TY - JOUR
T1 - Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases
T2 - Evolution of local motifs
AU - Cramer Pedersen, Martin
AU - Robins, Vanessa
AU - Mortensen, Kell
AU - Kirkensgaard, Jacob J.K.
N1 - Publisher Copyright:
© 2020 The Author(s).
PY - 2020/9/1
Y1 - 2020/9/1
N2 - Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by 'topological proximity', a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.
AB - Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by 'topological proximity', a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.
KW - molecular dynamics
KW - persistent homology
KW - quasi-crystal
KW - self-assembly
KW - topology
UR - http://www.scopus.com/inward/record.url?scp=85093113395&partnerID=8YFLogxK
U2 - 10.1098/rspa.2020.0170
DO - 10.1098/rspa.2020.0170
M3 - Article
SN - 1364-5021
VL - 476
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2241
M1 - 20200170
ER -