Probing a Nonequilibrium Einstein Relation in an Aging Colloidal Glass

Abou, Bérengère; Gallet, François

doi:10.1103/physrevlett.93.160603

Cited by 122 publications

(161 citation statements)

References 25 publications

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“…The ageing properties of Laponite have triggered lots of effort and debate about the exact nature of these nonergodic states, in particular, about whether the material is actually a "gel" or a (Wigner) "glass" [30,32,33,34,35,36,37,38]. Moreover, due to their out-of-equilibrium nature, Laponite suspensions were used to test possible violations of the fluctuationdissipation theorem (FDT) [39,40]. Several recent microrheology experiments tend to prove that the effective temperature cannot be distinguished from the bath temperature, so that the FDT remains valid [41,42], but such results are still under debate [43].…”

Section: Structure and Rheology Of Laponite Suspensionsmentioning

confidence: 99%

Shear-induced fragmentation of laponite suspensions

et al. 2009

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Simultaneous rheological and velocity profile measurements are performed in a smooth Couette geometry on Laponite suspensions seeded with glass microspheres and undergoing the shear-induced solid-to-fluid (or yielding) transition. Under these slippery boundary conditions, a rich temporal behaviour is uncovered, in which shear localization is observed at short times, that rapidly gives way to a highly heterogeneous flow characterized by intermittent switching from plug-like flow to linear velocity profiles. Such a temporal behaviour is linked to the fragmentation of the initially solid sample into blocks separated by fluidized regions. These solid pieces get progressively eroded over time scales ranging from a few minutes to several hours depending on the applied shear ratė γ. The steady-state is characterized by a homogeneous flow with almost negligible wall slip. The characteristic time scale for erosion is shown to diverge below some critical shear rateγ ⋆ and to scale as (γ −γ ⋆ ) −n with n ≃ 2 aboveγ ⋆ . A tentative model for erosion is discussed together with open questions raised by the present results.

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Section: Structure and Rheology Of Laponite Suspensionsmentioning

confidence: 99%

Shear-induced fragmentation of laponite suspensions

et al. 2009

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“…We measure the equal-time fluctuations of this local oscillator and show that, in an ergodic phase, the temperature of the oscillator T o equals the environment temperature T bath of the system, as required by equilibrium statistical mechanics. Significantly, when we repeat the measurements in an aging glass we find a higher temperature and T o > T bath .All experiments to date on colloidal glasses [3,4,5] have relied on active, driven measurements. We conduct our experiments instead in a quasi-static limit which has several advantages.…”

mentioning

confidence: 99%

“…All experiments to date on colloidal glasses [3,4,5] have relied on active, driven measurements. We conduct our experiments instead in a quasi-static limit which has several advantages.…”

mentioning

confidence: 99%

Measurement of Effective Temperatures in an Aging Colloidal Glass

2006

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We study the thermal fluctuations of an optically confined probe particle, suspended in an aging colloidal suspension, as the suspension transforms from a viscous liquid into an elastic glass. The micron-sized bead forms a harmonic oscillator. By monitoring the equal-time fluctuations of the tracer, at two different laser powers, we determine the temperature of the oscillator, To. In the ergodic liquid the temperatures of the oscillator and its environment are equal while, in contrast, in a nonequilibrium glassy phase we find that To substantially exceeds the bath temperature.Understanding the slow dynamics of glasses is one of the most fascinating yet difficult challenges in statistical physics. One question which has attracted considerable interest is whether the dynamical fluctuations of a glass can be characterized by a non-equilibrium temperature. A rigorous thermodynamic temperature is strictly impossible to define for an aging glass, which remains far from thermal equilibrium even on long-time scales. Nevertheless various groups [1,2] have proposed "effective" temperatures with many of the properties expected for an equilibrium temperature. These ideas lead to the surprising prediction of two distinct temperatures in an aging glass [1]. The fast rattling modes of particles inside the cage constituted by neighbors thermalize rapidly to the temperature of the environment, T bath , while the much slower structural rearrangement of these cages are supposed to be characterized by a second temperature, T eff , which mean-field models predict should exceed T bath . To date most of the support for this striking two-temperature picture has emerged from simulation results [2] on idealized glasses. Experiments have so far produced conflicting results. Studies of colloidal glasses have reported that T eff increases [3], remains unchanged [4], or even decreases [5] with age in contrast to measurements on structural [6] and spin glasses [7] which have revealed effective temperature warmer than the bath temperature.In this Letter, we report the temperature of a micrometer-sized sphere immersed in an aging colloidal suspension, as the suspension transforms from a fluid to a glass. The particle, captured in an optical trap, constitutes a microscopic harmonic oscillator whose fluctuations probe the nonequilibrium dynamics of the aging glass. We measure the equal-time fluctuations of this local oscillator and show that, in an ergodic phase, the temperature of the oscillator T o equals the environment temperature T bath of the system, as required by equilibrium statistical mechanics. Significantly, when we repeat the measurements in an aging glass we find a higher temperature and T o > T bath .All experiments to date on colloidal glasses [3,4,5] have relied on active, driven measurements. We conduct our experiments instead in a quasi-static limit which has several advantages. First, the experiments are simpler because there is no need to characterize the complete time-dependent response of the system. Second, the lack of an ...

