Stability of the A15 phase in diblock copolymer melts

Where Biology and Traditional Polymers Meet: The Potential of Associating Sequence-Defined Polymers for Materials Science

Polymers with precisely defined monomeric sequences present an exquisite tool for controlling material properties by harnessing both the robustness of synthetic polymers and the ability to tailor the inter- and intramolecular interactions so crucial to many biological materials. While polymer scientists traditionally synthesized and studied the physics of long molecules best described by their statistical nature, many biological polymers derive their highly tailored functions from precisely controlled sequences. Therefore, significant effort has been applied toward developing new methods of synthesizing, characterizing, and understanding the physics of non-natural sequence-defined polymers. This perspective considers the synergistic advantages that can be achieved via tailoring both precise sequence control and attributes of traditional polymers in a single system. Here, we focus on the potential of sequence-defined polymers in highly associating systems, with a focus on the unique properties, such as enhanced proton conductivity, that can be attained by incorporating sequence. In particular, we examine these materials as key model systems for studying previously unresolvable questions in polymer physics including the role of chain shape near interfaces and how to tailor compatibilization between dissimilar polymer blocks. Finally, we discuss the critical challenges-in particular, truly scalable synthetic approaches, characterization and modeling tools, and robust control and understanding of assembly pathways-that must be overcome for sequence-defined polymers to attain their potential and achieve ubiquity.

The C36 Laves phase in diblock polymer melts

The C14 and C15 Laves phases form as micelle packing structures in many types of soft matter, but the related C36 phase, which consists of alternating C14-type and C15-type layers, has not been observed in any such system. To understand this absence in the context of diblock polymers, we used self-consistent field theory to relate the morphology and energetics of C36 to other known mesophases. Two case studies were conducted: blends of AB diblock polymers with A homopolymers (where A forms the micelle core), in which C14 and C15 have stability windows, and neat AB diblock melts, in which Laves phases are metastable. Laves phases exhibit nearly identical micelle morphologies and nearly degenerate free energies, with the free energy of C36 being a near-perfect bisector of the C14 and C15 free energies in all cases, revealing an intrinsic symmetry in free energy that is attributed solely to the structural relationship between the phases in which the packing of C36 is intermediate between C14 and C15. Based on this connection between structure and free energy, C36 is thus not expected to form in flexible diblock polymers, since C14 and C15 can always form instead via facile mass transfer.

Open-source platform for block polymer formulation design using particle swarm optimization

Facile exploration of large design spaces is critical to the development of new functional soft materials, including self-assembling block polymers, and computational inverse design methodologies are a promising route to initialize this task. We present here an open-source software package coupling particle swarm optimization (PSO) with an existing open-source self-consistent field theory (SCFT) software for the inverse design of self-assembling block polymers to target bulk morphologies. To lower the barrier to use of the software and facilitate exploration of novel design spaces, the underlying SCFT calculations are seeded with algorithmically generated initial fields for four typical morphologies: lamellae, network phases, cylindrical phases, and spherical phases. In addition to its utility within PSO, the initial guess tool also finds generic applicability for stand-alone SCFT calculations. The robustness of the software is demonstrated with two searches for classical phases in the conformationally symmetric diblock system, as well as one search for the Frank-Kasper [Formula: see text] phase in conformationally asymmetric diblocks. The source code for both the initial guess generation and the PSO wrapper is publicly available.

Emergence of Hexagonally Close-Packed Spheres in Linear Block Copolymer Melts

The hexagonally close-packed (HCP) sphere phase is predicted to be stable across a narrow region of linear block copolymer phase space, but the small free energy difference separating it from face-centered cubic spheres usually results in phase coexistence. Here, we report the discovery of pure HCP spheres in linear block copolymer melts with A = poly(2,2,2-trifluoroethyl acrylate) ("F") and B = poly(2-dodecyl acrylate) ("2D") or poly(4-dodecyl acrylate) ("4D"). In 4DF diblocks and F4DF triblocks, the HCP phase emerges across a substantial range of A-block volume fractions (circa f_A = 0.25-0.30), and in F4DF, it forms reversibly when subjected to various processing conditions which suggests an equilibrium state. The time scale associated with forming pure HCP upon quenching from a disordered liquid is intermediate to the ordering kinetics of the Frank-Kasper σ and A15 phases. However, unlike σ and A15, HCP nucleates directly from a supercooled liquid or soft solid without proceeding through an intermediate quasicrystal. Self-consistent field theory calculations indicate the stability of HCP is intimately tied to small amounts of molar mass dispersity (Đ); for example, an HCP-forming F4DF sample with f_A = 0.27 has an experimentally measured Đ = 1.04. These insights challenge the conventional wisdom that pure HCP is difficult to access in linear block copolymer melts without the use of blending or other complex processing techniques.

