve a first order liquid to hexatic transition and a continuous hexatic to crystal transition (Thorneywork et al 2017 Phys. Rev. Lett. 118 158001). Here, we expand upon this work by considering the behaviour of the bond-orientational correlation time and Frank's constant in the region of these phase transitions. We also consider the excess entropy, as calculated from the radial distribution functions, for a wide range of area fractions covering the liquid, hexatic and crystal phases. In all cases, the behaviour of these quantities further corroborates the previously reported melting scenario of 2D colloidal hard spheres.

Structural correlations and cooperative dynamics in supercooled liquids

The relationships between diffusivity and the excess, pair and residual multiparticle contributions to the entropy are examined for Lennard-Jones liquids and binary glassformers, in the context of approximate inverse power law mappings of simple liquids. In the dense liquid where diffusivities are controlled by collisions and cage relaxations, Rosenfeld-type excess entropy scaling of diffusivities is found to hold for both crystallizing as well as vitrifying liquids. The crucial differences between the two categories of liquids emerge only when local cooperative effects in the dynamics result in significant caging effects in the time-dependent behaviour of the single-particle mean square displacement. In the case of glassformers, onset of such local cooperativity coincides with onset of deviations from Rosenfeld-type excess entropy scaling of diffusivities and increasing spatiotemporal heterogeneity. In contrast, for two- and three-dimensional liquids with a propensity to crystallise, the onset of local cooperative dynamics is sufficient to trigger crystallization provided that the liquid is sufficiently supercooled that the free energy barrier to nucleation of the solid phase is negligible. The state points corresponding to onset of transient caging effects can be associated with typical values, within reasonable bounds, of the excess, pair, and residual multiparticle entropy as a consequence of the isomorph-invariant character of the excess entropy, diffusivity and related static and dynamic correlation functions.