Considering multi-body systems of monodisperse hard Brownian particles, it remains challenging to predict the forms of order that can emerge in their dense assembled structures. Surprisingly, here, using Monte Carlo simulations, we show that tetratic-ordered phases emerge in a dense two-dimensional system of hard kites that are rotationally asymmetric and have opposite 72° and α ≈ 90° internal angles. We observe a new tetragonal rectangular crystal (TRX) phase possessing (quasi-)long-range fourfold molecular-orientational order. We propose a method based on local polymorphic configurations of neighboring particle pairs (LPC-NPPs) to understand this emergent tetratic order and show that LPC-NPPs can be useful for predicting orientational order in such systems. To examine the dependence of the tetratic order on α, we apply LPC-NPP analysis to other hard kites for 54° ≤ α ≤ 144°. Our work provides insight into the creation of novel ordered materials by rationally designing particle shape based on anticipated LPC-NPPs.
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 fractions 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 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 collective motion of rounded squares with different corner-roundness ζ is studied by molecular dynamics (MD) simulation in this work. Three types of translational collective motion pattern are observed, including gliding, hopping and a mixture of gliding and hopping. Quantitatively, the dynamics of each observed ordered phase is characterized by both mean square displacement and van Hove functions for both translation and rotation. The effect of corner-roundness on the dynamics is further studied by comparing the dynamics of the rhombic crystal phases formed by different corner-rounded particles at a same surface fraction. The results show that as ζ increases from 0.286 to 0.667, the translational collective motion of particles changes from a gliding-dominant pattern to a hopping-dominant pattern, whereas the rotational motion pattern is hopping-like and does not change in its type, but the rotational hopping becomes much more frequent as ζ increases (i.e., as particles become more rounded). A simple geometrical model is proposed to explain the trend of gliding motion observed in MD simulations.
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