Particle deformability stabilizes hexatic order and suppresses crystallization

Abstract

We show that two-dimensional systems of deformable particles undergo a continuous liquid-hexatic transition upon compression or cooling, but no hexatic-solid transition-even at zero temperature and high density. Numerical simulations reveal that solid-like configurations do not possess a lower energy than hexatic ones, so that at low temperatures the hexatic phase is thermodynamically favored due to its higher entropy. Dislocation condensation, necessary for solid formation, is suppressed as the system accommodates strain via particle shape changes, responding affinely to compression. Our findings identify a generic route by which microscopic mechanical properties control defect energetics and reshape phase behavior in two dimensions, with broad relevance for soft and biological materials such as microgels and epithelial tissues.

Figures (10)

• Figure 1: (a) Zoomed-in view of the investigated system, highlighting the polymer-ring description of the particles, represented in different colors, and (b) configuration of the system at $\rho = 1.32$ and $T = 0.1$. Translational (c) and bond-orientational (d) correlation function at $T = 0.1$, for diverse values of the density. The translational correlation function $c(r)$ decays exponentially at all densities, indicating that the system does not enter the solid phase. In contrast, $g_6(r)$, which decays exponentially at low densities, exhibits a slow power-law decay for $\rho \gtrsim 1.26$, signaling the transition from the liquid to the hexatic phase. The inset of (c) illustrates the static structure factor at $\rho = 1.36$. The smearing of the first peaks is consistent with the loss of translational order. The data in (c) and (d) are averaged over 10 independent realizations.
• Figure 2: Equilibrium phase diagram for systems of deformable particles. At each density, diamonds mark the highest temperature at which we have estimated the system to be in the hexatic phase, and circles mark the lowest temperature of the liquid phases. The line is a guide to the eye. The white circle denotes the jamming transition density estimated by compressing the system at $T=0$.
• Figure 3: Dependence of the defect density (a) on the temperature, at $\rho = 1.36$, and (b) on the density, at $T=0.1$. Data are averaged over 10 independent simulations, and error bars represent the standard deviations.
• Figure 4: Translational (a) and bond-orientational (b) correlation function of an ideal solid at T = 0 (red), and of the configuration attained after heating it to $T=0.1$ (blue). Heating destroys positional order while retaining bond-orientational order. (c) Upon heating, the peak value of the static structure factor exponentially decays to an asymptotic low value on a melting time $t_m$. Error bars show standard deviations from ten independent runs. (d) Temperature dependence of $t_m$. The dashed line corresponds to $t_m \propto T^{-1/2}$. The uncertainties reflect the standard errors from the exponential fits.
• Figure 5: (a) Density dependence of the elastic energy upon quasistatic compression, for systems prepared in liquid-like, hexatic-like, and solid phases. (b) The symmetries of the initial configuration are preserved during compression, as demonstrated by the bond-orientational correlation functions at the highest attained density. (c) Representative snapshots of the system with particles colored according to the scalar product between the local sixfold bond-orientational order parameter and its average across all particles.