Hierarchical Dynamics of As2P2S8 Quasi-Molecular Units in a

Jun 1, 2009 - On the other hand, over the entire temperature range, the 31P NMR spin−lattice relaxation results from fast cage-rattling dynamics of ...
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Hierarchical Dynamics of As2P2S8 Quasi-Molecular Units in a Supercooled Liquid in the As-P-S System: A 31P NMR Spectroscopic Study E. L. Gjersing and S. Sen* Department of Chemical Engineering and Materials Science, UniVersity of California DaVis, DaVis, California 95616

H. Maekawa Department of Metallurgy, Graduate School of Engineering, Tohoku UniVersity, Sendai 980-8579 Japan

B. G. Aitken Glass Research DiVision, Corning Incorporated, Corning, New York 14831 ReceiVed: February 15, 2009; ReVised Manuscript ReceiVed: May 4, 2009

The dynamics of As2P2S8 quasi-molecular units caged in an As-S network in the supercooled chalcogenide liquid of composition (As2S3)90(P2S5)10 have been studied near the glass transition region (Tg ) 468 e T e 628 K) using 31P NMR line shape analysis and spin-lattice relaxation techniques. 31P NMR line shape analysis indicates the presence of isotropic rotational reorientation of As2P2S8 quasi-molecular units at frequencies on the order of tens of kilohertz at T < 540 K. At higher temperatures, the time scale of intramolecular bondbreaking and rearrangement is coupled to that of shear/structural relaxation of the surrounding network. On the other hand, over the entire temperature range, the 31P NMR spin-lattice relaxation results from fast cage-rattling dynamics of the same molecules at frequencies in the megahertz to gigahertz range. When taken together, these results imply the presence of serial hierarchical dynamics in which the fast rattling of As2P2S8 quasi-molecular units trapped in their cages coexists with slower isotropic rotational reorientation. The shear or R-relaxation involves cooperative rearrangement of the surrounding As-S network and, consequently, relaxation of the cages that provides feedback to the fast rattling dynamics over the entire temperature range. Introduction The chalcogenides have proven to be an interesting and diverse class of inorganic glass formers, displaying a rich array of structures and dynamics distinct from their oxide counterparts. Although the oxide glasses are generally known to form chemically ordered continuous random networks, chalcogenides show extensive violation of chemical order and have the ability to form both network and molecular structures.1 For instance, glasses in the binary P-Se system and pseudobinary Ge-doped As-S system can be predominantly molecular in nature, with the structure being dominated by P4Se3 and As4S3 molecules, respectively.2–4 On the other hand, stoichiometric glasses in Ge-As-X (X ) S, Se, Te) systems are characterized by a corner-shared network of GeX4 tetrahedra and AsX3 pyramids.5–10 Between these two extremes, structures in which molecules and networks coexist can be found. Examples of such structures are seen in a binary AsxS1-x system in which AsS3/2 pyramidal units cross-link to form a networked structure near stoichiometry and excess arsenic in S-deficient glasses is incorporated as As4S4 molecules embedded in the As-S network.11 Conversely, some of the excess sulfur in very S-rich glasses is present as molecular S8 rings that are similarly contained within the network of corner-shared AsS3/2 pyramids.12 The atomic-scale dynamical processes associated with structural relaxation in the glass transition range in supercooled chalcogenide liquids are also distinct from those encountered in oxide liquids. For example, previous high-temperature nuclear * Corresponding author.

