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Motility-Induced Crystallization and Rotating Crystallites

Max Philipp Holl1,2,3,*,†, Alina Barbara Steinberg3,*,‡, Michael te Vrugt4,§, and Uwe Thiele3,5,║

  • 1Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Espoo 00076, Finland
  • 2Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Espoo 00076, Finland
  • 3Institute of Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
  • 4Institute of Physics, Johannes Gutenberg University Mainz, 55128 Mainz, Germany
  • 5Center for Nonlinear Science (CeNoS), University of Münster, Corrensstrasse 2, 48149 Münster, Germany

  • *These authors contributed equally to this work.
  • †Contact author: max.holl@aalto.fi
  • ‡Contact author: a_stei52@uni-muenster.de
  • §Contact author: tevrugtm@uni-mainz.de
  • ║Contact author: u.thiele@uni-muenster.de; www.uwethiele.de
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Phys. Rev. Lett. 135, 158301 – Published 6 October, 2025

DOI: https://doi.org/10.1103/m3dy-53yc

Abstract

Active soft matter frequently shows motility-induced phase separation, where self-propelled particles condensate into clusters with an inner liquidlike structure. Such activity may also result in motility-induced crystallization into clusters with an inner crystalline structure. We derive a higher-order active phase-field-crystal model and employ it to study the interplay of passive (i.e., thermodynamic) and active (i.e., motility-induced) condensation or evaporation and crystallization or melting. Stability and morphological phase diagrams indicate the various occurring phase coexistences and transitions, e.g., the destruction of passive clusters in the case of a density-independent effective velocity and the possible creation of active clusters in the case of a density-dependent effective velocity. Finally, simple and complex rotating crystallites are discussed, including states of time-periodic chirality.

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Phys. Rev. Lett. 135, 158301– Published 6 October, 2025
  • Received 14 August 2024
  • Revised 28 July 2025
  • Accepted 8 September 2025
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