4700
J . Phys. Chem. 1990, 94, 4700-4705
that result from the modeling of deuterium quadrupolar splittings are perhaps a little surprising. The original impetus for examining alkane solutes in a nematic solvent was based on the idea that these flexible solutes would acquiesce to the nematic mean field and thereby exhibit considerably perturbed properties relative to isotropic state. In fact, much coarser attempts to model alkane solute behavior were suggestive of such perturbation^.^^-'^ Herein, we conclude that conformer probabilities and properties in the nematic state are not very different from those in the isotropic
state; Le., the alkane conformers are highly oriented in the liquid crystal while these solutes sample many conformations of comparable internal energy. Acknowledgment. We thank J. G. L. Pluyter, C.-D. Poon, and D. L. Harris for help with the NMR measurements and K. D. Mar for advice with the graphics. This work was supported by subcontracts from the Liquid Crystalline Polymer Research Center, University of Connecticut (DARPA/ONR Contract No. N0014-86-K-0772),and Los Alamos National Laboratory (DOE subcontract 9-X59-7021-R-I) and by the NSF (capital equipment grant CHE 8821 173).
( I 3) Samulski, E. T. Ferroelectrics 1980, 30, 83. (14) Samulski, E. T. Isr. J . Chem. 1983, 23, 329. ( I 5) Samulski, E. T. Polymer 1985, 26, 177. (16) Janik, 8.;Samulski, E. T.; Toriumi, H. J . Phys. Chem. 1987, 91, 1842.
Registry No. Pentane, 109-66-0; hexane, 110-54-3; heptane, 142-82-5; octane, 1 11-65-9; hexadecane, 544-76-3.
HCI/H20 SolldPhase Vapor Pressures and HCI Solubility in Ice David R. Hanson and Konrad Mauersberger* School of Physics and Astronomy, University of Minnesota, Minneapolis. Minnesota 55455 (Received: August 8, 1989; In Final Form: December 5, 1989)
A study of the HCI/H20 binary system at low temperatures is presented, and applicationsto the polar stratosphereare discussed. A phase diagram constructed for low HCI partial pressures includes the tri- and hexahydrates as well as solid solutions of HCI in ice. Results of two experiments strongly suggest that the solubility of HCI in ice is low, less than 0.01 mol % for
stratospheric conditions. Previous measurements have shown HCI to be orders of magnitude more soluble in bulk ice. The nitric acid trihydrate crystal, which is formed above ice condensation temperatures in the polar stratosphere, shows a much greater ability to absorb HCI than does pure ice for HCI pressures characteristic of the stratosphere.
Introduction Since the discovery of the south polar ozone hole, heterogeneous chemistry on ice and ice mixtures has been proposed to explain the formation of active chlorine. Such a chemistry includes the removal of odd nitrogen species, particularly HN03, from the gas phase via condensation into the nitric acid trihydrate (NAT) or ice mixtures that are observed as polar stratospheric clouds (PSCs). In addition, stratospheric HCI has to be deposited onto these cloud particles to participate in heterogeneous reactions. A summary of those and other processes has been presented by Solomon.' While the formation of NAT particles has been established in laboratory tests2 and also found in field meas~rements,~ the solubility of HCI in ice has not been completely resolved. HCI will form, as a binary mixture with water, a number of hydrates and solid solutions whose thermodynamic properties must be known to predict the behavior under stratospheric conditions. Historically, Pickering? R ~ p e r tand , ~ Vuillard6 measured the freezing points of HCI solutions and identified several crystal hydrates: the mono-, di-, tri-, and hexahydrates. A number of investigators7+' determined the vapor pressures of HCI solutions near room temperature, which were extrapolated by Wofsy et aI.Io
and Toon et al." to stratospheric temperatures. They concluded that HCI could condense, on the order of a few mol %, onto PSC particles composed of ice. Substantial discrepancies exist in solubility and partition coefficient measurements of HCI in water ice. Early work at low HCI concentrations indicates that HCI is incorporated into single-crystal ice at a very low level. DeMicheli and Iribarne,I2 Gross,I3and Seiden~tickerl~ measured the distribution or partition coefficient of HCI in single-crystal ice grown near 0 "C about 100-1000 times lower than that measured by Wofsy et a1.I0 at much lower temperatures. These earlier workers noted the difficulty in growing single-crystal ice at higher HCI concentrations and lower temperatures. More recently, Gross et al., in a series of p u b l i ~ a t i o n s , l ~ - ~ ~ demonstrated that the HCl/ice partition coefficient was concentration independent for crystals grown from starting concentrations of 10"-10-' M (mole/liter). They eliminated solute concentration gradients by vigorous stirring in the liquid and slowly growing the crystal. They determined a distribution coefficient of 0.0027 for HCI in ice. At liquid concentrations above 0.10 M (0.18 mol %), the crystals became cloudy and the "apparent"
