Block Copolymers beneath the Surface: Measuring and Modeling Complex Morphology at the Subdomain Scale

Nonaffinity of Liquid Networks and Bicontinuous Mesophases

Amphiphiles self-assemble into a variety of bicontinuous mesophases whose equilibrium structures take the form of high-symmetry cubic networks. Here, we show that the symmetry-breaking distortions in these systems give rise to anomalously large, nonaffine collective deformations, which we argue to be a generic consequence of "mass equilibration" within deformed networks. We propose and study a minimal "liquid network" model of bicontinuous networks, in which acubic distortions are modeled by the relaxation of residually stressed mechanical networks with constant-tension bonds. We show that nonaffinity is strongly dependent on the valency of the network as well as the degree of strain-softening or strain-stiffening tension in the bonds. Taking diblock copolymer melts as a model system, liquid network theory captures quantitative features of two bicontinuous phases based on comparison with self-consistent field theory predictions and direct experimental characterization of acubic distortions, which are likely to be pronounced in soft amphiphilic systems more generally.

Epitaxial Growth of Surface Perforations on Parallel Cylinders in Terraced Films of Block Copolymer/Homopolymer Blends

Due to incommensurability between initial thickness and interdomain distance, thermal annealing inevitably produces relief surface terraces (islands and holes) of various morphologies in thin films of block copolymers. We have demonstrated three kinds of surface terraces in blend films: polygrain terraces with diffuse edges, polygrain terraces with step edges, and pseudo-monograin terraces with island coarsening. The three morphologies were obtained by three different thermal histories, respectively. The thermal histories were imposed on blend films, which were prepared by mixing a homopolystyrene (hPS, 6.1 kg/mol) with a weakly segregated, symmetry polystyrene-block poly(methyl methacrylate) (PS-b-PMMA, 42 kg/mol) followed by spin coating. At a given weight-fraction ratio of PS-b-PMMA/hPS = 75/25, the interior of the blend films forms parallel cylinders. Nevertheless, the surface of the blend films is always dominated by a skin layer of perforations, which epitaxially grow on top of parallel cylinders. By oxygen plasma etching at various time intervals to probe interior nanodomains, the epitaxial relationship between surface perforations and parallel cylinders has been identified by a scanning electron microscope.

Synthesis and physical properties of polyhydroxyalkanoate (PHA)-based block copolymers: A review

Polyhydroxyalkanoates (PHAs) are a group of natural polyesters that are synthesised by microorganisms. In general, their thermoplasticity and (in some forms) their elasticity makes them attractive alternatives to petrochemical-derived polymers. However, the high crystallinity of some PHAs - such as poly(3-hydroxybutyrate) (P3HB) - results in brittleness and a narrow processing window for applications such as packaging. The production of copolymeric PHA materials is one approach to improving the mechanical and thermal properties of PHAs. Another solution is the manufacture of PHA-based block copolymers. The incorporation of different polymer and copolymer blocks coupled to PHA, and the resulting tailorable microstructure of these block copolymers, can result in a step-change improvement in PHA-based material properties. A range of production strategies for PHA-based block copolymers has been reported in the literature, including biological production and chemical synthesis. Biological production is typically less controllable, with products of a broad molecular weight and compositional distribution, unless finely controlled using genetically modified organisms. By contrast, chemical synthesis delivers relatively controllable block structures and narrowly defined compositions. This paper reviews current knowledge in the areas of the production and properties of PHA-based block copolymers, and highlights knowledge gaps and future potential areas of research.

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.