Enhancing ion transport in charged block copolymers by stabilizing low symmetry morphology: Electrostatic control of interfaces

Recently, the interest in charged polymers has been rapidly growing due to their uses in energy storage and transfer devices. Yet, polymer electrolyte-based devices are not on the immediate horizon because of the low ionic conductivity. In the present study, we developed a methodology to enhance the ionic conductivity of charged block copolymers comprising ionic liquids through the electrostatic control of the interfacial layers. Unprecedented reentrant phase transitions between lamellar and A15 structures were seen, which cannot be explained by well-established thermodynamic factors. X-ray scattering experiments and molecular dynamics simulations revealed the formation of fascinating, thin ionic shell layers composed of ionic complexes. The ionic liquid cations of these complexes predominantly presented near the micellar interfaces if they had strong binding affinity with the charged polymer chains. Therefore, the interfacial properties and concentration fluctuations of the A15 structures were crucially dependent on the type of tethered acid groups in the polymers. Overall, the stabilization energies of the A15 structures were greater when enriched, attractive electrostatic interactions were present at the micellar interfaces. Contrary to the conventional wisdom that block copolymer interfaces act as "dead zone" to significantly deteriorate ion transport, this study establishes a prospective avenue for advanced polymer electrolyte having tailor-made interfaces.

Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles

A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and n-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of n-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.

Crowding-Induced Unconventional Phase Behaviors in Dendritic Rodlike Molecules via Side-Chain Engineering

Dendritic molecules with a fanlike or conelike conformation are common molecular building blocks to construct supramolecular columnar or spherical phases. Although it is well-accepted that the preferred molecular conformation of dendritic molecules dictates their packing schemes, manipulation of this crucial parameter usually requires significant changes in molecular structures and tedious synthetic efforts. Herein, we report a simple yet highly efficient strategy to tune the molecular conformation of dendritic rodlike molecules by adjusting the length of alkyl side chains tethered to the rods. Strikingly, tiny chemical structure differences can largely change the "crowding" near the branching point to induce the "fanlike to conelike" conformational transitions and thus result in the formation of diverse supramolecular structures, including the columnar phase, double gyroid phase, and the unconventional Frank-Kasper σ and A15 phases. Our study provides a practical platform for further investigation of unconventional structure formation and phase transitions in soft matter.

Reevaluation of Poly(ethylene-alt-propylene)-block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth

Reanalysis of an asymmetric poly(ethylene-alt-propylene)-block-polydimethylsiloxane (PEP-PDMS) diblock copolymer first investigated in 1999 has revealed a rich phase behavior including a dodecagonal quasicrystal (DDQC), a Frank-Kasper σ phase, and a body-centered cubic (BCC) packing at high temperature adjacent to the disordered state. On subjecting the sample to large amplitude oscillatory shear well below the σ-BCC order-order transition temperature (T_OOT), small-angle X-ray scattering evidenced the emergence of a twinned BCC phase that, on heating, underwent a phase transition to an unusually anisotropic DDQC state. Surprisingly, we observe no evidence of this apparent epitaxy on heating or cooling through the equilibrium σ-BCC transition. We rationalize these results in terms of a shear-induced order-order transition and an apparent BCC-DDQC epitaxy favored by micelle translation-mediated ordering dynamics far below T_OOT.

Deep learning-based estimation of Flory-Huggins parameter of A-B block copolymers from cross-sectional images of phase-separated structures

In this study, deep learning (DL)-based estimation of the Flory-Huggins χ parameter of A-B diblock copolymers from two-dimensional cross-sectional images of three-dimensional (3D) phase-separated structures were investigated. 3D structures with random networks of phase-separated domains were generated from real-space self-consistent field simulations in the 25-40 χN range for chain lengths (N) of 20 and 40. To confirm that the prepared data can be discriminated using DL, image classification was performed using the VGG-16 network. We comprehensively investigated the performances of the learned networks in the regression problem. The generalization ability was evaluated from independent images with the unlearned χN. We found that, except for large χN values, the standard deviation values were approximately 0.1 and 0.5 for A-component fractions of 0.2 and 0.35, respectively. The images for larger χN values were more difficult to distinguish. In addition, the learning performances for the 4-class problem were comparable to those for the 8-class problem, except when the χN values were large. This information is useful for the analysis of real experimental image data, where the variation of samples is limited.

