The performance of thermoplastic elastomers composed of block copolymers is dependent upon the molecular bridges linking together the discrete minority domains. Here we devise a strategy for calculating the bridging statistics for complex block copolymer architectures, using self-consistent field theory. The method is demonstrated on (AB) M stars with M identical diblock arms. The fraction of molecules forming bridges, νb, is found to increase rapidly with M to values well beyond that of conventional ABA triblock copolymers. Once M is of order 10, virtually all molecules form bridges, and furthermore their arms tend to be distributed equally among neighboring minority domains. These high bridging fractions combined with the tendency of single molecules to bridge multiple domains make diblock-arm stars an excellent candidate for improved thermoplastic elastomers.

Block polymer self-assembly typically translates molecular chain connectivity into mesoscale structure by exploiting incompatible blocks with large interaction parameters (χ ij ). In this article, we demonstrate that the converse approach, encoding low-χ interactions in ABC bottlebrush triblock terpolymers (χ AC ≲ 0), promotes organization into a unique mixed-domain lamellar morphology, which we designate LAM P . Transmission electron microscopy indicates that LAM P exhibits ACBC domain connectivity, in contrast to conventional three-domain lamellae (LAM 3 ) with ABCB periods. Complementary small-angle X-ray scattering experiments reveal a strongly decreasing domain spacing with increasing total molar mass. Self-consistent field theory reinforces these observations and predicts that LAM P is thermodynamically stable below a critical χ AC , above which LAM 3 emerges. Both experiments and theory expose close analogies to ABA′ triblock copolymer phase behavior, collectively suggesting that low-χ interactions between chemically similar or distinct blocks intimately influence self-assembly. These conclusions provide fresh opportunities for block polymer design with potential consequences spanning all self-assembling soft materials.block polymer | self-assembly | polymer nanostructure | domain spacing | LAM P B lock polymers are a diverse class of soft materials capable of self-assembling into complex periodic nanostructures. Synthetic command over composition, dispersity, sequence, and molecular architecture enables control over the mesoscopic order and macroscopic thermal, mechanical, rheological, and transport properties (1-4). The phase behavior of "simple" linear AB diblock copolymers is universally parameterized by the segregation strength χ AB N and relative volume fraction f, where χ AB represents the effective Flory-Huggins binary interaction parameter and N is the total volume-averaged degree of polymerization. Mixing behavior, captured through the mean-field concept of χ AB , is central to block polymer self-assembly: the competing demands of minimizing interfacial energy and maximizing configurational entropy only favor microphase separation when A-B interactions are repulsive (χ AB > 0) (5, 6). Extension to higher-order multiblock polymers introduces additional interaction parameters (χ ij ) that impact self-assembly and properties (7). For example, introducing a mutually incompatible C block (χ AC > 0, χ BC > 0) generates a host of new morphologies dictated by the chain connectivity (ABC, ACB, or BAC) and intrinsic χ ij -values (8, 9). In this rich phase space, designing multiblock polymers with a combination of miscible and immiscible blocks can also access new structures and impart useful functions (10, 11). Perhaps the best-known examples of such systems are linear ABA′ triblock copolymers (χ AB > 0, χ AA′ ≈ 0): their high-value industrial applications as thermoplastic elastomers are entirely enabled by A/A′ mixing and chain connectivity, which together create physically cross-linked materials with ex...

Field theoretic simulations are used to predict the equilibrium phase diagram of symmetric blends of AB diblock copolymer with A-and B-type homopolymers. Experiments generally observe a channel of bicontinuous microemulsion (BμE) separating the ordered lamellar (LAM) phase from coexisting homopolymer-rich (A þ B) phases. However, our simulations find that the channel is unstable with respect to macrophase separation, in particular, A þ B þ BμE coexistence at high T and A þ B þ LAM coexistence at low T. The preference for three-phase coexistence is attributed to a weak attractive interaction between diblock monolayers.

Recent field-theoretic simulations of symmetric ternary blends of A- and B-type homopolymers with AB diblock copolymer [VorselaarsB. Vorselaars, B. 117801Phys. Rev. Lett.2020125predicted three-phase coexistence between bicontinuous microemulsion (BμE) and two homopolymer-rich phases. The present study begins by repeating their grand-canonical simulations over longer durations in simulation boxes of different sizes to ensure that the prediction was not an artifact of nonequilibrium effects or finite system sizes. The coexistence is then demonstrated in canonical simulations, where the three phases are explicitly separated by interfaces. From those simulations, we extract the interfacial widths, the interfacial tensions, the domain size in the BμE phase, and the copolymer concentration in each phase. The latter results are used to improve the accuracy of the previous phase diagram.

Field-theoretic simulations (FTSs) are performed on ternary blends of A- and B-type homopolymers of polymerization N and symmetric AB diblock copolymers of polymerization N. Unlike previous studies, our FTSs are conducted in three-dimensional space, with the help of two new semi-grand canonical ensembles. Motivated by the first experiment to discover bicontinuous microemulsion (BμE) in the polyethylene-polyethylene propylene system, we consider molecules of high molecular weight with size ratios of α ≡ N/N = 0.1, 0.2, and 0.4. Our focus is on the A + B coexistence between the two homopolymer-rich phases in the low-copolymer region of the phase diagram. The Scott line, at which the A + B phases mix to form a disordered melt with increasing temperature (or decreasing χ), is accurately determined using finite-size scaling techniques. We also examine how the copolymer affects the interface between the A + B phases, reducing the interfacial tension toward zero. Although comparisons with self-consistent field theory (SCFT) illustrate that fluctuation effects are relatively small, fluctuations do nevertheless produce the observed BμE that is absent in the SCFT phase diagram. Furthermore, we find evidence of three-phase A + B + BμE coexistence, which may have been missed in the original as well as subsequent experiments.