Stability of the A15 phase in diblock copolymer melts

Parsimonious Topology Based on Frank-Kasper Polyhedra in Metal-Organic Frameworks

A new topology previously unknown in metal-organic frameworks (MOFs) provides an important clue to uncovering a new series of polyhedral MOFs. We report a novel MOF crystallized in a parsimonious mep topology based on Frank-Kasper (FK) polyhedra. The distribution of angles in a tetrahedral arrangement (T-O-T) is crucial for the formation of FK polyhedra in mep topology. This finding led us to investigate the T-O-T angle distribution in related zeolites and zeolitic imidazolate frameworks (ZIFs). Unlike zeolites, it is extremely difficult to achieve high T-O-T angles in ZIFs, which prevents the formation of some FK topologies. Density functional theory (DFT) total energy calculations support a correlation between T-O-T angles and the feasibility of new tetrahedron-based FK frameworks. This result may lead to innovative ways of accessing new cellular topologies by simple chemical tweaking of T-O-T angles.

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.

Chromatographic Separation: A Versatile Strategy to Prepare Discrete and Well-Defined Polymer Libraries

ConspectusThe preparation of discrete and well-defined polymers is an emerging strategy for emulating the remarkable precision achieved by macromolecular synthesis in nature. Although modern controlled polymerization techniques have unlocked access to a cornucopia of materials spanning a broad range of monomers, molecular weights, and architectures, the word "controlled" is not to be confused with "perfect". Indeed, even the highest-fidelity polymerization techniques─yielding molar mass dispersities in the vicinity of Đ = 1.05─unavoidably create a considerable degree of structural and/or compositional dispersity due to the statistical nature of chain growth. Such dispersity impacts many of the properties that researchers seek to control in the design of soft materials.The development of strategies to minimize or entirely eliminate dispersity and access molecularly precise polymers therefore remains a key contemporary challenge. While significant advances have been made in the realm of iterative synthetic methods that construct oligomers with an exact molecular weight, head-to-tail connectivity, and even stereochemistry via small-molecule organic chemistry, as the word "iterative" suggests, these techniques involve manually propagating monomers one reaction at a time, often with intervening protection and deprotection steps. As a result, these strategies are time-consuming, difficult to scale, and remain limited to lower molecular weights. The focus of this Account is on an alternative strategy that is more accessible to the general scientific community because of its simplicity, versatility, and affordability: chromatography. Researchers unfamiliar with the intricacies of synthesis may recall being exposed to chromatography in an undergraduate chemistry lab. This operationally simple, yet remarkably powerful, technique is most commonly encountered in the purification of small molecules through their selective (differential) adsorption to a column packed with a low-cost stationary phase, usually silica. Because the requisite equipment is readily available and the actual separation takes little time (on the order of 1 h), chromatography is used extensively in small-molecule chemistry throughout industry and academia alike. It is, therefore, perhaps surprising that similar types of chromatography are not more widely leveraged in the field of polymer science as well.Here, we discuss recent advances in using chromatography to control the structure and properties of polymeric materials. Emphasis is placed on the utility of an adsorption-based mechanism that separates polymers based on polarity and composition at tractable (gram) scales for materials science, in contrast to size exclusion, which is extremely common but typically analyzes very small quantities of a sample (∼1 mg) and is limited to separating by molar mass. Key concepts that are highlighted include (1) the separation of low-molecular-weight homopolymers into discrete oligomers (Đ = 1.0) with precise chain lengths and (2) the efficient fractionation of block copolymers into high-quality and widely varied libraries for accelerating materials discovery. In summary, the authors hope to convey the exciting possibilities in polymer science afforded by chromatography as a scalable, versatile, and even automated technique that unlocks new avenues of exploration into well-defined materials for a diverse assortment of researchers with different training and expertise.

