Aging of the Nonlinear Optical SusceptibilityNonlinear optics susceptibility of liquids e. g. organicdye solutions have been widely stu<strong>di</strong>ed by examiningnonlinear refraction of thermal origin and nonlinearabsorption of electronic origin. However in ourknowledge optical nonlinear response variations inpresence of structural dynamics slowing down(aging) in soft materials such as colloidalsuspensions have not been considered. With thisaim, we investigated on a system of Laponite claypowder <strong>di</strong>spersed in dye Rhodamine-B aqueoussolution, <strong>di</strong>splaying high thermal nonlinear opticalresponse and the gelation process characteristic ofthe clay suspension [1].We performed Z-scan [2] and dynamic lightscattering (DLS) measurements to show that opticalnonlinearities exhibit the same aging behaviour ofstructural dynamics of a system.We present, as an example, in Fig. 1 Z-scan curves(A) of 0.6mM RhB aqueous solution at 2.2 wt % clay<strong>di</strong>spersion at increasing waiting time t wcorrespon<strong>di</strong>ngly to the correlation functions (B),from which is evident the dynamics slowing down ofthe system for increasing aging time. In Fig. 1A isalso reported the 0.6 mM RhB solution transmittancecurve (open circles) and it is worth noticing thatoptical nonlinearities are influenced by Laponitepresence and more interestingly dye nonlinearsusceptibility does vary in the clay matrix undergoingaging. The transmittance curves in Fig. 1A are typicalof beam defocusing nonlinear systems in this casewith thermal lens-like behaviour, in fact, as it is wellknown, dye molecules are characterized by stronglight absorption giving rise to refractive indexgra<strong>di</strong>ent due to the thermal effect. MoreoverRhodamines are characterized by nonlinear saturableabsorption as a result of excited-state or two photonabsorption well described in [3]. We used theanalytical description of Z-scan method reported in[4] to estimate both nonlinear refractive index andabsorption coefficient of the 0.6 mM RhB- Laponite<strong>di</strong>spersions at <strong>di</strong>fferent clay concentrations. In Fig 2Aand Fig 3A mean relaxation times τ m given by fittingDLS data and nonlinear absorption coefficients fromZ-scan measurements are reported vs. tw. Thespecific t w dependence of τ m(t w) and α 2(t w) leads toconsider a scaling law, that makes all data collapseFig. 1: Z-scan spectra (A) and DLS correlationfunctions (B) of Laponite 2.2 wt % <strong>di</strong>spersion inRhB 0.6 mM water solution for <strong>di</strong>fferent waitingtimes t w and correspon<strong>di</strong>ng fits (full lines). In A isalso reported RhB 0.6 mM scan (open circles).Fig. 2: Mean relaxation time τ m vs. waiting time t w(A) and vs. the scaled variable µ τ t w (B) in loglinearscale at various clay concentrations; full linesin (A) are the fitted curves.on a single master curve. This curves are reportedrespectively in Fig. 2B and Fig. 3B as functions ofµ τ t w and µ α t w, being µ τ and µ α fitting parameters [5].From our analysis it emerges that the two timescales µ τ -1 and µ α -1 are comparable showing that thenonlinear optical susceptibility does age andmoreover it exhibits the same aging behaviour ofstructural dynamics.Fig. 3: Nonlinear absorption coefficient α 2 vs. waitingtime t w (A) and vs. the scaled variable µ α t w (B) atvarious clay concentrations; full lines in (A) are thefitted curves.References[1] B. Ruzicka, L. Zulian and G. Ruocco, Phys. Rev.Lett. 93, 258301 (2004);[2] M. Sheik-Bahae, A. A. Said, Tai-Huei Wei, D. J.Hagan and E. W. Van Stryland, IEEE J. Quant. El. 26(4), 760 (1990);[3] N. K. M. Naga Scrivinas, S. Venugopal Rao andD. Narayana Rao, J. Opt. Soc. Am. B 20 (12), 2470(2003);[4] R. E. Samad and N. D. Vieira, J. Opt. Soc. Am. B15(11) (1998);[5] N. Ghofraniha, C. Conti, G. Ruocco, preprint.AuthorsN. Ghofraniha (a), C. Conti (b,c), G. Ruocco (d,c).(a) SMC-INFM-CNR, Università <strong>di</strong> Roma, Italy.(b) Research Center “Enrico Fermi”.(c) SOFT INFM-CNR, Università <strong>di</strong> Roma, Italy(d) <strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong>, Università <strong>di</strong> Roma, Italy.71SOFT Scientific <strong>Report</strong> 2004-06
Scientific <strong>Report</strong> – 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 red<strong>di</strong>sh 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 an<strong>di</strong>n 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 resultsin<strong>di</strong>cate 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 longitu<strong>di</strong>nal 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 hydrodynamicpre<strong>di</strong>ction, obtained assuming v∞ to be the limitinghigh frequency sound speed.The correspon<strong>di</strong>ng 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 in<strong>di</strong>cates the existence of an ad<strong>di</strong>tional 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 <strong>di</strong>vided 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 hdrodynamicspre<strong>di</strong>ction.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’Etu<strong>di</strong>esNucleaires, Grenoble, (FR) (c) <strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong>,Università <strong>di</strong> Perugia, (IT) (d) INFM CRS-SOFT c/oUniversità <strong>di</strong> Roma ″La <strong>Sapienza</strong>″ , Roma, (IT).SOFT Scientific <strong>Report</strong> 2004-0672
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