Relaxation dynamics and aging in structural glasses

Relaxation dynamics and aging in structural glassesB. Ruta, Y. Chushkin, G. Monaco, L. Cipelletti, V. M. Giordano et al. Citation: AIP Conf. Proc. 1518, 181 (2013); doi: 10.1063/1.4794566 View online: http://dx.doi.org/10.1063/1.4794566 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1518&Issue=1 Published by the American Institute of Physics. Additional information on AIP Conf. Proc.Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors

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Relaxation dynamics and aging in structural glassesB. Ruta∗, Y. Chushkin∗, G. Monaco∗, L. Cipelletti†, V. M. Giordano∗∗, E. Pineda‡

and P. Bruna§

∗European Synchrotron Radiation Facility, BP220, F-38043 Grenoble, France†Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France.

CNRS, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France.∗∗LPMCN, Université Claude Bernard Lyon 1 and CNRS, 69622, Villeurbanne, France.

‡Departament de Física i Enginyeria Nuclear, ESAB, Universitat Politècnica de Catalunya, c/ Esteve Terradas8, 08860 Castelldefels, Spain.

§Departament de Física Aplicada, EPSC, Universitat Politècnica de Catalunya, c/ Esteve Terradas 5, 08860Castelldefels, Spain.

Abstract. We present a study of the atomic dynamics in a Mg65Cu25Y10 metallic glass former both in the deep glassystate and in the supercooled liquid phase. Our results show that the glass transition is accompanied by a dynamicalcrossover between a faster than exponential shape of the intermediate scattering function in the glassy state and a slowerthan exponential shape in the supercooled liquid. While the crossover temperature is independent on the previous thermalhistory, both the relaxation rate and the shape of the relaxation process depend on the followed thermal path. Moreover, thetemperature dependence of the the structural relaxation time displays a strong departure from the Arrhenius-like behavior ofthe corresponding supercooled liquid phase, and can be well described in the Narayanaswamy-Moynihan framework with alarge non-linearity parameter.Keywords: glasses, relaxation dynamics, x-ray photon correlation spectroscopyPACS: 64.70.pe,81.40.Cd,64.70.pv

INTRODUCTION

Many disordered materials, like molecular glasses, poly-mers, gels and other soft materials undergo structuralarrest and physical aging. In fact, following differentexperimental routes, like varying the temperature, thepacking fraction, or the polymer concentration, thesematerials can be driven in an out-of-equilibrium con�g-uration, where the dynamics slows down enormously,and strongly depends on the sample age or waiting timetw [1, 2, 3].The physical quantity that captures this slowing downof the particle motion is the structural relaxation time,τ , which is proportional to the shear viscosity andrepresents the time necessary for shear relaxation. Thetemporal and temperature dependence of the structuralrelaxation time can be experimentally investigated bymeasuring, for instance, the evolution of the intermediatescattering function f (q, t) which describes the decay ofthe density �uctuations on a length scale ∼ 2π/q, with qbeing the scattering vector. The investigation of f (q, t)at the atomic scale allows therefore getting informationon the evolution of the relaxation dynamics at the in-terparticle distance and to shed light on the mechanismunderlying the dynamics in out-of-equilibrium systems.While many works have been devoted to the compre-hension of the single particle behavior in different soft

materials [3, 4], only very recent studies on metallicglasses report on the direct evolution of the intermedi-ate scattering function in the glassy state [5, 6, 7, 8].These works suggest that the dynamics is not frozenin the glassy state and that structural relaxation oc-curs on atomic scale even if the system has not fullyequilibrated. These results are in agreement also withpreviously reported studies of dielectric relaxations[9, 10, 11, 12, 13, 14, 15]. In some cases, the temporalevolution of the dynamics can be furthermore rescaledinto a single master curve, leading to the validity of thetime-waiting time superposition principle in the arrestedstate [5, 6, 8, 11, 12, 15].The experiments on metallic glasses have suggesteda non diffusive nature for the atomic dynamics in thearrested state, whose origin is however debated [6, 7, 8].While in one case the observed atomic dynamics hasbeen associated to the onset of a crystallization process[7], in other works, it has been interpreted in termsof relaxations of internal stresses stored in the systemduring the quenching [6, 8], as in the case of manyout-of-equilibrium soft materials [3, 4].All the above mentioned works on metallic glassesrepresent the �rst experimental studies on the atomicrelaxation dynamics in structural glasses, which willobviously require many additional investigations.In the present work, we focus on both the temporal

