9034
J . Phys. Chem. 1991, 95, 9034-9036
at T = 400 s from those obtained a t shorter T values. The normalized hole depth, h(r)/h(O),is plotted vs T in Figure 3 (circles), and refilling of the hole is seen to level off when magnetization transfer due to exchange has reached equilibrium, after which spin-lattice relaxation completes the process. The point (here 62%) where hole filling levels off depends upon the initial width of the hole, Le., the fraction of the spins inverted. The lifetime of the hole can be obtained by subtracting this equilibrium depth, and as shown in Figure 3, a semilog plot of the difference yields T,, Thole = 260 f 30 ws. Since k = 1 /hex, this procedure yields k = (1.9 f 0.2) X IO3 s-l in good agreement with the line-shape simulations. It is important to note that, for any kind of large-angle jumps, the rate of hole recovery is always slower than the rate of exchange and quite dependent upon the original width of the hole. This is due to the fact that during an exchange event some spins do not change quadrupolar frequency, and the number of such spins scales with the number of spins initially inverted. Ultimately, when the whole spectrum is uniformly inverted magnetization transfer is invisible and recovery is governed solely by T,.I4Thus, one should always expect T,, C T~~~~ < TI. It is clear that one can choose whether to generate a narrow hole, from which a more accurate measure of the exchange rate can be made without line-shape simulation, or a wider hole, which generates larger perturbations elsewhere in the spectrum. The results presented above show that the use of selective pulses on inhomogeneously broadened deuterium NMR spectra may be quite useful in dynamics studies, especially when TI is long, since the desired information-jump angle and rate-is available at
Supercritical Phase Separation in H,O-N,
short pulse spacings. The hole-burning experiments allow a distinction to be made between large and small-angle molecular motion, a feature they have in common with 2D exchange experi~nents.'~J~ The latter yield this information in a more clearcut fashion, but the advantage of the hole-burning experiments is that a measure of the jump rate can be obtained in the same experiment in a reasonable amount of time. In this respect hole-burning experiments may yield information more efficiently than measurements of spin-lattice relaxation ani~otropy.'-~Line-shape calculations of spin-alignment spectra6 present an alternative, since like the hole-burning experiment, results can be obtained at short pulse spacings. A potential disadvantage is that the asymmetric perturbation associated with Jeener-Broekaert excitation requires time-consuming diagonalization of large Liouville matrices for each pulse sequence i n t e r ~ a l . ~ More . ' ~ importantly, the use of monitoring pulses much less than 90°" results in lower signalto-noise ratio in the spin-alignment experiments. The optimal approach to getting dynamic information from powder line shapes is being studied herels and e l s e ~ h e r e . ~ ~ * ~ ~
Acknowledgment. This work was supported by grant CHE9000427 from the National Science Foundation. (16) Schwartz, L. J.; Millhauser, G. L.; Freed, J. H. Chem. Phys. Lett. 1986, 127, 60. (17) Jeener, J.; Broekaert, P. Phys. Rev. 1967, 157, 232.
(18) Lin, T.-H.; Huo, S.; Vold, R. R. To be published. (19) English, A. D. Presented at the 32nd ENC, St. Louis, MO,April 1991. (20) Vold, R.L.; Hoatson, G. L. Private communication.
Mixtures
Marc Costantino* and Steven F. Ricet Department of Chemistry and Materials Science, L-369, Lawrence Livermore National Laboratory, Livermore, California 94550 (Received: August 5, 1991; In Final Form: September 18, 1991)
We report phase separation of supercritical mixtures of H20and N2 at pressures to 2.1 GPa and temperatures to 830 K on the 75 mol % water isopleth. The composition is fixed by loading a diamond anvil cell with a known mixture at temperatures above 400 O C and pressures above 150 MPa. We measure the pressure using the pressure dependence of the Sm3+:YAG fluorescence line at 6178 A. The shape of the coexistence curve for this isopleth implies a critical curve with a relatively weak dependence of the phase separation pressure on the temperature.