( I ) Solomon, S. Reu. Geophys. 1988, 26, 131. (2) Hanson, D.; Mauersberger, K. Geophys. Res. Lett. 1988, I S , 855. (3) Fahey, D. W.; Kelly, K . K.; Ferry, G. V.; Poole, L. R.; Wilson, J . C.; Murphy, D. M.; Loewenstein, M.; Chan, K. R. J . Geophys. Res., in press. (4) Pickering, S. U . Ber. Dtsch. Chem. Ges. 1893, 26, 277. (5) Rupert, F. F. J . Am. Chem. SOC.1909, 31, 851. (6) Vuillard, G. C. R . Acad. Sci. 1955, 241, 1308. (7) Miller, E. J . Chem. Eng. Dura 1983, 28, 363. (8) Perry, R. H.; Chilton, C. H.; Kirkpatrick, S.D. Chemical Engineers Handbook, Sth ed.; McGraw-Hill: New York, 1973. (9) Fritz, J. J.; Fuget, C. R. Ind. Eng. Chem., Chem. Eng. Data Ser. 1956,
(10) Wofsy, S. C.; Molina, M. J.; Salawitch, R. J.; Fox, L. E.; McElroy, M. B. J . Geophys. Res. 1988, 93, 4442. ( I I ) Toon, 0. B.; Hamill, P.; Turco, R. F.; Pinto, J. Geophys. Res. Lett. 1986, 13, 1284. (12) DeMicheli, S. M.; Iribarne, J. V. J . Chim. Phys. 1963, 60, 767. ( I 3) Gross, G. W. J . Colloid Interface Sci. 1967, 25, 270. (14) Seidensticker, R. G. J . Chem. Phys. 1972, 56, 2853. (15) Gross, G. W.: McKee, C.; Wu,C. J . Chem. Phys. 1975, 62, 3080. (16) Gross, G. W.; Wu, C.; Bryant, L.; McKee, C . J . Chem. Phys. 1975, 62, 3085. (17) Gross, G. W.; Wong, P. M.; Humes, K. J . Chem. Phys. 1977, 67, 5264. (18) Gross, G. W.; Gutjahr, A.; Caylor, K . J . Phys. Coll. 1987, CI, 527.
I . IO.
0022-3654/90/2094-4700$02.50/0
0 1990 American Chemical Society
HCI/H20 Solid-Phase Vapor Pressures distribution coefficient rose steeply. They attributed this to interface breakdown and occlusion of liquid droplets. They also postulated the existence of a solubility limit for HCI in single crystal ice of about 0.0008 mol %. Wolff et aI.l9 studied the incorporation and movement of HCI within the structure of ice using X-ray analysis. They showed that HCI is not easily incorporated into ice crystals at low temperatures. From these experiments they derived an upper limit for the partition coefficient of 0.002. Molina et aL20 found that HCI had a large affinity for ice in several experiments, for temperatures as low as 185 K. Because large amounts of HCI were taken up, they stated that HCI is probably dissolved in bulk ice rather than adsorbed on surfaces. In these experiments, the bulk ice was observed to be polycrystalline, the vapor-deposited ice appeared as a frost, and the HCI partial pressures were about a 100 times greater than those found in the stratosphere. Ice samples were grown by Wofsy et a1.I0 at temperatures characteristic of the stratosphere, in starting solutions between 3 and 14 mol % HCI. Some samples were made by vapor deposit of water with HCI. For both these sets of measurements, the ice was observed to be frosty in appearance, and the partition coefficient was determined to be 0.25-0.30. Hanson and Mauersbergerz1measured the pressure vs composition behavior of HCI in small amounts of vapor deposited ice and NAT. They also presented a treatment of the HCI/H20 system using the Gibbs-Duhem relation and the partition coefficient of Wofsy et al.IO The measurements, performed at 200 K and HCI pressures typical of the stratosphere, implied that HCI was physically absorbed in ice without dissociation. They also corroborated the partition coefficient measurements of Wofsy at the 200 K three-phase equilibrium. The dissolved HCI content was about one-third the concentration of the liquid when the HCI pressure was near Torr. At stratospheric HCI pressures near IOd7 Torr, however, only 0.03 mol % was dissolved into ice while Wofsy predicted over 1%. In addition, it was found that the amount of absorbed HCI (at 200 K and an HCI pressure of IO-’ Torr) was about 20 times higher in NAT than in ice. The study of the HCI/H20 system has been continued to obtain a broader understanding of its thermodynamic properties and to investigate the discrepancies in the solubilities, as discussed above. This paper reports on results in the following areas: A new phase diagram