J. Phys. Chem. 1984, 88, 159-162 molecules held together by a weak N-N bond. The N=O stretching frequencies (1 866 and 1762 cm-’) and the force constant of 14.49 mdyn/A are only slightly lower than the valued3 for free NO: vNo = 1876 cm-l and f N o = 16.0 mdyn/A. The corresponding frequency and force constant values for as-N203are 1858 cm-’ and 15.04 mdyn/A. The force constant for the weak N-N linkage was calculated to be only 0.32 mdyn/A for N202;for N2O3 this stretching constant is 0.57 mdyn/A. Since each of these values has an uncertainty of about 0.1 mdyn/A, the difference may not be highly significant. Nonetheless, the N-N bond is clearly (13) J. Laane and J. R. Ohlsen, Prog. Inorg. Chem., 27,465 (1980), and refrences therein.
759
extremely weak in both cases. For comparison, the nitrogennitrogen bond in N 2 0 has a force constantI3 of 18.5 mdyn/A, ON=N02- has a force constanti4 of 7.9 mdyn/A, and N2032has a valueI5 of 4.4 mdyn/A. A typical N-N single bond may be expected to have a force constant of about 4 mdyn/A. Acknowledgment. This work was sponsored by the National Science Foundation. Registry No. (I4NO),, 16824-89-8; (”NO)2, 61925-25-5; (‘5N’80)2, 88296-32-6. (14) L.-H. Chen and J. Laane, J . Raman. Specfrosc.,14, 284 (1983). (15) F. T. Bonner, M. J. Akhtar, T.-V. King, L.-H. Chen, a n d T . Ishida, J . Phys. Chem., 85, 4051 (1981).
Nonexistent Glass Transition for Amorphous Solid Water D. R. MacFarlane and C. A. Angell* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: August 9, 1983)
In an attempt to characterize the nature of the glass transition in vitreous water we have vapor deposited the amorphous solid directly in a differential scanning pan, and studied its warm-up behavior under high-sensitivity conditions. Notwithstanding the use of many preparation variations and DSC scanning cycles known to maximize the thermal manifestation of the “glass transition”, no transition anywhere in the region expected from binary solution extrapolations has been detected. Rather, the material remains unrelaxed up to the onset of crystallization commencing abruptly in the range 150-162 K depending on deposition conditions. We interpret the observation by reference to known (network glass + “modifier”) system behavior.
Introduction For the frequency with which its experimentally determined behavior confounds the most confident predictions, water is, among known substances, without peer. This contribution documents another in a series of such predictive failures, each of which has in the past led to a new and useful understanding of the nature of this extraordinary substance. We are concerned in this work with the nature of amorphous solid (or vitreous) water (ASW). This material and its relationship to liquid water is currently in focus because of the apparent success that independent laboratories seem to have had recently1i2in suppressing the crystallization phenomenon during ultrafast cooling of initially liquid water samples. The resulting product is an X-ray amorphous form of the substance which shows behavior during subsequent warm-up which is generally, and in some cases exactly, similar to the behavior of the amorphous solid water which is produced by vapor deposition of dilute gas molecules on a cold substrate^.^ That the glassy looking material deposited from the low-pressure vapor is amorphous to X-rays was first shown by Burton and Oliver4 in 1932. In 1966 McMillan and Loss reported a glass transition in such deposits some 20 K below the temperature of crystallization, but the thermal effect was later denied in the work of Ghormley.6 Subsequently, adiabatic calorimetry studies by Sugisaki et al.7 showed an increase in heat capacity, which is ( I ) Brugeller, P.; Mayer, E.Nature (London) 1980, 288, 569. 1980, 288,
