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J. Phys. Chem. B 2007, 111, 9758-9761
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MAS NMR Spectroscopic Study of Structural Relaxation, Aging, and Memory Effect at the Atomic Scale in a Borosilicate Glass Sezen Soyer Uzun and Sabyasachi Sen* Department of Chemical Engineering and Materials Science, UniVersity of California at DaVis, One Shields AVenue, DaVis, California 95616 ReceiVed: March 20, 2007; In Final Form: June 15, 2007
Relaxation kinetics of boron coordination environments in a borosilicate glass in response to temperature jumps has been monitored using 11B magic-angle spinning (MAS) NMR spectroscopy. The relaxation time scale of the BO4/BO3 ratio is found to be closely comparable with those of the bulk properties, namely, refractive index and viscosity, showing a close connection with one another. Samples partially equilibrated at a low temperature, when subjected to a positive temperature jump, display an initial rapid decrease followed by an increase in the BO4/BO3 ratio. This reversal in the trend of the variation of the BO4/BO3 ratio has been interpreted to be the signature of a memory effect, and the implications are discussed within the framework of the potential energy landscape model of glassy dynamics.
1. Introduction Borosilicate glasses are technologically important materials that have found a variety of applications in modern technologies ranging from liquid crystal display substrates to host materials for encapsulation of radioactive wastes.1,2 These applications depend on how these materials undergo changes in atomic structure and properties when cooled from liquid into a glass. Thus, knowledge of these temperature-dependent changes should lead a better understanding of the processing conditions for manufacturing materials with the desired properties. As the glass-forming liquid is cooled, the atomic structure undergoes relaxation.3,4 Unfortunately, our current understanding of these relaxation phenomena is largely based on phenomenological kinetic models that often suffer from the lack of a direct microscopic understanding of the atomic-scale processes that accompany structural relaxation.5,6 Previous studies have investigated permanent temperaturedependent changes in the equilibrium structure in inorganic glasses and liquids using various spectroscopic and diffraction techniques.7-17 These studies were carried out both in situ in the liquid state as well as ex situ on glasses with different fictive temperatures Tf resulting from cooling the parent liquid at different rates. Some of these temperature-dependent structural changes include the formation of three- and four-membered rings in silica, transformation of BO4 units to BO3 units in borates, Si Q-speciation and formation of pentacoordinated SiO5 groups in silicates, and AlO5 to AlO4 transformation in boroaluminates with increasing temperature.11-17 On the other hand, in situ hightemperature 29Si, 11B, and 17O NMR exchange spectroscopic studies have shown that the average time scale of chemical exchange between Si atoms belonging to different Q-species or between B atoms in BO3 and BO4 species corresponds very well with the time scale of shear or structural relaxation in simple silicate or borate liquids.7-10 However, the relationship between the permanent changes in the equilibrium structure and the dynamic structural fluctuations resulting from chemical exchange in a glass-forming liquid has not been addressed in the literature.