of the HCI/H20 system has been constructed from vapor pressure measurements over solid and liquid phases at low temperatures. The solubility has been investigated by using vapor pressure measurements over pure ice and HCI-ice solutions and applying Raoult’s law. Finally, the dependence of the HCI solubility measurements on the surface/volume ratio of the solvent was examined. Experimental Section The configuration of the apparatus is similar to the one used in earlier experiments with HN0,2,22and HCL2I The main part is a gold-plated stainless steel chamber that is at room temperature where vapor pressures are measured. Connected to the chamber are a glass coldfinger (still) where the condensed substrate is maintained at constant temperature, a high-precision capacitance manometer, vacuum lines for gas supply and pumpout, and a mass spectrometer gas analysis system.23 A small amount of gas is continuously sampled from the main chamber and formed into a molecular beam to be analyzed by the mass spectrometer. In this way, the partial pressures of HCI and H 2 0 as well as impurities such as 02,N2, and others are monitored. Calibrations of the analysis system are performed before and after actual HCI/H20 measurements. The lowest pressures to be monitored (19) Wolff, E.W.; Mulvaney, R.; Oates, K. Geophys. Res. Leu. 1989, 16, 487. (20) Molina, M. J.; Tso, T. L.; Molina, L. T.;Wang, F. C. Science (Washington. D.C.) 1987, 238, 1253. (21) Hanson, D.; Mauersberger, K. Geophys. Res. Lerr. 1988, I S , 1507. (22) Hanson, D.; Mauersberger, K . J . Phys. Chem. 1988, 92, 6167. (23) Mauersberger, K.; Finstad, R. Reo. Sci. Insrrum. 1979, 50, 1612.
The Journal of Physical Chemistry, Vol. 94, No. 11, I990 4701
o~
i
Log PH20,Torr Figure 1. HCI/H20 phase diagram. The figure shows the HCI and H,O pressure regions over which phases are stable. A few temperature isotherms are also included. Measurements were performed along the phase boundaries and also over the single phases liquid and trihydrate: small open and closed circles are symbols for measurements over bulk solutions, and pluses for vapor-deposited substrates. The dashed lines are estimated coexistence curves for the hexahydrate. The curved line is the vapor pressures over a supercooled liquid at 190 K. Isotherms for solid phases at 180, 190, and 200 K are shown. The dotted line represents stratospheric pressures of H20 and HCI for mixing ratios of 3 ppm and 2 ppb, respectively.
in the main chamber are HCI partial pressures of approximately Torr. The capacitance manometer has a I-Torr full range and a resolution of 5 X IO” Torr on the lowest scale. The system with the mass spectrometer is bakeable at 200 OC to maintain ultrahigh vacuum conditions. The substrate is condensed into the cold still from either pure or mixed vapors made in the main chamber, allowing the determination of the amount condensed. Vapor pressures above the substrates are established as the temperature of the coldfinger is regulated. A small correction is applied due to the temperature difference between the vapor directly over the substrate and the vapor in the main ~ h a m b e r . ~In~ a. ~number ~ of tests, after the vapor pressure measurements, the substrate was warmed and vaporized, and the vapor analyzed to determine its composition. This paper presents a number of different experiments performed on the HCI/HzO system using the apparatus described above. More experimental detail will be provided as the results of each investigation are presented. Results (1) H C I / H 2 0 Phase Diagram. To provide a better understanding of the behavior of the solid phases formed in HCI/H20 mixtures, the vapor pressures over liquid and solid phases were investigated at low temperatures. The following procedure was used to grow the trihydrate crystal: Vapor depositions of H 2 0 in the presence of about 5 mTorr of HCI were made at temperatures of 170-190 K. Initially, a thin, translucent film appeared, probably the supercooled liquid. Irregular, opaque solid particles began to form, and the film slowly diminished. Crystal growth was accelerated by raising the composition of the supercooled film to 20-25 mol % HCI through increasing the HCI pressure and cooling to 170 K. After the solid was sufficiently grown, the remaining film could be removed by pumping on the substrate, although it may disappear upon (24) Poulter, K. F.; Rodgers, M.-J.; Nash, P. J.; Thompson, T.J.; Perkins, M. P. Vacuum 1983, 33, 31 1. (25) Yasumoto, I . J . Phys. Chem. 1980, 84, 589.