Introduction Phase separation of binary mixtures at pressures and temperatures above the critical point of the least volatile member is common, even among simple fluids.'-3 If one or both of the componcnts have a nonspherical potential, we might expect interesting structures in the coexistence surface of the miscible and immiscible phases and the resulting critical line.es The details of the P-T-x coexistence surface are important in many practical applications, including chemical processing, toxic waste disposal, and detonation physics. Many of these systems have been studied at pressures and temperatures accessible to classical pressure vessel^.^ Recently, Schouten and co-workers have extended the pressure range using the diamond anvil cell.3 These systems also provide a rich environment for developing a theoretical description of molecular interactions as a function of density. Experimental work in the H20-N2 system, in particular, offers an exceptional opportunity to test a priori statistical mechanical calculations for the equation of state for nonsphericaf
'
Present address: Sandia National Laboratories, Livermore, CA 9455 1 0969.
0022-365419112095-9034$02.50/0
potentials. For example, Ree has predicted that, at pressures near 33 GPa and temperatures near 4000 K, H20and N, are immiscible.I0 Among the important points in Ree's work are two approximations that simplify the computer calculations: (1) ( I ) Schneider, G. M. Ado. Chem. Phys. 1970, 1 7 , I .
(2) Streett, W.B.; Erickson. A. L.; Hill, J. L. E. Phys. Earth Planet. Inter. 1972, 6 , 69.
(3) N2-He: van der Bergh, L. C.; Schouten, J. A. Chem. Phys. Lett. 1988, 145, 471. H,-He: van der Bergh, L. C.; Schouten, J. A,; Trappeniers, N. J. Physica 1987, 141A. 524. Ne-Xe: van den Bergh, L. C., Schouten, J. A.; Trappaniers, N. J. Physica 1985, 132A, 537. (4) Franck, E. U. J. Pure Appl. Chem. 1974, 38, 449. ( 5 ) Franck, E. U. Mater. Res. SOC.Symp. Proc. 1984, 22 (II), 95 (Proceedings of lhe 9Ih AIRAPT International High Pressure Conference, Albany, N Y , 1983; Homan, C., MacCrone, R. K., Whalley, E., Eds.). (6) Christoforakos, M.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 780. (7) Prokhorov, V. M.; Tsiklis, D. S. Russ. J . Phys. Chrm. (Engl. Trawl.) 1970, 44, I173 (translated from: Zh. Fiz. Khim, 1970, 44, 2069). (8) Japas, M. L.; Franck, E. U. Eer. Bunsen-Ges. P h j s . Chem. 1985,89, 793. (9) Franck, E. U. N u i d Phase Equilib. 1983, 10, 21 1. (10) Ree, F. H. J. Chem. Phys. 1986, 84, 5845.
0 1991 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9035
-
Closure nut
-
Bearlngs
Rotatlngstem
r Thermocouple well
-
Packlng
-Main seallng rlng
-
Statlonary frame
- anvil Dlamond cell
-
Thermocouple well
Pressure Input
4 1c m k -
Figure 1. Apparatus to load a supercritical mixture of water and nitrogen into the diamond anvil cell. The pressure vessel is made of Rent-41 and is designed for use to 1 GPa at 700 OC.
nonspherical potentials are represented by a temperature-dependent spherical potential, and (2) a simple averaging scheme is used to represent the interaction between unlike molecules. Prediction of the phase diagram by minimizing the Gibbs free energy provides a sensitive test of these assumptions. Unfortunately, the calculations are not expected to be accurate at the easily accessible pressures of 1 GPa and below and at temperatures below about 1500 K. We have, therefore, undertaken a program to make these phase separation measurements at pressures to 40 GPa and at as high temperature as possible. As a first step, we have developed an apparatus, based on a heated diamond anvil cell (DAC), designed to make pressure-temperature-composition phase diagram measurements to pressures in excess of 30 GPa and at temperatures to about 1200 K. This Letter describes the initial results of this research, viz., the coexistence curve for the miscible/immiscible phases along the 75 mol % water isopleth at pressures to 2.1 GPa and temperatures to 830 K.
Experimental Section There are four major steps in the experiment. First, we obtain a sample of a known H20-N2 mixture in the diamond anvil cell by loading the DAC in a larger pressure vessel. Next we heat the DAC in a vacuum furnace to the transition temperature. We then observe the transition by imaging the sample region onto a video camera. Finally, we measure the transition pressure using the shift of the 6178-A fluorescence line of Sm3+:YAG. The primary measurement concerns are the H20-N2 composition and the pressure. We fix the composition of the sample mixture in the DAC by loading the cell while it is immersed in a known mixture in the miscible phase. In this procedure, we place a measured amount of doubly distilled, deaerated water (conductivity
