Mesoscale networks and corresponding transitions from self-assembly of block copolymers

Equilibrium phase behavior of gyroid-forming diblock polymer thin films

Thin-film confinement of self-assembling block polymers results in materials with myriad potential applications-including membranes and optical devices-and provides design parameters for altering phase behavior that are not available in the bulk, namely, film thickness and preferential wetting. However, most research has been limited to lamella- and cylinder-forming polymers; three-dimensional phases, such as double gyroid (DG), have been observed in thin films, but their phase behavior under confinement is not yet well understood. We use self-consistent field theory to predict the equilibrium morphology of bulk-gyroid-forming AB diblock polymers under thin-film confinement. Phase diagrams reveal that the (211) orientation of DG, often observed in experiments, is stable between nonpreferential boundaries at thicknesses as small as 1.2 times the bulk DG lattice parameter. The (001) orientation is stable between modestly B-preferential boundaries, where B is the majority block, while a different (211)-oriented termination plane is stabilized by strongly B-preferential boundaries, neither of which has been observed experimentally. We then describe two particularly important phenomena for explaining the phase behavior of DG thin films at low film thicknesses. The first is "constructive interference," which arises when distortions due to the top and bottom boundaries overlap and is significant for certain DG orientations. The second is a symmetry-dependent, in-plane unit-cell distortion that arises because the distorted morphology near the boundary has a different preferred unit-cell size and shape than the bulk. These results provide a thermodynamic portrait of the phase behavior of DG thin films.

Topology Effect on Order-Disorder Transition of High-χ Block Copolymers

This work aims to systematically examine the topology effect on the self-assembly of block copolymers. Compositionally, symmetric polystyrene-block-polydimethylsiloxane block copolymers (BCPs) with different chain topologies (diblock, three-arm star-block, and four-arm star-block) and various molecular weights are synthesized. These purposely designed block copolymers are used as a model system to investigate the topology effect on order-to-disorder transition temperature (T ODT) by temperature-resolved small-angle X-ray scattering experiments. An increase of the T ODT is observed when the arm number of BCPs with equivalent arm length (i.e., molecular weight) is increased from one to four. Based on the random-phase approximation (RPA), Flory-Huggins interaction parameter (χ) is determined from the regression of the measured T ODT. The observation by differential scanning calorimetry also demonstrates the shifting of the endothermic peak from the order-to-disorder transition of star-blocks to the higher temperature region, consistent with the scattering experiments and the RPA prediction.

Sequential Self-Assembly of Polystyrene-block-Polydimethylsiloxane for 3D Nanopatterning via Solvent Annealing

This study aims to develop a strategy for the fabrication of multilayer nanopatterns through sequential self-assembly of lamella-forming polystyrene-block-polydimethylsiloxane (PS-b-PDMS) block copolymer (BCP) from solvent annealing. By simply tuning the solvent selectivity, a variety of self-assembled BCP thin-film morphologies, including hexagonal perforated lamellae (HPL), parallel cylinders, and spheres, can be obtained from single-composition PS-b-PDMS. By taking advantage of reactive ion etching (RIE), topographic SiO2 monoliths with well-ordered arrays of hexagonally packed holes, parallel lines, and hexagonally packed dots can be formed. Subsequently, hole-on-dot and line-on-hole hierarchical textures can be created through a layer-by-layer process with RIE treatment as evidenced experimentally and confirmed theoretically. The results demonstrated the feasibility of creating three-dimensional (3D) nanopatterning from the sequential self-assembly of single-composition PS-b-PDMS via solvent annealing, providing an appealing process for nano-MEMS manufacturing based on BCP lithography.

Frank-Kasper-like network phase from self-assembly of high-χ star-block copolymers

By taking advantage of the effects of solvent selectivity and topology on high-χ block copolymer (BCP) for self-assembly, network phases with high packing frustration can be formed in self-assembled polystyrene-b-polydimethylsiloxane (PS-b-PDMS). Apart from gyroid with trigonal structure and diamond with tetrahedral structure, a peculiar network phase with space group of [Formula: see text] (Frank-Kasper structure) can be found in six-arm star-block PS-b-PDMS as evidenced by small-angle x-ray scattering. Electron tomography results reveal the network phase with alternating connection of three and four struts. The observed phase behaviors suggest that the network formation is built from the bisectors of dispersive spheres in the Frank-Kasper phase, instead of building connections among them, and thus decipher the origins of complex phase formation due to the adaptive character of malleable mesoatoms.