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The Journal of Physical Chemistry, Vol. 94, No. 11, 1990
warming to 190 K. The vapor pressures over the crystal could be manipulated by adding or removing vapor. Vapor pressure measurements were made at 180, 190,200, and 205 K and the results are plotted as pluses in Figure I , which is a revised HCI/H20 phase diagram of Hanson and Mauersberger.21 Lines added to the first three temperatures are isotherms drawn through the data in accord with the Gibbs-Duhem relation. For a binary system, this relation states that the slope of an isotherm, presented in a plot such as Figure I , is the negative of the ratio of the constituents in the condensed phase, in the case of the trihydrate, 0.75 H 2 0 to 0.25 HCI. The associated phase boundaries and the isotherms for the other phases will be discussed below. Periodically, the composition of the substrate was measured by vaporizing it and analyzing the resultant vapor with the mass spectrometer system. The composition of the trihydrate averaged about 24 mol 5% HCI, close to the stoichiometric value. Also shown in the figure is a line for the supercooled liquid at I90 K. This line was obtained by extrapolating liquid HCI vapor pressure data to 190 K8,9 and calculating the H 2 0 pressures by using the Gibbs-Duhem equation and assuming that the pressure over a 13.6 mol 5% solution at 190 K is the ice pressure.26 The H 2 0 pressures obtained in this manner were about 40% less than the extrapolated values of Perry.8 Measurements were also made over the initially deposited film with no crystal present, and the results lie on the line obtained through extrapolation. Binary mixtures have three-phase equilibria where two condensed phases and vapor coexist. These equilibria form characteristic lines on phase diagrams, and a set of solid/liquid coexistences was presented by Wofsy et a1.I0 and Hanson and Mauersberger.21 The current, solid lines in Figure l are the pressures over coexisting phases, drawn through the measurements presented here. This new phase diagram includes the hexahydrate. The small open circles are the “ice”/liquid vapor pressures of Hanson and Mauersberger*I performed over bulk solutions, and the triangles are trihydrate/liquid coexistences performed over the vapor-deposited substrates discussed above. The coexistence was obtained by growing the trihydrate and adding water vapor until the vapor pressures became constant, which indicated that a second condensed phase arose, the liquid. For a given temperature, the partial pressures over two coexisting phases are uniquely determined. We attempted to grow the hexahydrate from the vapor in two ways: by temperature cycling a vapor-deposited 6:1 H,O/HCI mixture or through establishing the coexistence of the hexahydrate with either “ice” or trihydrate by manipulating partial pressures, as described above. No crystalline-like deposit arose, and the initial supercooled film was seen to persist after repeated temperature cycling of a 6: I mixture between 190 and 170 K . We were also unable to establish a coexistence involving the hexahydrate through manipulating the partial pressures over the “ice” or trihydrate substrate. We believe we obtained one of the metastable threephase equilibria, either “ice”/supercooled liquid, “ice”/trihydrate, or trihydrate/supercooled liquid, because vapor pressures were near these metastable coexistence curves as given by Wofsy et a1.I0 and Hanson and Mauersberger.21 Vuillard6 noted the difficulty in crystallizing the hexahydrate from solution, and Pickering4 never produced consistent results in the composition range of the hexahydrate. The vapor pressures of the supercooled liquid are very close to the expected pressures over the hexahydrate, as shown in Figure I , where the 190 K isotherms for the supercooled liquid and the hexahydrate are compared. As a result, the supercooled liquid could persist at temperatures well into the hexahydrate stability region, and thus growing the hexahydrate through the vapor phase becomes difficult. For these reasons, Vuillard’s melting point curve and the liquid vapor pressure data were utilized to produce a liquid/hexahydrate coexistence curve. Estimates of the three-phase lines between two solid phases can be made on the basis of previous measurements. The dashed lines are solid coexistence curves for trihydrate/hexahydrate and (26) Jancso, G.; Pupezin, J.; Van Hook, W . A. J . Phys. Chem. 1970, 7 4 , 2984.
