Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional “telegraph” process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.

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.

Over the past decade, a wealth of complexity has been reported in the packing of compositionally asymmetric, particle-forming diblock copolymer melts, beginning with the discovery of the Frank−Kasper σ phase and continuing with subsequent discoveries of a dodecagonal quasicrystal and the C14, C15, and A15 phases. First identified by self-consistent mean-field theory (SCFT), blending diblock copolymers has proven to be a useful strategy in extending these packings to new chemistries and length scales. However, much of the immense phase space created on blending two copolymers remains unexplored. Herein, we expand on our previous work investigating binary blends of polystyrene-block-1,4-polybutadiene diblock copolymers, focusing on binary mixtures with a constant corona (majority) block length and a range of ratios of core (minority) block lengths. Small-angle X-ray scattering and transmission electron microscopy conducted with 5 narrow dispersity diblock copolymers and the associated blends uncovered a rich phase space including 12 distinct nanostructures. Notably, in agreement with SCFT predictions, we document a C14 Laves phase at low fractions of the larger copolymer in a mixture of high and low molecular weight components. However, experiments and SCFT calculations reveal that this window is truncated by close packing when the smaller copolymer is weakly segregated. Moreover, we find that even a modest difference in core block lengths is sufficient to stabilize the σ phase, highlighting the impact of core block dispersity in previous studies as well as the utility of blending in accessing these complex particle phases.

Bottlebrush block copolymers are emerging as promising materials for designing advanced materials with a number of unique properties engendered by densely grafted architectures. We used self-consistent field theory (SCFT) to determine how the stability of the double gyroid phase in a diblock copolymer melt is affected by converting one or both of the blocks of a linear diblock copolymer to a bottlebrush architecture. For architecturally symmetric polymers, the dominant effect of the bottlebrush is increasing segregation strength, whereupon the gyroid stability regions are effectively the same as linear diblock copolymers at equivalent segregation. In contrast, architectural asymmetry produced by coil–bottlebrush block polymers significantly impacts the gyroid stability region as a result of conformational asymmetry, which promotes spontaneous curvature. Gyroid is more stable when the coil blocks are in minority domains, which relieves packing frustration at the center of the gyroid nodes than in majority domains. Our results suggest that architectural asymmetry in bottlebrush block polymers can be a powerful design tool.

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.