Intradomain Textures in Block Copolymers: Multizone Alignment and Biaxiality

Prasad, Ishan; Seo, Yongsok; Hall, Lisa M.; Grason, Gregory M.

doi:10.1103/physrevlett.118.247801

Cited by 21 publications

(24 citation statements)

References 45 publications

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“…The isotropic -gyroid transition occurs at densities between r g ¼ 0.52 (k u ¼ 2.4) and r g ¼ 0.55 (k u ¼ 4.5), the systems adopting a super-structure characterized by two interpenetrating channel networks (see figure 7). The interdigitating curved bilayers indicate a smectic order on the gyroid minimal surface (note related work on possible nematic ordering in block copolymers [45]). In this phase, the pear-shaped particles are able to traverse the simulation box isotropically, through both in-leaflet diffusion and leaflet to leaflet flip-flop.…”

Section: Phase Diagrammentioning

confidence: 92%

Purely entropic self-assembly of the bicontinuous Ia 3 d gyroid phase in equilibrium hard-pear systems

et al. 2017

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We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia[Formula: see text]d structure by entropic self-assembly, extending the previous observations of Barmes (2003, 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison (2006, 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression-decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.

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Section: Phase Diagrammentioning

confidence: 92%

Purely entropic self-assembly of the bicontinuous Ia 3 d gyroid phase in equilibrium hard-pear systems

et al. 2017

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“…To analyze the intra-domain structure of chain packing in more detail, we compute the polar orientational order parameter, t A (x), of A block segments using methods described in ref. [36],…”

Section: Geometric Analysis Of Spherical Domainsmentioning

confidence: 99%

Stable Frank–Kasper phases of self-assembled, soft matter spheres

Reddy

Buckley

Arora

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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138

248

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SignificanceFormation of complex Frank–Kasper phases in soft matter systems confounds intuitive notions that equilibrium states achieve maximal symmetry, owing to an unavoidable conflict between shape and volume asymmetry in space-filling packings of spherical domains. Here we show the structure and thermodynamics of these complex phases can be understood from the generalization of two classic problems in discrete geometry: the Kelvin and Quantizer problems. We find that self-organized asymmetry of Frank–Kasper phases in diblock copolymers emerges from the optimal relaxation of cellular domains to unequal volumes to simultaneously minimize area and maximize compactness of cells, highlighting an important connection between crystal structures in condensed matter and optimal lattices in discrete geometry.

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“…Moreover, scattering experiments [i.e., wide-angle X-ray scattering (WAXS)] were conducted but no mesophase characteristic signature can be identified in the patterns. While melt BCPs are typically described as "amorphous," microphase separation necessarily introduces anisotropy in the packing of segments as measured by nonvanishing orientational order parameters (29), even in the absence of strong orientational interactions between segments (i.e., interactions which would give rise to thermotropic isotropic/nematic transitions). Therefore, microphase separation, which induces at least some measure of orientational order of segments within the domain, has the effect of enhancing or amplifying otherwise weakly anisotropic tendencies of intersegment forces between segments (30), such as intersegment forces that favor twisted (cholesteric) packing.…”

Section: Resultsmentioning

confidence: 99%

Generalizing the effects of chirality on block copolymer assembly

Wang

Yang

Hsu

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

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We explore the generality of the influence of segment chirality on the self-assembled structure of achiral–chiral diblock copolymers. Poly(cyclohexylglycolide) (PCG)-based chiral block copolymers (BCPs*), poly(benzyl methacrylate)-b-poly(d-cyclohexylglycolide) (PBnMA-PDCG) and PBnMA-b-poly(l-cyclohexyl glycolide) (PBnMA-PLCG), were synthesized for purposes of systematic comparison with polylactide (PLA)-based BCPs*, previously shown to exhibit chirality transfer from monomeric unit to the multichain domain morphology. Opposite-handed PCG helical chains in the enantiomeric BCPs* were identified by the vibrational circular dichroism (VCD) studies revealing transfer from chiral monomers to chiral intrachain conformation. We report further VCD evidence of chiral interchain interactions, consistent with some amounts of handed skew configurations of PCG segments in a melt state packing. Finally, we show by electron tomography [3D transmission electron microscope tomography (3D TEM)] that chirality at the monomeric and intrachain level ultimately manifests in the symmetry of microphase-separated, multichain morphologies: a helical phase (H*) of hexagonally, ordered, helically shaped tubular domains whose handedness agrees with the respective monomeric chirality. Critically, unlike previous PLA-based BCP*s, the lack of a competing crystalline state of the chiral PCGs allowed determination that H* is an equilibrium phase of chiral PBnMA-PCG. We compared different measures of chirality at the monomer scale for PLA and PCG, and argued, on the basis of comparison with mean-field theory results for chiral diblock copolymer melts, that the enhanced thermodynamic stability of the mesochiral H* morphology may be attributed to the relatively stronger chiral intersegment forces, ultimately tracing from the effects of a bulkier chiral side group on its main chain.

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Intradomain Textures in Block Copolymers: Multizone Alignment and Biaxiality

Cited by 21 publications

References 45 publications

Purely entropic self-assembly of the bicontinuous Ia 3 d gyroid phase in equilibrium hard-pear systems

Purely entropic self-assembly of the bicontinuous Ia 3 d gyroid phase in equilibrium hard-pear systems

Stable Frank–Kasper phases of self-assembled, soft matter spheres

Generalizing the effects of chirality on block copolymer assembly

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