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C. A. ANGELLAND D. B. HELPHREY
Corresponding States and the Glass Transition for Alkali Metal Nitrates by C. A. Angell* and D. B. Helphrey Department of Chemistry, Purdue University, Lafayette, Indiana
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(Received August 10,1070)
Publication costs assisted by the National Science Foundation
In order to establish a set of corresponding temperatures for the much-studied molten alkali metal nitrates, estimates of the “ideal” glass transition temperatures for NaN03 and KN03are made from available thermodynamic data and shown consistent with “experimental” glass transition temperatures obtained by extrapolation from binary solution (hydrate melt) data. T, values are obtained in the same manner for the other alkali metal nitrates, Li, Rb, and csxo3, the spread of values among the five salts found being only Bo, thereby largely justifying isothermal comparisons of their properties despite the 160” spread in melting points. The order-disorder transition in sodium nitrate is examined and the relation of this class of transition to the glass transition phenomenon is considered. Equations from a zeroth-order, order-disorder theory for the glass transition are used to give a qualitative account of the change in heat capacity at the glass transition for sodium nitrate. The alkali metal nitrates are among the most studied of molten salts. Since it has proved possible to correlate, and simplify interpretation of, a number of aspects of the physicochemical behavior of binary fused salt solutions by recognizing that these liquids all tend on cooling towards a glassy condition reached at a characteristic temperature for each liquid,l it is of interest to decide whether definite glass transition temperatures can be measured or inferred for the pure alkali nitrates. The purpose of this short paper is to affirm that such temperatures can be assigned, by predicting theoretical glass transition temperatures using only equilibrium thermodynamic data, and then showing that very reasonable extrapolations of measured glass transition temperatures in appropriate binary solutions are in good accordance with the thermodynamic predictions. These values turn out to conflict with previous estimates based on cation charge/radius ratios, while confirming a previously noted parallel in the relaxational behavior of lithium and sodium ions in their nitrate melts. According to our ideas these studies define a useful set of corresponding temperature bases for use in interpreting other physicochemical properties of the solutions. That they also provide a novel means of detecting interactions between ionic species in these melts will be shown in subsequent papers. The thermodynamic estimates of the alkali metal nitrate glass transition temperatures are based on the observation, first made by Kauzmann,2 that the rate at which entropy is lost from a supercooling liquid is generally so much greater than that at which entropy is lost from the stable crystalline phase cooling in the same temperature region, that were it not for the intervention of the glass transition phenomenon the liquid would reach a state of lower entropy than the crystal well before the temperature could fall to 0°K. The glass trmsition phenomenon, at which the heat capacity changes rather abruptly under nonequilibrium condiThe Journal of Physical Chemistry, Vol. 76, N o . 16,1971
tions to a value essentially that of the crystal, always intervenes before this interesting equilibrium problem can be resolved. Although Hauzmann considered the resolution of the equilibrium problem to lie in an impending irreversible crystallization, Gibbs and Dimarzioa argued that the intervention of the glass transition was no accident but rather a direct consequence of the approach of the system to a configurational ground state. Their theory indicated a second order-thermodynamic transition at a temperature To consequent on the vanishing of the liquid excess entropy. Regardless of whether the normal liquid regime is terminated by such a second-order transition or by a (dynamically more appealing) rapid decrease in heat capacity, as for an “Einstein” crystal, as kT falls below some critical energy related to the energy spacing of the implied configurational microstates (see Discussion), it is clear that in the metastable equilibrium phase C, and C, must change value before 0 ° K and that the lower limit on the temperature at which the change has to occur during cooling can be determined from known heat capacity data for the liquid and crystalline states and the entropy of fusion. A suitable graphical method of finding this limiting t e m p e r a t ~ r ecalled , ~ in this work the “ideal glass transition temperature,” is shown in Figure 1 for the cases of NaN03, and KNO3, for which excellent thermodynamic data are available in the work of Shmidt.5 It is assumed that the supercooled liquid retains the same temperature-independent heat capacity as its exhibits above the melting point. This (1) (a) C. A. Angell, J . Phys. Chem., 70, 2793 (1966); (b) J . Chem. Phys., 46, 4673 (1967). (2) W. Kauzmann, Chem. Rev., 43, 219 (1948). (3) J. H. Gibbs and E. A. Dimarzio, J . Chem. Phys., 28, 373 (1958). (4) C. A. Angell and C. T. Moynihan, “Molten Salts: Characterization and Analysis,” G. Mamantov, Ed., Marcel Deklrer, New York, N. Y . , 1969, p 315.
CORRESPONDING STATES AND THE GLASS TRANSITION FOR ALKALI METALNITRATES value of C, is extrapolated into the supercooled region to a point (To)at which the area between the crystalline heat capacity curve and the extrapolated liquid heat capacity curve is exactly equal to the total area representing the entropy of fusion plus the entropies of all solid-state transitions occurring above To. By this construction, then, the supercooled liquid would have the same total entropy as the stable crystalline phase at TO. Discounting the unlikely case in which the amorphous phase has a lower vibrational heat capacity than the stable crystalline form (usually it is observed to be slightly larger), To therefore stands as a lower limit of the temperature range through which the supercooled liquid could persist with constant heat capacity.
