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A method of determining the globally stable morphologies of block copolymers using a framework composed of a genetic algorithm (GA) in conjunction with self-consistent field theory (SCFT) is described. We present results from benchmark testing of this GA-SCFT technique on the canonical AB diblock copolymer melt, for which the theoretical phase diagram has long been established. The GA-SCFT algorithm successfully predicts many of the conventional mesophases from random initial conditions in large, three-dimensional simulation cells, including HEX, LAM, and BCC, over a broad composition range and weak to moderate segregation strength. However, the GA-SCFT method is currently not effective at recovery of network phases, such as the gyroid structure, or for the BCC phase in the strong segregation limit. These challenges may be partially attributed to the large density of defective states seen in large simulation cells and at higher segregation strengths. [ABSTRACT FROM AUTHOR]

We review the latest developments in computational methods for direct simulation of fully fluctuating field theories of polymeric assemblies. In this context, we describe a newly developed theoretical and computational framework for accurately computing fluctuation-corrected phase diagrams of mesostructured polymer systems and report the first such complete phase diagram for a diblock copolymer melt. The method is based on complex Langevin sampling of a UV regularized field-theoretic model, with Helmholtz free energies computed using thermodynamic integration. UV regularization ensures that the free energies do not have an arbitrary reference; they can be compared between incommensurate phases, permitting for the first time the computation of order-order transitions with fluctuation corrections. We further demonstrate that computed free energies are accurate in the disordered phase by comparison to perturbation theory on the one-loop level. Importantly, we note that our method uses no uncontrolled approximations beyond the initial definition of a coarse-grained molecular model for the polymer melt or solution. The method can be applied straightforwardly to melts and solutions containing multiple species with diverse polymer architectures. [ABSTRACT FROM AUTHOR]

Solvent vapor annealing is a promising, flexible platform for controlling the self-assembly of block copolymer thin films. However, the ability for static solvent annealing alone to provide sufficient bias to generate vertically oriented features is limited. Here, we use dynamical field theory simulations to investigate the morphology dynamics and capacity for pattern selection of a cyclic solvent annealing process. We find that the swell step selectively strains features oriented parallel to the substrate, reducing their stability with respect to disorder, while vertically oriented domains remain stable through the full cycle. This memory effect may be exploited to systematically improve feature orientation with wide operating margins and favorable kinetics compared to static solvent or cyclic thermal annealing. In aggregate, these results suggest a simple, robust method for orienting features in solvent annealed block copolymer films, potentially obviating the need for external fields while minimizing the total annealing time. [ABSTRACT FROM AUTHOR]

The promise of ABC triblock terpolymers for improving the mechanical properties of thermoplastic elastomers is demonstrated by comparison with symmetric ABA/CBC analogs having similar molecular weights and volume fraction of B and A/C domains. The ABC architecture enhances elasticity (up to 98% recovery over 10 cycles) in part through essentially full chain bridging between discrete hard domains leading to the minimization of mechanically unproductive loops. In addition, the unique phase space of ABC triblocks also enables the fraction of hard-block domains to be higher ( f hard ≈ 0.4) while maintaining elasticity, which is traditionally only possible with non-linear architectures or highly asymmetric ABA triblock copolymers. These advantages of ABC triblock terpolymers provide a tunable platform to create materials with practical applications while improving our fundamental understanding of chain conformation and structure-property relationships in block copolymers., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

The small specific entropy of mixing of high molecular weight polymers implies that most blends of dissimilar polymers are immiscible with poor physical properties. Historically, a wide range of compatibilization strategies have been pursued, including the addition of copolymers or emulsifiers or installing complementary reactive groups that can promote the in situ formation of block or graft copolymers during blending operations. Typically, such reactive blending exploits reversible or irreversible covalent or hydrogen bonds to produce the desired copolymer, but there are other options. Here, we argue that ionic bonds and electrostatic correlations represent an underutilized tool for polymer compatibilization and in tailoring materials for applications ranging from sustainable polymer alloys to organic electronics and solid polymer electrolytes. The theoretical basis for ionic compatibilization is surveyed and placed in the context of existing experimental literature and emerging classes of functional polymer materials. We conclude with a perspective on how electrostatic interactions might be exploited in plastic waste upcycling., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

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.

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.

The usual understanding in polymer electrolyte design is that an increase in the polymer dielectric constant results in reduced ion aggregation and therefore increased ionic conductivity. We demonstrate here that in a class of polymers with extensive metal-ligand coordination and tunable dielectric properties, the extent of ionic aggregation is delinked from the ionic conductivity. The polymer systems considered here comprise ether, butadiene, and siloxane backbones with grafted imidazole side-chains, with dissolved Li + , Cu 2+ , or Zn 2+ salts. The nature of ion aggregation is probed using a combination of X-ray scattering, electron paramagnetic resonance (in the case where the metal cation is Cu 2+ ), and polymer field theory-based simulations. Polymers with less polar backbones (butadiene and siloxane) show stronger ion aggregation in X-ray scattering compared to those with the more polar ether backbone. The T g -normalized ionic conductivities were however unaffected by the extent of aggregation. The results are explained on the basis of simulations which indicate that polymer backbone polarity does impact the microstructure and the extent of ion aggregation but does not impact percolation, leading to similar ionic conductivity regardless of the extent of ion aggregation. The results emphasize the ability to design for low polymer T g through backbone modulation, separately from controlling ion-polymer interaction dynamics through ligand choice.

