J. Phys. Chem. B 2008, 112, 9053–9057
9053
Secondary Relaxation Behavior in a Strong Glass Lina Hu and Yuanzheng Yue* Key laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong UniVersity, Jinan 250061, China, and Section of Chemistry, Aalborg UniVersity, DK-9000 Aalborg, Denmark ReceiVed: December 12, 2007; ReVised Manuscript ReceiVed: April 28, 2008
In the present paper we study the enthalpy relaxation behavior of the hyperquenched GeO2 (HQGeO2) glass, one of the strongest glass systems. By applying the hyperquenching-annealing-calorimetry approach, we have found that unlike fragile glasses the strong HQGeO2 glass relaxes in a manner that all the secondary relaxation units contribute to the primary relaxation. By analyzing dynamic properties of the secondary relaxation, we have identified two typical features of the Johari-Goldstein relaxation in the HQGeO2 glass. First, the quantitative relationship observed here between Eβ and Tg agrees well with the empirical relation of the JG relaxation. Second, the characteristic relaxation time of the GeO2 glass at Tg is found to be about 10 s, larger than that of relatively fragile glasses. These results verify that the JG peak in strong glasses is hidden by the R peak in the dielectric loss curves. 1. Introduction In contrast to the primary (R) relaxation, the secondary (β) relaxation, especially the so-called “Johari-Goldstein” (JG) relaxation,1–1 has attracted more and more scientific attention. The JG relaxation is the precursor of the R relaxation.2,3 Although considerable progress has been made in studying dynamic properties of the genuine JG relaxation,4 the physical nature of the local JG motion is still far from a thorough understanding. It has been found that for strong glasses,5,6 neither JG peak nor JG shoulder are observed in dielectric loss curves, but the excess wing is exhibited. Fragile glasses, however, usually exhibit a distinct JG relaxation peak. Some researchers attributed the lack of the JG peak for strong glasses to the fact that the characteristic JG relaxation time, τJG, is not much shorter than the primary relaxation time, τR, or that the JG peak is too small to be observed.4,7 However, some researchers assume that the JG relaxation does not exist in strong glasses at all.8 The two-order-parameter model9 attributes the JG relaxation to the restricted rotational motion in metastable solid-like regions and therefore this motion exists only below the melting temperature Tm. According to this model, the JG relaxation tends to be absent in strong glass formers and the excess wing is due to the motion different from that involved in the JG behavior. Whether the excess wing is associated with the JG relaxation or only is related to the high-frequency part of the primary R relaxation is still under debate.10,11 From the problems stated above, we can say that it is of great importance to study the secondary relaxation behavior in strong glasses. However, such study is seldom reported in literature. This is due to the fact that the methods (e.g., dielectric, mechanical, and NMR spectroscopes) usually used for probing the secondary relaxation of fragile liquids are not applicable to the archetypal strong glasses. The reasons for this could be as follows. First, the loss spectrum of strong glasses lacks a peak or a shoulder on the high frequency side. Second, the typical network structure relaxes around the temperature at which the frequencies of the spectroscopic measurements are utilized.1,12 * Corresponding author. E-mail:
[email protected]. Tel: 0045 9940 8522. Fax: 0045 9635 0558.
Figure 1. Illustration of the relation between the decrease in enthalpy and the excitation level on the potential energy hypersurface of a glass forming system. The relaxation mechanism in a hyperquenched glass with a fictive temperature Tf above Tg corresponds to the fast relaxation mechanism in liquids at T ) Tf. The standard glasses were obtained at the cooling rate of 20 K/min.