Particle Dynamics in a Diblock-Copolymer-Based Dodecagonal Quasicrystal and Its Periodic Approximant by X-Ray Photon Correlation Spectroscopy

Temperature-dependent x-ray photon correlation spectroscopy (XPCS) measurements are reported for a binary diblock-copolymer blend that self-assembles into an aperiodic dodecagonal quasicrystal and a periodic Frank-Kasper σ phase approximant. The measured structural relaxation times are Bragg scattering wavevector independent and are 5 times faster in the dodecagonal quasicrystal than the σ phase, with minimal temperature dependence. The underlying dynamical relaxations are ascribed to differences in particle motion at the grain boundaries within each of these tetrahedrally close-packed assemblies. These results identify unprecedented particle dynamics measurements of tetrahedrally coordinated micellar block polymers, thus expanding the application of XPCS to ordered soft materials.

Coil-Helix Block Copolymers Can Exhibit Divergent Thermodynamics in the Disordered Phase

Chiral building blocks have the ability to self-assemble and transfer chirality to larger hierarchical length scales, which can be leveraged for the development of novel nanomaterials. Chiral block copolymers, where one block is made completely chiral, are prime candidates for studying this phenomenon, but fundamental questions regarding the self-assembly are still unanswered. For one, experimental studies using different chemistries have shown unexplained diverging shifts in the order-disorder transition temperature. In this study, particle-based molecular simulations of chiral block copolymers in the disordered melt were performed to uncover the thermodynamic behavior of these systems. A wide range of helical models were selected, and several free energy calculations were performed. Specifically, we aimed to understand (1) the thermodynamic impact of changing the conformation of one block in chemically identical block copolymers and (2) the effect of the conformation on the Flory-Huggins interaction parameter, χ, when chemical disparity was introduced. We found that the effective block repulsion exhibits diverging behavior, depending on the specific conformational details of the helical block. Commonly used conformational metrics for flexible or stiff block copolymers do not capture the effective block repulsion because helical blocks are semiflexible and aspherical. Instead, pitch can quantitatively capture the effective block repulsion. Quite remarkably, the shift in χ for chemically dissimilar block copolymers can switch sign with small changes in the pitch of the helix.

Confinement-induced self-assembly of a diblock copolymer within a non-uniform cylindrical nanopore

The self-assembly of a diblock copolymer melt confined within a non-uniform cylindrical nanopore is studied using the self-consistent field theory. The non-uniformity manifests in the form of a converging-diverging cylindrical nanopore. The axial variation in pore diameter presents a range of curvatures within the same confinement pore as opposed to a single curvature in a uniform-diameter cylindrical pore. The introduction of multiple curvatures leads to the formation of novel microstructures not accessible in uniform cylindrical confinement. The well-known equilibrium structures like a single helix, double helices, and concentric lamella under cylindrical confinement transition into new morphologies such as hyperboloidal phases, microstructures containing rings with a bead, rings with spheres, and a squeezed helical phase as the pore diameter varies axially. The converging-diverging geometry of the confining pore renders the helical phases seen in the cylindrical pore less favorable. A phase diagram in the parametric space of the block fraction and the ratio of the smallest and largest pore radii has been constructed to depict the order-order transition of various microstructures. The ratio of radii, a measure of the non-uniformity of the pore, along with the pore length brings out some interesting morphologies. The mechanism of these structural transitions is understood as the interplay between the variation in pore curvature attributed to the non-uniformity, the spontaneous curvature of the block copolymer interface, and the enthalpic interaction between the segregated blocks.

Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions

Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained (CG) approaches in k-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher order contributions. We propose a systematic framework for constructing a faithful Fourier-space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular CG models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parameterization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems.