Gradient Transformation of the Double Gyroid to the Double Diamond in Soft Matter

Transitions between gyroid and diamond intercatenated double network phases occur in many types of soft matter, but to date, the structural pathway and the crystallographic relationships remain unclear. Slice and view scanning electron microscopy tomography of a diblock copolymer affords monitoring of the evolving shape of the intermaterial dividing surface, allowing structural characterization of both the majority and minority domains. Two trihedral malleable mesoatoms combine to form a single tetrahedral mesoatom in a volume additive manner while preserving network topology, as the types of loops, the number of mesoatoms in a loop, minority domain strut lengths, and directions that connect a given mesoatom to its neighbors evolve across a 150 nm wide transition zone (TZ). The [111]DD direction is coincident with the [110]DG direction so that the (111)DD and (110)DG planes define the boundaries of the TZ. Selection of the particular crystal orientations and direction and width of the transition zone is to minimize the cost of morphing the mesoatoms from one structure to the other, by maximizing like-block continuity and minimizing the variation of the surface curvature and thickness of the domains across the TZ. Such coherent continuity of the independent, intercatenated networks across the transition zone is critical for applications such as graded mechanical trusses where the pair of different networks are joined to provide different mechanical properties for adjacent grains or could serve as a nanoscale anode/cathode allowing super charging and discharging provided the networks are continuous and rigorously separate.

Tetrahedron clusters serving as a platform for foam-like structure design

There are a number of exceptional examples indicating the unique position of tetrahedral symmetry in the vast landscape of different spatial organization pathways which can be sampled by matter. This work shows that the design and analysis of relatively simple tetrahedron clusters can lead to the formulation of a new type of dendritic structure together with unique periodic frameworks resembling clathrates and foams. A simple sequential protocol leading from regular tetrahedron clusters to more complex structural motifs can be employed to determine interesting repetitive building units. Accordingly, four different hierarchical superstructures are introduced, in which the dominant population of nodes is based on tetrahedral symmetry. The introduced architectures could be of particular interest for the field of regenerative medicine and metamaterial engineering.

Thermodynamically stable plumber's nightmare structures in block copolymers

Block copolymer self-assembly affords diverse nanostructures, spanning from spheres and cylinders to networks, offering meticulous control over properties and functionalities at the nanoscale. However, creating thermodynamically stable network structures with high packing frustration remains a challenge. In this study, we report a methodology to access diverse network structures such as gyroid, diamond, and primitive phases from diblock copolymers using end group and linker chemistry. The stability of the medial packing of polymer chain ends (plumber's nightmare structure) over skeletal aggregation (gyroid) is attributed to the interplay between the strength of the end-end interactions and the initial shape of the curvature. Our study establishes an approach to develop tailored network structures from block copolymers, providing an important platform for using block copolymers in nanotechnology applications.

Emergence of layered nanoscale mesh networks through intrinsic molecular confinement self-assembly

Block copolymer self-assembly is a powerful tool for two-dimensional nanofabrication; however, the extension of this self-assembly concept to complex three-dimensional network structures is limited. Here we report a simple method to experimentally generate three-dimensional layered mesh morphologies through intrinsic molecular confinement self-assembly. We designed triblock bottlebrush polymers with two Janus domains: one perpendicular and one parallel to the polymer backbone. The former enforces a lamellar superstructure that intrinsically confines the intralayer self-assembly of the latter, giving rise to a mesh-like monoclinic (54°) M¹⁵ network substructure with excellent long-range order, as well as a tetragonal (90°) T¹³¹ mesh. Numerical simulations show that the spatial constraints exerted on the polymer backbone drive the assembly of M¹⁵ and yield T¹³¹ in the strong segregation regime. This work demonstrates that intrinsic molecular confinement is a viable path to bottom-up assembly of new geometrical phases of soft matter, extending the capabilities of block copolymer nanofabrication.