Therefore, to probe the secondary relaxation in strong glasses, a different method from those generally used in fragile liquids should be applied. In this work, we apply the hyperquenchingannealing-calorimetric scan (HAC) approach. The basic idea of our attempts is to slow down the motions with higher frequency than the frequency range involved in the primary relaxation in order to see what happens to the higherfrequency relaxation behavior. To do so, the method of hyperquenching would be particularly useful, since the potential energy states trapped using hyperquenching relax more rapidly than those trapped during slow quenching, and mainly contribute to the secondary relaxation as shown in Figure 1. All the potential energy states over the temperature range from Tf of the hyperquenched glass to that of the standard glass could be observed in real time window during the following enthalpy recovery procedure. In this way, we may find the characteristics of the secondary relaxation in strong glasses. By comparisons in the JG relaxation between the quenched and the annealed samples of some rigid molecules,13,14 it has been found that the
10.1021/jp711696p CCC: $40.75 2008 American Chemical Society Published on Web 07/08/2008
9054 J. Phys. Chem. B, Vol. 112, No. 30, 2008
Hu and Yue
Figure 2. Typical heat capacity (Cp) curves of hyperquenched GeO2 glasses. Cp1 and Cp2 represent the heat capacity curves measured during the first and second upscan of the DSC measurement, respectively. Tonset is the onset temperature, at which the release of enthalpy starts, and Teq is the temperature, at which Cp1 ) Cp2. The inset: the second upscan Cp curve of the standard bulk GeO2 glass, which is denoted by Cp3.
HAC approach may make the secondary relaxation more visible and more separable from the primary relaxation. 2. Experimental methods Germanium dioxide glass (GeO2: fragility index m ) 17-20),15 one of archetypal strongest glasses, were prepared from GeO2 powder with a purity of 99.98%. In order to minimize the water content of the GeO2 glass, the powder was repeatedly dried in a platinum crucible under dry air. The dried powder was then melted at 1873 K in a platinum crucible and held at this temperature for 1 h. The hyperquenching of the GeO2 glass was realized by means of continuous fiber drawing from the GeO2 melt. The continuous GeO2 glass fibers, drawn at the constant rate of 20 m/s, have the average diameter of 3.5 µm. On the infrared (IR) absorption curves of these fibers, no peak at 3560-1 cm due to the hydroxyl group could be observed. According to the method introduced previously,16 the cooling rate of the hyperquenched fibers was calculated to be about 106 K/s. For relaxation study, the annealing (or aging) of glasses is often performed to obtain the decay pattern of enthalpy. The fiber samples were annealed in a furnace under ambient atmosphere at selected temperatures in the range between 0.5Tg and 0.9Tg (in Kelvin) for various durations. A differential scanning calometer (DSC) (Netszch Jupiter STA 449C) was used for the heat capacity (Cp) measurements with the following procedure. The annealed samples were held for 5 min at 333 K, and heated to 973 K at the rate of 20 K/min and then immediately cooled at the rate of 20 K/min. Subsequently, the glasses were subjected to the second upscan and downscan using the same procedure as mentioned above. Glasses subjected to the first downscan, i.e., the samples cooled at 20 K/min are termed as the “standard glasses”. Furthermore, the second upscan Cp curve of the standard glass is termed as the “standard curve”. To determine the Cp curve of the fibers, both baseline and reference sample (here sapphire) were measured. 3. Results and Discussion 3.1. Abnormal Enthalpy Relaxation Manner of Hyperquenched GeO2 Glasses (HQGeO2). Figure 2 shows the typical heat capacity curves of HQGeO2 during the first and second upscans (Cp1 and Cp2, respectively), as well as the second upscan curve of the corresponding bulk sample (see Cp3 in the inset of Figure 2). It is seen that the first heating upscan shows a broad exothermic peak, reflecting the release of the excess enthalpy of the hyperquenched fibers. According to the area-match
Figure 3. Influence of annealing duration on the energy release of hyperquenched glasses (a) GeO2 annealed at 565 K for different durations; (b) basaltic fibers annealed at 723 K for different durations.19
