Solid-phase nucleation free-energy barriers in truncated cubes: interplay of localized orientational order and facet alignment.

The nucleation of ordered phases from the bulk isotropic phase of octahedron-like particles has been studied via Monte Carlo simulations and umbrella sampling. In particular, selected shapes that form ordered (plastic) phases with various symmetries (cubic and tetragonal) are chosen to unveil trends in the free-energy barrier heights (ΔG*'s) associated with disorder to order transitions. The shapes studied in this work have truncation parameter (s) values of 0.58, 0.75, 0.8 and 1. The case of octahedra (s = 1.0) is studied to provide a counter-example where the isotropic phase nucleates directly into a (Minkowski) crystal phase rather than a rotator phase. The simulated ΔG*'s for these systems are compared with those previously reported for hard spheres and truncated cubes with s = 0.5 (cuboctahedra, CO) and s = 2/3 (truncated octahedra, TO). The comparison shows that, for comparable degrees of supersaturation, all rotator phases nucleate with smaller ΔG*'s than that of the hard sphere crystal, whereas the octahedral crystal nucleates with a larger ΔG*. Our analysis of near-critical translationally ordered nuclei of octahedra shows a strong bias towards an orientational alignment which is incompatible with the tendency to form facet-to-facet contacts in the disordered phase, thus creating an additional entropic penalty for crystallization. For rotator phases of octahedra-like particles, we observe that the strength of the localized orientational order correlates inversely with ΔG*. We also observe that for s > 0.66 shapes and similar to octahedra, configurations with high facet alignment do not favor high orientational order, and thus ΔG*'s increase with truncation.

SSAGES: Software Suite for Advanced General Ensemble Simulations.

Molecular simulation has emerged as an essential tool for modern-day research, but obtaining proper results and making reliable conclusions from simulations requires adequate sampling of the system under consideration. To this end, a variety of methods exist in the literature that can enhance sampling considerably, and increasingly sophisticated, effective algorithms continue to be developed at a rapid pace. Implementation of these techniques, however, can be challenging for experts and non-experts alike. There is a clear need for software that provides rapid, reliable, and easy access to a wide range of advanced sampling methods and that facilitates implementation of new techniques as they emerge. Here we present SSAGES, a publicly available Software Suite for Advanced General Ensemble Simulations designed to interface with multiple widely used molecular dynamics simulations packages. SSAGES allows facile application of a variety of enhanced sampling techniques-including adaptive biasing force, string methods, and forward flux sampling-that extract meaningful free energy and transition path data from all-atom and coarse-grained simulations. A noteworthy feature of SSAGES is a user-friendly framework that facilitates further development and implementation of new methods and collective variables. In this work, the use of SSAGES is illustrated in the context of simple representative applications involving distinct methods and different collective variables that are available in the current release of the suite. The code may be found at: https://github.com/MICCoM/SSAGES-public.

Molecular pathways for defect annihilation in directed self-assembly.

Over the last few years, the directed self-assembly of block copolymers by surface patterns has transitioned from academic curiosity to viable contender for commercial fabrication of next-generation nanocircuits by lithography. Recently, it has become apparent that kinetics, and not only thermodynamics, plays a key role for the ability of a polymeric material to self-assemble into a perfect, defect-free ordered state. Perfection, in this context, implies not more than one defect, with characteristic dimensions on the order of 5 nm, over a sample area as large as 100 cm(2). In this work, we identify the key pathways and the corresponding free energy barriers for eliminating defects, and we demonstrate that an extraordinarily large thermodynamic driving force is not necessarily sufficient for their removal. By adopting a concerted computational and experimental approach, we explain the molecular origins of these barriers and how they depend on material characteristics, and we propose strategies designed to overcome them. The validity of our conclusions for industrially relevant patterning processes is established by relying on instruments and assembly lines that are only available at state-of-the-art fabrication facilities, and, through this confluence of fundamental and applied research, we are able to discern the evolution of morphology at the smallest relevant length scales-a handful of nanometers-and present a view of defect annihilation in directed self-assembly at an unprecedented level of detail.

Simultaneous estimation of free energies and rates using forward flux sampling and mean first passage times.

