Equilibrium Morphologies Research Articles

A versatile lattice Boltzmann model for immiscible ternary fluid flows

We propose a lattice Boltzmann color-gradient model for immiscible ternary fluid flows, which is applicable to the fluids with a full range of interfacial tensions, especially in near-critical and critical states. An interfacial force for N-phase systems is derived and then introduced into the model using a body force scheme, which helps reduce spurious velocities. A generalized recoloring algorithm is applied to produce phase segregation and ensure immiscibility of three different fluids, where an enhanced form of segregation parameters is derived by considering the existence of Neumann’s triangle and the effect of the equilibrium contact angle in a three-phase junction. The proposed model is first validated by two typical examples, namely, the Young-Laplace test for a compound droplet and the spreading of a droplet between two stratified fluids. It is then used to study the structure and stability of double droplets in a static matrix. Consistent with the theoretical stability diagram, seven possible equilibrium morphologies are successfully reproduced by adjusting the interfacial tension ratio. By simulating near-critical and critical states of double droplets where the outcomes are very sensitive to the model accuracy, we show that the present model is advantageous to three-phase flow simulations and allows for accurate simulation of near-critical and critical states. Finally, we investigate the influence of interfacial tension ratio on the behavior of a compound droplet in a three-dimensional shear flow, and four different deformation and breakup modes are observed.

Advancing the computational methodology of rigid rod and semiflexible polymer systems: A new solution to the wormlike chain model with rod‐coil copolymer calculations

ABSTRACTA wormlike chain model for rod type blocks in a rod‐coil diblock copolymer is implemented in the self‐consistent field theory (SCFT) formalism. A pseudo‐spectral method is used to solve for the single‐chain partition function of this copolymer system. Orientation degrees of freedom are discretized using Lebedev sphere rules such that orientation integrations are carried out through a Lebedev quadrature, an approach not used previously in tandem with the pseudo‐spectral method. Phase behavior in the rigid‐rod limit as a function of rod segment volume fraction, Flory–Huggins interaction parameter χ, degree of polymerization N, and rod contour length ratio β are examined in detail in one and two dimensions. Examples extending to three dimensions are included. Semiflexible behavior via the rod bending rigidity κ is explored. An approximation is used for rigid‐rods that do not need spherical harmonics leading to increased speed in finding equilibrium morphologies. The results show that standing vertical structures may be more easily produced with rigid‐rod blocks compared to coil‐coil lamellae, an important feature in nanolithographic applications. Suggestions are made for using the model in future molecular orientation studies where the model can be used with inverse search methods to measure the values of the model parameters for the real systems. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 29–39

Mesoscopic Simulation Assistant Design of Immiscible Polyimide/BN Blend Films with Enhanced Thermal Conductivity

The mesoscopic simulation technique was applied to describe the phase separation behavior of polyimide blends and used for design of immiscible polyimide/BN blend films with enhanced thermal conductivity. The simulation equilibrium morphologies of different poly(amic acid) (PAA) blend systems were investigated and compared with optical images of corresponding polyimide blend films obtained by experiment. The immiscible polyimide blend films containing nano-/micro-sized BN with vertical double percolation structure were prepared. The result indicated that the thermal conductivity of polyimide blend film with 25 wt% nano-sized BN reached 1.16 W/(m·K), which was 236% increment compared with that of the homogenous film containing the same BN ratio. The significant enhancement in thermal conductivity was attributed to the good phase separation of polyimide matrix, which made the inorganic fillers selectively localized in one continuous phase with high packing density, consequently, forming the effective thermal conductive pathway.

Influence of the particle shape on the equilibrium morphologies of supracolloidal magnetic filaments

We investigate the equilibrium morphologies of linear and ring-shaped magnetic filaments made from crosslinked ferromagnetic spherical or ellipsoidal colloidal particles. Using Langevin dynamics simulations, we calculate the radius of gyration and total magnetic moment of a single filament at zero field and different temperatures, analyzing the influence of the particles shape, the strength of their magnetic moment and the filament length. Our results show that, among such parameters, the shape of the particles has the strongest qualitative impact on the equilibrium behavior of the filaments.