Recently, glassy dynamics near the transition range has been described successfully within the framework of a potential energy landscape (PEL) model. In this model the dynamics near the glass transition is visualized as the exploration of a (3N + 1)-dimensional potential energy hypersurface by a system of N particles where the potential energy is a function of particle coordinates.18-22 This energy hypersurface has nonoverlapping basins each of which corresponds to one inherent structure or configuration with an energy that is characteristic of the temperature at which the structure is in equilibrium. The diverging relaxation time on cooling a liquid then corresponds to a drastic lowering of the number of available configurational states or entropy as the system becomes trapped in a basin and can no longer explore nontrivial alternative configurations in separate basins due to the lack of thermal energy. Direct experimental observation of the details of the potential energy hypersurface of a glass-forming liquid remains an impossible task. However, recent experiments on gels and polymers show evidence of intermittent, heterogeneous dynamics in the form of spontaneous but random switching between distinct configurations at low temperatures close to and even below the glass transition temperature, Tg.23-25 Similar experimental evidences are still lacking in the case of inorganic glass-formers. It has recently been suggested that the aging dynamics of a glassforming liquid, during its evolution toward equilibrium following a temperature jump, proceeds along a sequence of structural configurations that are different from those explored in equilibrium.18 Detailed structural studies of the aging dynamics of glasses can therefore provide important constraints for this hypothesis. This article reports the results of a high-resolution 11B magicangle spinning (MAS) NMR spectroscopic study of time dependence of the structural evolution of various borate species in a complex borosilicate glass following temperature jumps. The relaxation kinetics of BO3 and BO4 speciation are compared with the kinetics of refractive index and shear relaxation in these glasses in order to gain a fundamental understanding of the atomic-scale processes associated with aging dynamics. The
10.1021/jp072223i CCC: $37.00 © 2007 American Chemical Society Published on Web 07/28/2007
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influence of an underlying PEL on the borate speciation dynamics is also investigated. 2. Experimental Section 2.1. Sample Synthesis. The composition of the borosilicate glass used in this study can be expressed in wt % as 70% SiO2, 11% B2O3, 7% K2O, 9% Na2O, and 3% BaO. This particular glass composition has been chosen since the time and temperature dependence of relaxation of the refractive index and density of this glass, variously known as Corning code 8370 and BSC 517, have been studied in the glass transition range (Tg ∼ 555 °C) in extensive detail by others in the past.26-29 Therefore, it provides an opportunity to directly compare variations in macroscopic properties with corresponding changes in the short-range structure. Glass samples were synthesized from high-purity oxide reagents which were mixed thoroughly, melted at 1450 °C for about 2 h in Pt crucibles, and then quenched to room temperature. The first step in the protocol for relaxation kinetics experiments consisted in annealing millimeter-sized chunks of glass samples at 585 °C for 1 h in order to obtain identical starting fictive temperature Tf for all samples. A subset of these glass samples was then annealed at 530 °C while another subset was annealed at 470 °C, for time periods ranging from several minutes to several hours, and subsequently rapidly quenched in air. A third subset of samples was annealed at 470 °C for 100 h and subsequently annealed at 530 °C for various periods of time followed by rapid quenching in air. Previous refractive index relaxation studies on this glass composition have shown that samples with initial Tf ) 585 °C, when held at 470 °C for ∼100 h, acquire similar density and refractive index as those that have been completely equilibrated at 530 °C.29 Therefore, the third subset of glass samples provides an opportunity to investigate the atomic-scale details of the structural relaxation phenomena in the time-temperature space where the two relaxation curves corresponding to annealing at 530 and 470 °C cross over. It may be noted here that such experiments are typically denoted as “crossover experiments” in the literature.18,29 2.2. 11B MAS NMR. Relative changes in the BO4/BO3 ratio in all samples with different time-temperature histories were monitored by 11B MAS NMR spectroscopy. The 11B NMR spectra of all glass samples were collected with a 4 mm Bruker MAS probe and a Bruker Avance 500 spectrometer equipped with a widebore ultrashield magnet operating at a Larmor frequency of 160.4 MHz for 11B. Crushed glass samples were spun in Si3N4 and ZrO2 rotors at 15 kHz. All 11B MAS spectra were collected using nonselective rf pulses with 15° tip angle (0.6 µs) and with a recycle delay of 2 s. Approximately 5001000 free induction decays (FIDs) were averaged to obtain each spectrum. 3. Results The evolution of the 11B MAS NMR spectra of the borosilicate glass with initial Tf ) 585 °C as a function of annealing time at T ) 530 °C is shown in Figure 1. Similar spectral evolution is also observed for samples annealed at 470 °C. The broad powder pattern and the narrow Gaussian line shape in these spectra can be readily assigned to BO3 and BO4 species, respectively (Figure 1).11 Direct simulation of these spectra is difficult due to the heterogeneous broadening of the BO3 line shape. Instead, these spectra are all normalized to the highest intensity of the BO3 line shape, and consequently, the relative intensity of the BO4 peak maximum was used as a relative
Figure 1. 11B MAS NMR spectra of the borosilicate glass with initial Tf ) 585 °C, as a function of annealing time at 530 °C. Spectra, in the order of increasing intensity of the BO4 peak, correspond to annealing times of 0, 1, 4, and 6 h, respectively.
