Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Non Equilibrium Dynamics and ComplexityNon-Ergodicity in Locally Ordered SystemsThe current interest in studying the structurallyarrested states of matter is based on searching for abasic mechanism underlying the onset of theparticle-blocking of motion, common to differentclasses of systems.Suppose a tagged particle is trapped in a transientcage made by its nearest neighbours, which arecaged themselves. With decreasing temperature, theparticle becomes progressively more confined in itscage and partakes correlated collisions.Subsequent diffusion out of the cage needs acooperative rearrangement of many particles andprovides long-range transport motion, which slowsdown drastically as the temperature is lowered. Thiscage effect mechanism can be regarded as themicroscopic origin of the eventual structural arrest ofa simple liquid that occurs at the glass-transition. Inmore complex systems like associated and covalentliquids, the ubiquitous class of liquids including waterand silica, the cage effect manifests a differentnature since molecules are blocked in energeticcages of hydrogen or covalent bonds, and bondbreaking and formation is needed for diffusion tooccur. This is why finding a unique paradigm toexplain the particle dynamics and the particle cagingof different classes of systems actually constitutes abig challenge for condensed matter physics.f Qf Q0.90.80.70.6Q=2 nm -10.50.951.00.90.80.70.95Q=4 nm -10.900.900.850.850.80Q=7 nm -1Q=10 nm -10.750.8050 100 150 200 250 300 50 100 150 200 250 300T(K)T(K)Fig. 1: Temperature dependence of the nonergodicityfactor f Q of m-toluidine for different Q-values. The solid lines are the best fits obtainedusing the square-root function predicted by theMCT.Intensity64200 2 4 6 8 10 12 14 16 18Q (nm -1 )Fig. 2 X-ray diffraction pattern (left axis) of liquidm-toluidine at ambient temperature taken from Ref.[2], compared with the parameter f Q c (right axis)obtained from the fit of the experimental f Q(T) data(open circles); full squares indicate the values of f Qat T=263 K - a temperature in the plateau region off Q(T) - for all the available Qs.1.00.80.6f QcOriginally, the mode coupling theory (MCT) wasproposed as an approximation approach for the cageeffect in liquids [1]. In its simplest version, thederived equations of motion for the densityfluctuationslead to a bifurcation of the long-timelimit of the density correlators, the so-called nonergodicity factor f Q, if a control parameter liketemperature crosses a critical value, T c. Within MCT,specific predictions are postulated for thetemperature and wave-vector dependence of f(Q,T):i) A square-root temperature behaviour below T c,i.e., f Q(T)=f c Q +h Q(1-T/T c) 1/2 , where f cQ is the criticalnon-ergodicity parameter and h Q the criticalamplitude at a fixed wavevector Q; ii) A Q-cdependence of f Q and of h Q that follows theoscillations of the static structure factor S(Q).While a large number of experimental and theoreticalworks have verified the MCT predictions in Van-der-Waals molecular liquids, few investigations havebeen devoted to associated and covalent liquids, andthe results are often not exhaustive. In these liquidsthe local order extends over several neighboringmolecules and reflects on a nontrivial Q behavior inthe low-Q region of the static structure factor, S(Q).We investigated a molecular system, m-toluidine,which is characterized by a spatial organization ofthe molecules induced by hydrogen bonds extendingover several molecular diameters and giving rise tonanometer size clusters [2]. The non-ergodicityfactor of supercooled and glassy m-toluidine hasbeen measured, through IXS experiments (beam lineID16-ESRF), in the mesoscopic Q range between 1and 10 nm -1 , around the prepeak in the staticstructure factor related to the local order (Q pp=5nm -1 ). We proved that the basic predictions of MCTabout the non-ergodicity factor hold in m-toluidine(see Figure 1 and Figure 2), providing experimentalevidence that the signature of the ergodic to nonergodictransition, valid for simple liquids, lives on inclustering systems [3]. Our findings suggest that theinitial stage of the cooperative rearrangements,where the cage effect dominates the moleculardynamics, exhibits a universal character, common tosimple liquids and liquids with a local order. Thisconcept is not so obvious, because it places on thesame level the structural arrest in simple and inlocally ordered liquids, though the cage formation iscontrolled by different mechanisms.References[1] W. Götze and L. Sjögren, Rep. Prog. Phys. 55,241 (1992).[2] D. Morineau et al., Europhys. Lett. 43, 195(1998); M. Descamps et al., Prog. Theor. Phys.Suppl. 126, 207 (1997).[3] L. Comez et al., Phys. Rev. Lett. 94, 155702(2005).Authors:L. Comez (a), S. Corezzi (b), G. Monaco (c), R.Verbeni (c), and D. Fioretto (a).(a) CRS-SOFT and Dipartimento di Fisica, Universitàdi Perugia, Perugia (Italy), (b) CRS-SOFT andDipartimento di Fisica, Università di Roma LaSapienza, Roma (Italy), (c) ESRF, Grenoble (France).SOFT Scientific Report 2004-0666