Translational and orientational excluded-volume fields encoded in particles with anisotropic shapes can lead to purely entropy-driven assembly of morphologies with specific order and symmetry. To ...elucidate this complex correlation, we carried out detailed Monte Carlo simulations of six convex space-filling polyhedrons, namely, truncated octahedrons, rhombic dodecahedrons, hexagonal prisms, cubes, gyrobifastigiums and triangular prisms. Simulations predict the formation of various new liquid-crystalline and plastic-crystalline phases at intermediate volume fractions. By correlating these findings with particle anisotropy and rotational symmetry, simple guidelines for predicting phase behaviour of polyhedral particles are proposed: high rotational symmetry is in general conducive to mesophase formation, with low anisotropy favouring plastic-solid behaviour and intermediate anisotropy (or high uniaxial anisotropy) favouring liquid-crystalline behaviour. It is also found that dynamical disorder is crucial in defining mesophase behaviour, and that the apparent kinetic barrier for the liquid-mesophase transition is much lower for liquid crystals (orientational order) than for plastic solids (translational order).
Mixtures of nanoparticles (NPs) with hybridizing grafted DNA or DNA-like strands have been shown to create highly tunable NP–NP interactions, which, if designed to give nonadditive mixing, could lead ...to a richer self-assembly behavior. While nonadditive mixing is known to result in nontrivial phase behavior in molecular fluids, its effects on colloidal/NP materials have been much less studied. Such effects are explored here via molecular simulations for a binary system of tetrahedral patchy NPs, known to self-assemble into the diamond phase. The NPs are modeled with raised patches that interact through a coarse-grained interparticle potential representing DNA hybridization between grafted strands. It was found that these patchy NPs spontaneously nucleate into the diamond phase, and that hard-interacting NP cores eliminated the competition between the diamond and BCC phases at the conditions studied. Our results also showed that while higher nonadditivity had a small effect on phase behavior, it kinetically enhanced the formation of the diamond phase. Such a kinetic enhancement is argued to arise from changes in phase packing densities and how these modulate the interfacial free energy of the crystalline nucleus by favoring high-density motifs in the isotropic phase and larger NP vibrations in the diamond phase.
Mixtures of nanoparticles (NPs) with hybridizing grafted DNA or DNA-like strands have been of particular interest because of the tunable selectivity provided for the interactions between the NP ...components. A richer self-assembly behavior would be accessible if these NP-NP interactions could be designed to give nonadditive mixing (in analogy to the case of molecular components). Nonadditive mixing occurs when the mixed-state volume is smaller (negative) or larger (positive) than the sum of the individual components’ volumes. However, instances of nonadditivity in colloidal/NP mixtures are rare, and systematic studies of such mixtures are nonexistent. This work focuses on patchy NPs whose patches (coarsely representing grafted hybridizing DNA strands) not only encode selectivity across components but also impart a tunable nonadditivity by varying their extent of protrusion. To guide the exploration of the relationship between phase behavior and nonadditivity for different patches’ designs, the NP–NP potential of mean force (PMF) and a nonadditive parameter were first calculated. For one-patch NPs, different lamellar morphologies were predominantly observed. In contrast, for mixtures of two-patch NPs and (fully grafted) spherical particles, a rich phase behavior was found depending on patch–patch angle and degree of nonadditivity, resulting in phases such as the gyroid, cylinder, honeycomb, and two-layered crystal. Our results also show that both minimum positive nonadditivity and multivalent interactions are necessary for the formation of ordered network mesophases in the class of models studied.
Bolapolyphiles constitute a versatile class of materials with a demonstrated potential to form a wide variety of complex ordered mesophases. In particular, cubic network phases (like the gyroid, ...primitive, and diamond phases) have been a target of many studies for their ability to create percolating 3D nanosized channels. In this study, molecular simulations are used to explore the phase behavior of bolapolyphiles containing a rigid rodlike core, associating hydrophilic core ends and a hydrophobic side chain with a multident architecture, i.e., where the branching pattern can vary from bident (two branches) to hexadent (six branches). Upon network phase formation, its skeleton is made up of “nodes” populated by the core ends and “struts” populated by the cores. It is shown that, by varying the side chain length, branching pattern, and attachment point to the core, one can alter the crowding around the cores and hence tune the nodal size and nodal valence (i.e., number of connecting struts) which lead to different types of network morphologies. For example, for a fixed total side chain length, having more branches generates a stronger crowding around the molecular core, driving them to form bundlelike domains with curvier interfaces that result in thinner struts. Also, attaching the lateral chain closer to one core end breaks the symmetry between the environments around the two core ends, leading to networks with bimodal nodal sizes. Importantly, since the characterization of (ordered or partially ordered) network phases is challenging given the potential incompatibilities between the simulation box size with the structure’s space group periodic symmetry and the effect of morphological defects, a detailed framework is presented to analyze and fully characterize the unit cell parameters and structure factor of such systems.