Leveraging Macromolecular Isomerism for Phase Complexity in Janus Nanograins

It remains intriguing whether macromolecular isomerism, along with competing molecular interactions, could be leveraged to create unconventional phase structures and generate considerable phase complexity in soft matter. Herein, we report the synthesis, assembly, and phase behaviors of a series of precisely defined regioisomeric Janus nanograins with distinct core symmetry. They are named B₂DB₂ where B stands for iso-butyl-functionalized polyhedral oligomeric silsesquioxanes (POSS) and D stands for dihydroxyl-functionalized POSS. While BPOSS prefers crystallization with a flat interface, DPOSS prefers to phase-separate from BPOSS. In solution, they form 2D crystals owing to strong BPOSS crystallization. In bulk, the subtle competition between crystallization and phase separation is strongly influenced by the core symmetry, leading to distinct phase structures and transition behaviors. The phase complexity was understood based on their symmetry, molecular packing, and free energy profiles. The results demonstrate that regioisomerism could indeed generate profound phase complexity.

Soft, malleable double diamond twin

A twin boundary (TB) is a common low energy planar defect in crystals including those with the atomic diamond structure (C, Si, Ge, etc.). We study twins in a self-assembled soft matter block copolymer (BCP) supramolecular crystal having the double diamond (DD) structure, consisting of two translationally shifted, interpenetrating diamond networks of the minority polydimethyl siloxane block embedded in a polystyrene block matrix. The coherent, low energy, mirror-symmetric double tubular network twin has one minority block network with its nodes offset from the (222) TB plane, while nodes of the second network lie in the plane of the boundary. The offset network, although at a scale about a factor of 10³ larger, has precisely the same geometry and symmetry as a (111) twin in atomic single diamond where the tetrahedral units spanning the TB retain nearly the same strut (bond) lengths and strut (bond) angles as in the normal unit cell. In DD, the second network undergoes a dramatic restructuring-the tetrahedral nodes transform into two new types of mirror-symmetric nodes (pentahedral and trihedral) which alternate and link to form a hexagonal mesh in the plane of the TB. The collective reorganization of the supramolecular packing highlights the hierarchical structure of ordered BCP phases and emphasizes the remarkable malleability of soft matter.

Network Phases with Multiple-Junction Geometries at the Gyroid-Diamond Transition

A novel phase sequence for the transition from the double diamond to the double gyroid cubic phases via two non-cubic intermediate phases, an orthorhombic Fmmm (O⁶⁹) phase and a hexagonal P6₃/m (H¹⁷⁶) phase, is reported for specifically designed bolapolyphiles composed of a linear rod-like bistolane core with sticky glycerol ends and two branched central and two linear peripheral side chains. These liquid crystalline (LC) phases represent members of a new class of unicontinuous network phases, formed by longitudinal rod bundles with polar spheres acting as junctions and the alkyl chains forming the continuum around them. In contrast to previously known bicontinuous cubic networks, they combine different junctions with different angles in a common structure, and one of them even represents a triple network instead of the usually found double networks. This provides new perspectives for the design of soft network phases with enhanced structural complexity, inspiring the search for new supramolecular networks, nano-particle arrays, and photonic band-gap materials.

Induced Circular Dichroism and Circularly Polarized Luminescence for Block Copolymers with Chiral Communications

Many sophisticated chiral materials are found in living organisms, giving specific functions and required complexity. Owing to the remarkable optical properties of chiral materials, they have drawn significant attention for the development of synthetic materials to give optical activities for appealing applications. In contrast to a top-down approach, the bottom-up approach from self-assembled systems with chiral host-achiral guest and achiral guest-chiral host for induced circular dichroism and induced circularly polarized luminescence has greatly emerged because of its cost-effective advantage with easy fabrication for mesoscale assembly. Self-assembled hierarchical textures with chiral sense indeed give significant amplification of the dissymmetry factors of absorption and luminescence (g_abs and g_lum ), resulting from the formation of well-ordered superstructures and phases with the building of chromophores and luminophores. By taking advantage of the microphase separation of block copolymers via self-assembly, a variety of well-defined chiral nanostructures can be formed as tertiary superstructures that can be further extended to quaternary phases in bulk or thin film. In this article, a conceptual perspective is presented to utilize the self-assembly of chiral block copolymers with chiral communications, giving quaternary phases with well-ordered textures at the nanoscale for significant enhancement of dissymmetry factors.