magnetic resonance (NMR) spectroscopic studies have indicated that structural relaxation and viscous flow in oxide liquids near the glass transition are controlled by the breaking and reforming of the bonds between network-forming Si, B, Al, and O atoms.1,13–15 The nature of the corresponding dynamical processes in chalcogenide liquids is not clear. The most widely studied chalcogenide liquids in this regard belong to the P-Se system in which the temperature dependence of the 31P and 77Se NMR line shapes has indicated that the glass transition is associated with P-Se bond breaking and chemical exchange between P4Se3 molecular units and the network.16,17 On the other hand, our recent high-temperature 31P NMR spectroscopic studies of a Ge- and P-doped arsenic sulfide glass of composition Ge3P1.3As50.7S45 have shown that the constituent PAs3S3 and As4S3 molecules in this glass undergo rapid isotropic tumbling motion, even at temperatures well below the glass transition temperature Tg, where the extrapolated structural relaxation time would nearly diverge.18 The results of that study have indicated that the translationally frozen PAs3S3 and As4S3 molecules in the glassy state are performing rotational dynamics, much like what is observed in plastic crystals. These unusual and remarkable results have prompted us to investigate the rotational dynamics of moleculelike entities and their relation to glass transition in other chalcogenide liquids where the structure is dominated by a network in which the molecules are embedded, such as those encountered in (As2S3)x(P2S5)1-x glasses. Previous NMR and Raman spectroscopic studies have conclusively shown that glasses in this system with x > 60 incorporate nearly all the

10.1021/jp901388j CCC: $40.75  2009 American Chemical Society Published on Web 06/01/2009

Dynamics of As2P2S8 Quasi-Molecular Units

J. Phys. Chem. B, Vol. 113, No. 25, 2009 8515 pulse (3 µs) and a recycle delay of 5 × T1 over a temperature range of ambient to up to 568 K. Approximately 300 scans were averaged to obtain the room temperature spectrum, and the hightemperature spectra were acquired through averaging of 64 scans. All 31P NMR spectra were externally referenced to an aqueous solution of 85% H3PO4. Results

Figure 1. Schematic representation of the local structure of (As2S3)90(P2S5)10 glass in which the As2P2S8 quasi-molecular unit, enclosed by the dashed curve, is embedded in a network defined by corner-shared AsS3 pyramids.

phosphorus atoms as As2P2S8 quasi-molecular units that are networked into the As-S matrix, as depicted in Figure 1.19–21 Here, we report high-temperature 31P NMR results of the dynamics of As2P2S8 quasi-molecular units in a supercooled liquid of composition (As2S3)90(P2S5)10 near its glass transition. This liquid has Tg ∼ 468 K and is very resistant to crystallization and stable under ambient conditions.19,20 The existence of a small concentration of As2P2S8 quasi-molecular units bonded to an As-S network in the structure of this glass provides an interesting opportunity to exploit these molecular units as probes of the glass transition dynamics using 31P NMR spectroscopy. 31 P static NMR line shapes and spin-lattice relaxation times, T1, near and above Tg have been analyzed to obtain the correlation times of the associated dynamical processes that control these NMR parameters. Finally, a mechanistic connection between these dynamical processes and primary (R) or shear relaxation and glass transition is established. Experimental Section The (As2S3)90(P2S5)10 glass was synthesized in an evacuated fused-silica ampule using a mixture of g99.9995% purity (metal basis) constituent elements. The mixture was then melted at 923 K for 24 h in a rocking furnace and quenched in cold water to produce the glass. Tg was determined by differential scanning calorimetry using a heating rate of 10 K/min and found to be ∼468 K. The viscosity in the 104-108 Pa s range was determined by the parallel plate technique. The Tg and viscosity data were found to be in excellent agreement with those published in the literature for this composition.19,20,22 Ambient temperature 31P static and magic-angle-spinning (MAS) NMR spectra were collected at a magnetic field strength of 11.7 T with a Bruker Avance 500 solid-state NMR spectrometer operating at 31P resonance frequency of 202.5 MHz. Crushed glass samples were loaded into ZrO2 rotors and placed in a 4 mm Bruker CPMAS probe. The MAS spectra were collected at spinning speeds of 8 kHz and 15 kHz with a 60° rf pulse (1.2 µs) and a recycle delay of 15 s. Approximately 450 free induction decays were averaged and Fourier-transformed to obtain each MAS spectrum. The corresponding static spectrum was collected in the same probe with a Hahn echo pulse sequence using a 90° pulse of 1.8 µs (180° pulse ) 3.6 µs) and recycle delay of 15 s; 5450 scans were averaged. Variable temperature NMR experiments were carried out at 7.0 T (31P resonance frequency of 121.54 MHz) on a Chemagnetics Infinity console. The crushed glass was placed in a vacuum-sealed quartz tube to prevent reaction with ambient oxygen. A home-built, static, high-temperature NMR probe was used to measure spin-lattice relaxation (SLR) times, T1, over a temperature range of ambient to up to 628 K using an inversion recovery pulse sequence. The variable temperature 31P NMR spectra were collected under static conditions with a single 90°

