The phase behavior of liquids confined in a slit geometry does not reveal a crossover from a three to a two-dimensional behavior as the gap size decreases. Indeed, the prototypical two-dimensional hexatic phase only occurs in liquids confined to a mo
nolayer. Here, we demonstrate that the dimensionality crossover is apparent in the lateral size dependence of the relaxation dynamics of confined liquids, developing a Debye model for the density of vibrational states of confined systems and performing extensive numerical simulations. In confined systems, Mermin-Wagner fluctuations enhance the amplitude of vibrational motion or Debye-Waller factor by a quantity scaling as the inverse gap width and proportional to the logarithm of the aspect ratio, as a clear signature of a two-dimensional behaviour. As the temperature or lateral system size increases, the crossover to a size-independent relaxation dynamics occurs when structural relaxation takes place before the vibrational modes with the longest wavelength develop.
Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time sub-diffusive transient, as observed in some experiments and recent stud
ies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behaviour, tissues of stiff cells having conventional glassy relaxation dynamics.
The phase diagram of the prototypical two-dimensional Lennard-Jones system, while extensively investigated, is still debated. In particular, there are controversial results in the literature as concern the existence of the hexatic phase and the melti
ng scenario. Here, we study the phase behaviour of 2D LJ particles via large-scale numerical simulations. We demonstrate that at high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. As the temperature decreases, the density range where the hexatic phase occurs shrinks so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.
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 potentia
ls, 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.
We investigate the translational and rotational relaxation dynamics of a crowded two-dimensional system of monodisperse Penrose kites, in which crystallization, quasi-crystallization, and nematic ordering are suppressed, from low to high area fractio
ns along the metastable ergodic fluid branch. First, we demonstrate a decoupling between both the translational and the rotational diffusion coefficients and the relaxation time: the diffusivities are not inversely proportional to the relaxation time, neither in the low-density normal liquid regime nor in the high-density supercooled regime. Our simulations reveal that this inverse proportionality breaks in the normal liquid regime due to the Mermin-Wagner long-wavelength fluctuations and in the supercooled regime due to the dynamical heterogeneities. We then show that dynamical heterogeneities are mainly spatial for translational degrees of freedom and temporal for rotational ones, that there is no correlation between the particles with the largest translational and rotational displacements, and that different dynamical length scales characterize the translational and the rotational motion. Hence, despite the translational and the rotational glass-transition densities coincide, according to a mode-coupling fit, translations and rotations appear to decorrelate via different dynamical processes.
The identification of the different phases of a two-dimensional (2d) system, which might be in solid, hexatic, or liquid, requires the accurate determination of the correlation function of the translational and of the bond-orientational order paramet
ers. According to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, in the solid phase the translational correlation function decays algebraically, as a consequence of the Mermin-Wagner long-wavelength fluctuations. Recent results have however reported an exponential-like decay. By revisiting different definitions of the translational correlation function commonly used in the literature, here we clarify that the observed exponential-like decay in the solid phase results from an inaccurate determination of the symmetry axis of the solid; the expected power-law behaviour is recovered when the symmetry axis is properly identified. We show that, contrary to the common assumption, the symmetry axis of a 2d solid is not fixed by the direction of its global bond-orientational parameter, and introduce an approach allowing to determine the symmetry axis from a real space analysis of the sample.
The suppression of density fluctuations at different length scales is the hallmark of hyperuniformity. However, its existence and significance in jammed solids is still a matter of debate. We explore the presence of this hidden order in a manybody in
teracting model known to exhibit a rigidity transition, and find that in contrary to exisiting speculations, density fluctuations in the rigid phase are only suppressed up to a finite lengthscale. This length scale grows and diverges at the critical point of the rigidity transition, such that the system is hyperuniform in the fluid phase. This suggests that hyperuniformity is a feature generically absent in jammed solids. Surprisingly, corresponding fluctuations in geometrical properties of the model are found to be strongly suppressed over an even greater but still finite lengthscale, indicating that the system self organizes in preference to suppress geometrical fluctuations at the expense of incurring density fluctuations.
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.
One of the central problems of the liquid-glass transition is whether there is a structural signature that can qualitatively distinguish different dynamic behaviors at different degrees of supercooling. Here, we propose a novel structural characteriz
ation based on the spatial correlation of local density and we show the locally dense-packed structural environment has a direct link with the slow dynamics as well as dynamic heterogeneity in glass-formers. We find that particles with large local density relax slowly and the size of cluster formed by the dense-packed particles increases with decreasing the temperature. Moreover, the extracted static length scale shows clear correlation with the relaxation time at different degrees of supercooling. This suggests that the temporarily but continuously formed locally dense-packed structural environment may be the structural origin of slow dynamics and dynamic heterogeneity of the glass-forming liquids.
We present an event-driven molecular dynamics study for hard ellipses and assess the effects of aspect ratio and area fraction on their physical properties. For state points in the plane of aspect ratio (k=1-9) and area fraction (phi=0.01-0.8), we id
entify three different phases, including isotropic, plastic and nematic states. The equation of state (EOS) is shown for a wide range of aspect ratios and is compared with the scaled particle theory (SPT) for the isotropic states. We find that SPT provides a good description of the EOS for the isotropic phase of hard ellipses. At large fixed phi, the reduced pressure p increases with k in both the isotropic and the plastic phases, and interestingly, its dependence on k is rather weak in the nematic phase. We rationalize the thermodynamics of hard ellipses in terms of particle motions. The plastic crystal is shown to form for aspect ratios up to k=1.4, while appearance of the stable nematic phase starts approximately at k=3. We quantitatively determine the locations of the isotropic-plastic (I-P) transition and the isotropic-nematic (I-N) transition by analyzing the bond-orientation correlations and the angular correlations, respectively. As expected, the I-P transition point is found to increase with k, while a larger k leads to a smaller area fraction where the I-N transition takes place. Moreover, our simulations strongly support that the two-dimensional nematic phase in hard ellipses has only quasi-long-range orientational order. The self-diffusion of hard ellipses is further explored and connections are revealed between the structure and the self-diffusion. We discuss the relevance of our results to the glass transition in hard ellipses. Finally, the results of the isodiffusivity lines are evaluated for hard ellipses and we discuss the effect of spatial dimension on the diffusive dynamics of hard ellipsoidal particles.
