Tackling the λ-transition in liquid Sulphur by InfraRed PhotonCorrelation SpectroscopyDeveloping a novel experimental technique, we appliedInfrared Ra<strong>di</strong>ation Photon Correlation Spectroscopy(IRPCS) to liquid sulphur in the λ transition region, i.e.where an abrupt increase in viscosity by four orders ofmagnitude has been observed upon heating within fewdegrees [1]. Accor<strong>di</strong>ng to basic para<strong>di</strong>gms, thisincrease in viscosity around T λ=159 °C should inprinciple trigger an equivalent increase of thestructural relaxation time τ α from the ps to the nsrange, accor<strong>di</strong>ng to the Maxwell equation η=G ∞·τ α, G ∞being the limiting short wavelength shear modulus.This should imply, in turn, the detection of a relaxationeffect crossing the GHz frequency domain by means oftechniques, like Brillouin light scattering (BLS), thatmeasure the longitu<strong>di</strong>nal elastic modulus, and a largeincrease in attenuation at ultrasonic frequencies. BLShas shown [2], on the contrary, a continuous smoothdecrease in the real and imaginary part of themodulus, testifying a decrease of τ α. Ultrasonicexperiments performed in the 1-10 MHz frequencywindow [3] <strong>di</strong>d non evidence, as well, any criticalvariation of the acoustic attenuation around T λ;sulphur thus escaped the established viscoelasticframework for over a century, warranting the title of “viscous but not viscoelastic liquid” [3]. IRPCS wasperformed using a <strong>di</strong>ode pumped solid state lasersource operating at λ = 1064 nm. The detector was aPerkin Elmer avalanche photo<strong>di</strong>ode retaining a 2%quantum efficiency at the probe wavelength, with a 50counts/s dark count and an after pulse probabilitylower than 3%. The 90° scattered ra<strong>di</strong>ation wascollected by a lens and collimated by means of an IRoptimized collimator from OZ-optics. The sample waskept in a home-made furnace whose temperature wasmeasured by a RTD and stabilized by a software PIDfeedback. The <strong>di</strong>gital signal coming out from the• Fig. 1: Reduced homodyne IR correlationfunctions at selected temperatures. Opensymbols are for TT λ. The temperature behaviour of thedetector was acquired by a PC and used to performreal time autocorrelation. Correlation functions werecollected at constant temperatures during an upscan inthe range 145
Scientific <strong>Report</strong> – Non Equilibrium Dynamics and ComplexityVibrational Dynamics and Viscous Flowin Glass Forming LiquidsThe connection between slow and fast degrees offreedom in glass forming materials has been in focusof several investigations for long times. On thetheoretical side, landscape based approachessuggest a correlation between the curvature of thepotential energy minima and the barrier heights. Onthe experimental side, a number of correlationsbetween the temperature dependence of theviscosity (fragility) and other quantities related tofast degrees of freedom gradually emerged. A newimpulse in this context has been stimulated by arecently reported result connecting fragility with thelow temperature behaviour of the non ergo<strong>di</strong>cityfactor.When reported on an Arrhenius plot, i.e. logarithm ofviscosity versus inverse temperature, practically allglass forming liquids stand in such a way that theycan be ordered accor<strong>di</strong>ng to their steepness at theglass transition temperature, T g. On a morequantitative groung, one defines the kinetic fragilitym as:m =limT →Tgd logηd(T T )Recent extensive inelastic x-ray scattering (IXS)measurements of the dynamic structure factor haveallowed to constitute a sizeable library of highfrequency (THz) dynamical properties of glasses. Inparticular, the IXS measurements allow for thedetermination of the non-ergo<strong>di</strong>city factor, f(Q,T),i.e. the long time limit of the normalized densitydensitycorrelation function. This quantity representsthe amount of decorrelation introduced by thevibrational dynamics, and it depends on both the (Tdependent)amplitude of the vibrations and thedegree of <strong>di</strong>sorder of the glassy structure.We show that the low temperature dependence ofthe non ergo<strong>di</strong>city factor for several glasses stands ina fashion similar to the one exhibited by a T g scaledArrhenius plot (best known as Angell plot). It isindeed possible to define a glass fragility as thederivative of f(Q,T) in the T=0 limit (there is almostno Q dependence in the small Q region of interesthere) .mαdf ( Q,T )= limT → 0 d(T T )This conceptually suprising link between vibrationalmotion in glasses and <strong>di</strong>ffusive processes insupercooled liquids represents a further aspect thatrequires to be clarified and, at the same time,suggests a new <strong>di</strong>rection of investigation for the theultimate understan<strong>di</strong>ng of the glass transitionphenomenology.ggfragility m12010080604020BeF 2silicaglycerolPB 1.4mTCP00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8SeoTPmtolsalolnBBFig. 1. Upper panel: Angell plot for a strong,interme<strong>di</strong>ate and fragile system. Middle panel: Glassfragility for the same three system. Lower panel:Correlation between liquid and glass fragilityReferences[1] C.A. Angell, Science, 267, 1924 (1995)[2] T. Scopigno, G. Ruocco, F. Sette and G. Monaco,Science 302, 850 (2003).[3] V.N. Novikov. A.P. Sokolov, Nature 431, 961 (2004)[4] J. Dyre, Nature Materials 3, 749, (2004)AuthorsG. Monaco (a), G. Ruocco (b,c), T. Scopigno (c), F.Sette (a).(a) ESRF, Grenoble, France.(b) Dip. Di <strong>Fisica</strong>, Univ. Di Roma, Roma, Italy.(c) CRS SOFT-INFM-CNR, Roma, Italy.αSOFT Scientific <strong>Report</strong> 2004-0674
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