Frank-Kasper Phases of Diblock Copolymer Melts: Self-Consistent Field Results of Two Commonly Used Models

We constructed phase diagrams of conformationally asymmetric diblock copolymer A-B melts using the polymer self-consistent field (SCF) calculations of both the dissipative particle dynamics chain (DPDC) model (i.e., compressible melts of discrete Gaussian chains with the DPD non-bonded potential) and the "standard" model (i.e., incompressible melts of continuous Gaussian chains with the Dirac δ-function non-bonded potential) in the χN-ε plane, where χN and ε characterize, respectively, the repulsion and conformational asymmetry between the A and B blocks, at the A-block volume fraction f = 0.2 and 0.3. Consistent with previous SCF calculations of the "standard" model, σ and A15 are the only stable Frank-Kasper (FK) phases among the five FK (i.e., σ, A15, C14, C15 and Z) phases considered. The stability of σ and A15 is due to their delicate balance between the energetic and entropic contributions to the Helmholtz free energy per chain of the system, which, within our parameter range, increases in the order of σ/A15, Z, and C14/C15. While in general the SCF phase diagrams of these two models are qualitatively consistent, A15 is not stable for the DPDC model at the copolymer chain length N = 10 and f = 0.3; any differences in the SCF phase diagrams are solely due to the differences between these two models.

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.

Discrete Miktoarm Star Block Copolymers with Tailored Molecular Architecture

Molecular architecture is a critical factor in regulating phase behaviors of the block copolymer and prompting the formation of unconventional nanostructures. This work meticulously designed a library of isomeric miktoarm star polymers with an architectural evolution from the linear-branched block copolymer to the miktoarm star block copolymer and to the star-like block copolymer (i.e., 3AB → 3(AB1)B2 → 3(AB)). All of the polymers have precise chemical composition and uniform chain length, eliminating inherent molecular uncertainties such as chain length distribution or architectural defects. The self-assembly behaviors were systematically studied and compared. Gradually increasing the relative length of the branched B1 block regulates the ratio between the bridge and loop configuration and effectively releases packing frustration in the formation of the spherical or cylindrical structures, leading to a substantial deflection of phase boundaries. Complex structures, such as Frank-Kasper phases, were captured at a surprisingly higher volume fraction. Rationally regulating the molecular architecture offers rich possibilities to tune the packing symmetry of block copolymers.

Assessment of the partial saddle point approximation in field-theoretic polymer simulations

Field-theoretic simulations are numerical treatments of polymer field theory models that go beyond the mean-field self-consistent field theory level and have successfully captured a range of mesoscopic phenomena. Inherent in molecularly-based field theories is a "sign problem" associated with complex-valued Hamiltonian functionals. One route to field-theoretic simulations utilizes the complex Langevin (CL) method to importance sample complex-valued field configurations to bypass the sign problem. Although CL is exact in principle, it can be difficult to stabilize in strongly fluctuating systems. An alternate approach for blends or block copolymers with two segment species is to make a "partial saddle point approximation" (PSPA) in which the stiff pressure-like field is constrained to its mean-field value, eliminating the sign problem in the remaining field theory, allowing for traditional (real) sampling methods. The consequences of the PSPA are relatively unknown, and direct comparisons between the two methods are limited. Here, we quantitatively compare thermodynamic observables, order-disorder transitions, and periodic domain sizes predicted by the two approaches for a weakly compressible model of AB diblock copolymers. Using Gaussian fluctuation analysis, we validate our simulation observations, finding that the PSPA incorrectly captures trends in fluctuation corrections to certain thermodynamic observables, microdomain spacing, and location of order-disorder transitions. For incompressible models with contact interactions, we find similar discrepancies between the predictions of CL and PSPA, but these can be minimized by regularization procedures such as Morse calibration. These findings mandate caution in applying the PSPA to broader classes of soft-matter models and systems.

Phase Behavior of Binary Blends of Diblock Copolymers: Progress and Opportunities

The phase behavior of binary blends of diblock copolymers has been examined extensively in the past decades. Experimental and theoretical studies have demonstrated that mixing two different block copolymers provides an efficient and versatile route to regulate their self-assembled morphologies. A good understanding of the principles governing the self-assembly of block copolymer blends has been obtained from the study of A1B1/A2B2 diblock copolymer blends. The second (A2B2) diblocks could act synergistically as fillers and cosurfactants to regulate the domain size and interfacial properties, resulting in the formation of ordered phases not found in the parent (A1B1 or A2B2) diblock copolymer melts. The study of A1B1/A2B2 block copolymer blends further provides a solid foundation for future research on more complex block copolymer blends.