4th International Symposium on Slow Dynamics in Complex SystemsAIP Conf. Proc. 1518, 181-188 (2013); doi: 10.1063/1.4794566

© 2013 American Institute of Physics 978-0-7354-1141-8/$30.00

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and temperature dependence of the relaxation dynamicsin a Mg65Cu25Y10 metallic glass former at the atomiclength scale. From a previous study we have obtained aclear evidence of a dynamical crossover on cooling thesystem across the glass transition temperature from thesupercooled liquid phase and of a complex hierarchy ofaging regimes in the glassy state [6]. Here we furtherdiscuss those results, focusing on the dynamics of a glassobtained with an extremely fast quenching from the hightemperature melt and subsequently slowly heated up tothe liquid phase. Our results show that the dynamicalcrossover is independent of the followed thermal path,which instead affects both the relaxation time and theshape of the intermediate scattering function. We further-more observe a strong departure from the Arrhenius-liketemperature dependence of the structural relaxation timein the liquid phase, which can be well described in termsof the well known Narayanaswamy-Moynihan theoryfor the structural relaxation in glasses [16, 17].

EXPERIMENTAL DETAILS

Metallic glasses of Mg65Cu25Y10 were obtained byprealloying Cu-Y ingots with the adequate ratio in anarc-melter furnace under a Ti-gettered argon atmosphereand then alloying with magnesium in an induction fur-nace. The high temperature melt (T ∼ 1250 K) was thenfast-quenched with a cooling rate of 106 K/s by injectingit on a copper spinning wheel in a melt spinner device.The resulting ribbons had a thickness of ∼33 μm and awidth of ∼2 mm. The amorphous structure of the sam-ples was checked by high resolution X-ray diffractionon the as-quenched samples and by measuring the staticstructure factor during the experiments.X-ray photon correlation spectroscopy (XPCS) exper-iments have been performed at the beamline ID10 atthe European Synchrotron Radiation Facility (ESRF)in Grenoble, France. An X-ray beam, produced byan undulator source, was focused by a Be compoundrefractive lens and 8 keV radiation was selected by asingle bounce crystal Si(111) monochromator operatingin a horizontal scattering geometry (energy bandwidthΔE/E ∼ 10−4). The beam was then re�ected by a Simirror working at a grazing incident angle of 0.2◦, inorder to suppress higher order harmonics. To select thespatially coherent part of the beam we used rollerbladeslits opened to 10× 10 μm, placed ∼ 0.18 m upstreamof the sample. The corresponding incident �ux was1.1×1010 photons/s/100 mA.Ribbons of Mg65Cu25Y10 were placed in a resistivelyheated furnace, providing a temperature stability of 0.1K. During all the experiments, the temperature of thesamples was changed by keeping a �xed heating or

cooling rate of 1 K/min.The scattered intensity was measured by an IkonMcharge-coupled device (CCD) from Andor Technologywhich consists of 1024 × 1024 pixels, with 13 × 13μm2 pixel size. The transmitted scattered intensity wascollected at a distance 0.68 m from the sample and ina wide angle con�guration, speci�cally at a scatteringangle 2θ = 36.5◦ with respect to the incident beam.In this way all pixels of the CCD were considered tobelong to the same wave vector q0 = 2.56± 0.04 Å−1,corresponding to the maximum of the static structurefactor of the system, allowing us to investigate thedynamics at the inter particle distance of 2π/q0 ∼ 2Å.Focusing on the slow dynamics, we collected time seriesof up to about 3000 images with 5 s or 7 s exposuretime per frame. The only limitation for very long timemeasurements was given by the overall instrumentalstability and by the re�lling mode of the storage ring,yielding an upper limit of several hours. The data weretreated and analyzed following the procedure describedin Ref. [18].Several XPCS experiments on different ribbons ofMg65Cu25Y10 were performed in order to check thereproducibility and consistency of the data.