Controlled Self-Assembly of Polystyrene-block-Polydimethylsiloxane for Fabrication of Nanonetwork Silica Monoliths

Herein, this work aims to carry out controlled self-assembly of single-composition block copolymer for the fabrication of various nanonetwork silica monoliths. With the use of lamellae-forming polystyrene-block-polydimethylsiloxane (PS-b-PDMS), nanonetwork-structured films could be fabricated by solvent annealing using a PS-selective solvent (chloroform). By simply tuning the flow rate of nitrogen purge to the PS-selective solvent for the controlled self-assembly of the PS-b-PDMS, gyroid- and diamond-structured monoliths can be formed due to the difference in the effective volume of PS in the PS-b-PDMS during solvent annealing. As a result, well-ordered nanonetwork SiO₂ (silica) monoliths can be fabricated by templated sol-gel reaction using hydrofluoric acid etched PS-b-PDMS film as a template followed by the removal of the PS. This bottom-up approach for the fabrication of nanonetwork materials through templated synthesis is appealing to create nanonetwork materials for various applications.

Enhanced dielectric permittivity of hierarchically double-gyroid nanocomposites via macromolecular engineering of block copolymers

It is a challenging task to realize the periodically bicontinuous gyroid nanostructures of flexible nanocomposites with high loading of functionalized nanoparticles, which could exhibit high dielectric permittivity for energy storage and electronic devices. Herein, with the aid of the concept of macromolecular engineering, we propose novel nanocomposites, composed of A'(A''B)_n miktoarm star copolymers and nanoparticles, to obtain a double-gyroid structure through self-consistent field theory coupled with density functional theory. By tailoring the architecture of this copolymer, a large window of the double-gyroid phase extending to a high loading concentration of nanoparticles is achieved, leading to a hierarchical structure of a percolation network of nanoparticles within the gyroid channels. Furthermore, the finite difference quasielectrostatic method is integrated to reveal an enhanced dielectric permittivity of the structured nanocomposites by increasing the loading concentration of nanoparticles. The simultaneous achievement of an ordered double-gyroid phase and high loading nanoparticles represents a crucial step toward the realization of fully three-dimensional network-like metamaterials via a rational molecular design of nanocomposites.

Self-Assembly of Lipid Mixtures in Solutions: Structures, Dynamics Processes and Mechanical Properties

The self-assembly of lipid mixtures in aqueous solution was investigated by dissipative particle dynamics simulation. Two types of lipid molecules were modelled, where three mixed structures, i.e., the membrane, perforated membrane and vesicle, were determined in the self-assembly processes. Phase behaviour was investigated by using the phase diagrams based on the tail chain lengths for the two types of lipids. Several parameters, such as chain number and average radius of gyration, were employed to explore the structural formations of the membrane and perforated membrane in the dynamic processes. Interface tension was used to demonstrate the mechanical properties of the membrane and perforated membrane in the equilibrium state and dynamics processes. Results help us to understand the self-assembly mechanism of the biomolecule mixtures, which has a potential application for designing the lipid molecule-based bio-membranes in solutions.