Shear-Modulated Rates of Phase Transitions in Sphere-Forming Diblock Oligomer Lyotropic Liquid Crystals

Hydration of the amphiphilic diblock oligomer C₁₆H₃₃(CH₂CH₂O)₂₀OH (C₁₆E₂₀) leads to concentration-dependent formation of micellar body-centered cubic (BCC) and Frank-Kasper A15 lyotropic liquid crystals (LLCs). Quiescent thermal annealing of aqueous LLCs comprising 56-59 wt % C₁₆E₂₀ at 25 °C after quenching from high temperatures established their ability to form short-lived BCC phases, which transform into long-lived, transient Frank-Kasper σ phases en route to equilibrium A15 morphologies on a time scale of months. Here, the frequency and magnitude of applied oscillatory shear show the potential to either dynamically stabilize the metastable BCC phase at low frequencies or increase the rate of formation of the A15 to minutes at high frequencies. Time-resolved synchrotron small-angle X-ray scattering (TR-SAXS) provides in situ characterization of the structures during shear and thermal processing. This work shows that the LLC morphology and order-order phase transformation rates can be controlled by tuning the shear strain amplitude and frequency.

Molecularly Informed Field Theories from Bottom-up Coarse-Graining

Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters). To overcome the weaknesses of both, we introduce a bottom-up coarse-graining methodology that leverages all-atom molecular dynamics to molecularly inform coarser field-theoretic models. Specifically, we use relative-entropy coarse-graining to parametrize particle models that are directly and analytically transformable into statistical field theories. We demonstrate the predictive capability of this approach by reproducing experimental aqueous poly(ethylene oxide) (PEO) cloud-point curves with no parameters fit to experimental data. This synergistic approach to multiscale polymer simulations opens the door to de novo exploration of phase behavior across a wide variety of polymer solutions and melt formulations.

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

A series of cubic network phases was obtained from the self-assembly of a single-composition lamellae (L)-forming block copolymer (BCP) polystyrene-block-polydimethylsiloxane (PS-b-PDMS) through solution casting using a PS-selective solvent. An unusual network phase in diblock copolymers, double-primitive phase (DP) with space group of [Formula: see text], can be observed. With the reduction of solvent evaporation rate for solution casting, a double-diamond phase (DD) with space group of [Formula: see text] can be formed. By taking advantage of thermal annealing, order-order transitions from the DP and DD phases to a double-gyroid phase (DG) with space group of [Formula: see text] can be identified. The order-order transitions from DP (hexapod network) to DD (tetrapod network), and finally to DG (trigonal planar network) are attributed to the reduction of the degree of packing frustration within the junction (node), different from the predicted Bonnet transformation from DD to DG, and finally to DP based on enthalpic consideration only. This discovery suggests a new methodology to acquire various network phases from a simple diblock system by kinetically controlling self-assembling process.

Architecture Effects in Complex Spherical Assemblies of (AB)n-Type Block Copolymers

Molecular architecture plays a key role in the self-assembly of block copolymers, but few studies have systematically examined the influence of chain connectivity on tetrahedrally close-packed (TCP) sphere phases. Here, we report a versatile material platform comprising two blocks with substantial conformational asymmetry, A = poly(trifluoroethyl acrylate) and B = poly(dodecyl acrylate), and use it to compare the phase behavior of AB diblocks, ABA triblocks, and (AB)_n radial star copolymers with n = 3 or 4. Each architecture forms TCP sphere phases at minority A block compositions (f_A < 0.5), namely, σ and A15, but with differences in the location of order-order phase boundaries that are not anticipated by mean-field self-consistent field theory simulations. These results expand the palette of polymer architectures that readily self-assemble into complex TCP structures and suggest important design considerations when targeting specific phases of interest.

