Delayed gravitational collapse of colloidal gels is characterized by initially slow compaction that gives way to rapid bulk collapse, posing interesting questions about the underlying mechanistic origins. Here we study gel collapse utilizing large-scale dynamic simulation of a freely draining gel of physically bonded particles subjected to gravitational forcing. The hallmark regimes of collapse are recovered: slow compaction, transition to rapid collapse, and long-time densification. Microstructural changes are monitored by tracking particle positions, coordination number, and bond dynamics, along with volume fraction, osmotic pressure, and potential energy. Together these reveal the surprising result that collapse can occur with a fully intact network, where the tipping point arises when particle migration dissolves strands in a capillary-type instability. While it is possible for collapse to rupture a gel network into clusters that then sediment, and hydrodynamic interactions can make interesting contributions, neither is necessary. Rather, we find that the "delay" arises from gravity-enhanced coarsening, which triggers the re-emergence of phase separation. The mechanism of this transition is a leap toward lower potential energy of the gel, driven by bulk negative osmotic pressure that condenses the particle phase: the gel collapses in on itself under negative osmotic pressure allowing the gel, to tunnel through the equilibrium phase diagram to a higher volume fraction "state". Remarkably, collapse stops when condensation stops, when gravitational advection produces a positive osmotic pressure, re-arresting the gel.
Cubic bicontinuous phases like the double gyroid (G), double diamond (D), and plumber’s nightmare (P) are of great practical interest for many emerging applications requiring highly regular nanoscale networks or porous materials. Such phases can be formed from A–B diblock copolymers by the addition of A-type homopolymer over a range of compositions and relative chain lengths. Particle-based molecular simulations were used to delineate the phase diagram in a region where self-consistent field theory predicts the presence of a G–D–P triple point. Since the simulation box size must be commensurate with the morphology-specific 3D unit cell size (which is not known a priori), accurate free energy estimates are required for a range of box sizes, particularly when multiple competing phases can occur at the conditions of interest. A variant of thermodynamic integration was implemented to obtain such free energies (and hence identify the stable phases and their optimal box sizes) by tracing a reversible path connecting the ordered and disordered phases. This method overcomes key limitations of free energy methods based on the evaluation of chemical potentials via molecular insertions. For the range of conditions simulated, evidence was found of D–G, D–P, and G–D–P phase coexistence, consistent with previous theoretical predictions. Our simulations also reveal key differences and similarities in the size and microstructure of the nodes and struts that make up the different types of bicontinuous networks.
T-shaped bolaamphiphiles (TBA) with a swallow-tail lateral chain have been found to provide a fertile platform to produce complex liquid crystalline phases that are accessible through changes of temperature and lateral chain length and design. In this work, we use molecular simulations of a simple coarse-grained model to map out the phase behavior of this type of molecules. This model is based on the premise that the crucial details of the fluid structure stem from close range repulsions and the strong directional forces typical of hydrogen bonds. Our simulations confirm that TBAs exhibit a rich phase behavior upon increasing the length of their lateral chain. The simulations detect a double gyroid phase and an axial-bundle columnar phase which bear some structural resemblance to those found in the experiment. In addition, simulations predict two cocontinuous phases with 3D-periodicity: the "single" diamond and the "single" plumber's nightmare phase. Our analysis of energetic and entropic contributions to the free energy of phases formed by TBA with either swallow-tail or linear side-chains suggest that the 3D-periodic network phases formed by the former are stabilized by the large conformation entropy of the side-chains.
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