The ambient temperature 31P static and MAS NMR spectra of the (As2S3)90(P2S5)10 glass obtained at 11.7 T are shown in Figure 2. These spectra can be simulated well with a single phosphorus site with nonaxial chemical shift anisotropy. These simulations yield the following principal components of the chemical shift tensor: δ11 ) 142 ppm, δ22 ) 111 ppm, and δ33 ) -28 ppm, resulting in an isotropic chemical shift δiso of ∼75 ppm, along with a chemical shift anisotropy CSA ) -103 ppm and an asymmetry parameter ηCSA ) 0.3 (Figure 2). These 31P NMR parameters are consistent with the 31P NMR results obtained at 9.4 T in a previous study on a glass sample with the same nominal composition.19 The ambient and high-temperature 31P static NMR spectra collected at 7.0 T are shown in Figure 3. At this magnetic field strength, the room-temperature 31P spectrum can be simulated well with the same principal components of the chemical shift tensor as those obtained at 11.7 T (Vide supra). The 31P static NMR line shape remains practically unchanged upon increasing the temperature to up to 498 K. Further increase in the temperature results in rapid motional narrowing of the 31P static NMR line shape into a symmetric Lorentzian centered at the δiso of ∼76 ppm at T ) 548 K via dynamical averaging of the chemical shift anisotropy. The width of this Lorentzian peak continues to decrease with increasing temperature at least up to T ) 568 K, beyond which it remains unchanged with further increase in temperature up to 628 K. These temperature-induced dynamical changes of the 31P NMR line shape are found to be completely reversible upon cooling, and no crystallization effects were ever observed in the NMR spectra. The 31P NMR spectral line shapes in Figure 3 have been simulated over the temperature range of 518 e T e 568 K using a model of isotropic reorientation or tumbling of the 31P chemical shift tensor, resulting in an “exchange” among N different orientations under the rigid molecule (T e 498 K) powder pattern. The analytic expression for the resulting line shape is given by the real part of g(ω), where g(ω) ) L/N[1 -(L/τNMR)] and L ) ∑j)1,N[i(ω - ωj) + 1/T2j + N/τNMR]-1, ωj is the frequency and T2j is the reciprocal of the intrinsic line width corresponding to the orientation j, and 1/τNMR is the frequency of the reorientational exchange or tumbling frequency of the 31P chemical shift tensor. In this analysis, the frequencies ωj corresponding to 400 orientations (N) were generated by taking that many angular steps through the expression for the rigid-molecule CSA powder pattern.23 The value of T2j has been kept constant at 0.2 ms for all orientations in all of the simulations. A single average temperature-dependent tumbling frequency τNMR-1 is found to be sufficient for simulation of all spectra (Figure 3). It may be noted that the 31P NMR line shape analysis performed here completely ignores any contribution from the homonuclear 31P-31P dipolar coupling. Although this does not present a problem at low temperatures where the line shape is controlled by CSA interaction, the effect of dipolar coupling on the line shape may become more important at higher temperatures. However, recent 31P NMR spin-echo measurements of 31P second-moment M2 in As2S3-P2S5 glasses have shown that for (As2S3)90(P2S5)10 glass as well as for As2P2S8

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Figure 2. Experimental (left) and simulated (right) 31P static (top) and MAS (middle and bottom) NMR spectra collected at 11.7 T. The MAS spectra were collected at sample spinning speeds of 8 kHz (middle) and 15 kHz (bottom).

