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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster: Nonlinear Dynamics, Pattern Formation, Granular Matter

DY 27.7: Poster

Mittwoch, 19. März 2025, 15:00–18:00, P4

Phase separation with long-range interactions — •Filipe Thewes, Yicheng Qiang, Oliver Paulin, and David Zwicker — Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

It is well known that long-range interactions affect phase separation. For instance, such interactions can suppress droplet coarsening, leading to microscopic pattern with selected length scales. This effect is widely exploited by nature -- from structure formation in living cells to food engineering by humans. Although the details of the transition from macroscopic phase separation to microscopic pattern formation are understood for particular systems, the general conditions for the existence of such transition remain unclear.

We propose a general field theoretical model that combines Flory's theory of phase separation and a broad class of long-range interactions. We then show that the particular details of these interactions are not relevant to the transition from macro phase separation to micro pattern formation and the most important parameter is the length-scale associated with the long-range interactions. We uncover the possibility of both first-order and second-order transitions as this length-scale crosses a threshold value, and we show how two macro phases can coexist with patterned phases. Extending these results to multi-component mixtures reveals even richer physics with multiple coexisting patterns. Our results open the possibility of systematic control of droplet sizes via different pathways, and depending on the nature of the phase transition, allow for an intricate design of pattern formation.

Keywords: phase separation; long-range interactions; pattern formation