Revealing the 3D Structure of Block Copolymers with Electron Microscopy: Current Status and Future Directions

Block copolymers (BCPs) are considered model systems for understanding and utilizing self-assembly in soft matter. Their tunable nanometric structure and composition enable comprehensive studies of self-assembly processes as well as make them relevant materials in diverse applications. A key step in developing and controlling BCP nanostructures is a full understanding of their three-dimensional (3D) structure and how this structure is affected by the BCP chemistry, confinement, boundary conditions, and the self-assembly evolution and dynamics. Electron microscopy (EM) is a leading method in BCP 3D characterization owing to its high resolution in imaging nanosized structures. Here we discuss the two main 3D EM methods: namely, transmission EM tomography and slice and view scanning EM tomography. We present each method's principles, examine their strengths and weaknesses, and discuss ways researchers have devised to overcome some of the challenges in BCP 3D characterization with EM- from specimen preparation to imaging radiation-sensitive materials. Importantly, we review current and new cutting-edge EM methods such as direct electron detectors, energy dispersive X-ray spectroscopy of soft matter, high temporal rate imaging, and single-particle analysis that have great potential for expanding the BCP understanding through EM in the future.

Local Chain Feature Mandated Self-Assembly of Block Copolymers

This work demonstrates an effective and robust approach to regulate phase behaviors of a block copolymer by programming local features into otherwise homogeneous linear chains. A library of sequence-defined, isomeric block copolymers with globally the same composition but locally different side chain patterns were elaborately designed and prepared through an iterative convergent growth method. The precise chemical structure and uniform chain length rule out all inherent molecular defects associated with statistical distribution. The local features are found to exert surprisingly pronounced impacts on the self-assembly process, which have yet to be well recognized. While other molecular parameters remain essentially the same, simply rearranging a few methylene units among the alkyl side chains leads to strikingly different phase behaviors, bringing about (i) a rich diversity of nanostructures across hexagonally packed cylinders, Frank-Kasper A15 phase, Frank-Kasper σ phase, dodecagonal quasicrystals, and disordered state; (ii) a significant change of lattice dimension; and (iii) a substantial shift of order-to-disorder transition temperature (up to 40 °C). Different from the commonly observed enthalpy-dominated cases, the frustration due to the divergence between the native molecular geometry originating from side chain distribution and the local packing environment mandated by lattice symmetry is believed to play a pivotal role. Engineering the local chain feature introduces another level of structural complexity, opening up a new and effective pathway for modulating phase transition without changing the chemistry or composition.

Development and optimization of amphiphilic self-assembly into nanostructured liquid crystals for transdermal delivery of an antidiabetic SGLT2 inhibitor

The anti-hyperglycemic sodium glucose co-transporter 2 inhibitor Canagliflozin (CFZ) represents a recent antihyperglycemic modality, yet it suffers from low oral bioavailability. The current work aims to formulate CFZ-loaded transdermal nanostructured liquid crystal gel matrix (NLCG) to improve its therapeutic efficiency. Pre-formulation study included the construction of pseudoternary phase diagrams to explore the effect of two conventional amphiphiles against amphiphilic tri-block copolymer in the formulation of NLCG. The influence of different co-solvents was also investigated with the use of monooleine as the oil. Physical characterization, morphological examination and skin permeation were performed for the optimized formulations. The formula of choice was further investigated for skin irritation and chemical stability. Pharmacodynamic evaluation of the successful formula was conducted on hyperglycemic as well as normoglycemic mice. In addition, oral glucose tolerance test was conducted. Results revealed the supremacy of Poloxamer for stabilizing and maximizing liquid crystal gel (LCG) area percentage that reached up to 12.6%. CFZ-NLCG2 isotropic formula showed the highest permeation parameters; maximum flux value of 7460 μg/cm² h and Q₂₄ of 5327 μg/cm². Pharmacodynamic evaluation revealed the superiority of the antihyperglycemic activity of CFZ-NLCG2 in fasting mice and its equivalence in the oral glucose tolerance test (OGTT) compared to the oral one. The obtained results confirmed the success of CFZ-NLCG2 in the transdermal delivery of CFZ in therapeutically effective concentration compared to the oral route, bypassing first pass effect; in addition, eliminates the possible gastrointestinal side effects related to the inhibition of intestinal sodium glucose co-transporter (SGLT) and maximizes its selectivity to the desired inhibition of renal SGLT.

