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Attraction tames two-dimensional melting: from continuous to discontinuous transitions
Two-dimensional systems may admit a hexatic phase and hexatic-liquid
transitions of different natures. The determination of their phase diagrams
proved challenging, and indeed those of hard-disks, hard regular polygons, and
inverse power-law potentials, have been only recently clarified. In this
context, the role of attractive forces is currently speculative, despite their
prevalence at both the molecular and colloidal scale. Here we demonstrate, via
numerical simulations, that attraction promotes a discontinuous melting
scenario with no hexatic phase. At high-temperature, Lennard-Jones particles
and attractive polygons follow the shape-dominated melting scenario observed in
hard-disks and hard polygons, respectively. Conversely, all systems melt via a
first-order transition with no hexatic phase at low temperature, where
attractive forces dominate. The intermediate temperature melting scenario is
shape-dependent. Our results suggest that, in colloidal experiments, the
tunability of the strength of the attractive forces allows for the observation
of different melting scenario in the same system.Comment: SI include
Role of cell deformability in the two-dimensional melting of biological tissues
The size and shape of a large variety of polymeric particles, including
biological cells, star polymers, dendrimes, and microgels, depend on the
applied stresses as the particles are extremely soft. In high-density
suspensions these particles deform as stressed by their neighbors, which
implies that the interparticle interaction becomes of many-body type.
Investigating a two-dimensional model of cell tissue, where the single particle
shear modulus is related to the cell adhesion strength, here we show that the
particle deformability affects the melting scenario. On increasing the
temperature, stiff particles undergo a first-order solid/liquid transition,
while soft ones undergo a continuous solid/hexatic transition followed by a
discontinuous hexatic/liquid transition. At zero temperature the melting
transition driven by the decrease of the adhesion strength occurs through two
continuous transitions as in the Kosterlitz, Thouless, Halperin, Nelson, and
Young scenario. Thus, there is a range of adhesion strength values where the
hexatic phase is stable at zero temperature, which suggests that the
intermediate phase of the epithelial-to-mesenchymal transition could be hexatic
type
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