Cage effect in supercooled molecular liquids: Local anisotropies and collective solid-like response

Abstract

Both local geometry and collective extended excitations drive the moves of a particle in the cage of its neighbours in dense liquids. The strength of their influence is investigated by the molecular dynamics simulations of a supercooled liquid of fully flexible trimers with semirigid or rigid bonds. The rattling in the cage is investigated on different length scales. First, the rattling anisotropy due to local order is characterized by two order parameters sensing the monomers succeeding or failing to escape from the cage. Then the collective response of the surroundings excited by the monomer-monomer collisions is considered. The collective response is initially restricted to the nearest neighbours of the colliding particle by a Voronoi analysis revealing elastic contributions. Then the long-range excitation of the farthest neighbours is scrutinised by searching spatially extended correlations between the simultaneously fast displacements of the caged particle and the surroundings. It is found that the longitudinal component has stronger spatial modulation than the transverse one with a wavelength of about one particle diameter, in close resemblance with experimental findings on colloids. It is concluded that the cage rattling is largely affected by solid-like extended modes.

Fast Vibrational Modes and Slow Heterogeneous Dynamics in Polymers and Viscous Liquids

“…At very short times (ballistic regime), MSD increases according to 〈r2(t)〉≅(3kBT/m)t2 and ISF starts to decay. The repeated collisions with the other monomers slow the displacement of the tagged one, as evinced by the knee of MSD at t∼12/Ω0∼0.17, where sans-serifΩ0 is an effective collision frequency, i.e., it is the mean small oscillation frequency of the monomer in the potential well produced by the surrounding ones kept at their equilibrium positions [64,67]. At later times, a quasi-plateau region, also found in ISF, occurs when the temperature is lowered and/or the density increased.…”

“…It is crucial to provide a robust criterion to assess the presence of the cage, which is anticipated to lack in liquids with high molecular mobility and fast relaxation. Compelling evidence of the cage effect is provided by the time velocity correlation function, which, after a first large drop due to pair collisions, reverses the sign since the monomer rebounds from the cage wall [64]. As an alternative route to reveal the cage effect, we consider the slope of MSD in the log-log plot Δ(t)≡∂prefixlog〈r2(t)〉∂prefixlogt…”

“…Henceforth, Cδu(r,τα) and Cu→(r,τα) will be referred to as modulus (or mobility) and direction DDC functions, respectively. Local anisotropies and collective elastic solid-like response to the rattling of the monomers in the cage of their neighbours play a central role in the DDC build-up [64].…”

Thermodynamic scaling of vibrational dynamics and relaxation

“…Therefore, it is noteworthy that a different definition for the timescale related to the GT modifies the expression of Eq.3 only by shifting for a constant value. Eq.3 has been tested on experimental data [72,75,77,80,81,87] as well as numerical models of polymers [38,39,[72][73][74]82], colloids [76] and atomic liquids [39,73,75]. Douglas and coworkers developed a localization model predicting the alternative master curve F F M ( u 2 ) ∝ u 2 −3/2 relating the structural relaxation time and the fast mobility [56,78,79].…”

Looking at the dynamical heterogeneity in a supercooled polymer system through isoconfigurational ensemble

“…The identification of a correlation between the structure and dynamic heterogeneity would allow us to discover the universal origin of slow dynamics in the glassy state. There have been many interesting studies in the last years trying to relate the heterogeneous dynamics with structural aspects, [12][13][14][15][16][17][18][19][20][21][22][23] but there are also other approaches suggesting that structure is not dominant in the glass transition. 24 In particular, the iso-configurational ensemble method (ICEM) ideated by Widmer-Cooper and Harrowel 25 appears as a very useful tool for this objective.…”