The role of entropic interactions, often subtle and sometimes crucial, on the structure and properties of soft matter has a well-recognized place in the classic and modern scientific literature. ...However, the lessons learned from many of those studies do not always form part of the standard arsenal of strategies that are taught or used for
de novo
studies relevant to the engineering of new materials. Fortunately, a growing number of examples exist where entropic effects have been designed
a priori
to achieve a desired or new outcome. This tutorial review describes some recent such examples, selected to illustrate the potential benefits of a more pro-active approach to harnessing the often overlooked power of entropy.
Although often fought against or designed accidentally, the intelligent design of entropy can lead to novel materials and phase behaviours.
Molecular simulations of coarse-grained diblock copolymers (DBP) were devised to unveil correlations between microstructure and ionic mobility (μ) in the limit of high salt dilution. It is found that ...three key microstructural features had a significant effect on ion transport: the extent of microdomains mixing (β), the local unit-cell tortuosity of the conductive domain (λ), and the local fluctuations in the density (ρ) of the polymer matrix. While the β effect has been previously studied in some detail for lamellae morphology, the effects of ρ nonhomogeneities and λ have received much less attention. To control the local fluctuations in ρ, a polymer design variant is explored that incorporates a second conductive block (A′) that is incompatible with the other two blocks (A′–A–B). It is found that increasing the fraction of A′ beads increases the frequency and amplitude of the local ρ depleted regions within the conductive domain, resulting in an increase in μ. Additionally, the effect of morphology on μ was examined by varying the volume fraction of the constitutive blocks and utilizing the different blocks as the conductive domains. It is shown that μ for various defect-free morphologies and chain lengths can be correlated to β and λ via a single universal curve.
This work aims to deepen our understanding of the molecular origin of the recently observed phenomenon of polymer cooperative adsorption onto faceted nanoparticle (NP) surfaces. By exploring a large ...parameter space for polymer/NP interactions through coarse-grained (CG) molecular dynamics (MD) simulations, it is found that consistent with experiments the presence or absence of cooperativity is related to solvent quality and relative interaction strengths between the polymer and the adsorbent. Specifically, positive cooperativity is associated with stronger polymer–polymer interaction than polymer–surface interactions and vice versa for negative cooperativity. This contrast in interaction energies manifests in positive cooperativity (i.e., increased affinity) and negative cooperativity (i.e., decreased affinity) as concentration increases. It is also found that increasing chain length strengthens cooperativity effects and that the nanoscale confinement of polymer chains to the adsorbing facet (due to weaker affinity to corners and edges) enhances positive cooperativity but weakens negative cooperativity. Moreover, adsorption onto a spherical NP shows stronger positive cooperativity but weaker negative cooperativity compared with adsorption onto a cubic NP of equal surface area. It was further found that as polymer bulk concentration increases, the free energy of adsorption decreases in positive cooperativity, increases in negative cooperativity, and is independent of concentration in noncooperative systems consistent with the phenomenological explanation of cooperativity. We further found that positive cooperativity is associated with growing fluctuations in the adsorption density at critical bulk polymer concentrations. This behavior can be attributed to the competition between enthalpic gains and entropic losses upon adsorption. Overall, our results shed light on the microscopic origin of cooperative adsorption and the role of solvent quality, which can be leveraged in, for example, controlling NP growth into target shapes and designing NP catalysts with improved performance.
The simulation of homogeneous liquid to vapor nucleation is investigated using three rare-event algorithms, boxed molecular dynamics, hybrid umbrella sampling Monte Carlo, and forward flux sampling. ...Using novel implementations of these methods for efficient use in the isothermal-isobaric ensemble, the free energy barrier to nucleation and the kinetic rate are obtained for a Lennard-Jones fluid at stretched and at superheated conditions. From the free energy surface mapped as a function of two order parameters, the global density and largest bubble volume, we find that the free energy barrier height is larger when projected over bubble volume. Using a regression analysis of forward flux sampling results, we show that bubble volume is a more ideal reaction coordinate than global density to quantify the progression of the metastable liquid toward the stable vapor phase and the intervening free energy barrier. Contrary to the assumptions of theoretical approaches, we find that the bubble takes on cohesive non-spherical shapes with irregular and (sometimes highly) undulating surfaces. Overall, the resulting free energy barriers and rates agree well between the methods, providing a set of complementary algorithms useful for studies of different types of nucleation events.
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