characteristic of the glass transition, at a somewhat lower temperature than that of McMillan and Los, but the complete transition could not be observed because of crystallization of the deposit at the low temperature of 136 K. In 1970 Angell and Sares showed that the glass transition temperature predicted by extrapolation of binary solution data on many salt water systems was consistent with the TBreported by McMillan and Los, and this was subsequently supported by extrapolations involving a number of molecular liquids? including some whose glass transition temperatures fell at lower values. Most workers would agree that the extrapolation of these data, to yield Tg(H20) = 139 K as shown in Figure 1, carries conviction. Angell and Sare also showed, using an entropy argument going back to Kauzrnann,lo that the extrapolated glass transition temperature could not be reconciled with the observed heat capacity of liquid water. As a result, they anticipated that, in the supercooled state of water, an anomalous decrease in heat capacity would be encountered. Subsequent experiments’ ‘ - I 3 in the supercooled region revealed, characteristically, an anomaly which ran in the opposite sense. Angell et al.13attempted to rationalize the increase in supercooled water heat capacity by postulating a A-type transition just below the limit of observation. As a result of this the heat capacity, it was asserted, would plunge to a low value thereby postponing the entropy catastrophe to temperatures compatible with McMillan and Los’ glass transition temperature. Johari14subsequently showed that if one accepted the heat capacity rise observed at 132 K by Sugisaki et al.’ as the glass transition
579. (2) (a) Dubochet, J.; McDowell, A. W. J . Microsc. 1981, 124, RP3-RP4. (b) Dubochet, J.; Lepault, J.; Freeman, R. Ibid. 1982, 128, 219. (3) For a complete review see the comprehensive article by M. S.Sceats and S.A. Rice in ’Water, A Comprehensive Treatise”; Franks, F., Ed.; Plenum: New York, 1982; p 115. (4) Burton, E. F.; Oliver, W. F.Proc. R . Soc. (London), Ser. A 1935,153, 166. (5) McMillan, J. A.; Los, S.C. J . Chem. Phys. 1965, 42, 829. (6) Ghormley, J. A. J . Chem. Phys. 1967, 48, 503. (7) Sugisaki, M.; Suga, H.; Seki, S.J . Chem. SOC.Jpn. 1968, 41, 2591.
(8) Angell, C. A.; Sare, E. J. J . Chem. Phys. 1970, 52, 1058. (9) Sare, E. J.; Angell, C. A. J. Solution Chem. 1973, 2, 53. (IO) Kauzmann, W. Chem. Rev. 1948, 43, 219. (11) Rasmussen, D. H.; MacKenzie, A. P.; Tucker, J. C.; Angell, C. A. Science 1973, 18, 4079. (12) Rasmussen, D.H.; MacKenzie, A. P. J . Chem. Phys. 1973,59, 5003. (13) Angell, C. A.; Shuppert, J.; Tucker, J. C. J . Phys. Chem. 1973, 77, 3092. (14) Johari, G. P. Phil. Mag. 1977, 35, 1077
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sensitively enough to detect glass transitions which might have been overlooked in previous DTA studies.
Experimental Section
4001 100
T,
Tg/K
/OC
300
0
200 -100
loo
20
40
60
80
100
mole ‘10 component 2 Figure 1. composition dependence of T,in a variety of aqueous binary systems, showing common extrapolation to T,(H,O) = 139 K. Adapted from Figure 6, Chapter 1 of “Water: A Comprehensive Treatise”,Vol. 7, F. Franks, Ed., Plenum Press, New York, 1982. Data for NH40Ac and Na2Si03from E. J. Sare, Ph.D. Thesis, Purdue University, 1971. Data for hydrated sodium silicate glasses from R. J. Bartholomew, J . Non-Cryst. Solids, 56, 331 (1983).