The impact of intramolecular polydispersity on the self-assembly of ABn miktoarm star copolymers

The self-assembly behaviors of AB_n miktoarm star copolymers as one typical type of asymmetric architecture have been studied well in the past few decades due to their deflected phase boundaries. In particular, recently, they have attracted renewed theoretical interest due to their expanded spherical phase region that stabilizes complex Frank-Kasper spherical phases. However, previous theoretical studies have never considered AB_n copolymers with unequal arm lengths, which is more or less the case for synthesized copolymers. In this work, we investigate the self-assembly behaviors of AB_n miktoarm star copolymers with unequal B-arms using self-consistent field theory. We propose an intramolecular polydispersity index (iĐ) to quantify the distribution of unequal B-blocks. Accordingly, we further propose a simple quantity of an effective arm number n_equ = n/iĐ for quantitatively comparing the phase boundaries between various AB_n copolymer samples with different arm numbers or different distributions of B-blocks. Our results indicate that different AB_n copolymers with equal n_equ exhibit similar phase diagrams. On the other hand, we also found that the phase boundaries of two different samples with same n_equ are not exactly overlapped. We speculate that the effect of spontaneous curvature may be mainly controlled by n_equ, but the packing frustration of B-blocks may also be dependent on the other quantities that are closely related to the shape of the distribution of B-arms, such as higher order polydispersity indexes.

Liquid-Like States in Micelle-Forming Diblock Copolymer Melts

Large cell self-consistent field theory (SCFT) solutions for a neat, micelle-forming diblock copolymer melt, initialized using the structure of a Lennard-Jones fluid, reveal the existence of a vast number of liquid-like states, with free energies of order 10^-3 k_BT per chain higher than the body-centered cubic (bcc) state near the order-disorder transition (ODT). Computation of the structure factor for these liquids at temperatures below the ODT indicates that their intermicellar distance is slightly swollen compared to bcc. In addition to providing a mean-field picture of the disordered micellar state, the number of liquid-like states and their near-degeneracy with the equilibrium bcc morphology suggest that self-assembly of micelle-forming diblock copolymers navigates a rugged free energy landscape with many local minima. This picture provides a basis for the anomalously slow ordering kinetics of particle-forming diblock copolymer melts observed in experiments.

Combining particle and field-theoretic polymer models with multi-representation simulations

Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.

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.

Experimental and Computational Evaluation of Self-Assembled Morphologies in Diblock Janus Bottlebrush Copolymers

Diblock Janus-type "A-branch-B" bottlebrush copolymers (di-JBBCPs) consist of a backbone with alternating A and B side chains, in contrast to the side chain arrangement of conventional bottlebrush copolymers. As a result, A and B blocks of di-JBBCPs can microphase-separate perpendicular to the backbone, which is located at the interface between the two blocks. A reparametrized dissipative particle dynamics (DPD) model is used to theoretically investigate the self-assembly of di-JBBCPs and to compare with the experimental results of a range of polystyrene-branch-polydimethylsiloxane di-JBBCPs. The experimentally formed cylinder, gyroid, and lamellar morphologies showed good correspondence with the model phase diagram, and the effect of changing volume fraction and backbone length is revealed. The DPD model predicts a bulk-stable perforated lamella morphology together with two unconventional spherical phases, the Frank-Kasper A15 spheres and the hexagonally close-packed spheres, indicating the diversity of morphologies available from complex BCP molecular architectures.

Tuning conformational asymmetry in particle-forming diblock copolymer alloys

Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer "alloy"). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner-Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation.

