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3 About the Nature of the Structural Glass Transition: an Experimental Approach 3 About the Nature of the Structural Glass Transition: An Experimental Approach J. K. Kr¨uger1,2, P. Alnot1,3, J. Baller1,2, R. Bactavatchalou1,2,3,4, S. Dorosz1,3, M. Henkel1,3, M. Kolle1,4,S.P.Kr¨uger1,3,U.M¨uller1,2,4, M. Philipp1,2,4,W.Possart1,5, R. Sanctuary1,2, Ch. Vergnat1,4 1 Laboratoire Europ´een de Recherche, Universitaire Sarre-Lorraine-(Luxembourg) [email protected] 2 Universit´edu Luxembourg, Laboratoire de Physique des Mat´eriaux,162a, avenue de la Fa¨ıencerie, L-1511 Luxembourg, Luxembourg 3 Universit´eHenriPoincar´e, Nancy 1, Boulevard des Aiguillettes, Nancy, France 4 Universit¨atdes Saarlandes, Experimentalphysik, POB 151150, D-66041 Saarbr¨ucken, Germany 5 Universit¨at des Saarlandes, Werkstoffwissenschaften, POB 151150, D-66041 Saarbr¨ucken, Germany Abstract. The nature of the glassy state and of the glass transition of structural glasses is still a matter of debate. This debate stems predominantly from the kinetic features of the thermal glass transition. However the glass transition has at least two faces: the kinetic one which becomes apparent in the regime of low relaxation frequencies and a static one observed in static or frequency-clamped linear and non-linear susceptibilities. New results concerning the so-called α-relaxation process show that the historical view of an unavoidable cross-over of this relaxation time with the experimental time scale is probably wrong and support instead the existence of an intrinsic glass transition. In order to prove this, three different experimental strategies have been applied: studying the glass transition at extremely long time scales, the investigation of properties which are not sensitive to the kinetics of the glass transition and studying glass transitions which do not depend at all on a forced external time scale. 3.1 Introduction Synthetic glassy materials are known for more than 8000 years. Neverthe- less, the question about the nature of the glassy state and of the thermal glass transition (TGT) of structural (or canonical) glasses is still open [1–26]. Usually, synthetic glasses belong to the class of structural (canonical) glasses which behave mechanically as solids, but which have an amorphous, that means a liquid-like, structure. In other words, glasses are hybrids which have similarities as well with solids as with liquids. This hybrid nature also be- comes obvious in the course of the transformation from the liquid to the J.K. Kr¨uger et al.: About the Nature of the Structural Glass Transition: An Experimental Approach, Lect. Notes Phys. 716, 61–159 (2007) DOI 10.1007/3-540-69684-9 3 c Springer-Verlag Berlin Heidelberg 2007 62 J.K. Kr¨uger et al. Fig. 3.1. Schematic drawing of the effect of slow and fast cooling on the mass density ρ of (a) a crystallisable and (b) a non-crystallisable liquid. ρl: mass density of the equilibrium liquid, ρc: mass density of the crystalline state, ρsc: mass density of the under-cooled liquid, ρg: mass density of the glassy state glassy state. On cooling the glass-forming liquid, the transition from the liq- uid to the glassy state is accompanied by experimental features which may be attributed to phase transitions as well as to under-cooling effects (Figs. 3.1a,b, 3.2). Under-cooling means that the temperature of the liquid sample can be de- creased faster than certain of its physical properties do respond. For instance, crystallization of a liquid may be prevented by fast cooling if the viscosity of the liquid increases much faster than nucleation takes place. As a result a super-cooled liquid is obtained. Figure 3.1a shows schematically this situation for the mass density ρ for slow and fast cooling. Below the melting tempera- ture Tm the liquid becomes super-cooled and is therefore out of equilibrium. The degree of metastability of the super-cooled state depends amongst other parameters on the glass-forming liquid itself and on the temperature devi- ation ∆T =(Tm − T ). As a matter of fact the mass density curve of the super-cooled state is a direct continuation of the equilibrium liquid state. At still lower temperatures around the so-called thermal glass transition temper- ature Tg the mass density curve ρ(T ) shows a kink-like anomaly (Fig. 3.1a). Depending on the sharpness of this kink the volume expansion coefficient αV shows a step-like anomaly at Tg. Figure 3.1b schematically shows for com- parison the temperature behaviour of the mass density of a non-crystallisable liquid (e.g. atactic polymers). The only temperature induced anomaly which remains is the kink-like anomaly of ρ(T ) at the glass transition temperature Tg. The