Predicting Surface Energies and Particle Morphologies of Boehmite (γ-AlOOH) from Density Functional Theory

Particle morphology is an important property affecting the reactivity of solid phases. The aluminum oxyhydroxide boehmite (γ-AlOOH) is one example for which particle morphology has relevance to geochemistry, environmental management, and catalysis. Accurate predictions of the morphology of boehmite particles are currently missing, and the dependence of these predictions on the level of theory and complexity of the physics involved is not known. Density functional theory calculations were therefore performed for a wide range of exchange-correlation (XC) functionals, including a hybrid functional, to calculate the energetics of the four main low-index surfaces of boehmite ((100), (010), (001), and (101)) in aqueous conditions and predict equilibrium and growth morphologies. The results highlight the critical need for converged plane-wave basis sets to obtain accurate surface energies as well as the strong influence the XC functional can have on surface energies and water adsorption energies. The predicted m...

Self-Templated Generation of Triggerable and Restorable Nonequilibrium Micelles.

Conditional variations can lead to micellar transformations resulting in various (equilibrium) morphologies. However, creating differently shaped assemblies under the same final conditions (same ingredients, composition, temperature, etc.) is challenging. We present a thermoresponsive polyelectrolyte system allowing a pathway-dependent preparation of kinetically stable spherical star-like or cylindrical micelles. In more detail, a temperature-induced structure switch is used to generate equilibrated interpolyelectrolyte complex (IPEC) micelles of different morphologies (templates) below and above the lower critical solution temperature in the presence of plasticizer (salt). Then, lowering the salt concentration at a specific temperature kinetically freezes the formed IPECs, keeping the respective microstructural information encoded in the frozen IPEC also at other temperatures. Hence, different nonequilibrium morphologies at the same final conditions are provided. The salt-triggered transition from nonequilibrium to equilibrium micelles can be repeated for the same sample, highlighting a system with an on-demand changeable and restorable structure.

The role of shelf morphology and antecedent setting in the preservation of palaeo-shoreline (beachrock and aeolianite) sequences: the SE African shelf

On the SE African shelf, a submerged shoreline at a depth of 60 m is examined and its attributes compared between two shelf sectors with different morphologies, yet similar energy regimes. The aim is to assess the controls of antecedent conditioning on shoreline development and later preservation from transgressive ravinement. Using a combination of multibeam bathymetry and single-channel seismic profiles, the stratigraphy and morphology of the shoreline is investigated. Low-gradient bedrock examples reveal several distinctive seismic facies, including onlapping chaotic reflector packages which are interpreted as calcarenite rubble fields. These palaeo-shorelines possess planform equilibrium morphologies, including parabolic dunes and blowout forms along with relict shore platforms. They are strongly associated with incised valleys of last glacial maximum age which underlie the shoreline locations; these provide wide, back-barrier accommodation space during transgression. In contrast, palaeo-shorelines on the steeper-gradient shelf have a simpler stratigraphic arrangement. They are not as well preserved, are generally covered by thick drapes of sediment, and lack the elaborate planform morphologies of their lower-shelf gradient equivalents. Isolated incised valleys and the steep bedrock gradient limit accommodation space. The comparison indicates that antecedent bedrock slope and available accommodation are amongst the dominant controls on overstepping, and thus potential preservation, of palaeo-shorelines on the shelf. Lower-gradient shelves not only promote rapid shoreline translation but, together with wide, sandy back-barrier accommodation, also foster larger barrier volumes. In suitable climates such as in the Mediterranean and other sub-tropical areas, the ensuing shoreline stability promotes rapid and effective cementation of the barrier. In comparison, steep bedrock profiles with limited back-barrier accommodation have much lower preservation potential. Transgressive ravinement is more focussed on steep slopes, effectively removing more material during the ravinement process. The more dynamic environment may also reduce the effectiveness of diagenesis. The potential of beachrock and aeolianite palaeo-shorelines as submerged sea-level indicators may be optimal in low-gradient settings in Mediterranean to subtropical environments.

How geometric frustration shapes twisted fibres, inside and out: competing morphologies of chiral filament assembly.

Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure-finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. 'frustration escape'). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.