for amorphous water, then Angell et al.’s argument was unsupportable. Johari argued instead that amorphous solid water must be thermodynamically disconnected from ordinary and supercooled water. In the meantime, a series of elegant experiments by Rice and c o - ~ o r k e r s ~ *established ~ * - ~ ~ that the structure of amorphous solid water obtained by vapor deposition was exactly what one might expect for the low-temperature configurational ground state for liquid water, viz., a fully connected but spatially random network of hydrogen-bonded water molecules containing a statistical number of bent bonds sufficient to provide for loss of long-range positional order. Angell and TuckerI7 attempted to save the connectability of ASW and supercooled water by showing, from extrapolation of aqueous solution observations, that the heat capacity change at 132 K observed by Sugisaki et al.’ and central Johari’s argument was probably too high, for reasons unspecified. Rice et ale’*argued along the same lines though suppressed the glass transition completely. Clearly a repetition of the Sugisaki et al. heat capacity determinations was needed to resolve this issue. For the present study we reasoned that if, instead of adiabatic calorimetry, the measurements could be made by differential scanning calorimetry, then data of about f 2 % accuracy covering the range from below 130 K to the temperature of crystallization of ASW (158-166 K) observed by Rice and c o - ~ o r k e r s , ~ McMillan and Los,~Ghormley,6 and Skripov and co-w~rkers’~ could be obtained. In view of the great sensitivity of the DSC-2, it was felt that measurements could be made on samples small enough to avoid any surface crystallization induced problems, and (15) Narten, A. H.; Venkatesh, C. G.; Rice, S.A. J . Chem. Phys. 1976, 64, 1106. (16) Venkatesh, C. G.; Rice, S. A.; Bates, J. B. J . Chem. Phys. 1975,63, 1065. (17) Angell, C. A,; Tucker, J. C. J . Phys. Chem. 1980, 84, 268. (18) Rice, S. A.; Bergren, M.;Swingle, L. Chem. Phys. Lett. 1978,59, 14. (19) Koverda, V. P.; Skripov, V. P.; Bogdanov, H. M. Sou. Phys. Crystallogr. 19, 19, 379.
The obvious difficulty standing in the way of a DSC study of vapor deposited ASW is the provision of a suitable amorphous sample in a DSC pan in the sample chamber of the DSC instrument. Ways of mounting a Dewar flask around the DSC head to permit studies to liquid helium temperatures were discussed some time ago with Rice, but, in addition to the obvious construction difficulties, these would have involved decommissioning a DSC which was being actively used in other programs. Before deciding on such a course we have sought, with some success, ways of producing a suitable deposit in a DSC pan external to the calorimeter, and then affected a cold transfer to the DSC. The adequacy of the cold transfer step is quickly determined by the subsequent presence or absence of a crystallization peak consistent in size with (Le., smaller by a reasonable margin than) the subsequent fusion peak. Samples of mass up to 5 mg were prepared by depositing water vapor which was metered into a vacuum deposition apparatus at a rate of 0.07 mg h-l, (s 2-pm film thickness h-l) about the maximum rate recommended by Sceats and Rice3to ensure a fully amorphous deposit. The total deposition time typically amounted to 48 h. Temperature in the DSC pan was continuously monitored by a fine thermocouple in contact with the pan exterior. When the pan was “glued” to the heat sink with a drop of propylene glycol, its temperature was found to remain below 90 K throughout the deposition. Using liquid nitrogen-precooled tweezers, we placed the sample pan in a liquid nitrogen-containing transfer vessel, which was then placed in the DSC head-protecting drybox. The DSC sample pan cover was displaced sufficiently to expose the sample pan but not the reference pan (in order that maximum machine cooling could be maintained during the transfer) and immediately prior to removing the sample from the transfer flask, liquid nitrogen was poured into the sample pan in the DSC head to establish a temporary cold gas blanket which protected the sample during the few seconds in which it was being removed from the transfer vessel and positioned into the pan compartment of the DSC head. With practice, this operation could be repeated with consistent success. The sample was then scanned between 110 and 150 K, using an instrument sensitivity which would cause pen displacement half of full scale for the case where the heat capacity is that reported by Sugisaki et ale7After an initial exciting result (a well-defined glass transition) was shown to be an artifact due to a film of silicone oil being used at that time as a heat transfer medium between the DSC pan and the heat sink in the deposit apparatus, it quickly became evident that no glass transition or any other thermal effect was to be found in this scanning range. To provide for the possibility that ACp might be unexpectedly small, the sample was annealed at various temperatures below the expected Tgin order to build up an enthalpy deficiency. In the case of ordinary glass-forming substances this would lead to a substantial overshoot in the apparent heat capacity during an up-scan (see for instance the sharp peaks in ref 20). However all such efforts completely failed to find any trace of a glass transition phenomenon in this range. All samples, for which the appropriate deposition conditions were met, showed sharp crystallizations commencing at 158-166 K, and concluding at 159-166 K, usually but not always preceeded by a small shoulder some 2 K before the sharp rise of the crystallization exotherm. A scan for the deposit which gave the highest crystallization peak temperature (166 K) is shown in Figure 2 at two sensitivities. In the range 130-155 K a sensitivity of 10 mcal s-l was used. The pen displacements expected for this sample mass in the case of glass transitions with the ACp values reported in ref 1 at 132 K, and in ref 17 (by extrapolation) at 140 K, are shown as dashed lines. For the range 150-170 K a smaller sensitivity suitable for dis(20) Boehrn, L.; Ingram, M. D.; Angell, C. A. J . Non-Cryst. Solids 1981, 44, 305.