question marks in Fig. 3.1a,b stress the open question about the origin of this kink: is it purely due to a super-cooling effect (Fig. 3.1b) or to a further super-cooling effect (Fig. 3.1a) or does there exist an intrinsic event which causes this kink-like anomaly of the mass density? Assuming that the density-kink is purely kinetically conditioned (“kinetic hypothesis”) 3 About the Nature of the Structural Glass Transition 63 Fig. 3.2. Schematic drawing of the evolution of a structural glass transition. Mass density ρ = ρ(T ): the graphics (a) to (f) show the temporal evolution of the mass density ρ at fixed temperature T the temperature position of this kink should shift to lower temperatures if the cooling rate is slowed down. Time-domain investigations, as schematically drawn in Fig. 3.2a–d, help to elucidate the validity of the “kinetic hypothesis”. For the thought (time-domain) experiment of Fig. 3.2 we assume that the mass density ρ is measured in a static way by determining at every temper- ature T the mass and the volume of the sample. At high temperatures, far above the freezing temperature Tg, mass-density and volume-changes equili- brate as fast as the temperature of the sample does. After a temperature step −∆T the mass density responds almost instantaneously (Fig. 3.2a). As a mat- ter of fact, on approaching the glass transition temperature Tg from above by temperature steps −∆T , the recovery of the mass density ρ takes more and more time t, i.e. ρ(t) is less and less able to follow a temperature step −∆T (Fig. 3.2b,c). This is due to the fact that glass-forming liquids exhibit inter- nal degrees of freedom with relaxation times τα, which become very large on approaching Tg from above and which even show a certain tendency to di- verge in a temperature interval below Tg (Fig. 3.2e–f). The experimental time needed to equilibrate the new temperature after a temperature jump −∆T is assumed to be τm. If at sufficiently high temperatures τm τα then the mass density ρ is in internal equilibrium. If the recovery time of the mass density τα becomes larger than the experimental time constant of the temperature ad- justment τm, the mass density ρ(t) shows relaxation behaviour (Fig. 3.2a–d). This relaxation behaviour has been interpreted as the result of cooperative 64 J.K. Kr¨uger et al. interaction of the molecules close the glass transition (e.g. [2]) and is called the α-relaxation process. In order to bring the mass density ρ(T ) still to equilibrium the experi- mental time constant τm has to be increased sufficiently in order to realize τm τα or at least τm >τα. For the understanding of the thermal glass transition the exciting question arises how the process develops in an equi- librium experiment when decreasing the temperature as slowly as possible (Fig. 3.2a–f). If on cooling, at a certain temperature Tg the α-relaxation time τα increases so strongly that τα becomes comparable to τm and even exceeds τm in that case the “bending temperature” Tg is indicative for the fact that the mass density ρ(T ) falls out of “equilibrium” (Fig. 3.2a–3.2d–f). In the following this will be denoted as time trap [15]. If on the other hand, the mass density curve shows a kink at Tg although the time trap could be avoided, in that case Tg represents an intrinsic transition temperature (Fig. 3.2a–3.2c,e,f). The α-relaxation phenomenon is typical for the glass transition in liquids and will be discussed in Sect. 3.4 of this article as the dynamical aspect of the thermal glass transition. Thus, as a consequence of the strongly increasing α-relaxation times in the vicinity of Tg, there exists an inherent risk for every experiment performed to measure non-equilibrium properties close to Tg. If the time for temperature equilibration and/or for the equilibration of the measured quantity exceeds the “patience of the experimentalist”, non-equilibrium properties are mea- sured. If, as argued in literature ( see any text book on glasses, e.g. [2]), the relaxation time τ of the α-relaxation process diverges at a temperature ∼ α T0 = (Tg − 40) K then the cross-over between τα and the experimental time scale is unavoidable. If the experiment of interest was driven too fast and as a consequence captivated in the “time-trap” a so-called ageing process is possi- ble on a long time scale. This process brings eventually the physical quantity of interest to its equilibrium value. This specific “kinetic” face of the glass transition and the question under which conditions quenched physical prop- erties will age towards their equilibrium values will be discussed in Sect. 3.3. Whether τα (T ) really diverges at a temperature T0 is rather questionable.
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