Figure 3. Experimental 31P static NMR spectra of (As2S3)90(P2S5)10 glass and supercooled liquid at temperatures indicated (left) and corresponding simulated spectra (right). The frequencies of isotropic rotational reorientation used to simulate these spectra are given alongside each spectrum. See text for details of the simulation procedure.

The variation of 31P T1 in the temperature range of 298 e T e 628 K is shown in Figure 4. T1 remains nearly unchanged with increasing temperature up to T ∼ Tg (468 K), beyond which it sharply drops with further increase in temperature to up to 628 K. This result indicates the onset of some dynamic process that takes control of 31P spin-lattice relaxation at temperatures above Tg. The slope of the temperature dependence of ln T1 yields an activation energy of ∼111 kJ mol-1 in the temperature range Tg (468 K) e T e 530 K (Figure 4). At T > 530 K, the activation energy changes somewhat discontinuously to ∼132 kJ mol-1 and then decreases continuously in a non-Arrhenius fashion to ∼65 kJ mol-1 at the highest temperatures (Figure 4). Figure 4. Temperature dependence of the 31P spin-lattice relaxation time, T1. Dotted lines are guides to the eye showing a crossover from an Arrhenius temperature dependence in the temperature range Tg e T e 530 K to a non-Arrhenius temperature dependence at T > 530 K.

quasi-molecular units, M2 is on the order of ∼(1.0-1.5) × 106 rad2 s-2 corresponding to a maximum dipolar line width of ∼0.5 kHz. This dipolar contribution to 31P NMR line width is substantially smaller than the intrinsic line width (1/πT2j) of ∼1.6 kHz chosen for the line shape analyses. Therefore, any effect of P-P dipolar interaction on the τNMR-1 values derived from the 31P NMR line shape analyses can be safely neglected.

Discussion The nonaxial symmetry of the 31P NMR line shape and the lack of any significant temperature dependence of this line shape over the range of 298 e T e 498 K imply the absence of (i) any rapid rotation of the As2P2S8 quasi-molecular units about any single axis and (ii) any isotropic reorientation of these units at rates faster than a few kilohertz (Figures 2, 3). 31P NMR line shapes in the temperature range of 518 e T e 568 K indicate rapid isotropic reorientational averaging of the 31P CSA for the two P atoms in the As2P2S8 unit in the (As2S3)90(P2S5)10 supercooled liquid at rates that increase from several kilohertz

Dynamics of As2P2S8 Quasi-Molecular Units

J. Phys. Chem. B, Vol. 113, No. 25, 2009 8517 that the dynamical process responsible for 31P spin-lattice relaxation (SLR) at these temperatures is strongly coupled to the glass transition (Figure 4). The temperature dependence of the 31P T1 data above Tg needs to be modeled to obtain correlation times for the dynamical process responsible for 31P SLR in the (As2S3)90(P2S5)10 supercooled liquid. For the spin-1/2 31P nucleus, the two possible mechanisms of SLR involve the fluctuation of dipole-dipole (DD) or CSA interactions such that 1/T1 ) 1/T1,DD + 1/T1,CSA. The 1/T1,DD and 1/T1,CSA can be calculated using the following relations:28

1/T1,DD ) 0.3(µ0 /4π)2γ4p2(1/r6)[(τDD /(1 + ω2τDD2)) + (4τDD /(1 + 4ω2τDD2))] (1) Figure 5. Comparison between the temperature dependences of τshear (solid line) calculated from viscosity data using the Maxwell relation, τNMR (b) obtained from 31P NMR line shape simulations and τCSA (() calculated from 31P T1 data. Open circles and triangles represent τshear obtained from viscosity data of Tver’yanovich and Somov22 and from viscosities determined in this study, respectively. Solid line is a fit using Tamman-Vogel-Fulcher expression: Log τshear ) -14.9 + 2073/(T - 339). Dotted lines indicate Arrhenius behavior of τNMR and τCSA with similar activation energies at T < 540 K.