Self-assembly of surfactant aqueous solution confined in a Janus amphiphilic nanotube

In recent years, Janus amphiphilic nanotubes with complex surfaces have been synthesized. However, the self-assembly behaviour of surfactant solutions confined in a Janus amphiphilic nanotube has not been investigated so far. We performed molecular simulations to investigate the morphologies and phase diagrams of a surfactant confined in Janus amphiphilic nanotube consisting of both hydrophobic and hydrophilic surfaces. We derived a phase diagram of the representative snapshots of equilibrium morphologies. Morphologies that were not observed in the bulk eventuated in confined systems. Moreover, the self-assembled structures were found to be dependent on the spatial confinement. Furthermore, the self-assembled structures confined in hydroneutral and Janus amphiphilic nanotubes were compared. The results suggested that the self-assembled structures confined in the Janus amphiphilic nanotube resembled that confined in the hydroneutral nanotube owing to a strong confinement effect. Further developments in controlling the morphologies and self-assemblies will greatly advance their applications of these materials in nanofluidic devices, or for nanopatterning.

Length controlled kinetics of self-assembly of bidisperse nanotubes/nanorods in polymers

While there is a growing body of work that supports the self-assemblies of nanotubes and nanorods, little attention has been devoted to understand the relation between their length and the kinetics of self-assembly in polymer composites. Using dissipative particle dynamics (DPD) method, we simulated the temporal developments of equilibrium microstructures of nanotube dispersions with a bimodal length distribution in polymer matrix. The nanotube/polymer models were developed with different sets of interactions between the components. The equilibrium morphologies obtained for nanotubes are in good agreement with those proposed by previous experimental and theoretical studies. We found that long nanotubes could self-assemble into ordered honeycomb-like bundles as validated with the structure factor calculations. The self-assembly kinetics was quantitatively estimated at different stages and length scales using the variations in the pair-correlation functions. It was observed that the kinetics slowed down particularly in the initial stages of the self-assembly. This was mainly ascribed to the spatial interferences of bidisperse nanotubes as evidenced by laser scanning microscopy and simulated mean-squared-displacements (MSD). Furthermore, the developed microstructures were assessed in terms of the effective nanotube volume derived from Monte Carlo (MC) calculations and the frequency of nanotube-nanotube contacts. The simulations reported herein contribute to a microscopic interpretation of the literature results, and the findings of this paper contribute meaningfully to the design strategies aimed at achieving novel nanocomposites with optimal physical properties.

Modeling Iron–Gold Nanoparticles Using a Dedicated Semi-Empirical Potential: Application to the Stability of Core–Shell Structures

Core–shell nanoparticles made from iron embedded in gold have a strong potential interest in nanomedicine, the Au shell providing an efficient biocompatible coating for the magnetic Fe core. With the aim of determining theoretically the equilibrium morphologies of Fe–Au nanoparticles in a broad size range and with different compositions, a semiempirical many-body Fe–Au potential was designed combining well-established models for the pure metals and introducing dedicated contributions for the interactions involving mixed elements. The potential was parametrized against various energetic properties involving impurities, intermetallics, and finite clusters obtained using density functional calculations in the generalized gradient approximation. The potential was tested to investigate Fe–Au nanoparticles near equiconcentration containing about 1000–2000 atoms at finite temperature using parallel tempering Monte Carlo simulations initiated from the core–shell structure. The core–shell nanoparticles are found to be thermally stable up to about 800 K, at which point the gold outer layer starts to melt, with the iron core remaining stable up to approximately 1200 K. In contrast, the alternative potential developed by Zhou and co-workers (Zhou, X. Z.; Johnson, R. A.; Wadley, H. N. G. Phys. Rev. B, 2004, 69, 144113) predicts a strong tendency for mixing, the core–shell structure appearing energetically metastable. The two models also predict significantly different vibrational spectra.

A finite element approach to self-consistent field theory calculations of multiblock polymers

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.

Morphology Control of Poly(styrene-block-dimethylsiloxane) by Simple Blending with Trimethylsilylated Silicate Nanoparticles.