THEORETICAL BACKGROUND

The quantity measured in a multispeckle XPCS experi-ment is the autocorrelation function of the intensity �uc-tuations

g2(q, t) =

⟨⟨Ip(q, t1)Ip(q, t1+ t)

⟩p

⟩t1⟨

〈I(q, t1)〉p⟩t1

⟨〈I(q, t1)〉p

⟩t1

, (1)

where Ip(q, t1) and Ip(q, t1 + t) correspond to the inten-sity measured on the pixel p at the time t1 and t1+t, 〈...〉pis the ensemble average over all the pixels of the detectorwhich correspond to the same wave vector q, and 〈...〉t1is the temporal average over all times t1.At small and large delay times equation (1) becomes

limt→0g2(q, t) =

⟨⟨Ip(q, t1)2

⟩p

⟩t1⟨

〈I(q, t1)〉p⟩2

t1

= 1+ γ(q) (2)

andlimt→∞

g2(q, t) = 1, (3)

respectively. Here γ is the normalized variance of theintensity �uctuations and is related to the ratio betweenthe coherent and the scattering volume [4].Information on the dynamics can be obtained from the

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FIGURE 1. a) Normalized intensity auto-correlation func-tions measured on heating the sample from the glassy state upto the supercooled liquid phase (Tg= 405 K). The black arrowindicates the direction of temperature changes, from low tohigh T . From right to left, T= 318, 348, 383, 413, 415 and 417K. b, Same data reported as a function of t/τ .

intermediate scattering function f (q, t), which is relatedto g2(q, t) by means of the Siegert relation [19, 20]

g2(q, t) = 1+ γ(q) | f (q, t)|2 , (4)

being f (q, t) = S(q, t)/S(q), where

S(q, t)=1

N [b2(q)]

N

∑n=1

N

∑m=1

⟨bn(q)bm(q) · eiq[rn(0)−rm(t)]

⟩

(5)and S(q) =

∫S(q, t)dt are the dynamic and static

structure factor, respectively. Here N is the numberof scatterers, b2(q) the scattering amplitude averagedover the size distribution of the scatterers, and rn(t) theposition of the scatterer n at the time t [4].

RESULTS AND DISCUSSIONS

The intermediate scattering function of glass-formers canbe well described by using the empirical KohlrauschWilliams Watt (KWW) model function [21]

f (q, t) = fq(T ) · e−(t/τ)β(6)

In this expression, τ is the structural relaxation time, βdescribes the shape of the relaxation, and fq(T ) is thenonergodicity factor.Following equation (4) the intensity correlation functionsmeasured with XPCS can then be described by

g2(q, t) = 1+A(q,T ) · e−2(t/τ)β(7)

where A = γ(q) fq, γ(q) being the parameter in theSiegert relation.Figure 1 a) shows a selection of normalized intensityautocorrelation functions for q0 = 2.56 ± 0.04 Å−1.The data were taken by performing several isothermalruns, for increasing values of the temperature, and arehere reported together with the best-�t lines obtained byusing relation (7).Contrary to the common opinion of a frozen dynamicsin the glassy state, the normalized correlation functionsdisplay a full decay to zero even at the lowest investigatetemperature which is ∼ 100 K below the calorimetricglass transition temperature Tg = 405 K. It is importantto stress here that the observed decorrelation does notimply that the system is ergodic at all lenght scale, butsimply that structural rearrangements can occur at theatomic length scale [6, 22]. Indeed, Mg65Cu25Y10 isknown to show structural changes implying aging ofsome physical properties at room temperature (0.7Tg)[23, 24].On increasing the temperature, the dynamics gets fasterdue to thermal motions and the decay shifts towardshorter time scales. Similarly to previous results onmetallic glasses [6, 7, 8], the shape of the correlationcurves in the glassy state displays a faster than expo-nential decay and can be well described by relation (7)with an exponent β ∼ 1.5, independent on the temper-ature. This anomalous compressed behavior cannot beexplained with a distribution of single exponential relax-ation times, as it would be within the current theoriesfor glasses [16, 17, 22], and persists up to Tg. At tem-peratures above Tg the shape of g2(t) drastically changesand can be described by a stretched exponent β ∼ 0.88,also independent of the temperature. This latter behavioris typical of supercooled liquids and can be explainedwithin both the spatially dynamical homogeneous sce-nario and the heterogeneous one [25]. However severalsimulations and experiments have directly establishedthat the dynamical slowing down encountered in glass

