Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Non Equilibrium Dynamics and ComplexityRubberlike Dynamics in Sulphur Above the λ-TransitionTemperatureAt 432 K (Tλ) and ambient pressure, liquid sulphurundergoes a rather peculiar reversible transitionbetween a yellow low viscosity fluid to a reddish highviscosity one. This phenomenon, known as λtransition, is marked by anomalous behaviour inmany physical properties. In particular, the shearviscosity increases by at least 4 orders of magnitude[1] and a λ-like singularity is found in thetemperature dependence of the heat capacity [2].The transition is generally attributed to a reversiblepolymerization process: the S8 units of the lowtemperaturemolecular liquid tend to open above Tλand to polymerize, thus giving rise to a solution ofpolymers in monomeric S8 molecules.An inelastic x-ray scattering (IXS) study of the highfrequency acoustic dynamics of sulphur across Tλhas been performed [3], measuring the wavenumber (q) and energy (E) dependence of thedynamic structure factor S(q,E) at five temperaturesacross Tλ. At each temperature, spectra werecollected at values of q between 1 and 15 nm -1 andin the ±20 meV energy range. The resulting spectraare characterized by a quasielastic contribution andan inelastic Brillouin doublet. The data have beenfitted to a DHO model function and thus described interms of three relevant quantities: the energyposition Ω of the Brillouin peak, its FWHM, 2Γ, andthe ratio of the elastic to the total spectral intensityfq.At all the investigated temperatures, a linear qdependence of Ω and a quadratic dependence of 2Γhas been identified up to q ~4 nm -1 . These resultsindicate that liquid sulphur behaves as a viscoelasticliquid, and that, at the high frequencies probed byIXS, its unrelaxed elastic properties are beingmeasured.The sound velocity v∞ has been derived from theslope of Ω(q) and the longitudinal kinematic viscosityν l, as well, from 2Γ(q). The velocity (fig. 1, top) is40% higher than that measured with ultrasonictechniques; the low-q limit of the experimental fqvalues is in agreement with the hydrodynamicprediction, obtained assuming v∞ to be the limitinghigh frequency sound speed.The corresponding viscoelastic transition, whichtakes place between the MHz and the THz frequencyrange probed by IXS, is most likely the structuralrelaxation, that characterizes the dynamics of allliquids. The data show that the structural relaxationexperiences fundamentally no change at Tλ (fig. 1,top): the structural relaxation is thus, surprisingly,not responsible for the increase of the shear viscosityacross the λ transition.By supposing that structural relaxation is the onlyone active in liquid sulphur and using a constantratio between ν l and ν t (the kinematic shearviscosity), a strong increase of the ultrasonicacoustic attenuation should be expected. Theabsence of this feature in the data (fig. 1, bottom)clearly indicates the existence of an additional lowfrequency relaxation.This low frequency relaxation can be attributed toentanglement coupling among polymeric chains,typical of concentrated solutions of linear uncrosslinkedpolymers. Results available in the literaturecan be used to guess a characteristic time in the msrange and a strength in the order of 10 5 Pa for theshear modulus.References[1] R.F. Bacon and R. Fanelli , J. Am. Chem. Soc.65, 639 (1943).[2] F. Feher and E. Hellwig, Z. Anorg. Allg. Chem.294, 63 (1958)[3] G. Monaco, L. Crapanzano, R. Bellissent, W.Crichton, D. Fioretto, M.Mezouar, F. Scarponi And R.Verbeni, Phys. Rev. Lett. 95, 255502 (2005)• Fig. 1: Temperature dependance of a) soundvelocity and b) line-width divided by q 2 . TheIXS results (■) are reported together withultrasound data. In a) the dotted line puts inevidence the change in the temperaturecoefficient of v ∞ at T λ. In (b) the dashed curveis the zero-frequency, symple hdrodynamicsprediction.AuthorsG. Monaco (a), L. Crapanzano (a), R. Bellissent (b),W. Crichton (a), D. Fioretto (c,d), M. Mezouar (a), F.Scarponi (c,d) and R. Verbeni (a)(a) ESRF, Grenoble, (FR) (b) Centre d’EtudiesNucleaires, Grenoble, (FR) (c) Dipartimento di Fisica,Università di Perugia, (IT) (d) INFM CRS-SOFT c/oUniversità di Roma ″La Sapienza″ , Roma, (IT).SOFT Scientific Report 2004-0672