Dynamics and Equilibration Mechanisms in Block Copolymer Particles

Self-assembly of block copolymers into interesting and useful nanostructures, in both solution and bulk, is a vibrant research arena. While much attention has been paid to characterization and prediction of equilibrium phases, the associated dynamic processes are far from fully understood. Here, we explore what is known and not known about the equilibration of particle phases in the bulk, and spherical micelles in solution. The presumed primary equilibration mechanisms are chain exchange, fusion, and fragmentation. These processes have been extensively studied in surfactants and lipids, where they occur on subsecond time scales. In contrast, increased chain lengths in block copolymers create much larger barriers, and time scales can become prohibitively slow. In practice, equilibration of block copolymers is achievable only in proximity to the critical micelle temperature (in solution) or the order-disorder transition (in the bulk). Detailed theories for these processes in block copolymers are few. In the bulk, the rate of chain exchange can be quantified by tracer diffusion measurements. Often the rate of equilibration, in terms of number density and aggregation number of particles, is much slower than chain exchange, and consequently observed particle phases are often metastable. This is particularly true in regions of the phase diagram where Frank-Kasper phases occur. Chain exchange in solution has been explored quantitatively by time-resolved SANS, but the results are not well captured by theory. Computer simulations, particularly via dissipative particle dynamics, are beginning to shed light on the chain escape mechanism at the molecular level. The rate of fragmentation has been quantified in a few experimental systems, and TEM images support a mechanism akin to the anaphase stage of mitosis in cells, via a thin neck that pinches off to produce two smaller micelles. Direct measurements of micelle fusion are quite rare. Suggestions for future theoretical, computational, and experimental efforts are offered.

Bayesian modeling of pattern formation from one snapshot of pattern

Partial differential equations (PDEs) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a method, referred to as Bayesian modeling of PDEs (BM-PDEs), to estimate the best dynamical PDE for one snapshot of a objective pattern under the stationary state without ground truth. We apply BM-PDEs to nontrivial patterns, such as quasicrystals (QCs), a double gyroid, and Frank-Kasper structures. We also generate three-dimensional dodecagonal QCs from a PDE model. This is done by using the estimated parameters for the Frank-Kasper A15 structure, which closely approximates the local structures of QCs. Our method works for noisy patterns and the pattern synthesized without the ground-truth parameters, which are required for the application toward experimental data.

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.

Effect of Molecular Architecture and Symmetry on Self-Assembly: A Quantitative Revisit Using Discrete ABA Triblock Copolymers

The inherent statistical heterogeneities associated with chain length, composition, and architecture of synthetic block copolymers compromise the quantitative interpretation of their self-assembly process. This study scrutinizes the contribution of molecular architecture on phase behaviors using discrete ABA triblock copolymers with precise chemical structure and uniform chain length. A group of discrete triblock copolymers with varying composition and symmetry were modularly synthesized through a combination of iterative growth methods and efficient coupling reactions. The symmetric ABA triblock copolymers self-assemble into long-range ordered structures with expanded domain spacings and enhanced phase stability, compared with the diblock counterparts snipped at the middle point. By tuning the relative chain length of two end blocks, the molecular asymmetry reduces the packing frustration, and thus increases the order-to-disorder transition temperature and enlarges the domain sizes. This study would serve as a quantitative model system to correlate the experimental observations with the theoretical assessments and to provide quantitative understandings for the relationship between molecular architecture and self-assembly.

Droplet-like Defect Annihilation Mechanisms in Hexagonal Cylinder-Forming Block Copolymers

The annihilation of typical individual defects in hexagonal cylinder-forming block copolymers is investigated using the self-consistent field theory (SCFT) in conjunction with the string method. Usually, defect removal in two-dimensional hexagonal patterns involves reorganizing the cylindrical domains. Unlike atoms in solid crystals, the self-assembled cylindrical domains of block copolymers are "soft". Thus, the kinetic motions of the cylindrical domains resemble liquid droplets. Dislocations in hexagonal patterns are eliminated via creating and removing cylindrical domains. Our results show that new cylindrical domains are created via either a nucleation-like process or a fission-like process, whereas excessive domains are eliminated via a fusion-like or evaporation-like process. For weakly segregated block copolymers, the nucleation-like and evaporation-like processes are preferred.