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 761
Glass Transition for Amorphous Solid Water
Expected from ref 7 Expected from ref 17
130
I40
150
160
170
Figure 2. DSC scan of vapor-deposited amorphous water in the range 125-175 K showing featureless behavior in the range where a glass transition is expected from extrapolations,and sharp crystallization at 164 K. Noise level is about double the line width. Some scans were conducted at 5 X this sensitivity.
playing the whole crystallization isotherm was used. In all, a dozen separate samples were prepared and studied. The crystallization product was, as expected, ice ICjudging by the small exotherm at 177 K (185 K in ref 5 ) for ice I,. Some samples were cycled repeatedly between 130 and 147 K, without showing any signs of devitrification. Such samples also crystallized sharply in the same manner as those scanned only once. Two samples were prepared at deposition rates such that some crystalline material in the deposit was to be expected. These samples yield warm-up curves in which the sharp crystallization was preceded by a shoulder of variable size commencing at about 150 K.
Discussion In view of the high quality of calorimetric investigations for which the Osaka University group3 is so well reputed, we must be concerned at the apparent discrepancy between the present results and theirs. The first suspicion is that our deposit is already in a microcrystalline state and that the thermal effect seen at 166 K is just a grain growth phenomenon. This would require, however, that the preparations of most other workers (including the thinnest, most slowly deposited, samples of Rice and colleagues which survived in the amorphous state to > 160 K on reheating3 and which also passed spectroscopic tests for impurity incorporation) also were microcrystalline, since their crystallization phenomena are consistent with ours. On the other hand, it has always seemed a little paradoxical that water, which has proven so difficult to vitrify from the liquid ~ t a t e ,and ’ ~ for ~ ~which ~ ~ the nucleation rates are by all calculations expected to be so high, should be capable in amorphous solid form of exhibiting a glass transition during warm-up. It is well-known from the extensive studies of metallic glasses” that most marginal glasses even when formed from initially liquid states fail to exhibit a glass transition during warm-up, and this tendency to move directly to the crystalline state, bypassing the supercooled liquid state completely, is even more pronounced for the vapor-deposited unstable metal glass compositions. The reason for the latter findings is essentially that, when a “liquid” is caught by one means or another in an amorphous state far below its homogeneous nucleation temperature Thrit is in a doubly unstable region and can move toward the crystalline state and the internally equilibrated amorphous state at comparable rates. The bigger the gap ( Th- T,) the greater the drive toward (21) Martin, S. W.;Cooper, E. I.; Angell, C . A. J . Am. Cerum. SOC.1983,
66, C153.
(22) Dubochet, J.; Lepault, J.; Freeman, R.; Berryman, J . A.; Homo, J . U.J . Microsc. 1982, 128, 219. (23) Angell, C . A. Annu. Rev. Phys. Chem. 1983, 34, 593. (24) Polk, E.; Giessen, W.C . ‘Metallic Glasses”; Gilrnan, J. J.; Learny, H. J. Ed.; American Society for Metals: Metals Park, OH, 1978; Chapter 1.
T/K
Figure 3. Comparison of warm-up behavior of vapor-deposited solid amorphous water with that of the glass-forming aqueous solution LiC1.11H20, showing a glass transition in the latter followed by crystallization at a temperture 152 K well below that at which ASW crystallizes. The sensitivityof the LiCI.1 1H20scan is greater than for the ASW scan.