to a few megahertz with increasing temperature (Figure 3). The corresponding dynamical process may involve either an isotropic tumbling of the entire As2P2S8 unit (Figure 1) or intramolecular P-S and As-S bond-breaking and rearrangement, resulting in a local averaging of the CSA at the 31P nuclides. The time scale τNMR for this process is compared with the shear or R-relaxation time scale, τshear, of the supercooled liquid in Figure 5. The τshear values are obtained from viscosity data using the Maxwell relation: τshear ) η/G∞ where η is the shear viscosity and G∞ is the infinite frequency shear modulus, taken to be a temperatureindependent constant with a value of ∼3 × 1010 Pa, typical of a wide variety of glass-forming liquids near Tg.24 It is clear from Figure 5 that at T g 540 K (Tg + 70 K), τNMR and τshear are in good agreement, implying a strong coupling between the structural rearrangement of the As-S network and the averaging of the 31P CSA, presumably via As-S and P-S bond-breaking and rearrangement within the As2P2S8 units with a corresponding activation energy of ∼240 kJ mol-1. This dynamical scenario, in which the As2P2S8 units are continuously formed and annihilated at the shear/structural relaxation time scale, is somewhat intuitively expected. More interestingly, at temperatures below ∼540 K, the τNMR sharply decouples from τshear with a lower activation energy of ∼130 kJ mol-1 (Figure 5). This decoupling between τNMR and τshear is in sharp contrast with the results obtained in previous studies on purely molecular organic glass-forming liquids, where the rotational diffusion time scales of the molecules remain strongly coupled to τshear near the glass transition region.25–27 Therefore, close to the glass transition, the dynamics responsible for the averaging of the 31P CSA remain significantly faster than the structural relaxation of the As-S matrix, with the latter being the rate-controlling factor for shear or R-relaxation. Therefore, the observed decoupling of τNMR from τshear strongly suggests that at T < 540 K, the isotropic averaging of the 31P CSA must result from rotational reorientation of the As2P2S8 units via a low-energy pathway that may involve local bondbreaking without global structural relaxation. The sharp change in the temperature dependence of the 31P T1 across Tg and its rapidly decreasing value at T > Tg indicate

1/T1,CSA ) (1/15)γ2B02(∆σ)2[2τCSA /(1 + ω2τCSA2)]