Room temperature 3D printing of super-soft and solvent-free elastomers

Super-soft elastomers derived from bottlebrush polymers show promise as advanced materials for biomimetic tissue and device applications, but current processing strategies are restricted to simple molding. Here, we introduce a design concept that enables the three-dimensional (3D) printing of super-soft and solvent-free bottlebrush elastomers at room temperature. The key advance is a class of inks comprising statistical bottlebrush polymers that self-assemble into well-ordered body-centered cubic sphere phases. These soft solids undergo sharp and reversible yielding at 20°C in response to shear with a yield stress that can be tuned by manipulating the length scale of microphase separation. The addition of a soluble photocrosslinker allows complete ultraviolet curing after extrusion to form super-soft elastomers with near-perfect recoverable elasticity well beyond the yield strain. These structure-property design rules create exciting opportunities to tailor the performance of 3D-printed elastomers in ways that are not possible with current materials and processes.

Formation of a C15 Laves Phase with a Giant Unit Cell in Salt-Doped A/B/AB Ternary Polymer Blends

Salt-doped A/B/AB ternary polymer blends, wherein an AB copolymer acts as a surfactant to stabilize otherwise incompatible A and B homopolymers, display a wide range of nanostructured morphologies with significant tunability. Among these structures, a bicontinuous microemulsion (BμE) has been a notable target. Here, we report the surprising appearance of a robust C15 Laves phase, at compositions near where the BμE has recently been reported, in lithium bis(trifluoromethane) sulfonimide (LiTFSI)-doped low-molar-mass poly(ethylene oxide) (PEO)/polystyrene (PS)/symmetric PS-b-PEO block copolymer blends. The materials were analyzed by a combination of small-angle X-ray scattering (SAXS), ¹H NMR spectroscopy, and impedance spectroscopy. The C15 phase emerges at a high total homopolymer volume fraction ϕ_H = 0.8 with a salt composition r = 0.06 (Li⁺/[EO]) and persists as a coexisting phase across a large area of the isothermal phase diagram with high PS homopolymer compositions. Notably, the structure exhibits a huge unit cell size, a = 121 nm, with an unusually high micelle core volume fraction (f_core = 0.41) and an unusually low fraction of amphiphile (20%). This unit cell dimension is at least 50% larger than any previously reported C15 phase in soft matter, despite the low molar masses used, unlocking the possibility of copolymer-based photonic crystals without compromising processability. The nanostructured phase evolution from lamellar to hexagonal to C15 along the EO60 isopleth (ϕ_{PEO,homo-LiTFSI}/ϕ_H = 0.6) is rationalized as a consequence of asymmetry in the homopolymer solubility limit for each block, which leads to exclusion of PS homopolymer from the PS-b-PEO brush prior to exclusion of the PEO homopolymer, driving increased interfacial curvature and favoring the emergence of the C15 Laves phase.

Impact of Architectural Asymmetry on Frank-Kasper Phase Formation in Block Polymer Melts

In recent decades, the discoveries of complex low-symmetry phases in soft matter have inspired advances in molecular and materials design. However, understanding the mechanisms underlying symmetry selection across soft matter remains an important challenge in materials science. Block polymers represent attractive model materials because they permit wide synthetic tunability and provide access to multiple length scales (1-100 nm). However, to date the block polymer design space has been largely limited to variations in molecular weight, block volume fraction, and conformational asymmetry. The molecular architecture-the way in which chains are connected-offers rich potential but remains relatively unexplored in experimental block polymers. Our work bridges this gap, connecting molecular architecture, space-filling demands, and symmetry selection in block polymer self-assembly. Three series of block polymers were synthesized by living polymerization, tuning the architectural asymmetry across the linear-b-linear and linear-b-bottlebrush limits. The bottlebrush architecture amplifies two key ingredients for the formation of Frank-Kasper phases: high conformational asymmetry and high self-concentration. Analysis by small-angle X-ray scattering provides insight into the impact of architectural asymmetry on block polymer self-assembly. Increasing the asymmetry between blocks opens the complex phase window, expanding opportunities to tune symmetry selection in block polymer melts.