Figure 2. Evolution of the normalized intensity of the BO4 peak (also a relative measure of the BO4/BO3 ratio) in the 11B MAS NMR spectra of the borosilicate glass with initial Tf ) 585 °C, as a function of annealing time at 530 °C (open squares) and at 470 °C (open circles). The solid line represents the nonlinear least-squares fit of eq 1 to the 530 °C relaxation data. The dashed line is a straight-line fit to the 470 °C relaxation data. The inset shows the behavior of the 530 °C annealing curve at short times.
measure of the BO4/BO3 ratio for each spectrum. It may be noted here that such an approach is strictly valid only when the 11B NMR line shapes and widths corresponding to the BO and 3 BO4 species are independent of the thermal history of the glass, as observed in the present study. Moreover, the applicability of this approach to the spectral data analysis has been confirmed in a recent study on a simple sodium borosilicate glass where an independent measure of the BO4/BO3 ratio is available from direct NMR line shape simulation.30 The variation of the BO4/ BO3 ratio as a function of annealing time at 530 and 470 °C is shown in Figure 2. It is clear from Figure 2 that the BO4/BO3 ratio in the glass structure increases on annealing at a temperature lower than the initial Tf ) 585 °C. The BO4/BO3 ratio reaches its new equilibrium value at 530 °C within a few hours, while it monotonically increases at 470 °C for annealing times of at least up to 120 h indicating only partial equilibration in the latter case due to extremely long relaxation time scale. The kinetics of relaxation of the BO4/BO3 ratio as a function of time
9760 J. Phys. Chem. B, Vol. 111, No. 33, 2007
Uzun and Sen increases with time. The increasing trend continues until the BO4/BO3 ratio reaches the equilibrium value at 530 °C (Figure 3). 4. Discussion
Figure 3. Evolution of the normalized intensity of the BO4 peak (also a relative measure of the BO4/BO3 ratio) in the 11B MAS NMR spectra of the borosilicate glass, as a function of annealing time at 530 °C. The glass samples were annealed at 585 °C for 1 h and subsequently at 470 °C for 100 h prior to the temperature jump to 530 °C. The solid horizontal line represents the equilibrium value of the BO4 peak intensity at 530 °C.
t at 530 °C can be fitted well with a simple exponential functional form:
Pe - P t ) exp - [(t/τ)] Pe - P0
(1)
In this equation τ represents the relaxation time for the BO4/ BO3 ratio P and the subscripts 0, t, and e represent the values of P at t ) 0, at any time t, and the final value at equilibrium, respectively. Nonlinear least-squares fitting of eq 1 yields τ ) 1.1 ( 0.1 h for borate species relaxation at 530 °C (Figure 2). The average shear relaxation time τshear for this borosilicate glass at 530 °C can be calculated from the corresponding shear viscosity η at this temperature (1013.5 Pa‚s), available in the literature31 using the Maxwell relation:
τshear ) η/G∞
(2)
where G∞ represents the infinite frequency shear modulus of the liquid which is nearly independent of temperature and can be treated as a constant ∼(2-3) × 1010 Pa, for a wide variety of glass-formers.32 This calculation yields τshear in the range of 0.30-0.45 h. This value is in agreement with the borate speciation relaxation time scale of ∼1.1 h at 530 °C, especially when one considers the fact that τshear is close to the stress relaxation time and is often faster than the structural relaxation time by at least a factor of 3. On the other hand, analysis of previously published relaxation data τd for the refractive index and therefore for the density of this glass under identical annealing conditions shows a simple exponential relaxation process with a relaxation time τd ∼ 1.2 ( 0.1 h, again in excellent agreement with the borate speciation relaxation time scale.29 Finally, the evolution of the BO4/BO3 ratio of the borosilicate glass samples with initial Tf ) 585 °C that were annealed subsequently at 470 °C for 100 h followed by annealing at 530 °C for various periods of time is shown in Figure 3. The relative BO4/BO3 ratio initially decreases below the equilibrium value at 530 °C, and the decreasing trend continues until t ) 1 h, i.e., annealing at 530 °C for 1 h (Figure 3). This trend reverses at longer annealing times, and the BO4/BO3 ratio