the crystalline state.25 When the time scale for nucleation (escape from metastability) becomes shorter than that for internal liquid-state relaxation, then it must always be the former which is observed. This line of thought suggests that the reason the glass transition has not been seen in the present study is that it has in fact nof been reached before crystallization has set in. (For a clear example, see the sequence of DSC traces at the edge of the glass-forming region in an inorganic glass system in ref 21.) This important conclusion is strongly supported by the observation that, in the case of lithium chloride water solutions near the edge of their glassforming regime, crystallization occurs, after a well-defined and easy-to-determine glass transition, at a temperature significantly below the temperature at which amorphous solid water crystallizes (see Figure 3). That water, with its much greater drive toward crystallization, should survive in the supercooled state further above its T8 than does a recognized glass-forming composition in the binary system is difficult to rationalize. Consequently, we conclude that the “normaln glass transition temperature for vitreous water (which could only be observed in the presence of a nucleus-destroying Maxwell demon, hence has no real existence) lies above 160 K. Note Added in Proof. Further support for this conclusion may be drawn from the clever dielectric loss studies of ASW by Koverda et al. (Koverda, V. P.; Skokov, V. W.; Faizillin, M. Z.; Bogdanov, N. M.; Skripov, V. P. Russ. J . Phys. Chem. Glasses 1977, 186). These authors showed that tan 6 at 1000 Hz for the vapor deposit starts to rise exponentially from the baseline at N 135 K reaching a value of 0.04 at the crystallization temperature. For an (easily) glass-forming liquid with a dielectric constant similar to that of water, viz., propylene carbonate, Johari and Goldstein (Johari, G. P.; Goldstein, M. J . Chem. Phys. 1979, 53, 2372) showed the same value of tan b at 1000 H z was reached in a similar manner (as a secondary relaxation) some 7 K below the normal calorimetric glass transition temperature at 163 K. The peak value of the primary relaxation for this case is tan 6 = 0.99 and is reached at 8 K above the calorimetric T,. In making these correlations we are taking exception to Koverda et al.’s discussion in which the initial tan 6 rise was taken as implying a glass transition at the point of initial tan 6 increase, at 135 K. Although it is basically fatuous to discuss the character of a glass transition which cannot be observed (except for a Maxwell demon-protected amorphous solid), it is valid to discuss why crystallization with or without prior T, does not occur close to the temperature expected by extrapolation of the numerous binary solution data. The most reasonable interpretation takes note of the well-formed random tetrahedral network structure possessed by ASW3,15,’6and assumes that the addition of network-breaking
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impurities must have the same effect on the kinetic rigidity of the amorphous phase as is observed, through glass transition temperature vs. composition studies, in the better known “network + modifier” systems, Si02+ sodium oxide, and ZnCI, modifier chloides.26-2* In each case the disruption of the network leads to a rapid decrease in Tgup to a limit where Tgbecomes at least temporarily independent of composition. In the region of steeply decreasing glass transition temperatures, major fragments of the initial network still exist. In the case of the aqueous system it is these fragments which produce the easy nucleation of ice. It seems reasonable, then, that by the point in composition where glass formation can be observed in normally cooled aqueous solutions the glass transition temperature should have reached its composition-independent regime. It should be possible to confirm this interpretation by thermal studies of vapor-deposited binary amorphous solids formed by, e.g., deposition from H202+ H 2 0 vapors in equilibrium with H 2 0 2 + H 2 0 solutions of known concentrations. We are at the moment unable to account for the observations of McMillan and Los,’ and Sugisaki et al.’ The heat released on crystallization in our study was 1.5 0.1 kJ mol-’, based on quantitative study of three samples. This is in reasonable agreement with the maximum value, 1.64 kJ mol-’, reported by Sugisaki et al. Ghormley, whose DTA traces also show no glass transition, reported a slightly larger heat of crystallization, 1.8 kJ mol-‘.6 An important consequence of this discussion is the new light it throws on the problem raised by Johari.14 Johari argued, on the basis of the increase of heat capacity at 130 K reported by Sugisaki et al.,’ that the rate of increase of entropy in the supercooled liquid was too great to be compatible with the known entropy of water at the limit of C, measurement at -38 0C.29 Johari concluded that the amorphous solid was thermodynamically
unconnected to the normal pressure liquid state, and suggested that it might bear a closer relation to the high-pressure polymorphs of ice. But if, as we have concluded above, the amorphous state cannot commence producing entropy at a liquidlike rate at temperatures less than 160 K (or even higher, as would be the case if one were to heat the sample at a rate sufficient to avoid the crystallization and connect directly to the liquid), then the problem raised by Johari simply goes away. This leaves the ground free to establish the hoped-for connections between the vapor-deposited amorphous solid and the snap-quenched liquid, which are apparently now being tentatively established experimentally through the identification of an amorphous solid from rapidly quenched liquid in the work of Brugeller and Mayerz1and Dubochet et aLZ2 Although there are some unexplained differences between jet-quenched and vapor-deposited ASW X-ray patterns in the reports of Brugeller Mayer,’ Dubochet et aL30have recently given good electron diffraction and kinetic evidence for indistinguishability of the liquid-route and vapor-route forms. Their characterizations were performed under identical conditions to minimize ambiguities. The warm-up behavior of an initially vitreous sample when heated as rapidly as-or more rapidly than-was necessary to vitrify it remains a matter for speculation. It now seems it would look more like the suggestion of Rice et aLL8than that of Angell and T ~ c k e r ;however, ’~ if supercooled water is characterized by fast “normal” configurational relaxations as well as by slow “anomalous” configuration relaxation modes, then the warm-up curve should still show two relaxation steps rather than the single step considered in ref 18.
