Dynamic arrest in a liquid of symmetric dumbbells: Reorientational hopping for small molecular elongations

Abstract

We present extensive molecular dynamics simulations of a liquid of symmetric dumbbells, for constant packing fraction, as a function of temperature and molecular elongation. For large elongations, translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. The odd rotational degrees of freedom remain ergodic at all investigated temperature and the temperature dependence of the corresponding characteristic time is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of a type-A transition temperature for the odd rotational degrees of freedom, distinct from the type-B transition associated with the arrest of the translational and even rotational ones, as predicted by the mode-coupling theory for the glass transition. The ideal mode-coupling theory (MCT) equations have been recently solved in the site-site representation for a system of symmetric hard dumbbell molecules [1,2], as a function of the packing fraction ϕ and the elongation ζ. Interestingly enough, the theory predicts two different dynamic arrest scenarios, on varing ϕ and ζ (see Fig. 1 in Ref.[1]). For large elongations, it is predicted that all rotational correlation functions are strongly coupled to the translational degrees of freedom and dynamic arrest takes place at a common ϕ value, ϕ B c (ζ). According to MCT, the transition is of type-B, i.e. the long time limit of translational and rotational correlation functions jumps discontinuosly from zero to a finite value at the ideal glass transition line. The ideal glass transition line (the B-line) has a non-monotonic shape in the ϕ−ζ plane, with a maximum at ζ = 0.43. The B-line continues for small elongations until the hard sphere limit at ζ = 0 is reached. However, for small elongations ζ < ζ c = 0.345, theory predicts a novel different scenario: only the translational and the even rotational degrees of freedom freeze at the B-line. Here even and odd refer to the parity of the order l of the rotational correlator C l (t) = P l (ê(t)·ê(0)) , where P l is the Legendre l-polynomial andê(t) is a unity vector along the molecular axis at time t. The odd-l rotational degrees of freedom freeze at higher values of the packing fraction, namely at an A-line ϕ The A-and B-lines separate the ϕ − ζ plane in three dynamic regions: an ergodic fluid, a completely arrested state, and an intermediate state (located between the Aand B-lines) which is the amorphous analog of a plastic crystal. In such a state, each molecule remains trapped in the cage formed by the neighbouring molecules, but is able to perform 180 o rotations within the cage, which lead to relaxation for the odd-l but not for the even-l rotational correlators. An analogous scenario is predicted by molecular MCT for the case of hard-ellipsoids in the limit of small aspect ratio [3].In order to test these predictions, we have recently carried out ...

Anomalous dynamic arrest in a mixture of large and small particles

“…This behavior resembles features characteristic of MCT transitions of the type-A, which are defined by a zero value of the critical non-ergodicity parameter, in contrast to the finite value defining stan- dard type-B transitions. A recent realization of this scenario has been reported for a system of dumbbell molecules [39,40,41]. While for moderate molecular elongations a standard relaxation scenario is observed, for small elongations angular correlators exhibit features analogous to those of Fig.…”

Crystal nucleation of colloidal hard dumbbells

“…13. [34][35][36][37][38] Increasing the supersaturation will lower G * , but D l will decrease as well, while at lower supersaturation the barrier height will only increase. As a result, the nucleation of CP1 phase of hard dumbbells is severely hindered by a high free energy barrier at low supersaturations and slow dynamics at high supersaturations, which explains why the CP1 phase of colloidal hard dumbbells has never been observed in experiments 18 or in direct simulations.…”

Glassy swirls of active dumbbells

“…Living realisations include reconstituted layer of confluent epithelial cells [13], where cell shape anisotropy plays a crucial role in the jammingunjamming transition [14], and jammed biofilms formed by a dense collection of rod-shaped bacteria. Likewise, shaken non-spherical grains at high packing densities constitute non-living examples [15].We perform Brownian dynamics simulations of a dense binary assembly of dumbbells [16][17][18][19] in 2-dimensions (see Fig. 1(a) and Supplementary Information [20] for details); the 50:50 mixture of A and B type dumbbells ensures amorphous steady state structures.…”