(2) where µ0 is the magnetic constant (4π × 10-7N/A2), γ is the gyromagnetic ratio (10.829 × 107rad/T s for the 31P nucleus), p is the reduced Planck’s constant (1.054 × 10-34 J s), r is the average intramolecular distance between the P-P pair in As2P2S8 units (3.79 Å)19, ω is the resonant frequency (121.5 MHz for 31P at 7.0 T), B0 is the magnetic field strength (7.05 T), ∆σ is the CSA (-103 ppm), and τDD and τCSA are the correlation times for dipole-dipole and CSA fluctuations, respectively. It is to be noted that calculations using eq 1 were made assuming that the only significant dipolar coupling for 31 P nuclides is associated with the intramolecular P-P pair in As2P2S8 units. A recent study of the 31P-31P dipolar coupling in this glass has shown this to be a completely valid assumption.19 Moreover, the following observations lend strong support to the validity of these assumptions: (a) 31P-33S dipolar coupling is negligible due to the low γ and extremely low natural abundance (0.76%) of the 33S nuclides, (b) 31P-75As dipolar coupling within the As2P2S8 units is weaker than 31P-31P dipolar coupling by more than a factor of 5 in its contribution to SLR due to the lower γ of the 75As nucleus and (c) intermolecular 31 P-31P dipolar coupling is also negligible, since the low P concentration in the glass is expected to result in a large average separation of ∼15 Å between intermolecular 31P-31P pairs. Equations 1 and 2 were iteratively solved to calculate τDD and τCSA from the experimentally measured T1 values at each temperature. These calculations indicate that the fluctuation of the DD interaction is at least an order of magnitude less efficient than that of the CSA interaction in causing the 31P SLR and, hence, 1/T1 ≈ 1/T1,CSA. The correlation time, τCSA, of the dynamical process that gives rise to CSA fluctuation and 31P spin-lattice relaxation in the temperature range Tg (468 K) e T e 628 K is compared in Figure 5 with τshear and τNMR. The τCSA decreases monotonically from ∼10-7 s at Tg to ∼ 10-10 s at 628 K and shows strong decoupling from both τshear and τNMR over the entire temperature range. The temperature dependence of τCSA is nearly Arrhenius for temperatures below ∼530 K, but it is non-Arrhenius at higher temperatures, similar to the behavior shown by τNMR, as discussed above. The relatively fast time scale of τCSA possibly corresponds to a highly restricted rattling motion of the As2P2S8 units over the entire temperature range. It is worth noting here that our preliminary in situ Raman spectroscopic studies of this glass and the corresponding supercooled liquid (to be published elsewhere) show the presence of a sharp band at 418 cm-1 corresponding to the characteristic breathing mode of the quasi-molecular As2P2S8

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Gjersing et al. step for the cooperative R-relaxation.34,35 Within the framework of this model, the time scale of J-G β-process (τβ) is expected to scale with the R-relaxation time scale (τR) in the region of decoupling as a power law: τR ∼ (τβ)1/(1-n). In this expression, (1 - n) ) β is the Kohlrausch-Williams-Watts exponent of the time dependence of the R-relaxation function: φ(t) ) exp[-(t/τR)β] that can be obtained independently from dielectric relaxation experiments.34,35 If one approximates τshear ) τR, then, indeed, the variation of τCSA over several orders of magnitude shows a power-law scaling given by τshear ∼ (τCSA)3.2 that yields β ∼ 0.3 for the (As2S3)90(P2S5)10 supercooled liquid (Figure 6). It should be noted in this regard that recent NMR studies have indicated that the J-G β-processes in organic molecular glasses do involve highly restricted reorientation of the molecules that could be similar to the cage-rattling dynamics of the As2P2S8 quasi-molecular units observed here.36

Figure 6. Log-log plot demonstrating the power-law scaling between τshear and τCSA. Dashed line with a slope of 3.2 is the linear least-squares best fit to the data. 21

units at temperatures of up to 600 K . This observation asserts that the As2P2S8 units do persist in the structure of the (As2S3)90(P2S5)10 supercooled liquid. It is well-known that molecules trapped in cages perform rattling motion in polymers and glasses near the glass transition region.29–31 The relaxation of these cages above Tg would result in a sharp change in the temperature dependence of these rattling dynamics and, hence, that of τCSA across Tg. The non-Arrhenius temperature dependence of τCSA at T > 530 K suggests a possible coupling between τCSA and τshear. Such a coupling is also intuitively expected, since the correlation time for the rattling dynamics is likely to be controlled by the temperature dependence of the time scale of the cage relaxation process, which would be identical to τshear. On the other hand, the Arrhenius temperature dependence of τCSA in the temperature range Tg e T e 530 K with an activation energy (∼111 kJ mol-1) similar to that of τNMR (∼130 kJ mol-1) may suggest a mechanistic connection between the slow tumbling and fast rattling dynamics of the quasi-molecular As2P2S8 units. When taken together, these results provide a picture of hierarchical dynamics of As2P2S8 quasi-molecular units in the supercooled (As2S3)90(P2S5)10 liquid associated with its glass transition. In this scenario, the regions of As-S network surrounding the As2P2S8 units act as cages. The As2P2S8 units, being trapped in their cages, perform fast (megahertz to gigahertz) rattling dynamics, and at T < 540 K, undergo slow (tens of kilohertz) isotropic tumbling. This latter dynamical process then corresponds to the intermittent escape of the As2P2S8 units from their cages. The R-relaxation occurs primarily via cooperative rearrangement of the surrounding As-S network and results in relaxation of the cages. The cage relaxation consequently affects the fast rattling dynamics of the molecules at T > Tg, thus providing a mechanistic and hierarchical connection between the slow and fast dynamical processes observed in this study. Finally, the suggested connection between τCSA and τShear, despite the large differences between these two time scales, is reminiscent of the coupling between the slow R-relaxation and the fast Johari-Goldstein (J-G) β-relaxation processes in glass-formers.32,33 Detailed studies on a wide variety of glassforming liquids have shown that, despite its temporal decoupling from the primary relaxation process, the J-G β-process can still be mechanistically related to the glass transition. In the coupling model scenario of Ngai and co-workers, the J-G β-process has been suggested to be the fundamental precursor

