Long-wavelength fluctuations and anomalous dynamics in 2-dimensional liquids

Abstract

Long-wavelength Mermin-Wagner fluctuations prevent the existence of translational long-range order, in two-dimensional systems at finite temperature. Their dynamical signature, which is the divergence of the vibrational amplitude with the system size, also affects disordered solids and washes out the transient solid-like response generally exhibited by liquids cooled below their melting temperature. Through a combined numerical and experimental investigation, here we show that long-wavelength fluctuations are also relevant at high temperature, where the liquid dynamics does not reveal a transient solid-like response. In this regime, they induce an unusual but ubiquitous decoupling between long-time diffusion coefficient D and structural relaxation time τ , where D ∝ τ −κ , with κ > 1. Long-wavelength fluctuations have a negligible influence on the relaxation dynamics only at extremely high temperatures, in molecular liquids, or extremely low densities, in colloidal systems.

Dynamics in two-dimensional glassy systems of crowded Penrose kites

“…This implies that the inverse proportionality between diffusion coefficient and relaxation time may break down with D ∝ τ −κ with κ > 1, not with κ < 1 as usually observed in the supercooled regime. Such a breakdown has been recently observed in a variety of different 2D models [18,45,[47][48][49]. This unusual breakdown is restricted to the liquid regime because upon supercooling the vibrational amplitudes decrease, so that the breakdown of the inverse proportionality becomes dominated by the dynamical heterogeneities, which promote κ < 1.…”

“…The translational relaxation dynamics of 2D systems has been recently shown to be strongly affected by the collective particle motion arising from the Mermin-Wagner long-wavelength fluctuations [24][25][26][27]45]. The effect of these fluctuations can be filtered out investigating the dynamics using CR measures, and indeed recent results have clarified [24][25][26][27]45] that when CR quanti- ties are considered the previously observed fundamental distinctions [46] between the glass transition in 2D and in 3D disappear. However, it remains unclear how these fluctuations affect the scaling relations between diffusion coefficient and relaxation time in both translation and rotation, also because all previous studies of the CR dynamics focused on systems with a radially symmetric interaction potential.…”

Cooperatively rearranging regions change shape near the mode-coupling crossover for colloidal liquids on a sphere

“…The presence of dynamical heterogeneities in the supercooled regime implies that D is no longer proportional to τ α , like in simple liquids, but instead scales as with κ < 1. Recent studies found that besides dynamical heterogeneities, MW fluctuations, which are prevalent in 2D, also contribute to altering the value of κ 20 . This implies that when MW fluctuations are removed using cage-relative measures, the exponent κ CR connecting the cage-relative diffusivity D CR and is different from κ with 1 ≥ κ CR > κ in the supercooled regime.…”

“…This implies that when MW fluctuations are removed using cage-relative measures, the exponent κ CR connecting the cage-relative diffusivity D CR and is different from κ with 1 ≥ κ CR > κ in the supercooled regime. In 3D liquids, where MW fluctuations have a lesser role, κ CR ≈ κ 20 . A change in the value of exponent between the normal and the cage-relative measures thus serves as a readout for the presence of MW fluctuations.…”

“…These fluctuations provide an additional channel for structural relaxation and transient particle localization, a signature feature of glassy dynamics in 3-dimensions, is absent. In fact, even in the normal liquid regime where such localization effects are absent, while in d = 3 the long-time diffusion constant with κ = 1, in d = 2 MW fluctuations result in an anomalous scaling with κ > 1 20 . MW fluctuations are also strongly system size-dependent and their effects diminish systematically on reducing system size 17 – 21 .…”