Competition brings out the best: modelling the frustration between curvature energy and chain stretching energy of lyotropic liquid crystals in bicontinuous cubic phases

Chen, Hao; Jin, Chenyu

doi:10.1098/rsfs.2016.0114

Cited by 19 publications

(28 citation statements)

References 50 publications

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“…This medial surface (or axis) is a geometric construction that produces a centred skeleton of the original shape (see [46] for a recent review). For the case of bicontinuous structures, it represents a generalized line graph that also provides a robust definition of local domain (or channel) size and hence relates to questions of chain stretching frustration and geometric homogeneity [44,47,48,49]. For an object defined by its bounding surface, for every surface point p with surface normal vector n( p), the corresponding medial surface point is defined as p þ d( p) .…”

Section: Rsfsroyalsocietypublishingorg Interface Focus 7: 20160161mentioning

confidence: 99%

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: Rsfsroyalsocietypublishingorg Interface Focus 7: 20160161mentioning

confidence: 99%

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

et al. 2017

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“…terminal boundaries lie along the medial set). As medial geometry encodes the shortest distance to the "center" of a complex morphology, previous studies have proposed that medial thickness can be used as a heuristic measure of packing frustration [17,20,35] or otherwise an ingredient in phenomenological models of its costs [37] in TPN morphologies. We next exploit a fully molecular description of TPN assembly, the SST of BCP melts, to test and establish the direct connections between the medial geometry of complex TPN, the underlying configurations of molecular constituents and the thermodynamic stability of the DG phase.…”

Section: Medial Anatomy Of Tpn Morphologiesmentioning

confidence: 99%

Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers

Reddy,

Dimitriyev,

Grason

2021

Preprint

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Triply-periodic networks are among the most complex and functionally valuable self-assembled morphologies, yet they form in nearly every class of biological and synthetic soft matter building blocks. In contrast to simpler assembly motifs -spheres, cylinders, layers -TPN assemblies require molecules to occupy variable local domain shapes, confounding attempts to understand their formation. Here, we examine the double-gyroid (DG) network phase of block copolymer (BCP) melts, a prototypical soft self-assembly system, by using a geometric formulation of the strong stretching theory (SST) of BCP melts. The theory establishes the direct link between molecular BCP packing, thermodynamics of melt assembly and the medial map, a generic geometric measure of the center of complex shapes. We show that "medial packing" is essential for thermodynamic stability of DG in strongly-segregated melts, reconciling a long-standing contradiction between infinite-and finitesegregation theories, corroborating our SST predictions at finite-segregation via self-consistent field calculations. Additionally, we find a previously unrecognized non-monotonic dependence of DG stability on the elastic asymmetry, the comparative entropic stiffness of matrix-forming to tubularnetwork forming blocks. The composition window of stable DG -intermediate to competitor lamellar and columnar phases -widens both for large and small elastic asymmetry, seemingly overturning the heuristic view that packing frustration is localized to the tubular domains. This study demonstrates utility of geometric optimization of medial tesselations for understanding in soft-molecular assembly. As such, the particular medial-based approach deployed here is readily generalizable to study packing frustration far beyond the case of DG morphologies in neat BCP assemblies.

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“…The results confirmed that the G surface is the most stable structure among the hyperbolic surface categories, followed by D and P surface structures. A recent publication indicated that bicontinuous phases are determined by the competition and compromise between the CMC and parallel surface models [150].…”

Section: Structure and Formation Mechanismmentioning

confidence: 99%

Bicontinuous cubic phases in biological and artificial self-assembled systems

2020

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Nature has created innumerable life forms with miraculous hierarchical structures and morphologies that are optimized for different life events through evolution over billions of years. Bicontinuous cubic structures, which are often described by triply periodic minimal surfaces (TPMSs) and their constant mean curvature (CMC)/parallel surface companions, are of special interest to various research fields because of their complex form with unique physical functionalities. This has prompted the scientific community to fully understand the formation, structure, and properties of these materials. In this review, we summarize and discuss the formation mechanism and relationships of the relevant biological structures and the artificial self-assembly systems. These structures can be formed through biological processes with amazing regulation across a great length scales; nevertheless, artificial construction normally produces the structure corresponding to the molecular size and shape. Notably, the block copolymeric system is considered to be an applicable and attractive model system for the study of biological systems due to their versatile design and rich phase behavior. Some of the phenomena found in these two systems are compared and discussed, and this information may provide new ideas for a comprehensive understanding of the relationship between molecular shape and resulting interface curvature and the selfassembly process in living organisms. We argue that the copolymeric system may serve as a model to understand these biological systems and could encourage additional studies of artificial self-assembly and the creation of new functional materials.

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Competition brings out the best: modelling the frustration between curvature energy and chain stretching energy of lyotropic liquid crystals in bicontinuous cubic phases

Cited by 19 publications

References 50 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

Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers

Bicontinuous cubic phases in biological and artificial self-assembled systems

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