Well-Ordered Nanonetwork Metamaterials from Block Copolymer Templated Syntheses

ConspectusThrough the morphological evolution to give highly optimized complex architectures at different length scales, fine-tuned textures for specific functions in living organisms can be achieved in nature such as a bone core with very complicated porous architecture to attain a significant structural efficiency attributed to delicately structured ligaments and density gradients. As inspired by nature, materials with periodic network structures (i.e., well-defined porous textures) in the nanoscale are appealing and promising for innovative properties. Biomimicking from nature, organic and/or inorganic nanonetworks can be synthetically fabricated, giving broadness and effectiveness when tuning the desired properties. Metamaterials are materials whose effective properties do not result from the bulk behavior of the constituent materials but rather mainly from their deliberate structuring. The performances of fabricating metamaterials will depend on the control of size, shape, order, and orientation of the forming textures. One of the appealing textures for the deliberate structuring is network architecture. Network materials possess self-supporting frameworks, open-cell character, high porosity, and large specific surface area, giving specific functions and complexity for diverse applications. As demonstrated by recent studies, exceptional mechanical performances such as negative thermal expansion, negative Poisson's ratio, and twisting under uniaxial forces can be achieved by the effect of the deliberate structuring with nanonetwork textures. In contrast to a top-down approach, a bottom-up approach is cost-effective, and also it can overcome the size limitation to reach nanoscale fabrication. It can be foreseen that network metamaterials with a feature size of tens of nanometers (referred as nanonetwork metamaterials) may provide new comprehension of the structure and property relationships for various materials. The self-assembly of block copolymers (BCPs) is one of the most used methods to build up well-ordered nanostructured phases from a bottom-up approach with precise control of size, shape, and orientation in the thin films for realistic applications. In this account, we summarize recent advancements in the fabrication of nanohybrids and nanoporous materials with well-ordered nanonetwork textures even with controlled helicity by combining block copolymer self-assembly and templated syntheses for mechanical and optical applications with superior properties beyond nature as metamaterials as well as chiral metamaterials with new properties for chiroptic applications such as chiral plasmonics, beam splitter, and negative refraction. The description of the fundamental facets of a nonconventional structure-property relationship with the characters of metamaterials and the state-of-the-art methodologies to fabricate nanonetworks using block copolymer self-assembly will stimulate research activities for the development of nanonetwork metamaterials with exceptional individual and multifunctional properties for futuristic devices.

Alternating Gyroid in Block Polymer Blends

Alternating gyroid is a lower symmetry variant of the double gyroid morphology, where the left-handed and right-handed chiral networks are physically distinct. This structure is of particular interest for photonic applications owing to predictions of a complete photonic band gap subject to the requirement of a large dielectric contrast between the individual networks and sufficient optical matching between one of the networks and the matrix. We provide evidence, via self-consistent field theory (SCFT), that stoichiometric blends of double-gyroid-forming AB and BC diblock copolymers with relatively immiscible A and C blocks should form an alternating gyroid morphology with complementary three-dimensional A and C networks that have a free energy that is nearly degenerate with two phase-separated double gyroid states. Solvent casting offers the potential for trapping this binary mixture of diblock copolymers in this metastable alternating gyroid phase. Theory further predicts that the addition of a minuscule amount (<1%) of ABC triblock terpolymer will open an alternating gyroid stability window in the resulting ternary-phase diagram. The surfactant-like stabilization produced by the triblock is relatively insensitive to its exact composition provided the B-block forms a sufficiently long bridge between the A-rich and C-rich networks. This blending strategy provides significant synthetic and material processing advantages compared to prevailing methods to produce an alternating gyroid phase in block polymers.

Block Copolymer Modified Nanonetwork Epoxy Resin for Superior Energy Dissipation

Herein, this work aims to fabricate well-ordered nanonetwork epoxy resin modified with poly(butyl acrylate)-b-poly(methyl methacrylate) (PBA-b-PMMA) block copolymer (BCP) for enhanced energy dissipation using a self-assembled diblock copolymer of polystyrene-b-poly(dimethylsiloxane) (PS-b-PDMS) with gyroid and diamond structures as templates. A systematic study of mechanical properties using nanoindentation of epoxy resin with gyroid- and diamond-structures after modification revealed significant enhancement in energy dissipation, with the values of 0.36 ± 0.02 nJ (gyroid) and 0.43 ± 0.03 nJ (diamond), respectively, when compared to intrinsic epoxy resin (approximately 0.02 ± 0.002 nJ) with brittle characteristics. This enhanced property is attributed to the synergic effect of the deliberate structure with well-ordered nanonetwork texture and the toughening of BCP-based modifiers at the molecular level. In addition to the deliberate structural effect from the nanonetwork texture, the BCP modifier composed of epoxy-philic hard segment and epoxy-phobic soft segment led to dispersed soft-segment domains in the nanonetwork-structured epoxy matrix with superior interfacial strength for the enhancement of applied energy dissipation.