4.1. Annealing Experiments at 530 and 470 °C. The observed increase in the BO4/BO3 ratios of the borosilicate glass on lowering of the Tf from 585 to 530 or 470 °C is consistent with previous reports of the Tf dependence of the well-known speciation reaction BO4 ) BO3 + NBO in borate and borosilicate glasses.12 For annealing at 530 °C a rapid rise to a lower equilibrium BO4/BO3 ratio is observed. On the other hand a slower rise is seen for heat treatment at 470 °C, and equilibrium is not achieved within the experimental time scale (Figure 2). These results agree well with the refractive index relaxation results previously reported.29 More interestingly, the strong similarity between the time scales of the relaxation kinetics of viscosity, index/density, and borate speciation near Tg clearly indicates a cause-and-effect relationship and a close mechanistic connection between changes in short-range atomic structure and macroscopic physical properties. Such one-to-one correspondence between the short-range coordination environment of B atoms in a complex borosilicate glass with relatively low concentration of B (11 wt % B2O3) and its global properties such as density and viscosity is remarkable. Considering the close connection between configurational entropy and viscous flow in a glass-forming liquid, the present results imply that a significant fraction of the temperature-dependent configurational changes near Tg in borosilicate glasses are controlled by the borate speciation.30,33 4.2. Crossover Experiment and Memory Effect. Annealing the borosilicate glass at 470 °C for 100 h results in a BO4/BO3 ratio that is slightly higher than the equilibrium value at 530 °C (Figures 2 and 3). Therefore, upon subsequent annealing of this glass at 530 °C it may be expected that the BO4/BO3 ratio would decrease monotonically and approach the equilibrium value at this temperature. Instead, the BO4/BO3 ratio in the glass structure decreases to a value that is significantly lower than the equilibrium value at 530 °C followed by a reversal of the trend and increases back toward the equilibrium value (Figure 3). Similar behavior, commonly known as “memory effect”, has previously been observed in crossover experiments in the case of relaxation of macroscopic properties such as refractive index and density in glasses. Macedo and Napolitano and later Narayanaswamy have postulated the presence of two or more relaxation times to explain the origin of the memory effect.34,35 Multiple relaxation times would result in nonexponential relaxation, which at first may seem to be in contradiction with our observation of a single-exponential relaxation of the borate speciation process at 530 °C. However, it may be noted that the same relaxation process may become nonexponential at lower temperatures near 470 °C where the memory effect is observed in this study. The presence of multiple relaxation times has been associated in previous studies with the presence of density and/or compositional fluctuations in the glass structure with regions of different densities and/or compositions being characterized by different relaxation times.36,37 It is possible that such regions are also characterized by different borate speciation relaxation times that can explain the observation of a memory effect associated with the relaxation of the BO4/BO3 ratio. In this model samples partially equilibrated at 470 °C will contain regions with fast relaxation that are characterized by high BO4/ BO3 ratio and regions with slow relaxation that are characterized by low BO4/BO3 ratio, compared to that characteristic of the