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formers is accompanied by the existence of a growingcorrelation length scale over which local dynamics isspatially correlated, thus supporting the heterogeneousscenario [26, 27, 28].As discussed in Ref. [6] the observed change at Tg corre-sponds to a dynamical equilibrium to out-of-equilibriumcrossover. In fact as it will be shown later, the curvesabove Tg correspond to stationary dynamics and thus tothe equilibrium supercooled liquid phase, while at lowertemperatures the system is in a metastable state and thedynamics depends both on the age of the sample, orwaiting time tw, and on the followed thermal path. Inorder to properly compare the different curves, the datain the glassy state are taken by subsequently heating thesystem and are here reported for the same waiting timefrom temperature equilibration.Differently from the data reported in Ref. [6], the liquidphase is here approached from the low temperatureglass. The data in Figure 1 a) show that the crossover isindependent of the thermal path and is a clear signatureof the dynamic glass transition. The in�uence of the pre-vious thermal treatment is instead fully contained in theshape parameter and in the structural relaxation time. Inparticular the faster the cooling rate, the larger is β andthe faster is τ [6]. The fact that the correlation functionsdecay more rapidly in a glass obtained with a fast cool-ing rate is a simple consequence of the earlier departurefrom the equilibrium liquid upon cooling, and thus ofthe kinetic nature of the glass transition [1]. The increasein the shape exponent is instead in agreement with thepreviously proposed stress relaxation driven dynamics[6]. The main idea is that the compressed behaviorarises from the presence of an heterogeneous stress�eld introduced in the system during the quench to anout-of-equilibrium con�guration, as observed also in alarge variety of soft materials, like gels and concentratedcolloidal suspensions [3, 29, 30, 31, 32, 33, 34, 35]. Inthis picture, a faster cooling rate would lead to a largeramount of internal stresses and consequently to a largervalue of the shape parameter.In the case of soft materials, the compressed behavior ofthe correlation functions is usually associated to ballisticrather than diffusive atomic motion and thus to a τ ∼ 1/qdependence of the structural relaxation time on the wavevector. Due to the weak scattered signal of our metallicglass, it was not experimentally possible to investigatedthe dynamics for wave vectors far from the �rst sharpdiffraction peak and to check therefore its q dependence.However, the presence of internal stresses, or excess freevolume in metallic glasses has been largely documentedin the literature [36, 37, 38, 39, 40], and is con�rmed inour glass by mechanical, rheological and calorimetricmeasurements [6, 41, 42].The independence of the shape parameter on temper-ature changes suggests the possibility to rescale the

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FIGURE 2. a, g2(t)measured at T=403 K by averaging overdifferent interval of times, while keeping �xed the age of thesample at tw=4400 s. The dashed and the dashed-dotted linescorrespond to the �t fo the data taken with ΔI = 3000 and6000 s, respectively b, Corresponding shape parameter β asa function of the integration time. The black line indicates thevalue of the shape parameter in the corresponding supercooledliquid phase.

observed dynamics in two families of master curves, oneassociated to the liquid phase and one to the glassy state.This scaling is shown in Figure 1 b) where the samecurves of Figure 1 a) are reported as a function of t/τ ,where τ is the structural relaxation time obtained fromthe analysis of the curves with a KWW model function(7). The marked evolution from stretched to compressedexponentials is con�rmed by the very different shape ofthe curves corresponding to the two different states. Thescaling of all the curves in both the liquid and the glassleads to the validity of a time-temperature superpositionprinciple in both the liquid and the glassy state [5, 15],and is in disagreement with a recent prediction of atemperature dependent β parameter in the glassy state[43].

As above mentioned, below Tg the dynamics is not sta-tionary and the correlation functions depend also on thesample age. In order to check the absence of any pos-sible artifact in the calculation of the g2(t) due to theevolution of the dynamics during the measurements, wecompared correlation functions obtained using differentsets of images, and thus intervals of time, while keep-ing �xed the age of the system. This is shown in Fig-ure 2 for data measured at T = 403 K and tw = 4400 s.The inset reports the corresponding shape parameter ob-tained from the analysis of the data with equation (7). Itis evident that the result of the �t is not affected by thechoice of the time interval over which the data are aver-

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FIGURE 3. Temperature dependence of the structural relax-ation time obtained from the analysis of the XPCS data follow-ing two different thermal paths (circles and stars). The arrowsindicate the followed thermal paths, while the dotted-dashedline is just a guide for the eye indicating the macroscopic equi-librium liquid data (empty triangles) taken from Ref. [41] andrescaled here in structural relaxation time units [6].