Discrete Block Copolymers with Diverse Architectures: Resolving Complex Spherical Phases with One Monomer Resolution

This work describes the first rigorous example of a single-component block copolymer system forming unconventional spherical phases. A library of discrete block polymers with uniform chain length and diverse architectures were modularly prepared through a combination of a step-growth approach and highly efficient coupling reactions. The precise chemical structure eliminates all the molecular defects associated with molar weight, dispersity, and compositional ratio. Complex spherical phases, including the Frank-Kasper phase (A15 and σ) and quasicrystalline phase, were experimentally captured by meticulously tuning the composition and architectures. A phase portrait with unprecedented accuracy was mapped out (up to one monomer resolution), unraveling intriguing details of phase behaviors that have long been compromised by inherent molecular weight distribution. This study serves as a delicate model system to bridge the existing gaps between experimental observations and theoretical assessments and to provide insights into the formation and evolution of the unconventional spherical phases in soft matter systems.

Symmetry breaking in particle-forming diblock polymer/homopolymer blends

Compositionally asymmetric diblock copolymers provide an attractive platform for understanding the emergence of tetragonally close-packed, Frank-Kasper phases in soft matter. Block-polymer phase behavior is governed by a straightforward competition between chain stretching and interfacial tension under the constraint of filling space at uniform density. Experiments have revealed that diblock copolymers with insufficient conformational asymmetry to form Frank-Kasper phases in the neat-melt state undergo an interconversion from body-centered cubic (bcc) close-packed micelles to a succession of Frank-Kasper phases (σ to C14 to C15) upon the addition of minority-block homopolymer in the dry-brush regime, accompanied by the expected transition from bcc to hexagonally packed cylinders in the wet-brush regime. Self-consistent field theory data presented here qualitatively reproduce the salient features of the experimental phase behavior. A particle-by-particle analysis of homopolymer partitioning furnishes a basis for understanding the symmetry breaking from the high-symmetry bcc phase to the lower-symmetry Frank-Kasper phases, wherein the reconfiguration of the system into polyhedra of increasing volume asymmetry delays the onset of macroscopic phase separation.

Rapid Generation of Block Copolymer Libraries Using Automated Chromatographic Separation

A versatile and scalable strategy is reported for the rapid generation of block copolymer libraries spanning a wide range of compositions starting from a single parent copolymer. This strategy employs automated and operationally simple chromatographic separation that is demonstrated to be applicable to a variety of block copolymer chemistries on multigram scales with excellent mass recovery. The corresponding phase diagrams exhibit increased compositional resolution compared to those traditionally constructed via multiple, individual block copolymer syntheses. Increased uniformity and lower dispersity of the chromatographic libraries lead to differences in the location of order-order transitions and observable morphologies, highlighting the influence of dispersity on the self-assembly of block copolymers. Significantly, this separation technique greatly simplifies the exploration of block copolymer phase space across a range of compositions, monomer pairs, and molecular weights (up to 50000 amu), producing materials with increased control and homogeneity when compared to conventional strategies.

Stabilizing Phases of Block Copolymers with Gigantic Spheres via Designed Chain Architectures

It is generally believed that the spherical domains self-assembled from AB-type block copolymers are composed of the minority A blocks with a volume fraction of f_A < 1/2. Breaking this generic rule so that the spherical domains are formed by the majority A blocks (f_A > 1/2) requires mechanisms to drastically expand the stable region of spherical packing phases. Self-consistent field theory predicts that dendron-like AB-type block copolymers, composed of G - 1 generations of A blocks connected with the outermost generation of B blocks, exhibit a stable region of spherical packing phases extending to f_A ∼ 0.7. The extremely expanded spherical regions shed light on the mechanisms governing the self-assembly of amphiphilic macromolecules, as well as provide opportunities to engineer complex spherical packing phases.

Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends

The observation of complex, Frank-Kasper (FK) particle packings in diblock polymer melts has until recently been limited to low molecular weight, conformationally asymmetric polymers. We report temperature-dependent small-angle X-ray scattering (SAXS) studies of blends of a sphere-forming poly(styrene-block-1,4-butadiene) (SB) diblock polymer (M_n = 33.3 kg/mol, Đ = M_w/M_n = 1.08, f_B = 0.18) with two different poly(1,4-butadiene) (B) homopolymer additives. When the B additive M_n is the same as that of the diblock core-forming B segment, these blends remarkably form tetrahedrally close-packed FK σ and Laves C14 and C15 phases with increasing B content. However, binary blends in which the B additive M_n is 60% of that of the diblock B segment form only the canonical body-centered cubic (BCC) particle packing and hexagonally-packed cylinders (HEXc). The observed phase behavior is rationalized in terms of "wet" and "dry" brush blending, whereby higher B M_n drives stronger localization of the homopolymer in the particle cores while preserving the interfacial area per SB diblock chain. The consequent packing constraints in these blends destabilize the BCC packing, and FK phases emerge as optimal minimal surface solutions to filling space at constant density while maximizing local particle sphericity.