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equilibrium value at 530 °C. Following the temperature jump from 470 to 530 °C the ensemble-averaged BO4/BO3 ratio initially decreases as the fast-relaxing regions try to reach equilibrium by lowering their BO4/BO3 ratio while the equilibration of slow-relaxing regions dominate at longer times and the average BO4/BO3 ratio increases. Moreover, this model of the memory effect also implies that once the glass reaches equilibrium such strong dynamical and structural heterogeneities cease to exist resulting in monotonic variation in structure and properties between equilibrium states. The structural relaxation scenario discussed above has interesting implications in understanding the origin of the memory effect within the framework of the PEL model of glassy dynamics.18 The equilibrium inherent structures in this landscape, explored by a glass-forming liquid such as the one studied here, are characterized by a narrow range of BO4/BO3 ratios corresponding to thermodynamic fluctuations. The ensembleaveraged value of this structural parameter in equilibrium is characteristic of the temperature of the system, and it decreases with temperature. Below glass transition this equilibrium temperature simply corresponds to the fictive temperature of the glass. However, this “single fictive temperature” concept cannot explain the aging dynamics when the glass is out of equilibrium immediately following a temperature jump.18 For example, it is clear from Figure 3 that following the temperature jump from 470 to 530 °C the BO4/BO3 ratio initially decreases and intersects the relaxation curve for 530 °C at which point the glass has the appropriate BO4/BO3 ratio to be in equilibrium at 530 °C. However, the glass structure seeks other configurations with lower BO4/BO3 ratios before coming back to the equilibrium. Therefore, in spite of having identical ensembleaveraged short-range structure in terms of borate speciation, the structural fluctuations of the glass at the intersection point following the temperature jump from 470 to 530 °C must be different from that of the equilibrium structure at 530 °C. The same must also be true for pairs of glass structures with identical BO4/BO3 ratio that are formed on either side of the minimum on the memory curve (Figure 3). These results directly demonstrate that a plethora of different structural configurations with identical ensemble-averaged short-range order can be explored by the glass during the aging dynamics.18 The memory effect can then be explained within the framework of the PEL if one assumes the following scenario. The inherent structures explored by the system under equilibrium vary over a narrow range. However, during aging following a downward/upward temperature jump from equilibrium the system explores a significantly wide range of structures in the PEL before reaching equilibrium and at various points during aging the ensembleaveraged structure may be identical. In this scenario the memory effect is expected to be more pronounced in fragile liquids than in strong liquids since the former are expected to have a larger number of minima in the PEL compared to that in the case of strong liquids.18-22 This hypothesis is corroborated by the recent observation that vitreous SiO2, which is one of the strongest glass-forming liquids, does not display any detectable memory effect in relaxation, whereas such effect has been observed in fragile vitreous B2O3.37,38 5. Conclusions Kinetics of the relaxation of boron coordination environments in a borosilicate glass following temperature jumps below Tg has been studied by 11B MAS NMR spectroscopy. The structural changes as a function of annealing time are monitored and correlated with the relaxation of macroscopic properties such