Conclusion In conclusion, the variable temperature 31P NMR spectra and line shape simulations combined with T1 relaxation time measurements imply the coexistence of at least two different dynamical processes associated with the As2P2S8 quasi-molecular units in the (As2S3)90(P2S5)10 supercooled liquid near Tg over the temperature range Tg (468 K) e T e 540 K. One such process is the random isotropic tumbling of the As2P2S8 units that control the 31P NMR line shapes. The characteristic time scale τNMR for this process decouples from τshear in an Arrhenius fashion at T < 540 K. On the other hand, the time scales τCSA calculated on the basis of the T1 measurements indicate the existence of a fast dynamical process that can be attributed to the rattling of the As2P2S8 units within cages formed by the surrounding As-S network. The isotropic tumbling of these units then represents occasional escapes of the As2P2S8 quasimolecular units from their cages. At T > 540 K, modeling of the 31P NMR line shape simulations yields the trivial result that the lifetime of the As2P2S8 units is controlled by structural relaxation of the supercooled liquid. On the other hand, the fast rattling of these units appears to be coupled to the R-relaxation process that controls the relaxation of the cages themselves, presumably via cooperative rearrangement of the As-S network. This cage relaxation, in turn, strongly affects the rattling dynamics of the As2P2S8 units at T > 540 K that can be described within the framework of coupling between R-relaxation and a J-G β-process. These dynamical processes are therefore mechanistically coupled with one other, despite their very different time scales, indicating the presence of hierarchical dynamics in the (As2S3)90(P2S5)10 supercooled liquid. Acknowledgment. This work was supported by NSF Grant DMR-0603933 to S.S. and NSF EAPSI Award 0813082 to E.L.G. H.M. wishes to express sincere gratitude for the financial support provided by CREST, JST under “Novel Measuring and Analytical Technology Contributions to the Elucidation and Application of Materials.” The authors wish to thank S. C. Currie for sample preparation and P. Yu, M. Ando, and Y. Noda for NMR support. References and Notes (1) Greaves, G. N.; Sen, S. AdV. Phys. 2007, 56, 1. (2) Aitken, B. G. J. Non-Cryst. Solids 2004, 345 and 346, 1. (3) Verrall, D. J.; Elliot, S. R. J. Non-Cryst. Solids 1989, 114, 34. (4) Verrall, D. J.; Elliot, S. R. Phys. ReV. Lett. 1988, 61, 974. (5) Sen, S.; Ponader, C. W.; Aitken, B. G. J. Non-Cryst. Solids 2001, 204, 293–295.