aged and that the obtained curves are clearly compressedwith a shape parameter β much larger than that of thecorresponding supercooled liquid (full line in the inset).Beyond this, one should also consider that aging wouldlead to a lower, more stretched, value of β , and not to theobserved compressed decay [12].The temperature dependence of the structural relaxationtimes is reported in Figure 3. Some of the data are alsoreported in Ref. [6]. Macroscopic values obtained fromliterature viscosity data [41] rescaled in times units arereported as well [6]. Full circles correspond to XPCSdata taken in the glassy state by slowly heating the as-quenched glass. The corresponding correlation curvesdisplay indeed a faster than exponential decay whichevolves with the sample age (see Figure 1). The two starsymbols are also taken in the glassy state, but on a dif-ferent, " fresh" as-quenched sample and following a dif-ferent thermal path (by heating and cosequently coolingthe glass, see arrows). Differently, full diamonds corre-spond to XPCS data measured in the supercooled liquidphase. They are in agreement with equilibrium macro-scopic data [41] and correspond to the stretched expo-nential decays shown in Figure 1.In the glassy state the structural relaxation time weaklydecreases with temperature and displays a strong depar-ture from the Arrhenius-like behavior observed in the su-percooled liquid phase. At about T ∼ 400 K, τ abruptlyincreases on increasing the temperature and then de-creases again, once the equilibrium liquid line is reached.This step-like behavior is likely to be just a consequence

of an annealing of the glass due to the slow heating as-sociated to density changes in the material close to Tg[40]. This behavior can in fact be viewed as a shift ofthe glass transition temperature, or �ctive temperature,of the fast-quenched glass to lower value (dashed-dottedline), associated with the slow temperature rate used dur-ing the experiment. If instead the system is continuouslyheated up to higher temperatures without having the timeto rearrange, no signature of the step is observed, and thesystem meets the equilibrium liquid line at higher tem-perature (star symbols in Figure 3).The observed non linearity of the structural relaxationtime can be well described in the Narayanaswamy-Moynihan framework by the relation

τ = τ0eq exp[x(Eeq/kBT )+(1− x)(Eeq/kBTf )], (8)

where x is the non-linearity parameter, with 0 < x < 1,Tf the �ctive temperature, and τ0eq and Eeq the pre-factorand activation energy describing the Arrhenius behaviorin the liquid phase [16, 17]. Considering only the data upto the step-like feature, we �nd x = 0.087 and Tf = 414K. The non-linearity parameter x simply correspondsto the ratio Eglass/Eeq between the activation ener-gies obtained from an Arrhenius �t to both the glassystate and the supercooled liquid, for which we �ndEglass = (29± 4) kJ/mol and Eeq = (330± 10) kJ/mol,in agreement with mechanical measurements [42].As previously discussed, the dynamics in the

glassy state strongly resembles that of out-of-equilibrium jammed soft materials, where the corre-lation functions decay faster than a single exponential[3, 29, 30, 31, 32, 33, 34, 35]. This similarity can befurther strengthened by looking at the evolution withaging in the glassy state. As discussed in Ref. [6], thecorrelation functions change with waiting time in acomplex way, which strongly resembles that followedby some soft materials, such as polymeric or colloidalgels and clays [30, 44, 45, 46]. In particular two differentaging regimes can be found: a fast, exponential growthof the structural relaxation time with waiting time forshort tw and high cooling rate, followed by an almostfrozen regime, where the evolution of the dynamics dueto aging takes too long with respect to our experimentaltime window. These different regimes are shown in Fig-ure 4 and compared to the dynamics in the supercooledliquid phase.The �rst fast regime is shown in Figure 4 a) whichreports the evolution with tw of the g2(t)− 1 measuredin the the deep glassy state, at T = 358 K. On increasingthe sample age, the decay of the curves clearly shiftstoward a longer time. This slowing down of the dy-namics can be well described by a unique empiricalexponential growth for all the investigated temperatures,being τ(T, tw) ∼ exp(tw/τ�) with τ� ∼ 7900 s being a

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FIGURE 4. Evolution of the dynamics in the glassy and su-percooled state. a Fast aging dynamics at T=358 K. bCrossoverfrom fast to slow aging dynamics at T=403 K. c Equilibriumdynamics in the supercooled liquid at T=408 K. In all panels,lines are the best �ts using the KWW model function (7).