method,17 the fictive temperature (Tf) of the hyperquenched fibers used in the present work is found to be 1103 K. The glass transition temperature (Tg) of the bulk sample equals to 792 K. For the sample obtained at the slow cooling rate of 10 K/min, the value of Tf corresponds to that of Tg.18 The Cpl data remains approximately constant within a large range of temperature, whereas the Cpg data fits the Einstein equation.17 At Tg, the Cp difference between the liquid and the glass, ∆Cp,l-s(Tg), is 0.6 J/gK, much smaller than that of fragile glasses, resulting in the distinct noise of the Cp curves in Figure 2. The area between the Cp1 and Cp2 curves corresponds to the trapped excess enthalpy relative to that stored in standard glasses. The temperature dependences of Cp were measured on the HQGeO2 samples annealed at different temperatures for various durations. Figure 3a shows a set of representative Cp measurements on the HQGeO2 samples annealed at T ) 565 K for various durations. For a comparison, the Cp curves of the hyperquenched basaltic fibers (a relatively fragile glass system) annealed at different temperatures for various durations are shown in Figure 3b.19 For both glass systems, it is seen that the area enclosed by the Cp2 and Cp1 curves decreases with the annealing duration. It indicates that the trapped excess energy is released during annealing, i.e., the structural configuration approaches a lower energy level. Here we focus on the differences in the relaxation manner between Figure 3a,b. One difference concerns the first endothermic peak that occurs to the hyperquenched basaltic glasses subjected to a certain degree of annealing (see Figure 3b). It has been reported that the DSC scan of the hyperquenched glasses after annealing (such as in polymers, metallic glasses and inorganic glasses) shows two endothermic peaks instead of only one observed in standard glasses.20–22 The first endothermic peak, which occurs prior to the exothermic peak (i.e., the energy release peak) below Tg, has been referred to as a “sub-Tg peak” or a “shadow Tg peak” or a prepeak.23,24 In this paper, the term “sub-Tg peak” is used. In Figure 3b, it is seen that besides the endothermic peak attributed to the glass transition above 900 K, the sub-Tg peak becomes more distinct with increasing the annealing time. In Figure 3a, however, no distinct sub-Tg peak can be observed.
Secondary Relaxation Behavior in a Strong Glass This phenomenon agrees with the fact that a smaller value of the nonlinearity x parameter in Tool-Narayanaswamy (TN) model generally corresponds to more distinct sub-Tg peak at higher temperatures.25,26 The existence of the sub-Tg peak means that during annealing some microregions with fast relaxation reach the lower energy states relative to the rest of glass and then return to the higher energy states during DSC upscan. They seem independent of other domains with slower relaxation and simply cause the Cp overshoot, since they are reproducible.24 Figure 3a,b shows that the position of the second endothermic peak (i.e., the Tg peak) is independent of the annealing time. For relatively fragile glasses, we often find one or more shoulders in the Cp curves. This suggests that at least two domains of relaxation processes exist below Tg. For basaltic glasses, a distinct shoulder has been observed in each curve (from about 770 K in curve a to about 885 K in curve f).19 For HQGeO2, however, no shoulders are observed (see Figure 3a). This phenomenon is similar to the lack of the secondary relaxation peak or shoulder in the dielectric loss spectrum. The lack of the sub-Tg peak or the shoulder indicates the less structural heterogeneity in glass. Therefore strong glass formers have more structural heterogeneity than fragile glass formers. Another difference in relaxation behavior between HQGeO2 and basaltic glasses (see Figure 3a,b) is described as follows. In Figure 3b, it is shown that extending the annealing time at a certain temperature only influences the shape of the Cp curves below Tg, leaving the Cp curve above Tg unaffected. This indicates that the annealing procedure does not influence the slow cooperative motion involved in the primary glass transition, but affects the secondary relaxation at high-frequency regions.27 Only after the high-frequency