Trimethylsilylated silicate nanoparticle (termed MQ resin, combining M Me3SiO1/2 and Q SiO4/2 units)/poly(styrene-block-polydimethylsiloxane) (PS-PDMS, 31K-15K, polydispersity PD = 1.15, weight-average molecular weight Mw = 45.5K) blends behave similarly to block copolymers with different PS/PDMS ratios. MQ is localized in the PDMS phase virtually extending the volume fraction in the block copolymer. This allows for microdomain morphology control beyond what can be achieved with the starting block copolymer. Synthesizing siloxane-containing block copolymers targeted at certain equilibrium morphologies can be time-consuming and in some cases technically challenging. This work shows that MQ is a robust morphology modifier, not limited by the occurrence of surface segregation and the high diffusion rates typically associated with homopolymer modification, as confirmed by looking at the PDMS/PS-PDMS reference. The convenient and robust structure control MQ nanoparticle modification of PS-PDMS provides could overcome one of the hurdles to adoption of block copolymer lithography.

Exploiting the Combined Influence of Morphology and Energy Cascades in Ternary Blend Organic Solar Cells Based on Block Copolymer Additives

In recent works, we demonstrated that donor-b-acceptor block copolymer compatibilizers can be utilized in donor–acceptor blends of conjugated homopolymer donors and PCBM acceptors to target equilibrium morphologies containing the interconnected, cocontinuous structures that are desired for efficient bulk heterojunction devices. In this article, we utilize a combination of morphology and device-level simulations to demonstrate that by tuning the photoelectronic properties of the block copolymer additives, the device characteristics of such ternary blend systems can be made to outperform the idealized morphologies envisioned in donor–acceptor systems. Explicitly, we propose that by appropriately choosing the HOMO and LUMO energy levels of the block copolymer additives, an energy cascade can be exploited to reduce charge recombination and increase fill factors. The resulting device performance of such ternary blends reflects the combined influence of morphology and energy cascades, and in some instances, ter...

Cornucopia of Nanoscale Ordered Phases in Sphere-Forming Tetrablock Terpolymers.

We report the phase behavior of a series of poly(styrene)-b-poly(isoprene)-b-poly(styrene)'-b-poly(ethylene oxide) (SIS'O) tetrablock terpolymers. This study was motivated by self-consistent field theory (SCFT) calculations that anticipate a rich array of sphere-forming morphologies with variations in the molecular symmetry parameter τ = NS/(NS + NS'), where N is the block degree of polymerization and the volume fraction of O is less than about 0.22. Eight SIS'O samples, with τ ranging from 0.21 to 0.73, were synthesized and investigated using small-angle X-ray scattering and transmission electron microscopy, yielding evidence of nine different spherical phases: hexagonal, FCC, HCP, BCC, rhombohedral (tentative), liquid-like packing, dodecagonal quasicrystal, and Frank-Kasper σ and A15 phases. At temperatures close to the order-disorder transition, these tetrablocks behave as pseudo-[SIS']-O diblocks and form equilibrium morphologies mediated by facile chain exchange between micelles. Transition from equilibrium to nonequilibrium behavior occurs at a temperature (Terg) several tens of degrees below the order-disorder transition temperature, speculated to be coincident with the loss of ergodicity, as chain exchange is arrested due to increased segregation strength between the core (O) and corona (SIS') blocks. Nonequilibrium ordered structures form when T < Terg; these are interpreted using SCFT calculations to elucidate the free energy landscape driving ordering in the S and I block matrix. These experiments demonstrate a profound dependence on phase stability with variations in τ and temperature, providing insights into the formation of ordered phase symmetry in this class of asymmetric multiblock polymers.

Designing Block Copolymers for Nanolithography using Mesoscale Modeling: Line-Space Graphoepitaxy

ABSTRACTDirected self-assembly (DSA) of block copolymers is a promising alternative nanolithographic technology aimed at producing sub-40 nm patterns. One important opportunity for DSA is the creation of periodic arrays of lines and spaces. The two most common methods for line-space applications are chemoepitaxy (typically using a lamella-forming PS-b-PMMA diblock) and graphoepitaxy (typically using cylinder-forming block copolymers with a Si-containing minority block). Mesoscale modeling, such as Self-Consistent Field Theory (SCFT), has by now become an important tool in formulation screening and predicting polymer morphologies and defect types and probabilities. Here, we use SCFT to study the morphology of cylinder-forming PS-b-PDMS diblocks in rectangular trenches with grafted PS-brushes. The targeted morphology is 2 cylinders per trench (3X multiplication). We compute phase diagrams and determine equilibrium morphologies as a function of brush thickness and guiding weir height. Using those equilibrium morphologies as starting points, we also compute structures and free energies of typical defects, including dislocation and disclination dipoles, broken lines, and bridges. The predicted defect structures and probabilities are in a reasonable qualitative agreement with recent experimental results.

