Dynamical Heterogeneity and Nonlinear Susceptibility in Supercooled Liquids with Short-Range Attraction

Abstract

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here we study in detail the behavior of nonlinear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard nonlinear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids. DOI: 10.1103/PhysRevLett.99.135701 PACS numbers: 64.70.Pf, 61.43.Fs, 82.70.Dd The underlying reasons for the dramatic increase in the viscosity of glass-forming liquids are not well understood. It has become increasingly clear that simple structural measures remain short-ranged close to the glass transition, and thus a growing simple static length scale does not appear to be implicated [1]. This has led to the search for a growing dynamical length scale that drives vitrification. Indeed, recent simulations [2 -7] and experiments [8][9][10][11][12][13] have given direct evidence for both a growing length scale and a dynamical scaling relating its growth to the rapidly increasing time scales that characterize the glass transition. The study of this key aspect of dynamical heterogeneity, as encoded in various multipoint dynamical susceptibilities, has opened up the ability both to extract absolute length scales associated with cooperative relaxation in glassy systems and to provide precise metrics for the testing of various theoretical approaches [5,14,15].The simplest model system that exhibits the expected dynamical behavior associated with more complicated glassy systems is the hard-sphere liquid. Here entropydriven crowding effects give rise to a characteristic dynamical behavior that includes a two-step nonexponential relaxation, a dramatic increase in relaxation times associated with small changes in volume fraction, and dynamical heterogeneity accompanied by a growing dynamical length scale [14]. Recently, it has been demonstrated via theory [16], simulation [17,18], and experiment [19,20] that another extreme glassy limit exists for simple spherical particles: that of the short-range attractive glassy state. Here strong short-ranged bonding between the particles can lead to extremely slow relaxation but with dramatically different dynamical characteristics. Dynamical heterogeneity also exists close to the attractive glassy state [17,[21][22][23] but has not been systematically characterized, and multipoint dynamical susceptibilities for such systems have not been measured or computed. The goal of this work is to investigate in detail the properties of standard nonlinear spatiotemporal susceptibilities at distinct points along the attractive glass line and to quantitatively and qua...

Dynamical fluctuation effects in glassy colloidal suspensions

“…New structural mechanisms for dynamic heterogeneity emerge, and very large single particle nongaussian effects have been observed in both experiment [79 • ,82,83 • ] and simulation [36 •• ,84 • ]. Qualitative differences of the multi-point dynamical susceptibilities of hard and sticky spheres have begun to be documented [85]. Such dramatically heterogeneous dynamics, including the presumably coupled activated processes of physical bond breakage and cage escape, remain essentially unaddressed by theory and represent a major challenge for the future.…”

Three-point susceptibilitiesχn(k;t)andχns(kSzamel1, Flenner2 2009Phys. Rev. E2030View full textAdd to dashboardCite

“…The wave vector dependence of four-point correlation function χ 4 (k; t) was monitored in two recent simulational investigations [23,24]. Both studies used Newtonian rather than Brownian dynamics and thus our findings cannot be directly compared to their results.…”

“…Roughly speak-ing, according to Berthier et al [8,9], Brownian system's four-point correlation function χ 4 (k; t), which is defined as the self part of the four-point dynamic density correlation function integrated over the whole space, is proportional to χ s n (k; t) 2 for a system in which the total number of particles can fluctuate and is proportional to χ s n (k; t) for a system with fixed total number of particles (note that the latter one is commonly used in numerical simulations). Following Berthier et al and assuming that mode-coupling theory gives at least qualitatively correct results for three-point susceptibility χ s n (k; t) we are faced with a striking conclusion that the there is no finite intrinsic [23] wave vector at which dynamic heterogeneities, as quantified by χ 4 (k; t), are the largest. More precisely, at a fixed time we can determine a finite characteristic wave vector, but with increasing time this wave vector is decreasing towards 0.…”

“…At present, the origin of the differences between our findings and the results of Refs. [23,24] is unclear.…”

“…The second study, Ref. [23], shows the dependence of the maximum value of χ 4 (k; t) [25] on the wave vector. It exhibits a broad maximum located at a wave vector slightly smaller than the peak position of the static structure factor.…”