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Thermally Driven Order-Disorder Transition in Two-Dimensional Soft Cellular Systems.

Marc Durand1, Julien Heu1

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This study explores order-disorder transitions in 2D cellular systems, revealing an intermediate hexatic phase. This finding extends the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory to systems with many-body interactions.

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Area of Science:

  • Soft Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Biological tissues and foams exhibit high deformability and low compressibility in packed 2D systems.
  • These systems naturally tessellate a plane and show transitions between ordered and disordered patterns.

Purpose of the Study:

  • To numerically investigate the order-disorder transition in 2D cellular systems driven by thermal agitation.
  • To extend the validity of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory to systems with many-body interactions.

Main Methods:

  • Utilized a modified cellular Potts model algorithm for rapid thermalization of extensive 2D systems.
  • Simulated monodisperse cellular systems undergoing thermal agitation.

Main Results:

  • The order-disorder transition closely follows KTHNY theory predictions for 2D solid melting.
  • Identified an intermediate hexatic phase, retaining orientational order but losing positional order.
  • Demonstrated the KTHNY melting scenario in soft cellular systems with many-body interactions.

Conclusions:

  • Soft cellular systems serve as macroscopic models for exploring KTHNY melting.
  • The study validates KTHNY theory in systems beyond traditional 2D solids.
  • Findings offer insights into structural changes in experimental systems like biological tissues and foams.