In this work, a method is proposed to simultaneously compute the transition rate constant and the free energy profile of a rare event along an order parameter connecting two well-defined regions of phase space. The method employs a forward flux sampling technique in combination with a mean first passage time approach to estimate the steady state probability and mean first passage times. These quantities are fitted to a Markovian model that allows the estimation of the free energy along the chosen order parameter. The proposed technique is first validated with two test systems (an Ising model and a model potential energy surface) and then used to study the solid-phase homogeneous nucleation of selected polyhedral particles.

Stochastic fusion simulations and experiments suggest passive and active roles of hemagglutinin during membrane fusion.

Influenza enters the host cell cytoplasm by fusing the viral and host membrane together. Fusion is mediated by hemagglutinin (HA) trimers that undergo conformational change when acidified in the endosome. It is currently debated how many HA trimers, w, and how many conformationally changed HA trimers, q, are minimally required for fusion. Conclusions vary because there are three common approaches for determining w and q from fusion data. One approach correlates the fusion rate with the fraction of fusogenic HA trimers and leads to the conclusion that one HA trimer is required for fusion. A second approach correlates the fusion rate with the total concentration of fusogenic HA trimers and indicates that more than one HA trimer is required. A third approach applies statistical models to fusion rate data obtained at a single HA density to establish w or q and suggests that more than one HA trimer is required. In this work, all three approaches are investigated through stochastic fusion simulations and experiments to elucidate the roles of HA and its ability to bend the target membrane during fusion. We find that the apparent discrepancies among the results from the various approaches may be resolved if nonfusogenic HA participates in fusion through interactions with a fusogenic HA. Our results, based on H3 and H1 serotypes, suggest that three adjacent HA trimers and one conformationally changed HA trimer are minimally required to induce membrane fusion (w = 3 and q = 1).

Localized orientational order chaperones the nucleation of rotator phases in hard polyhedral particles.

The nucleation kinetics of the rotator phase in hard cuboctahedra, truncated octahedra, and rhombic dodecahedra is simulated via a combination of forward flux sampling and umbrella sampling. For comparable degrees of supersaturation, the polyhedra are found to have significantly lower free-energy barriers and faster nucleation rates than hard spheres. This difference primarily stems from localized orientational ordering, which steers polyhedral particles to pack more efficiently. Orientational order hence fosters here the growth of orientationally disordered nuclei.

Extensions of the interfacial pinning method and application to hard core systems.

The precise estimation of the location of phase transitions is an essential task in the study of many condensed matter systems. A recently developed technique denoted interface pinning (IP) [U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B. 88, 094101 (2013); U. R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] can accurately estimate the location of fluid-solid transition using the NP(z)T ensemble for single-component systems by computing the free energy difference between a solid and a fluid. The IP method is extended here to be applicable to different ensembles for both single-component systems and binary mixtures. A more general scheme is also proposed for the extrapolation of properties targeting coexistence conditions. This framework is used to estimate the coexistence pressure for the isotropic-rotator phase transition for three single-component polyhedral systems and to estimate isotropic-crystal coexistence compositions for a binary mixture of hard cubes and spheres. In addition, by exploring various choices for the order parameter used to distinguish between the isotropic and ordered phases, it is found that volume provides a reasonable alternative to translational order parameters which can be either more expensive to calculate or unable to pin a two-phase interfacial state.

Coarse-Grained Simulation of Bottlebrush: From Single-Chain Properties to Self-Assembly.

Bottlebrush polymers consist of a linear backbone with densely grafted side chains. They are known to have a range of properties of interest, such as enhanced mechanical strength and rapid self-assembly into large domains, and have attracted attention as promising candidates for applications in photonics, lithography, energy storage, organic optoelectronics, and drug delivery. Here, we present a coarse-grained model of bottlebrush polymers that is able to reproduce their experimentally observed persistence lengths and chain conformations in the melt. The model is then used to investigate the morphologies of this class of materials for various chain architectures and grafting densities.

Mesoscale Simulations of Polymer Solution Self-Assembly: Selection of Model Parameters within an Implicit Solvent Approximation.

Coarse-grained modeling is an outcome of scientific endeavors to address the broad spectrum of time and length scales encountered in polymer systems. However, providing a faithful structural and dynamic characterization/description is challenging for several reasons, particularly in the selection of appropriate model parameters. By using a hybrid particle- and field-based approach with a generalized energy functional expressed in terms of density fields, we explore model parameter spaces over a broad range and map the relation between parameter values with experimentally measurable quantities, such as single-chain scaling exponent, chain density, and interfacial and surface tension. The obtained parameter map allows us to successfully reproduce experimentally observed polymer solution assembly over a wide range of concentrations and solvent qualities. The approach is further applied to simulate structure and shape evolution in emulsified block copolymer droplets where concentration and domain shape change continuously during the process.