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Acknowledgment. This work was supported by the Office of Naval Research under agreement No. N00014-78-C-0035. Registry No. Water, 7732-18-5
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(26) Green, R. L. J . Am. Ceram. S O ~1942, . 25, 83. (27) Easteal, A. J.; Angell, C. A. J . Phys. Chem. 1970, 74, 3987. (28) Paik, J. S.; Perepezko, J. H., J . Non-Cryst. Solids 1983, 56, 405.
(29) Angell, C. A.; Sichina, W. J.; Oguni, M. J . Phys. Chem. 1982, 86, 998. (30) Dubochet, J.; Adrian, M.; Vogel, R. H. Cryolrtters 1983, 4, 233.
Asymptotic Solutions of a Reduced Oregonator Model of the Belousov-Zhabotinsky Reaction Michael F. Crowley and Richard J. Field* Department of Chemistry, University of Montana, Missoula, Montana 5981 2 (Received: January 7, 1983; In Final Form: May 9, 1983)
Singular perturbation techniques have been used to find relatively simple, closed-form solutions to a reduced, two-variable version (due to Tyson) of the Oregonator model of the oscillatory Belousov-Zhabotinsky (BZ) reaction. The reduction is accomplished by assuming that the value of Y in the Oregonator very rapidly follows that of X . Thus, dY/dt is set equal to zero and an algebraic relation between X and Y obtained.
Introduction The Belousov-Zhabotinsky (BZ) reaction’ is the most thoroughly studied and understood oscillating chemical reaction.2 In its classic form it is the metal-ion-catalyzed oxidation and bromination of malonic acid by bromate ion in a strongly acid medium. It shows a striking variety of interesting and important behaviors in both batch and CSTR (continuous-flow, stirred tank (,l) Field, R. J. In “Theoretical Chemistry: Advances and Perspectives”;
Eyring, H., Henderson, D., Eds.; Academic Press: New York, 1978; Vol. 4, Chapter 2. (2) Field, R. J.; KBros, E.; Noyes, R. M.J . Am. Chem. SOC.1972, 94, 8649.
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reactor) experiments. These behaviors involve the concentrations of the oxidized and reduced forms of the metal-ion catalyst as well as those of various intermediate species and include the following: periodic2 and aperiodic3 temporal oscillations, bistability; hystere~is,~ and traveling waves.6 These phenomena are interesting and important not only because of the complex chemistry occurring but also because they are relatively easily (3) Turner, J. S.; Roux, J.-C.; McCormick, W. D.; Swinney, H. L. Phys. Lett. A 1981, H A , 9. (4) DeKepper, P.; Boissonade, J. J . Chem. Phys. 1981, 75, 189. ( 5 ) (a) Marek, M.; Svobodova, E. Biophys. Chem. 1975,3,263. (b) Janz, R. D.; Vanecek, D. J.; Field, R. J. J . Chem. Phys. 1980, 73, 3132. (6) Field, R. J.; Noyes, R. M. J . Am. Chem. SOC.1974, 96, 2001.
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