Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers
Abstract
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 – networks require molecules to occupy variable local environments, confounding attempts to understand their formation. Here, we examine the double-gyroid network phase by using a geometric formulation of the strong stretching theory of block copolymer melts, a prototypical soft self-assembly system. The theory establishes the direct link between molecular packing, assembly thermodynamics and the medial map, a generic measure of the geometric center of complex shapes. We show that “medial packing” is essential for stability of double-gyroid in strongly-segregated melts, reconciling a long-standing contradiction between infinite- and finite-segregation theories. Additionally, we find a previously unrecognized non-monotonic dependence of network stability on the relative entropic elastic stiffness of matrix-forming to tubular-network forming blocks. The composition window of stable double-gyroid widens for both large and small elastic asymmetry, contradicting intuitive notions that packing frustration is localized to the tubular domains. This study demonstrates the utility of optimized medial tessellations for understanding soft-molecular assembly and packing frustration via an approach that is readily generalizable far beyondmore »
- Publication Date:
- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1905447
- Grant/Contract Number:
- SC0022229; SC0014599
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Nature Communications
- Additional Journal Information:
- Journal Volume: 13; Journal Issue: 1; Related Information: https://doi.org/10.7275/s98r-sb17; Journal ID: ISSN 2041-1723
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; self-assembly; polymers; supramolecular crystals; nanostructured networks; applied mathematics; theory and computation
Citation Formats
Reddy, Abhiram, Dimitriyev, Michael S., and Grason, Gregory M. Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers. United States: N. p., 2022.
Web. doi:10.1038/s41467-022-30343-2.
Reddy, Abhiram, Dimitriyev, Michael S., & Grason, Gregory M. Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers. United States. https://doi.org/10.1038/s41467-022-30343-2
Reddy, Abhiram, Dimitriyev, Michael S., and Grason, Gregory M. Thu .
"Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers". United States. https://doi.org/10.1038/s41467-022-30343-2. https://www.osti.gov/servlets/purl/1905447.
@article{osti_1905447,
title = {Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers},
author = {Reddy, Abhiram and Dimitriyev, Michael S. and Grason, Gregory M.},
abstractNote = {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 – networks require molecules to occupy variable local environments, confounding attempts to understand their formation. Here, we examine the double-gyroid network phase by using a geometric formulation of the strong stretching theory of block copolymer melts, a prototypical soft self-assembly system. The theory establishes the direct link between molecular packing, assembly thermodynamics and the medial map, a generic measure of the geometric center of complex shapes. We show that “medial packing” is essential for stability of double-gyroid in strongly-segregated melts, reconciling a long-standing contradiction between infinite- and finite-segregation theories. Additionally, we find a previously unrecognized non-monotonic dependence of network stability on the relative entropic elastic stiffness of matrix-forming to tubular-network forming blocks. The composition window of stable double-gyroid widens for both large and small elastic asymmetry, contradicting intuitive notions that packing frustration is localized to the tubular domains. This study demonstrates the utility of optimized medial tessellations for understanding soft-molecular assembly and packing frustration via an approach that is readily generalizable far beyond gyroids in neat block copolymers.},
doi = {10.1038/s41467-022-30343-2},
journal = {Nature Communications},
number = 1,
volume = 13,
place = {United States},
year = {Thu May 12 00:00:00 EDT 2022},
month = {Thu May 12 00:00:00 EDT 2022}
}
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