The physics of Empty Liquids: from Patchy particles to Water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Facile self-assembly of colloidal diamond from tetrahedral patchy particles via ring selection

Diamond-structured crystals, particularly those with cubic symmetry, have long been attractive targets for the programmed self-assembly of colloidal particles, due to their applications as photonic crystals that can control the flow of visible light. While spherical particles decorated with four patches in a tetrahedral arrangement—tetrahedral patchy particles—should be an ideal building block for this endeavor, their self-assembly into colloidal diamond has proved elusive. The kinetics of self-assembly pose a major challenge, with competition from an amorphous glassy phase, as well as clathrate crystals, leaving a narrow widow of patch widths where tetrahedral patchy particles can self-assemble into diamond crystals. Here we demonstrate that a two-component system of tetrahedral patchy particles, where bonding is allowed only between particles of different types to select even-member rings, undergoes crystallization into diamond crystals over a significantly wider range of patch widths conducive for experimental fabrication. We show that the crystallization in the two-component system is both thermodynamically and kinetically enhanced, as compared to the one-component system. Although our bottom-up route does not lead to the selection of the cubic polytype exclusively, we find that the cubicity of the self-assembled crystals increases with increasing patch width. Our designer system not only promises a scalable bottom-up route for colloidal diamond but also offers fundamental insight into crystallization into open lattices.

DNA self-organization controls valence in programmable colloid design

Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence—the number of interparticle bonds—is a prerequisite for the assembly of complex architectures. The assembly can be directed via solid “patchy” particles with prescribed geometries to make, for example, a colloidal diamond. We demonstrate here that the nanoscale ordering of individual molecular linkers can combine to program the structure of microscale assemblies. Specifically, we experimentally show that covering initially isotropic microdroplets with N mobile DNA linkers results in spontaneous and reversible self-organization of the DNA into Z(N) binding patches, selecting a predictable valence. We understand this valence thermodynamically, deriving a free energy functional for droplet–droplet adhesion that accurately predicts the equilibrium size of and molecular organization within patches, as well as the observed valence transitions with N. Thus, microscopic self-organization can be programmed by choosing the molecular properties and concentration of binders. These results are widely applicable to the assembly of any particle with mobile linkers, such as functionalized liposomes or protein interactions in cell–cell adhesion.

Self-Assembly of Porous Structures From a Binary Mixture of Lobed Patchy Particles

We report simulation studies on the self-assembly of a binary mixture of snowman and dumbbell shaped lobed particles. Depending on the lobe size and temperature, different types of self-assembled structures (random aggregates, spherical aggregates, liquid droplets, amorphous wire-like structures, amorphous ring structures, crystalline structures) are observed. At lower temperatures, heterogeneous structures are formed for lobed particles of both shapes. At higher temperatures, homogeneous self-assembled structures are formed mainly by the dumbbell shaped particles, while the snowman shaped particles remain in a dissociated state. We also investigated the porosities of self-assembled structures. The pore diameters in self-assemblies increased with an increase in temperature for a given lobe size. The particles having smaller lobes produced structures with larger pores than the particles having larger lobes. We further investigated the effect of σ, a parameter in the surface-shifted Lennard-Jones potential, on the self-assembled morphologies and their porosities. The self-assembled structures formed at a higher σ value are found to produce larger pores than those at a lower σ.

Revealing pseudorotation and ring-opening reactions in colloidal organic molecules

Colloids have a rich history of being used as ‘big atoms’ mimicking real atoms to study crystallization, gelation and the glass transition of condensed matter. Emulating the dynamics of molecules, however, has remained elusive. Recent advances in colloid chemistry allow patchy particles to be synthesized with accurate control over shape, functionality and coordination number. Here, we show that colloidal alkanes, specifically colloidal cyclopentane, assembled from tetrameric patchy particles by critical Casimir forces undergo the same chemical transformations as their atomic counterparts, allowing their dynamics to be studied in real time. We directly observe transitions between chair and twist conformations in colloidal cyclopentane, and we elucidate the interplay of bond bending strain and entropy in the molecular transition states and ring-opening reactions. These results open the door to investigate complex molecular kinetics and molecular reactions in the high-temperature classical limit, in which the colloidal analogue becomes a good model.

Mikto-Arm Stars as Soft-Patchy Particles: From Building Blocks to Mesoscopic Structures

We present an atomistic molecular dynamics study of self-assembled mikto-arm stars, which resemble patchy-like particles. By increasing the number of stars in the system, we propose a systematic way of examining the mutual orientation of these fully penetrable patchy-like objects. The individual stars maintain their patchy-like morphology when creating a mesoscopic (macromolecular) self-assembled object of more than three stars. The self-assembly of mikto-arm stars does not lead to a deformation of the stars, and their shape remains spherical. We identified characteristic sub-units in the self-assembled structure, differing by the mutual orientation of the nearest neighbor stars. The current work aims to elucidate the possible arrangements of the realistic, fully penetrable patchy particles in polymer matrix and to serve as a model system for further studies of nanostructured materials or all-polymer nanocomposites using the mikto-arm stars as building blocks.