Motivated by the much discussed, yet unexplained, presence of macrovoids in polymer membranes, we explore the impact of Marangoni flows in the process of nonsolvent induced phase separation. Such flows have been hypothesized to be important to the formation of macrovoids, but little quantitative evidence has been produced to date. Using a recently developed multifluid phase field model, we find that roll cells indicative of a solutal Marangoni instability are manifest during solvent/nonsolvent exchange across a stable interface. However, these flows are weak and subsequently do not produce morphological features that might lead to macrovoid formation. By contrast, initial conditions that lead to an immediate precipitation of the polymer film coincide with large Marangoni flows that disturb the interface. The presence of such flows suggests a new experimental and theoretical direction in the search for a macrovoid formation mechanism.

The effect of dispersity on block polymer self-assembly was studied in the monodisperse limit using a combination of synthetic chemistry, matrix-assisted laser desorption ionization spectroscopy, and small-angle X-ray scattering. Oligo(methyl methacrylate) (oligoMMA) and oligo(dimethylsiloxane) (oligoDMS) homopolymers were synthesized by conventional polymerization techniques and purified to generate an array of discrete, semidiscrete, and disperse building blocks. Coupling reactions afforded oligo(DMS-MMA) block polymers with precisely tailored molar mass distributions spanning single molecular systems ( Đ = 1.0) to low-dispersity mixtures ( Đ ≈ 1.05). Discrete materials exhibit a pronounced decrease in domain spacing and sharper scattering reflections relative to disperse analogues. The order-disorder transition temperature ( T ODT ) also decreases with increasing dispersity, suggesting stabilization of the disordered phase, presumably due to the strengthening of composition fluctuations at the low molar masses investigated.

Multiblock polymers (MBPs) show great promise as a platform for synthesizing materials with highly customized nanostructures. In these systems, the subtle balance of chain configurational entropy and interactions between dissimilar block chemistries emerge a rich palette of self-assembled structural motifs that may be leveraged to impart novel functional, mechanical, or optical properties to the final material. Unfortunately, extensive study of MBP self-assembly has yielded few reliable heuristics for intuitively navigating the enormous molecular design space made available by modern polymer synthesis techniques. In order to make progress, new methods must be developed that allow researchers to efficiently screen molecular designs for achieving a desired state of self-assembly. Here, we introduce a platform for the automated discovery of tailored MBP formulations based on the Particle Swarm Optimization (PSO) method and a linear multiblock chain parametrization that enables continuous optimization of chain architecture. We apply the method to thin-film blends of linear ABC triblock polymers subject to lateral confinement, allowing all polymer and blend parameters to freely optimize in search of a prespecified, nontrivial target morphology. While we focus on pattern selection as a proof of principle, any computable equilibrium property can be optimized using the methods described here.

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

We report the creation of highly asymmetric lamellar structures with a well-designed miktoarm star block copolymer of the S(IS')3 type, where S and S' are polystyrenes of different lengths and I is poly(isoprene). The domain spacing can be tuned continuously from 37 nm to over 300 nm when the miktoarm star block copolymer is blended with suitable molecular weight polystyrene homopolymers. Beyond the unbinding transition of the lamellar phase, extremely asymmetric lamellar structures were obtained with up to 97 wt % polystyrene, remarkably leaving the poly(isoprene) layers intact at only 3 wt %!

Solvent evaporation has proven to be a remarkably successful tool for directing self-assembly in block copolymers, yet the microscopic mechanisms, processing history dependence and macroscopic control parameters influencing pattern selection remain poorly understood. Here, we leverage dynamical field theory simulations to clarify how copolymer self-assembly proceeds during evaporation. We find that cylinders in the vertical orientation tend to form under modest evaporation rates and relatively weak segregation strengths, and link this behavior to nontrivial, morphology-dependent density correlations present at the ordering front.

Control of interfacial interactions leads to a dramatic change in shape and morphology for particles based on poly(styrene-b-2-vinylpyridine) diblock copolymers. Key to these changes is the addition of Au-based surfactant nanoparticles (SNPs) which are adsorbed at the interface between block copolymer-containing emulsion droplets and the surrounding amphiphilic surfactant to afford asymmetric, ellipsoid particles. The mechanism of formation for these novel nanostructures was investigated by systematically varying the volume fraction of SNPs, with the results showing the critical nature that the segregation of SNPs to specific interfaces plays in controlling structure. A theoretical description of the system allows the size distribution and aspect ratio of the asymmetric block copolymer colloidal particles to be correlated with the experimental results.

Reactivity ratios were evaluated for anionic ring-opening copolymerizations of ethylene oxide (EO) with either allyl glycidyl ether (AGE) or ethylene glycol vinyl glycidyl ether (EGVGE) using a benzyl alkoxide initiator. The chemical shift for the benzylic protons of the initiator, as measured by (1)H NMR spectroscopy, were observed to be sensitive to the sequence of the first two monomers added to the initiator during polymer growth. Using a simple kinetic model for initiation and the first propagation step, reactivity ratios for the copolymerization of AGE and EGVGE with EO could be determined by analysis of the (1)H NMR spectroscopy for the resulting copolymer. For the copolymerization between EO and AGE, the reactivity ratios were determined to be r(AGE) = 1.31 ± 0.26 and r(EO) = 0.54 ± 0.03, while for EO and EGVGE, the reactivity ratios were r(EGVGE) = 3.50 ± 0.90 and r(EO) = 0.32 ± 0.10. These ratios were consistent with the compositional drift observed in the copolymerization between EO and EGVGE, with EGVGE being consumed early in the copolymerization. These experimental results, combined with density functional calculations, allowed a mechanism for oxyanionic ring-opening polymerization that begins with coordination of the Lewis-basic epoxide to the cation to be proposed. The calculated transition-state energies agree qualitatively with the observed relative rates for polymerization.