Triply periodic level surfaces as models for cubic tricontinuous block copolymer morphologies

Microphase separation in block copolymer systems forms well-defined, periodic structure on the sub-micron length scale. This structure arises from the system striving to satisfy the delicate balance of minimizing the area of contact between incompatible chain segments and maximizing the conformational entropy of the macromolecules. Candidate geometries satisfying these constraints possess intermaterial dividing surfaces (IMDS) of constant mean curvature. These include triply periodic, bicontinuous structures related to minimal surfaces. These structures, recently observed in microphase-separated block copolymer systems, also arise in phase-separated surfactant-water systems, indicating the two phenomena may be driven by similar physical mechanisms. A complete description of block copolymer phase morphology requires characterization of the long-range ordered single grain microdomain structure, the defect structures within grains, and the microstructure of the boundary region between grains. The type of structure observed is sensitive to the architecture, chemical composition, and molecular mass of the copolymers. Thermodynamic treatments using a geometrical description of the IMDS provide a means for probing the physics of phase morphology in block copolymers.

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Anatomy of triply-periodic network assemblies: characterizing skeletal and inter-domain surface geometry of block copolymer gyroids

Soft Matter ◽

10.1039/c8sm00078f ◽

2018 ◽

Vol 14 (18) ◽

pp. 3612-3623 ◽

Cited By ~ 11

Author(s):

Ishan Prasad ◽

Hiroshi Jinnai ◽

Rong-Ming Ho ◽

Edwin L. Thomas ◽

Gregory M. Grason

Keyword(s):

Block Copolymer ◽

Triblock Copolymers ◽

Surface Geometry ◽

Material Surfaces ◽

Triply Periodic ◽

Double Gyroid

Mesogeometric anatomy – 2D inter-material surfaces and 1D skeletons – extracted from triply-periodic, double-gyroid network assembled from triblock copolymers.

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Triply-periodic nanostructures in surfactant, block copolymer, and biomembrane systems, and simulation of TEMs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100150253 ◽

1993 ◽

Vol 51 ◽

pp. 884-885

Author(s):

David M. Anderson ◽

Tomas Landh

Keyword(s):

Liquid Crystalline ◽

Diblock Copolymers ◽

Cubic Phase ◽

List Type ◽

Interpenetrating Networks ◽

Triply Periodic ◽

Wide Range ◽

Bicontinuous Cubic ◽

Phase Liquid ◽

Dividing Surface

First discovered in surfactant-water liquid crystalline systems, so-called ‘bicontinuous cubic phases’ have the property that hydropnilic and lipophilic microdomains form interpenetrating networks conforming to cubic lattices on the scale of nanometers. Later these same structures were found in star diblock copolymers, where the simultaneous continuity of elastomeric and glassy domains gives rise to unique physical properties. Today it is well-established that the symmetry and topology of such a morphology are accurately described by one of several triply-periodic minimal surfaces, and that the interface between hydrophilic and hydrophobic, or immiscible polymer, domains is described by a triply-periodic surface of constant, nonzero mean curvature. One example of such a dividing surface is shown in figure 5.The study of these structures has become of increasing importance in the past five years for two reasons:1)Bicontinuous cubic phase liquid crystals are now being polymerized to create microporous materials with monodispersed pores and readily functionalizable porewalls; figure 3 shows a TEM from a polymerized surfactant / methylmethacrylate / water cubic phase; and2)Compelling evidence has been found that these same morphologies describe biomembrane systems in a wide range of cells.

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