relaxations are completed does the slow cooperative motion begin. Compared with Figure 3b, Figure 3a displays a different manner of relaxation behavior. With an increase of the annealing time, the shift of the exothermic peak in the secondary relaxation region is accompanied by that of the Tg peak in the primary relaxation region. Both peaks tend to match the Cp curve of the standard sample (cooled at 20 K/min), which is obtained using a upscanning rate of 20 K/min. This means that every relaxation unit involved in the secondary process contributes to the primary relaxation process. It is difficult to separate the slow cooperative motion from the fast local one. In terms of the potential energy landscape (PEL), the scenario shown in Figure 3a means that in strong glass formers the secondary relaxation and the primary relaxation generally occur in the same megabasins,28 and this is so-called “no β without R” picture.29 This picture is supported by Speedy’s work,30 where the density of the energy minimum for a N-molecule system with typical network structures is ∼ exp(1.2N), much smaller than those of fragile materials with different atomic packing.31 Note that the degree of the overlap between the secondary and the primary relaxations differs from one glass system to another, although the primary relaxation is the determining dynamics and set the finite time scale for glass transition as shown in Figure 3a,b. In a previous study,32 it has been suggested that the degree of the overlap between the R and the β relaxation is higher for strong glass formers than for fragile glasses. This finding is consistent with what is observed in Figure 4. As shown in Figure 4a, the Cp curve of the HQGeO2 glasses, which was subjected to a certain degree of annealing, overlaps that of the standard glass. In contrast, for relative fragile glasses, such overlap does not exist as shown in Figure 4b.33 3.2. Dynamical Mechanism of the Secondary Relaxation in Strong Glasses below Tg. The enthalpy relaxation of a HQGeO2 glass during a DSC upscan toward Teq is a process,
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Figure 4. Comparison of the heat capacity curves obtained at the upscan rate 20 K/min between hyperquenched glasses subjected to different degrees of annealing and the standard glasses. (a) GeO2; (b) basaltic glasses.33
Figure 5. Annealing duration (t) dependence of the normalized remaining excess enthalpy (∆Hrem/∆Htotal) in the HQGeO2 glasses annealed at different temperatures (0.5-0.9Tg), where ∆Hrem and ∆Htotal are the remaining excess enthalpy and the total excess enthalpy, respectively.
during which the energy states of the glass (with a Tf of 1103 K) approach those of the liquid under equilibrium condition. Instead of the cooperative motion involved in the primary relaxation, the high-frequency motion of structural relaxation, i.e., the secondary relaxation is expected to be dominant in the temperature range above Tg. This means that when the annealing temperature is below Tg, only the structural relaxation related to the secondary relaxation occurs, which results in a change of thermodynamic properties of a system. Figure 5 shows the time dependence of the normalized remaining enthalpy in the HQGeO2 glasses annealed at different temperatures between 0.5Tg and 0.9Tg. The releasable excess enthalpy in the fresh HQGeO2 glass is in the range of 14-16 J/g. The constants of the Kohlrausch function (φ(∆Hrem/∆Htot) ) exp[-(t/τβ)1-n] are determined for each annealing temperature. The characteristic relaxation time τβ decreases with increasing the annealing temperature. The value 1 - n is nearly a constant of 0.4 within the limit of error in the range of temperature from 565 to 660 K. The value 1 - n for the secondary relaxation below Tg is quite different from the reported value of 1 for the primary relaxation at equilibrium above Tg.34 It should be mentioned that the enthalpy of the standard glasses is used as a reference state for the fitting of Kohlrausch function to the data. This allows us to focus only on the dynamic mechanism of the secondary relaxation. In Figure 3, it seems that it is possible for the hyperquenched
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Figure 6. Dependence of the characteristic relaxation time (τβ) of the secondary relaxation below Tg on the reciprocal annealing temperature (1/Ta).
