Local Density Fluctuation Governs the Divergence of Viscosity Underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid

Abstract

If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a logarithmically diverging diffusivity in the long-time limit.In many two-dimensional ordering phenomena, fluctuations at long wavelengths are so strong that perfect order is destroyed. For example, the transition between a liquid and a crystalline solid is continuous or nearly continuous [1][2][3][4][5][6]. Recently, large-scale molecular dynamics (MD) simulations [7,8] and colloidal experiments [9, 10] have revealed that such long-wavelength fluctuations also exist in two-dimensional (2D) liquids that are rapidly cooled toward the glass transition. Although retaining a random amorphous structure, elastic vibrations appear as the rigidity emerges with the decrease in temperature. The excess of low-frequency phonons in two dimensions [7,11] leads to enhanced thermal elastic vibrations at long wavelengths. Even in the presence of these long-wavelength fluctuations, the structural relaxation in 2D and 3D supercooled liquids appears to be similar, once the effect of these fluctuations has been eliminated by introducing quantities that characterize the local switching between neighbor particles [7,9,10].The glass transition is marked by a drastic increase in macroscopic viscosity, which is intimately related to the divergence of the microscopic structural relaxation time. As such, theoretical and computational studies have focused on the dynamical mechanism of growth in the microscopic structural relaxation time, most typically the α-relaxation time [12][13][14][15], which is defined as the decay time of the autocorrelation function for the local density i.e., the intermediate scattering function. However, in two dimensions, the decay time is strongly suppressed by the long-wavelength thermal elastic vibrations [7-10], preventing the α-relaxation time from reflecting the microscopic structural relaxation time. Therefore, to enhance our understanding of 2D glass formation, it is essential to identify the relaxation time related to the viscosity divergence by taking the mechanical properties into account.When a liquid approaches the glass transition via rapid cooling, a transient elastic response emerges, giving rise to an intermediate plateau in the shear stress relaxation function and an increase in the overall viscosity. In a recent study, while the viscosity enhancement is similar between 2D and 3D glassforming liquids, the plateau in the stress relaxation function turns out to be less clear in two dimensions under light super-...

Long-wavelength fluctuations and dimensionality crossover in confined liquids

“…3(c), we observe that, while the standard relaxation time decreases logarithmically with L, the CR one is L independent. These results closely parallel those observed in strictly two-dimensional systems [19][20][21][22][23][24][25] and demonstrate that LW fluctuations sensibly affect the structural relaxation dynamics of confined liquids.…”

“…The size dependence of the relaxation dynamics of confined liquids offers an alternative and unexplored approach to investigate the dimensionality crossover. Indeed, two-dimensional systems differ from their threedimensional counterpart because Mermin-Wagner [18] * massimo@ntu.edu.sg long-wavelength (LW) fluctuations make their relaxation dynamics size dependent [19][20][21][22][23][24][25]. This alternative approach is also convenient as Mermin-Wagner fluctuations are always present in two-dimensional systems; conversely, the two-and the three-dimensional phase behaviour do not qualitatively differ in all systems [26][27][28].…”

An improved integration scheme for Mode-coupling-theory equations

“…Furthermore, the lognonug allows studying numerically the long-wavelength regime q → 0. This could be particularly interesting to study the long-wavelength properties of the structural glass transition in two dimensions, a topic that is recently receiving increasing attention [76,77]. The proposed integration scheme resorts completely on trapezoidal integration in the case of hard spheres, while for hard disks we introduced a mix of trapezoidal and analytical integration that allows us to deal successfully with the singularities appearing in the MCT kernel for d = 2.…”

Are strongly confined colloids good models for two dimensional liquids?

“…Using computer simulations, Flenner and Szamel showed that many typical features of glassy dynamics in 3D systems (e.g., the transient cage formation, the coupling between orientational and translational relaxations) are absent in 2D samples, indicating that the glass transitions in 2D and in 3D differ significantly [21]. However, later experiments [8,9] and simulations [22,23] have clearly demonstrated that this difference is induced by Mermin-Wagner fluctuations which refer to the phenomenon that particles in 2D can move significantly without obviously changing their local environments (neighbors). Once the influence of these long-length fluctuations has been removed by using cage-relative quantities, the 2D systems are found to display all typical features of glassy dynamics, just like their 3D counterparts [8,9,22,23].…”

“…However, later experiments [8,9] and simulations [22,23] have clearly demonstrated that this difference is induced by Mermin-Wagner fluctuations which refer to the phenomenon that particles in 2D can move significantly without obviously changing their local environments (neighbors). Once the influence of these long-length fluctuations has been removed by using cage-relative quantities, the 2D systems are found to display all typical features of glassy dynamics, just like their 3D counterparts [8,9,22,23]. Hence this issue is resolved and 2D colloidal suspensions can be used as valuable models of glass-forming systems [24].…”