Free energy cost to assemble superlattices of polymer-grafted nanoparticles

Mesoparticles consisting of a hard core and a soft corona like polymer-grafted nanoparticles (PGNPs) can assemble into various superlattice structures, in which each mesoparticle assumes the shape of the corresponding Wigner-Seitz (or Voronoi) cell. Conventional wisdom often perceives the stability of these superlattices in a mean-field view of surface area minimization or corona entropy maximization, which lacks molecular interpretation. We develop a simulation method to calculate the free energy cost to deform spherical PGNPs into Wigner-Seitz polyhedra, which are then relaxed in a certain crystalline superlattice. With this method, we successfully quantify the free energy differences between model BCC, FCC and A15 systems of PGNPs and identify BCC as the most stable structure in most cases. Analysis of polymer configurations in the corona, whose boundary is blurred by chain interpenetration, shows that the radial distribution of grafted chains and the corresponding entropy are almost identical between BCC and FCC, suggesting that the higher stability of the BCC structure cannot be explained by the mean-field description of the corona shape.

Multiple 2D crystal structures in bilayered lamellae from direct self-assembly of 3D systems of soft Janus particles

Numerous crystals and Frank-Kasper phases in two-dimensional (2D) systems of soft particles have been presented by theoretical investigations. How to realize 2D crystals or Frank-kasper phases by direct self-assembly of...

Adaptive Recombinant Nanoworms from Genetically Encodable Star Amphiphiles

Recombinant nanoworms are promising candidates for materials and biomedical applications ranging from the templated synthesis of nanomaterials to multivalent display of bioactive peptides and targeted delivery of theranostic agents. However, molecular design principles to synthesize these assemblies (which are thermodynamically favorable only in a narrow region of the phase diagram) remain unclear. To advance the identification of design principles for the programmable assembly of proteins into well-defined nanoworms and to broaden their stability regimes, we were inspired by the ability of topologically engineered synthetic macromolecules to acess rare mesophases. To test this design principle in biomacromolecular assemblies, we used post-translational modifications (PTMs) to generate lipidated proteins with precise topological and compositional asymmetry. Using an integrated experimental and computational approach, we show that the material properties (thermoresponse and nanoscale assembly) of these hybrid amphiphiles are modulated by their amphiphilic architecture. Importantly, we demonstrate that the judicious choice of amphiphilic architecture can be used to program the assembly of proteins into adaptive nanoworms, which undergo a morphological transition (sphere-to-nanoworms) in response to temperature stimuli.

Multiblock Elastomers TPEAA and TPEEA: Physical Structure and Properties

A three series of terpolymers composed of the blocks PTMO (M_PTMO = 1000 g/mol) or DLAol (M_DLAol = 540 g/mol), PA12 (M_PA12 = 2000 g/mol) and xGT (DP_xGT = 2) with various chemical compositions of ester block were obtained. The series differ in the chemical structure of the flexible block and weight content of the soft phase. The effect of the number of carbons dividing the terephthalate groups on the synthesis, structure and properties of these elastomers has been investigated. To confirm assumed chemical structure Carbon-13 (¹³C NMR) and Proton (¹H NMR) Nuclear Magnetic Resonance and Fourier-transform Infrared Spectroscopy (FT-IR) were used. The influence of chemical compositions of ester block on the thermal properties and the phase separation of obtained systems were defined by Differential Scanning Calorimetry (DSC), Dynamic Mechanical Thermal Analysis (DMTA) and Wide Angle X-ray Scattering (WAXS). The mechanical and elastic properties were evaluated.