J. Phys. Chem. B, Vol. 111, No. 33, 2007 9761 as refractive index and viscosity. The results indicate that the short-range structural unit has a one-to-one correspondence with refractive index and viscosity relaxation. The borate speciation relaxation displays a memory effect in crossover experiments indicating that structures with identical ensemble-averaged shortrange order can be produced by suitably altering the timetemperature history of the glass during aging. The memory effect can be qualitatively explained by considering that the glass/ liquid structure explores a significantly wider range of regions in the PEL during aging compared to those explored under equilibrium conditions. Acknowledgment. This work was supported by the National Science Foundation under Grant No. DMR-0603933. References and Notes (1) Cable, M., Parker, J. M., Eds. High-Performance Glasses; Chapman & Hall: New York, 1992. (2) Rawson, H. Glasses and Their Applications; Royal Institute of Metals: London, 1991. (3) Scherer, G. W. Relaxation in Glass and Composites; WileyInterscience: New York, 1986. (4) Richert, R., Blumen, A., Eds. Disorder Effects on Relaxational Processes; Springer-Verlag: Berlin, 1994. (5) Debenedetti, P. G. Metastable Liquids; Princeton University Press: Princeton, NJ, 1996. (6) Donth, E. The Glass Transition, Relaxation Dynamics in Liquids and Disordered Materials; Springer-Verlag: Berlin, 2001. (7) Farnan, I.; Stebbins, J. F. Science 1994, 265, 1206. (8) Stebbins, J. F.; Sen, S. In The Second International Conference on Borate Glasses, Crystals and Melts; Wright, A. C., Feller, S. A., Hannon, A. C., Eds.; Society of Glass Technology: Sheffield, U.K., 1997. (9) Stebbins, J. F.; Sen, S. J. Non-Cryst. Solids 1998, 224, 80. (10) Hassan, A. K.; Torell, L. M.; Borjesson, L.; Doweider, H. Phys. ReV. B 1992, 45, 12797. (11) Sen, S. J. Non-Cryst. Solids 1999, 253, 84. (12) Gupta, P. K.; Lui, M. L.; Bray, P. J. J. Am. Ceram. Soc. 1985, 68, C-82. (13) Sen, S.; Youngman, R. E. Phys. ReV. B 2002, 66, 134209. (14) Stebbins, J. F. Nature 1991, 351, 638. (15) Geissberger, A. E.; Galeener, F. L. Phys. ReV. B 1983, 28, 3266. (16) Kiczenski, T. J.; Du, L.-S.; Stebbins, J. F. J. Non-Cryst. Solids 2005, 351, 3571. (17) Maje´rus, O.; Cormier, L.; Calas, G.; Beuneu, B. Phys. ReV. B 2003, 67, 024210. (18) Sciortino, F. J. Stat. Mech. 2005, P05015. (19) Goldstein, M. J. Chem. Phys. 1969, 51, 3728. (20) Stillinger, F. S.; Weber, T. Science 1984, 225, 983. (21) Angell, C. A. Nature 1998, 393, 521. (22) Wales, D. J. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science: Cambridge, 2004. (23) Buisson, L.; Bellon, L.; Ciliberto, S. J. Phys.: Condens. Matter 2003, 15, S1163. (24) Cipelletti, L.; Bissig, H.; Trappe, V.; Ballesta, P.; Mazoyer, S. J. Phys.: Condens. Matter 2003, 15, S257. (25) Vidal Russell, E.; Israeloff, N. E. Nature 2000, 408, 695. (26) Ritland, H. N. J. Am. Ceram. Soc. 1955, 38, 86. (27) Ritland, H. N. J. Am. Ceram. Soc. 1956, 39, 403. (28) Ritland, H. N. J. Am. Ceram. Soc. 1954, 37, 370. (29) Spinner, S.; Napolitano, A. J. Res. Natl. Bur. Stand. (U.S.) 1966, A70, 147. (30) Sen, S.; Topping, T.; Yu, P.; Youngman, R. E. Phys. ReV. B 2007, 75, 094203. (31) Corning Glass Works. Properties of Corning’s Glass and Glass Ceramics Families; Corning, NY, 1979. (32) Brawer, S. Relaxation in Viscous Liquids and Glasses; American Ceramic Society: Columbus, OH, 1985. (33) Adam, G.; Gibbs, J. H. J. Chem. Phys. 1965, 43, 139. (34) Macedo, P. B.; Napolitano, A. J. Res. Natl. Bur. Stand. (U.S.) 1967, A71, 231. (35) Narayanaswamy, O. S. J. Am. Ceram. Soc. 1971, 54, 491. (36) Moynihan, C. T.; Schroeder, J. J. Non-Cryst. Solids 1993, 160, 52. (37) Koike, A.; Ryu, S.-R.; Tomozawa, M. J. Non-Cryst. Solids 2005, 351, 3797. (38) Chen, H. S.; Kurkjian, C. R. J. Am. Ceram. Soc. 1983, 66, 613.