Self-assembly of carbon nanotubes in polymer melts: simulation of structural and electrical behaviour by hybrid particle-field molecular dynamics.

Self-assembly processes of carbon nanotubes (CNTs) dispersed in different polymer phases have been investigated using a hybrid particle-field molecular dynamics technique (MD-SCF). This efficient computational method allowed simulations of large-scale systems (up to ∼1 500 000 particles) of flexible rod-like particles in different matrices made of bead spring chains on the millisecond time scale. The equilibrium morphologies obtained for longer CNTs are in good agreement with those proposed by several experimental studies that hypothesized a two level "multiscale" organization of CNT assemblies. In addition, the electrical properties of the assembled structures have been calculated using a resistor network approach. The calculated behaviour of the conductivities for longer CNTs is consistent with the power laws obtained by numerous experiments. In particular, according to the interpretation established by the systematic studies of Bauhofer and Kovacs, systems close to "statistical percolation" show exponents t ∼ 2 for the power law dependence of the electrical conductivity on the CNT fraction, and systems in which the CNTs reach equilibrium aggregation show exponents t close to 1.7 ("kinetic percolation"). The confinement effects on the assembled structures and their corresponding conductivity behaviour in a non-homogeneous matrix, such as the phase separating block copolymer melt, have also been simulated using different starting configurations. The simulations reported herein contribute to a microscopic interpretation of the literature results, and the proposed modelling procedure may contribute meaningfully to the rational design of strategies aimed at optimizing nanomaterials for improved electrical properties.

Recent advances of theoretical researches in morphologies of lipid vesicles

Lipid membrane is a continuous barrier between cell and organelle, providing relatively separate room for the vital biological reaction to take place and guarantee substance, energy and information exchange between cells and organelles. Helfrich proposed a spontaneous curvature model to describe the free energy of lipid bilayer. This article reviews the equations describing the equilibrium morphologies of closed lipid membranes and lipid membranes with free edge based on the spontaneous model, and some analytic solutions are provided as well. The practicality of proving linking condition for splitting vesicle is also discussed.

Rational Design of Thermally Stable, Bicontinuous Donor/Acceptor Morphologies with Conjugated Block Copolymer Additives.

The bicontinuous microemulsion (BμE) phase is an equilibrium morphology characterized by cocontinuous domains, high interfacial areas, and nanoscale domain dimensions. These characteristics make the BμE potentially suitable for use in organic photovoltaic applications. Here, we use a combination of simulations and experiments to investigate the equilibrium morphologies formed by a ternary blend of conjugated polymer, all-conjugated diblock copolymer, and fullerene derivative PCBM. Using coarse-grained simulations, we identify the blend compositions that are most likely to result in donor/acceptor morphologies resembling the BμE. Experimentally, we probe these compositions through transmission electron microscopy and grazing-incidence X-ray scattering measurements. We demonstrate that all-conjugated block copolymer additives can be used to produce thermally stable, cocontinuous donor/acceptor morphologies at higher additive contents and longer annealing times than previously reported. These results demonstrate that conjugated BCP compatibilizers can be used as a means to achieve equilibrium, cocontinuous morphologies in donor/acceptor blends.

Elucidating the Morphological Complexities of Linear Symmetric Triblock Polymers Confined Between Two Parallel Plates: A Self‐Consistent Field Theoretic Approach

Three dimensional self‐consistent field theoretic simulations have been performed to determine the equilibrium morphologies formed by linear ABC triblock polymer melts confined between two parallel plates that favor the middle block. Our primary goal is to elucidate the conditions under which the perpendicular lamella is stabilized, since this morphology plays a central role in many nanotechnology applications. Key factors, namely, the chain architecture, surface energy and the mismatch between the film thickness d and the bulk lamella period, L0, determine the final morphologies, e.g., perpendicular and parallel lamella, perforated lamella and wet substrate with parallel cylinders in the core, have been identified. Overall, our findings are fully consistent with the results of limited experimental studies focused on morphology development in thin films of triblock polymer melts. Finally, we have clearly demonstrated that ABC triblocks hold technological advantages over diblocks for nano‐lithographic fabrications.