Double Gyroid Morphologies in Precise Ion-Containing Multiblock Copolymers Synthesized via Step-Growth Polymerization

The double gyroid structure was first reported in diblock copolymers about 30 years ago, and the complexity of this morphology relative to the other ordered morphologies in block copolymers continues to fascinate the soft matter community. The double gyroid microphase-separated morphology has co-continuous domains of both species, and the minority phase is subdivided into two interpenetrating network structures. In addition to diblock copolymers, this structure has been reported in similar systems including diblock copolymers blended with one or two homopolymers and ABA-type triblock copolymers. Given the narrow composition region over which the double gyroid structure is typically observed (∼3 vol %), anionic polymerization has dominated the synthesis of block copolymers to control their composition and molecular weight. This perspective will highlight recent studies that (1) employ an alternative polymerization method to make block copolymers and (2) report double gyroid structures with lattice parameters below 10 nm. Specifically, step-growth polymerization linked precise polyethylene blocks and short sulfonate-containing blocks to form strictly alternating multiblock copolymers, and these copolymers produce the double gyroid structure over a dramatically wider composition range (>14 vol %). These new (AB) _n multiblock copolymers self-assemble into the double gyroid structure by having exceptional control over the polymer architecture and large interaction parameters between the blocks. This perspective proposes criteria for a broader and synthetically more accessible range of polymers that self-assemble into double gyroids and other ordered structures, so that these remarkable structures can be employed to solve a variety of technological challenges.

Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers

Triply-periodic networks are among the most complex and functionally valuable self-assembled morphologies, yet they form in nearly every class of biological and synthetic soft matter building blocks. In contrast to simpler assembly motifs – spheres, cylinders, layers – networks require molecules to occupy variable local environments, confounding attempts to understand their formation. Here, we examine the double-gyroid network phase by using a geometric formulation of the strong stretching theory of block copolymer melts, a prototypical soft self-assembly system. The theory establishes the direct link between molecular packing, assembly thermodynamics and the medial map, a generic measure of the geometric center of complex shapes. We show that “medial packing” is essential for stability of double-gyroid in strongly-segregated melts, reconciling a long-standing contradiction between infinite- and finite-segregation theories. Additionally, we find a previously unrecognized non-monotonic dependence of network stability on the relative entropic elastic stiffness of matrix-forming to tubular-network forming blocks. The composition window of stable double-gyroid widens for both large and small elastic asymmetry, contradicting intuitive notions that packing frustration is localized to the tubular domains. This study demonstrates the utility of optimized medial tessellations for understanding soft-molecular assembly and packing frustration via an approach that is readily generalizable far beyond gyroids in neat block copolymers.

Double-gyroid networks assemble in diverse soft materials, yet the molecular packing that underlies their complex structure remains obscure. Here, authors advance a theory that resolves a long-standing puzzle about their formation in block copolymers.

End-exclusion zones in strongly stretched, molten polymer brushes of arbitrary shape

Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. However, the parabolic brush limit fails to describe polymers grafted to convex curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has previously been shown that strongly stretched curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the theoretical analysis. While this "end-exclusion zone" has been successfully incorporated into the descriptions of brushes grafted onto the outer surfaces of cylinders and spheres, the behavior of brushes on surfaces of arbitrary curvature has not yet been studied. We present a formulation of the strong-stretching theory for molten brushes on the surfaces of arbitrary curvature and identify four distinct regimes of interest for which brushes are predicted to possess end-exclusion zones, notably including regimes of positive mean curvature but negative Gaussian curvature. Through numerical solutions of the strong-stretching brush equations, we report predicted scaling of the size of the end-exclusion zone, the chain end distribution, the chain polarization, and the free energy of stretching with mean and Gaussian surface curvatures. Through these results, we present a comprehensive picture of how the brush geometry influences the end-exclusion zones and exact strong-stretching free energies, which can be applied, for example, to model the full spectrum of brush geometries encountered in block copolymer melt assembly.