glasses to approach, and even surpass the energy level of the standard glass, if the annealing time is enough. By analyzing the data plotted in Figure 5, here we attempt to answer the question of whether the secondary relaxation in the HQGeO2 belongs to the JG relaxation type. Different from fast secondary relaxations,35,36 the JG relaxation has both qualitative and quantitative features, resulting in several commonly invoked criterions.4,7,37 In the qualitative aspect, Figure 3a shows that the secondary motion detected in Figure 5 is a precursor or a local step of the primary relaxation, which accords with the nature of the genuine JG relaxation. For a quantitative description, the annealing temperature Ta dependence of the τβ value is plotted in Figure 6, which is obtained from the data shown in Figure 5. As a result, two typical features of JG relaxation are observed in Figure 6. First, the τβ value exhibits the Arrhenius temperature dependence. Second, the activation energy Eβ of this behavior is 155.7 kJ/mol, equal to 23.5RTg. The quantitative relationship observed here between Eβ and Tg agrees well with the empirical relation of the JG relaxation found in polymers and small molecules.7,37 By extrapolating the Arrhenius temperature dependence of τβ to Tg, we obtain [log τβ(Tg)] ) 0.995. This value is in agreement with that predicted from the empirical linear relationship between log τβ(Tg) and 1 - n obtained by compilations of more than twenty fragile systems.38 According to the extended CM,38,39 the τβ(Tg) value of 10 s is relatively close to τ0,R(Tg) (about 40-100 s, depending on the type of the glass systems), since the n value at Tg is nearly zero for the HQGeO2 glass under equilibrium conditions. This correspondence between τβ(Tg) and 1 - n is another general feature of JG relaxation.38 In terms of whether the β relaxation peak is visible in liquids or not, the glass formers have been divided into two groups: L(liquid)-type and G(glass)-type.13,14 In contrast with G-type glasses, according to our results, GeO2 is more L-type like and its dynamic homogeneity accords with that predicted by Wagner et al. According to Dyre et al.,40 the annealing process leads to the appearance of the β relaxation peak in liquids, if Tg (i.e., the Tf of the HQGeO2 used in this work) is higher than the merging temperature TB, where the R and β relaxations cross each other. This view is supported by the experiments shown in Figure 7, which depicts the heating rate (equal to the prior cooling rate) dependence of the fictive temperature of the bulk GeO2 Glass. From Figure 7, the activation energy of the viscous flow of this glass in the temperature range around Tg is found to be 302 kJ. As is known, the relaxation time for the R process at Tg is about 100 s for most of oxide glasses.18 By taking this into account, the primary and secondary relaxations in the HQGeO2 glass will cross each
Hu and Yue
Figure 7. Dependence of the DSC upscan rate (q+) on the reciprocal fictive temperature (1/Tf) for bulk GeO2 glasses. Inset: heat capacity curves obtained at different DSC upscan rates equal to the prior downscan rates.
other at the TB of 1005 K, which is lower than the Tf of 1103 K. From the comparisons between TB and Tf and from the Dyre’s statement mentioned above,40 the JG relaxation must occur in the HQGeO2 glass and the annealing procedure will make the JG relaxation present. According to Salmon et al.,41 the JG relaxation is attributed to the motion involved in the intermediate-range order structure. As far as we know, the τJG(Tg) value of GeO2 is the largest among those of the materials of different microstructures investigated. For some fragile glasses, log[τJG(Tg)] is -9.4 (PES) to -1.3 (B2O3).38 This agrees with the fact that the overlap degree of the primary relaxation with the secondary relaxation is larger for the GeO2 glass than that for fragile glasses, as shown in Figure 3. A larger value of τJG(Tg) also implies that τJG(T) is close to τR(T) below TB. That is why strong glasses (n usually smaller than 0.4) do no show distinct secondary relaxation (only with two exceptions of the plastic crystal and cyclo-octanol42). 4. Conclusions By using the hyperquenching-annealing-calorimetric scanning method, we have observed abnormal enthalpy relaxation behavior in typical strong glasses in comparison to that in fragile glasses. A stronger glass former corresponds to the larger degree of the overlap between the primary and the secondary relaxations. The secondary relaxation in the strong GeO2 glass during annealing exhibits two key features of genuine JG relaxation. The characteristic relaxation time of the GeO2 glass at Tg is found to be about 10 s, larger than that of normal fragile glasses. This explains why no JG peak is observed by performing dielectric loss and dynamic mechanical measurements in strong glasses. Our results verify that the JG peak in strong glasses is in fact hidden by the R peak in the dielectric loss curves. Acknowledgment. This work was financially supported by a Danish-Chinese cooperation grant and by National Basic Research Program of China (Grant No. 2007CB613903) and National Natural Science Foundation of China (Grant No. 50631010). References and Notes (1) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. Johari, G. P. J. Chem. Phys. 1973, 58, 1766. Johari, G. P. J. Non-Cryst. Solids 2002, 307-310, 317. (2) Hensel-Bielowka, S.; Ziolo, J.; Paluch, M.; Roland, C. M. J. Chem. Phys. 2002, 117, 2317. (3) Paluch, M.; Roland, C. M.; Pawlus, S.; Zioło, J.; Ngai, K. L. Phys. ReV. Lett. 2003, 91, 115701. Ko¨plinger, J.; Kasper, G.; Hunklinger, S.
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