temperature independent parameter [6]. This regime hasbeen observed for all the data taken by subsequentlyheating the system, starting from room temperature(full circles in Figure 3). Here the system is far fromthe equilibrium liquid phase and still contains a largeamount of internal stresses, as con�rmed also by thelarge and temperature independent compressed value ofthe shape parameter. It is expected that the dynamics willchange when the system will start to release its stresses.This is in fact the case for very large waiting times orpartially annealed samples [6]. This situation is shown inFigure 4 b) for a sample which was partially annealed athigh temperature in the glassy state and then cooled backto a lower temperature (star symbols in Figure 3). Thedifferent thermal treatment is in fact just an alternativeway to produce a faster annealing and investigate thedynamics close to the equilibrium line. For short twthe correlation functions are similar to those reportedin panel a) and the aging is still fast. By contrast, on

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FIGURE 5. Comparison between the correlation functionmeasured at T=403 K in the glassy state in the slow agingregime (down triangles) and the one measured in the equilib-rium supercooled liquid phase at T=408 K (circles). The dataare reported as a function of the delay time rescaled by thestructural relaxation time.

increasing tw the shape of g2(t) clearly becomes lesscompressed leading to a tw-independent dynamics fortw ≥ 7000 s. The fact that the correlation functions do notdepend anymore on tw for several hours, could suggestthat the system has reached the equilibrium liquid line.However this is not the case. As shown in Figure 4 c)for data taken at 408 K, the supercooled liquid phase ischaracterized by stretched exponential functions (β < 1)which do not depend neither on tw nor on the previousthermal history. The data taken in the second slow agingregime of Figure 4 b) are instead still compressed butwith a value β ∼ 1.15 much lower than that measured atlower temperatures. Here the system is likely reachingthe liquid phase in a very slow way, as observed alsoin polymeric glasses and soft materials [2, 30]. Thedifference between the equilibrium liquid phase and thismetastable frozen glassy state is highlighted in Figure 5where a g2(t)− 1 measured in the second aging regime(Figure 4 b)) is compared with a curve correspondingto the supercooled liquid. For a better comparison, thedata are reported as a function of the time rescaled bythe structural relaxation time. Even if now the value of βin the glass is just ∼ 30% larger than in the supercooledliquid, the equilibrium/out-of-equilibrium dynamicalcrossover is still well marked.

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CONCLUSIONS

In conclusion we have investigated the atomic dynamicsin a metallic glass ofMg65Cu25Y10 by slowly heating thesystem from the deep glassy state up to the supercooledliquid phase. We �nd that the structural relaxation per-sist in the glassy state, and that the normalized intensitycorrelation functions display a full decay to zero, evenfor temperatures much lower than Tg. The measuredstructural relaxation times display a strong departurefrom the Arrhenius-like behavior observed in the su-percooled liquid phase and can be well described in theNarayanaswamy-Moynihan framework. The dynamicsin the glassy state is furthermore characterized by fasterthan exponential correlation functions and very differentaging regimes. These behaviors seems to be universal inmetallic glasses [8] and strongly resemble those reportedfor jammed soft materials, such as gels and concentratedcolloidal suspensions, suggesting a common origin[3, 29, 30, 31, 32, 33, 34, 35]. Indeed in all these materi-als, the observed dynamics seems to be associated to thepresence of internal stresses stored in the system whenit is quenched in an out-of-equilibrium con�guration.In the case of our metallic glass, these stresses can bethen released upon annealing the system, leading toa decrease in the shape parameter of the correlationfunctions and to a second, extremely slow, dynamicalregime. Further investigations are anyway required tofully characterized this regime. In particular, it wouldbe interesting to follow the complete equilibration fromthe glassy state and the corresponding changes in theshape of the correlation functions, a task which cannotbe obviously achieved in many soft materials.

ACKNOWLEDGMENTS

We gratefully thank M. Gonzalez-Silveira for the calori-metric measurements of the sample, and S. Capaccioliand W. Kob for stimulating discussions. We acknowl-edge H. Vitoux, K. L’Hoste, L. Claustre for technicalsupport during the XPCS experiments. EP and PB ac-knowledge �nancial support from CICYT Grant No.MAT2010-14907 and Generalitat de Catalunya GrantsNo. 2009SGR1225 and No. 2009SGR1251.

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