Testing Rigidity Transitions in Glass and Crystal Forming Dense Liquids: Viscoelasticity and Dynamical Gaps

Abstract

A computational study of rigidity for dense fluids of monodisperse and bidisperse hard-disks near a phase and a glass transition respectively is presented. To achieve this goal, the transversal part of the dynamical structure factor is calculated. In both cases, a viscoelastic behavior is obtained, with a dynamical gap determined by a critical wavevector k c. Transversal waves exist for k > k c while the maximal correlations happens at frequency ω = 0 for k < k c. In both cases k c goes to zero as the freezing point is approached. Both systems are able to fulfill a scaled dynamical law as a power law is found for the critical k c as a function of the packing. The obtained results indicate that this method gives an alternative to study rigidity and constraint theory in dense fluids, since it is possible to assign a number of floppy modes or broken constraints in the liquid by computing the number of modes below k c , as well as an effective average coordination number. Also, this suggests that the critical wavevector k c can serve as a suitable order parameter.

Gapped momentum states

“…In further agreement with (18), k g calculated from the dispersion curves increases approximately as 1 τ [33]. The emergence of k g has also been ascertained in hard disk models used to understand the rigidity transition in glasses and liquid-glass transition [34].…”

“…We observe that the first equation in (34) is identical to (13), resulting in the first solution in (35) as in (17). The second solution increases with time.…”

“…Here, the k-gap increases at low packing fractions. Because rigidity is related to propagating shear modes, the value of k g was interestingly proposed as an order parameter quantifying the rigidity transition [34].…”

“…This motion is analogous to diffusive particle jumps in the liquid responsible for the viscous ∝ 1 τ term in (13). Therefore, the dissipative ∝ 1 τ term in (32) and (34) describes the hopping motion of the field (via thermal activation or tunneling [57]) between different wells with frequency 1 τ . We refer to this term as dissipative, although we note that no energy dissipation takes place in the system as discussed above.…”