Precisely Encoding Geometric Features into Discrete Linear Polymer Chains for Robust Structural Engineering

Molecular shape is an essential parameter that regulates the self-organization and recognition process, which has not yet been well appreciated and exploited in block polymers due to the lack of precise and efficient modulation methods. This work (i) develops a robust approach to break the intrinsic symmetry of linear polymers by introducing geometric features into otherwise homogeneous chains and (ii) quantitatively highlights the critical contribution of molecular geometry/architecture to the self-assembly behaviors. Iteratively connecting homologous monomers of different side chains according to pre-designed sequences generates discrete polymers with exact chemical structure, uniform chain length, and programmable side-chain gradient along the backbone, which transcribes into diverse shapes. The precise chemistry eliminates all the defects and heterogeneities, providing a delicate platform for fundamental inquiries into the role of molecular geometry. A rich collection of unconventional complex phases, including Frank-Kasper A15 and σ phases, as well as a dodecagonal quasicrystal phase, were captured in these rigorous single-component systems. The self-assembly behaviors are strikingly sensitive to subtle variations of geometry, such that simply migrating a few methylene units among the side chains would generate substantial differences in lattice size or phase stability, or even trigger a phase transition toward distinct structures. The phenomena can be rationalized with a geometric argument that nonuniform side chain distribution leads to conformational mismatch between two immiscible blocks, resulting in varied interfacial curvatures and distinct lattice symmetries. The profound contribution demonstrates that molecular geometry is an effective and robust parameter for structural engineering.

Charged Block Copolymers: From Fundamentals to Electromechanical Applications

Charged block copolymers are promising materials for next-generation battery technologies and soft electronics. Although once it was only possible to prepare randomly organized structures, nowadays, well-ordered charged block copolymers can be prepared. In addition, theoretical and experimental analyses of the thermodynamic properties of charged polymers have provided insights into how to control nanostructures via electrostatic interactions and improve the ionic conductivity without compromising mechanical strength, which is crucial for practical applications. In this Account, we discuss methods to control the self-assembly and ion diffusion behavior of charged block copolymers by varying the type of tethered ionic moieties, local concentration of embedded ions with controlled electrostatic interactions, and nanoscale morphology. We discuss with particular emphasis on the structure-transport relationship of charged block copolymers using various ionic additives to control the phase behavior electrostatically as well as the ion transport properties. Through this, we establish the role of interconnected ionic channels in promoting ion-conduction and the importance of developing three-dimensional interconnected morphologies such as gyroid, orthorhombic Fddd (O⁷⁰) networks, body-centered cubic (bcc), face-centered cubic (fcc), and A15 structures with well-defined interfaces in creating less tortuous ion-conduction pathways. Our prolonged surge and synthetic advances are pushing the frontiers of charged block copolymers to have virtually homogeneous ionic domains with suppressed ion agglomeration via the nanoconfinement of closely bound ionic moieties, resulting in efficient ion conduction and high mechanical strength.Subsequently, we discuss how, by using zwitterions, we have radically improved the ionic conductivity of single-ion conducting polymers, which have potential for use in next-generation electrochemical devices owing to the constrained anion depletion. Key to the improvement stems from hierarchically ordered ionic crystals in nanodomains of the single-ion block copolymers through the self-organization of the dipolar/ionic moieties under confinement. By precisely tuning the distances between ionic sites and the dipolar orientation in the ionic domains with varied zwitterion contents, unprecedented dielectric constants close to those of aqueous electrolytes have been achieved, leading to the development of high-conductivity solid-state single-ion conducting polymers with leak-free characteristics. Further, using these materials, low-voltage-driven artificial muscles have been prepared that show a large bending strain and millisecond-scale mechanical deformations at 1 V in air without fatigue, exceeding the performance of previously reported polymer actuators. Finally, smart multiresponsive actuators based on tailor-made charged polymers capable of programmable deformation with high force and self-locking without power consumption are suggested as candidates for use in soft robotics.