A comparison of the far-infrared and low-frequency Raman spectra of glass-forming liquids
Introduction
The transition of glass-forming liquids from the lower-temperature glassy state to the higher-temperature viscous melt has long been a subject of considerable scientific interest, but the phenomenon of the glass transition is still not adequately understood. As this paper is appearing in the special issue to honour the contributions of Professor G.P. Johari to glass science, the work is presented to complement his findings.
Through experiments on glass-forming liquids several researchers have shown that at a cross-over (or critical) temperature, TC, 30 to 40°C above the glass transition temperature, Tg, the relaxation rate in general shows a departure from the Arrhenius dependence on temperature. The cross-over temperature in general depends on the system. The relaxation process governed by the non-Arrhenius process, due to the co-operative motion of molecules, is called the α process. However, the significant contribution made by Johari through his systematic experiments on simple glass-forming liquids has been to show the emergence of a rather fast additional process, β, compared with the α process. He also showed that the latter is generic to the glass transition and arises from the orientation of molecules situated in the interstices of the amorphous structure, created in the material as it is cooled down. The amorphous structure is present in the glassy state and hence the β process persists at temperatures much below Tg. The process is referred to as the Johari–Goldstein relaxation [1], [2], [3] as a consequence of Johari's collaboration with Goldstein on the theory of glass transition. Since the discovery, some researchers [4], [5] have argued that at higher temperatures the α and β processes appear to merge into one relaxation process. This may imply that the α process involving co-operative processes has really emerged at TC and that the β process may have always been present in the liquid. However, the experimental observations do not support this viewpoint and one of the present authors [6], [7] finds, as Johari had observed, that the α process is continuously present at all temperatures above Tg. The departure from Arrhenius behaviour at a certain temperature above Tg is due to the number of molecules involved in the co-operative process first increasing gradually and then increasing rapidly as the liquid approaches the glass transition temperature from above. The statistical distribution of the number of molecules in a cluster, together with the size of the cluster, leads to both a departure from the Arrhenius rate and the broadening of the dielectric loss curves as the system approaches Tg. In contrast, the β process emerges at some temperature, above Tg, and continues to persist to several degrees below Tg. The strength of the β process is dependent on the system, as some glass-forming systems produce bigger pores or voids in the structure than others. In the recent literature [8] the Johari–Goldstein process is labelled as β slow. The observation of the α process departing from an Arrhenius rate at a temperature above Tg fits with the predictions of the mode coupling theory (MCT) [9]; however, the mode coupling theory also predicts a faster relaxation process. It is not clear whether the predictions are related to the observation of the Johari–Goldstein β process or still another faster relaxation process. The latter may be related to the vibrations of molecules seen in the boson peak or librations in the far-infrared absorption spectrum.
The physical origin of such a fast process and its possible connection to the α relaxation remain the outstanding unsolved problems in glass science. In general, the interpretations of neutron data corresponding to the fast process are based on the mode coupling theory [9]. The theory predicts a fast relaxation process (βfast process) in the time scale of 1 to 10 ps. Some authors [10] have related the observed fast process to the vibrational properties of the softening of the glass structure. However, the major problem in the analyses and interpretation of the fast process is that additional low-frequency vibrational excitations also contribute to the dynamic structure factor S(q,ω) of the supercooled liquids and glasses in the same frequency range where the quasi-elastic contribution of the fast process is to appear. In the low-frequency Raman (LFR) spectra these kinds of excitations are very well known and give rise to the so-called “boson peak”. Taking into account LFR data, Sokolov et al. [11], [12] have recently shown that LFR spectra of fragile systems1 are mainly dominated by the relaxational contributions and the boson peak is not observed in some very fragile systems even at temperatures below Tg. Several studies with neutron diffraction also appear to support this empirical correlation [14]. However, the origin of the boson peak is still under discussion and whether or not the Poley peak seen in the far infrared (FIR) arises from similar processes.
The far-infrared spectra should complement the Raman spectra and in principle could throw additional light towards the understanding of the nature of the boson peak. The relative contribution of relaxational and vibrational processes to the molecular dynamics of amorphous solids can then be properly assessed. However, to date, relatively little experimental work on the far-infrared absorption of glass-forming liquids has been carried out and a comparison between the results obtained from the techniques is lacking. We have therefore studied the far-infrared and low-frequency Raman spectra of three glass-forming liquids: glycerol, glycerol triacetate (triacetin) and o-terphenyl. Glycerol and o-terphenyl are the most studied glass-forming liquids using a wide variety of techniques since these show interesting properties. These two liquids in the supercooled state have already been studied with different techniques including acoustic, dielectric, nuclear magnetic resonance (NMR) and Raman spectroscopy. However, to our knowledge, no far-infrared spectra have been measured previously on these glass-forming liquids.
Section snippets
Theoretical background
As a consequence of the molecules being locked in the interstices of the amorphous structure (as mentioned in Section 1), the molecules are also likely to rattle in the cage or undergo underdamped angular librations in addition to the orientational motions. These librations are partly responsible for the absorption of the far-infrared radiation in the wavenumber range 10 to 200 cm−1 or the frequency range 300 GHz to 6 THz. This absorption was observed, possibly for the first time, by Reid and
Experimental
The chemicals, glycerol, triacetin and o-terphenyl (OTP), were purchased from Aldrich. Glycerol (99.5% with <0.1% water) and triacetin and o-terphenyl (99% purity) were used without further purification. Glycerol and triacetin were inserted in a cell with two polyethylene (or poly-4-methyl-1-pentene (TPX)) windows at room temperature. The thickness of such a cell was approximately a few micrometres. OTP was placed on one of the windows and heated up to ∼340 K; with o-terphenyl melted on a second
Glycerol, triacetin
Fig. 1 shows the experimental Raman spectra (I(ν)) of glycerol in the temperature range 253–328 K. These spectra compare favourably with those previously observed by Wang and Wright [28] and Sokolov and co-workers [29]. The far-infrared and low-frequency Raman spectra (in R(ν) representation) of glycerol and triacetin at different temperatures in the wavenumber range from 15 to 250 cm−1 are shown in Fig. 2Fig. 3. The spectra are analysed in greater detail elsewhere [30]. In this paper, a
Conclusions
Far-infrared and low-frequency Raman spectra (15–500 cm−1) of three glass-forming liquids — glycerol, triacetin and o-terphenyl — have been reported in the temperature range 253 to 353 K. A comparison between the results given by the two techniques shows that several features of the spectra are different. In particular, βfast seen in the quasi-elastic Rayleigh line (and also the neutron scattering) is not seen in the corresponding dielectric/far-infrared studies; and whether βfast has any
Acknowledgements
The authors thank the European Commission for funding this work through the INTAS-96-1411 grant. DHC and OFN are grateful to the Danish National Science Research Council for general funding during this project. JKV thanks Forbairt, Ireland for a partial funding under its basic programme of research. We thank Sergey Tsvetkov for his help during the preparation of this paper.
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