Field theoretic approach for block polymer melts: SCFT and FTS

This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.

Synthesis and Self-Assembly of ABn Miktoarm Star Polymers

The stability of tetrahedrally close-packed (TCP) phases in block copolymer melts is predicted by theory to depend on molecular architecture, yet no experimental studies to date have probed its effect. Motivated by this open question, here we report an efficient synthesis of asymmetric AB_n miktoarm star polymers using functionalized sugars as cores for orthogonal grafting-from block copolymerizations. A combination of ring-opening and atom transfer radical polymerization produced model low dispersity materials comprising a single A = poly(lactide) (L) and multiple B = poly(dodecyl acrylate) (D) arms that amplify "conformational asymmetry" through two concerted effects: the mikto architecture and disparate block statistical segment lengths. Analyzing the self-assembly of LD₂ and LD₃ samples resulted in the discovery of two TCP phases, σ and A15, that remained stable to significantly higher A-block volume fractions as the number of B arms increased. These results experimentally establish the importance of conformational asymmetry and molecular architecture as powerful design tools for the self-assembly of block copolymers into nonclassical phases.

Molecular Engineering of Nanostructures in Disordered Block Polymers

A series of symmetric poly(methyl methacrylate-stat-styrene)-block-polylactide (P(MMA-s-S)-b-PLA) diblock terpolymers with nearly constant molar masses yet varying block interaction parameters were synthesized as a model system to probe the extent and utility of composition fluctuations in the disordered state. A combination of differential scanning calorimetry, dynamic mechanical analysis, and small-angle X-ray scattering revealed that a broad range of segregation strengths ranging from what we ascribe to essentially a mean-field disordered to a fluctuating disordered to an ordered system could be readily obtained by tuning the molar fraction of styrene in these diblocks. The P(MMA-s-S)-b-PLA diblocks were annealed above their order-disorder transition temperatures (T_ODT) and rapidly quenched to low temperatures to trap the disordered state via vitrification, as confirmed by scanning electron microscopy. Small-angle X-ray scattering and N₂ sorption analysis post-removal of PLA demonstrated that a transition from a very weakly structured, mean-field-like melt to a bicontinuous fluctuating disordered state occurred with increasing segregation strength. This work demonstrates that the extent of microphase segregation as well as the domain continuity of the disordered block polymer melt can be tuned using both synthetic design and thermal stimuli, guiding the design of disordered block polymers with targeted nanostructures that have potential technological utility.

Open-source code for self-consistent field theory calculations of block polymer phase behavior on graphics processing units

Self-consistent field theory (SCFT) is a powerful approach for computing the phase behavior of block polymers. We describe a fast version of the open-source Polymer Self-Consistent Field (PSCF) code that takes advantage of the massive parallelization provided by a graphical processing unit (GPU). Benchmarking double-precision calculations indicate up to 30× reduction in time to converge SCFT calculations of various diblock copolymer phases when compared to the Fortran CPU version of PSCF using the same algorithms, with the speed-up increasing with increasing unit cell size for the diblock polymer problems examined here. Where double-precision accuracy is not needed, single-precision calculations can provide speed-up of up to 60× in convergence time. These improvements in speed within an open-source format open up new vistas for SCFT-driven block polymer materials discovery by the community at large.

A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends

A renewed focus on the phase behavior of nominally single-component, compositionally asymmetric diblock copolymers has revealed a host of previously unanticipated Frank-Kasper (FK) and quasicrystalline phases. However, these periodic and aperiodic particle packings have thus far only been reported in low molecular weight, highly conformationally asymmetric diblock copolymers, leaving researchers with a relatively small library of polymers in which these phases can be studied. In this work, we report on a simple approach to access these morphologies: blending two diblock copolymers with the same corona block length and varied core block lengths. Compositionally symmetric and asymmetric polystyrene-b-1,4-polybutadiene (SB) diblock copolymers with constant corona block lengths were blended together and shown via small-angle X-ray scattering and transmission electron microscopy to order into the FK A15 and σ phases, as well as a dodecagonal quasicrystal, providing a route to various particle packings in high molecular weight diblock copolymer melts.