Self-Aligned Assembly of a Poly(2-vinylpyridine)-b-Polystyrene-b-Poly(2-vinylpyridine) Triblock Copolymer on Graphene Nanoribbons.

Directed self-assembly (DSA) of block copolymers is one of the most promising patterning techniques for patterning sub-10 nm features. However, at such small feature sizes, it is becoming increasingly difficult to fabricate the guiding pattern for the DSA process, and it is necessary to explore alternative guiding methods for DSA to achieve long-range ordered alignment. Here, we report the self-aligned assembly of a triblock copolymer, poly(2-vinylpyridine)-b-polystyrene-b-poly(2-vinylpyridine) (P2VP-b-PS-b-P2VP) on neutral graphene nanoribbons with the gap consisting of a P2VP-preferential silicon oxide (SiO2) substrate via solvent vapor annealing. The assembled P2VP-b-PS-b-P2VP demonstrated long-range, one-dimensional alignment on the graphene substrate in a direction perpendicular to the boundary of the graphene and substrate with a half-pitch size of 8 nm, which greatly alleviates the lithography resolution required for traditional chemoepitaxy DSA. A wide processing window is demonstrated with the gap between graphene stripes varying from 10 to 100 nm, overcoming the restriction on widths of guiding patterns to have commensurate domain spacing. When the gap was reduced to 10 nm, P2VP-b-PS-b-P2VP formed a straight-line pattern on both the graphene and the substrate. Monte Carlo simulations showed that the self-aligned assembly of the triblock copolymer on the graphene nanoribbons is guided at the boundary of parallel and perpendicular lamellae on graphene and SiO2, respectively. Simulations also indicate that the swelling of a system allows for rapid rearrangement of chains and quickly anneal any misaligned grains and defects. The effect of the interaction strength between SiO2 and P2VP on the self-assembly is systematically investigated in simulations.

Boundary-directed epitaxy of block copolymers.

Directed self-assembly of block copolymers (BCPs) enables nanofabrication at sub-10 nm dimensions, beyond the resolution of conventional lithography. However, directing the position, orientation, and long-range lateral order of BCP domains to produce technologically-useful patterns is a challenge. Here, we present a promising approach to direct assembly using spatial boundaries between planar, low-resolution regions on a surface with different composition. Pairs of boundaries are formed at the edges of isolated stripes on a background substrate. Vertical lamellae nucleate at and are pinned by chemical contrast at each stripe/substrate boundary, align parallel to boundaries, selectively propagate from boundaries into stripe interiors (whereas horizontal lamellae form on the background), and register to wide stripes to multiply the feature density. Ordered BCP line arrays with half-pitch of 6.4 nm are demonstrated on stripes >80 nm wide. Boundary-directed epitaxy provides an attractive path towards assembling, creating, and lithographically defining materials on sub-10 nm scales.

Defect Annihilation Pathways in Directed Assembly of Lamellar Block Copolymer Thin Films.

Defects in highly ordered self-assembled block copolymers represent an important roadblock toward the adoption of these materials in a wide range of applications. This work examines the pathways for annihilation of defects in symmetric diblock copolymers in the context of directed assembly using patterned substrates. Past theoretical and computational studies of such systems have predicted minimum free energy pathways that are characteristic of an activated process. However, they have been limited to adjacent dislocations with opposite Burgers vectors. By relying on a combination of advanced sampling techniques and particle-based simulations, this work considers the long-range interaction between dislocation pairs, both on homogeneous and nanopatterned substrates. As illustrated here, these interactions are central to understanding the defect structures that are most commonly found in applications and in experimental studies of directed self-assembly. More specifically, it is shown that, for dislocation dipoles separated by several lamellae, multiple consecutive free energy barriers lead to effective kinetic barriers that are an order of magnitude larger than those originally reported in the literature for tightly bound dislocation pairs. It is also shown that annihilation pathways depend strongly on both the separation between dislocations and their relative position with respect to the substrate guiding stripes used to direct the assembly.