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“…This second linear regime has a slope reduced by a violation factor, X , relative to equilibrium, and is described as having an effective temperature, T eff = T /X . Thus far, experiments studying the breakdown of the FDR in structural and soft colloidal glasses have focused on the quasi-equilibrium regime with t w > t − t w , and have given a range of results that have found strong [18][19][20] , weak 21 or nonexistent 22 FDR violations. The strong-ageing regime has been difficult to access in these systems, owing largely to instrumental and statistical challenges of measuring thermal noise at the very low frequencies required.…”

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Nanoscale non-equilibrium dynamics and the fluctuation–dissipation relation in an ageing polymer glass

Oukris

Israeloff

2009

Nature Phys

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Response functions 1 and fluctuations 2 measured locally in complex materials should equally well characterize mesoscopic-scale dynamics. The fluctuation-dissipation relation (FDR) relates the two in equilibrium, a fact used regularly, for example, to infer mechanical properties of soft matter from the fluctuations in light scattering 3 . In slowly evolving non-equilibrium systems, such as ageing spin 4,5 and structural glasses 6,7 , sheared soft matter 8 and active matter 9 , a form of FDR has been proposed in which an effective temperature 10 , T eff , replaces the usual temperature, and universal behaviour is found in mean-field models 10,11 and simulations 6-8,12 . Thus far, only experiments on spin-glasses 13 and liquid crystals 14 have succeeded in accessing the strong-ageing regime, where T eff > T and possible scaling behaviour are expected. Here we test these ideas through measurements of local dielectric response and polarization noise in an ageing structural glass, polyvinyl acetate. The relaxation-time spectrum, as measured by noise, is compressed, and by response, is stretched, relative to equilibrium, requiring an effective temperature with a scaling behaviour similar to that of certain mean-field spin-glass models.The FDR expresses the equilibrium thermal fluctuations of an observable, O, in terms of available thermal energy, k B T (where k B is the Boltzmann constant), and the linear response of that observable to an applied field, F (ref. 10). It also relates the time (t ) dependence of the fluctuations, found in the autocorrelation function, C(t ) = δO(t + t )δO(t ) t , and the time-dependent susceptibility, χ (t ) = O(t )/F , where F is applied at t = 0. In equilibrium, C(t ) should contain the same information about the dynamics that is found in χ (t ), such as the spectrum of relaxation times. This is seen clearly in plotting χ (t ) versus C(t ) and obtaining a straight line, with a negative slope inversely proportional to temperature 10 . Deviations from the FDR have been intensively studied theoretically in ageing or driven glassy systems, both on the macroscale 8,10 and nanoscale 12 . Ageing occurs in glassy materials that have been quenched from high to low temperature. During ageing, the response functions depend both on time, t , and on the age of the system since the quench, t w . However, χ (t , t w ) and C(t , t w ) need not have the same dependence. This can be understood conceptually by viewing ageing dynamics as hopping on a tilted energy landscape 11 : energy-lowering transitions cause more rapid decorrelation than is possible by thermal energy alone. Prominent glass-transition models 15 place fragile structural glasses 6,16 in the same universality class as mean-field p-spin models with single-step replica symmetry breaking 17 . In such models 10 and simulations of structural glasses 7 , the χ (t ,t w ) versus C(t ,t w ) asymptotically collapse (with increasing t w ) to a single scaling Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA. *e-mail: n...

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Probing a Nonequilibrium Einstein Relation in an Aging Colloidal Glass

Cited by 122 publications

References 25 publications

Shear-induced fragmentation of laponite suspensions

Shear-induced fragmentation of laponite suspensions

Measurement of Effective Temperatures in an Aging Colloidal Glass

Nanoscale non-equilibrium dynamics and the fluctuation–dissipation relation in an ageing polymer glass

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