Dynamics of As2P2S8 Quasi-Molecular Units (6) Sen, S.; Ponader, C. W.; Aitken, B. G. Phys. ReV. B 2001, 64, 104202. (7) Sen, S.; Aitken, B. G. Phys. ReV. B 2002, 66, 134204. (8) Aitken, B. G.; Ponader, C. W. J. Non-Cryst. Solids 2000, 274, 124. (9) Soyer Uzun, S.; Sen, S.; Benmore, C. J.; Aitken, B. G. J. Phys. Chem. C 2008, 112, 7263. (10) Soyer Uzun, S.; Sen, S.; Benmore, C. J.; Aitken, B. G. J. Phys.: Condens. Matter 2008, 20, 335105. (11) Blachnik, R.; Hoppe, A. J. Non-Cryst. Solids 1979, 34, 191. Mamedov, S.; Georgiev, D. G.; Qu, T.; Boolchand, P. J. Phys.: Condens. Matter 2003, 15, S2397. (12) Bychkov, E.; Miloshova, M.; Price, D. L.; Benmore, C. J.; Lorriaux, A. J. Non-Cryst. Solids 2006, 352, 63. (13) Farnan, I.; Stebbins, J. F. Science 1994, 265, 1206. (14) Stebbins, J. F.; Sen, S. J. Non-Cryst. Solids 1998, 224, 80. (15) Sen, S. Phys. ReV. B 2008, 78, 100201. (16) Maxwell, R.; Eckert, H. J. Phys. Chem. 1995, 99, 4768. (17) Maxwell, R.; Eckert, H. J. Am. Chem. Soc. 1993, 115, 4747, 1994, 116, 682. (18) Gjersing, E. L.; Sen, S.; Yu, P.; Aitken, B. G. Phys. ReV. B 2007, 76, 214202. (19) Santagneli, S. H.; Skripatchev, I.; Ribeiro, S. J. L.; Messaddeq, Y.; Schneider, J. Chem. Mater. 2007, 19, 5493. (20) Tverjanovich, A.; Kru¨ger, M.; Soltwisch, M.; Quitmann, D. J. NonCryst. Solids 1991, 130, 236.

J. Phys. Chem. B, Vol. 113, No. 25, 2009 8519 (21) Koudelka, L.; Pisarcik, M.; Gutenev, M. S.; Blinov, L. N. J. NonCryst. Solids 1991, 134, 86. (22) Tver’yanovich, A. S.; Somov, D. Y. Inorg. Mater. 1996, 32, 1009. (23) Mehring, M. Principles of High Resolution NMR in Solids; SpringerVerlag: Berlin, 1983. (24) Stebbins, J. F. In Structure, Dynamics and Properties of Silicate Melts; Stebbins, J. F.; McMillan, P. F.; Dingwell, D. B., Eds.; Reviews in Mineralogy, 1995, 32, 191. (25) Swallen, S. F.; Bonvallet, P. A.; McMahon, R. J.; Ediger, M. D. Phys. ReV. Lett. 2003, 90, 015901. (26) Ediger, M. D. Annu. ReV. Phys. Chem. 2000, 51, 99. (27) Cicerone, M. T.; Ediger, M. D. J. Chem. Phys. 1996, 104, 7210. (28) Bakhmutov, V. I. Practical NMR Relaxation for Chemists; John Wiley & Sons: London, 2004. (29) Leporini, D.; Jeschke, G. Philos. Mag. 2004, 84, 1567. (30) Kasper, A.; Bartsch, E.; Sillescu, H. Langmuir 1998, 14, 5004. (31) Doliwa, B.; Heuer, A. Phys. ReV. Lett. 1998, 80, 4915. (32) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. (33) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1971, 55, 4245. (34) Ngai, K. L.; Paluch, M. J. Chem. Phys. 2004, 120, 857. (35) Capaccioli, S.; Shahin Thayyil, M.; Ngai, K. L. J. Phys. Chem. B 2008, 112, 16035. (36) Vogel, M.; Ro¨ssler, E. J. Chem. Phys. 2001, 114, 5802.

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