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and 224”K, respectively. That for NHdNOz falls lower at 165”K, while for AgKOs a higher TO,-260°K, is indicated for the improbable case in which C, (liquid) continues to increase well below TB. Rleasurement of an experimental quantity to compare with these calorimetric “ideal” glass temperatures presents problems. Although the formation of glasses from pure NaK03 and KNO3 by quenching tiny liquid droplets has been reported by Tammann and Elbrachter,’ our attempts t o produce useful experimental amounts of such glasses for glass transition temperature determinations have not to date been successful. Lowmelting mixtures of nitrates may be obtained as thin sheets of glassy appearance by pressure pulse splat quenching onto copper sheet at - 196”; however, except for some compositions in the LiK03-NH4N03 system these preparations exhibited a succession of irreversible crystallizations rather than a glass transition during warm-up.* There is also some doubt that glass transition temperatures measured in the eutectic regions of such systems would provide an accurate guide to the glass temperatures of the pure salts because of deviations from T , additivity indicated by electrical conductance measurements.lb Finally we have chosen to estimate T , for pure nitrates by extrapolations of glass temperatures measured over substantial glass-forming composition regions in “hydrate melt” type binary solut i o n ~in , ~which T, seems t o be a quite linear function of composition. Changes in T , across these systems are small and molar volumes in a representative case, Ca(N03)2*4HzO KNO3, are found to be additive within experimental error.1° Thus although calorimetric data are not available to establish ideal mixing behavior, it seems the extrapolations should be fairly reliable. For the present work the hydrate Cd(N03)2#4H20 w7as chosen as the second component. This salt has properties very similar to those of Ca(N03)2-4H20but the Cd2+ion appears, from pmr studies,l’ to bind the water molecules somewhat more strongly than Ca2ithus reducing the effects of constitutional changes due to water displacement into the alkali metal cation coordination with increasing alkali nitrate concentration.l 2
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1 , . . a ,
40
, *
,
7 0 m
200
403
I
m m
Temp. O K
Figure 1. Heat capacity plots for KNOI and NaNOa crystal and liquid, showing estimation of “ideal” glass temperatures.
Only for NaN03 and KN03 among the alkali nitrates are sufficient heat capacity data available for this calculation to be performed. Suitable data are also available for AgN0S5~and NH4N036although the anomalous increasing liquid heat capacity for AgNOa, and the presence of no less than four solid state transitions, and some uncertainty in the liquid heat capacity for NHr NOa, make the calculation less reliable in these cases. The “ideal” glass temperatures for sodium and potassium nitrates are found (from Figure 1) to lie at 218
(5) (a) V. A. Sokolov and N. E. Shmidt, Tzu. Sekt. Fiz. Khim. Anal. Inst. Obshch. Neorg. Khim. Akad. Nauk S‘SSR, 26, 123 (1955); (b) V. A. Sokolov and N. E. Shmidt, ibid., 27, 217 (1956); (c) The results of these authors for sodium nitrate have been confirmed to 0.2% by the more recent work of W. C. Reinsborough and F. W. Wetmore, A m t . J . Chem., 20, 1 (1967). AgNOa was also studied by the latter authors. (6) 111. Nagatani, T. Seiyama, M. Sakiyama, H. Suga, and S. Seki, Bull. Chem. Soc. Jap., 40, 1833 (1967). (7) G. Tammann and E. Elbrachter, 2.Anorg. Allg. Chem., 267, 268 (1932). (8) D. B. Helphrey, unpublifihed work. LiNOs (40%) NHdNOs (60%) yielded a T, of 231 O K , while for 1: 1 AgNOa TINO3 eutectic, T, was found, surprisingly, at a higher temperature, 242’K. (9) C. A. Angell, J . Electrochem. SOC.,112, 1225 (1965). (10) J. Braunstein, L. Om, and W. Macdonald, J. Chem. Eng. Data, 12, 415 (1967). (11) C. T. Moynihan, C. R. Smalley, C. A . Angell, and E. J. Sare, J . Phys. Chem., 73, 2287 (1969).
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The Journal of Physical Chemistry, Vol. 76, No. 16, 1971
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C . A. AWGELL AND D. B. HELPHREY trace as indicated in the inset to Figure 2 , and values are believed accurate to =t1". -e---
Results
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Results for the five Cd(l\-O&-4Hz0 X(l)NOa systems studied and an independently obtained set of I1.7T, and thus make glass-forming ability improbable. It may be that the methods of estimation of glass temperatures utilized in this work will prove helpful in seeking more general correlations between the energetic characteristics of solid-state transition phenomena and those of the glass transition, and thereby assist in developing a better understanding of the liquid state.
Acknowledgments. Thanks are due t o I