Hanson and Mauersberger “ice”/hexahydrate which were produced by assuming that they are parallel in the phase diagram (one implication of this is that the hexahydrate is stable at all temperatures below 203 K) and that the vapor pressure isotherms over the hexahydrate have a slope of -6. The slope of these lines were slightly different than the corresponding liquid vapor pressure lines, as was found for the H N 0 3 / H 2 0 system.2,22 The estimated curve for “ice”/ hexahydrate coexistence is also the lower boundary for the HCI pressure over the hexahydrate. An attempt was made using bulk mixtures to measure the trihydrate/hexahydrate coexistence curve, and the results are discussed below. The dotted line in the figure is H 2 0 and HCI partial pressures corresponding to mixing ratios of 3 ppm and 2 ppb, respectively, for an altitude range of 12-20 km (a pressure range of 160-40 mbar) over the south pole. Only under very cold conditions, when frost points corresponding to 0.3 ppm H 2 0 would be reached, could the hexahydrate form in coexistence with ”ice”. Such temperatures are not found in the lower stratosphere, even during polar winter,27,28and thus, for the HCI/H20 system, the HCI-in-ice solid solution (“ice”) forms in the atmosphere. This condition would have to be revised if measurements show that the HCI pressures over the ”ice”/hexahydrate coexistence are greatly different from the estimates in Figure 1 . A removable glass still was also connected to the chamber, and vapor pressures were measured over bulk liquids near the eutectic solutions of 0.128 and 0.151 mole fraction HCL6 The results are presented as small closed circles in Figure 1 with lines drawn through the data and the mole fraction HCI indicated. Measurements were performed over solutions of x = 0.132 and 0.146, and the pressures were found to be in agreement with respect to the measurements over the eutectic solutions. The line labeled 0.1 18 presented here is drawn through data over an x = 0.1 18 mole fraction solution, taken during the same runs as previous data.21 The HCI pressures at the freezing points for the eutectics lie about 30%over the quadruple points inferred from ice/liquid and trihydrate/liquid measurements discussed earlier. This implies that there is a systematic error in either the bulk liquid or liquid/solid coexistence vapor pressures measured here or that the eutectic liquids have a lower HCI content than that reported by Vuillard, possibly 0.126 and 0.148 mole fraction. The upper ends of the two estimated hexahydrate coexistence curves are taken to lie halfway between the quadruple points taken from the measured vapor pressures over the 0.128 and 0.15 1 mole fraction solutions and the quadruple points inferred from the liquid/solid coexistences reported here. Some of these solutions were frozen to measure the three-phase equilibria, particularly the trihydrate/hexahydrate. The x = 0.146 solution was frozen by supercooling to 77 K and warming to 180 K, whereupon crystals formed on top of the bulk near the glass surface. The crystals began to grow quickly, and the whole bulk crystallized in about 1 min. Assuming that the composition of the hexahydrate does not vary significantly from the stoichiometric ratio, 0.1429 mole fraction, an x = 0.146 solution, at temperatures below 200 K, should form a mixture of the tri- and hexahydrates and the vapor pressures should be found on the trihydrate/hexahydrate coexistence curve. The data represented by large open circles were taken over the frozen solution at 200, 195, and 190 K and lie near the estimated curve. Since thermodynamic equilibrium between two bulk solids is difficult to obtain, these data are considered to be a rough check of the estimated curve. ( 2 ) Solid Solutions of HCl in Ice. For stratospheric applications, solid solutions of HCI in ice are of particular importance since partial pressures of HCI and H 2 0 would form “ice” rather than any of the hydrates, as demonstrated above and in previous publications.l0.”S2’ A 12.6 mol % HCI solution begins to freeze out “ice” at 200 K.6,4 A partition coefficient of O.3I0 leads to “ice” (27) Newman, P. A,; Lamich, D. J.; Gelman, M.; Schoeberl, M. R.; Baker, W.; Krueger, A . J. Meterological Atlas of the Southern Hemisphere Lower Stratosphere for August and September 1987. NASA Technical Memoran-
dum 4049, Report no. NASA TM-4049, 1988. (28) Rosen, J. M.; Hofmann. D. J.; Carpenter, J. R.; Harder, J. W . Geophys. Res. Lett. 1988, IS, 859.
The Journal of Physical Chemistry, Vol. 94, No. 11, 1990 4703
HCI/H20 Solid-Phase Vapor Pressures
+ 8
+ ++
0, nz
a
f =1
-8 0
I
\
I
I 1
2
\f=2 4
1
6
8
1 .o
10
HCI, mol-%
0.01
0.001
X, mol-%
Figure 2. Percent difference in H 2 0 pressure for doped and pure ice samples vs amount of HCI in the sample. The lines labeled f = 1, 2 are
Figure 3. Pressure of HCI vs composition in the substrate was measured
along with the amount of substrate. The five ranges of substrates are 0.1-0.4,0.4-1.5, 1.5-6.0, 30-50, and 200-300 pmol and are labeled A, B, C, D, and E, respectively. The line labeledf= 1 is the result found in Hanson and Mauersberger?’ where substrates between 0.4 and 4 pmol were used.
expected H 2 0 pressure deviations of an ideal solution for large amounts of HCI incorporated into the ice.
containing 4 mol % HCI while the much lower partition coefficient of 0.002717-18 leads to “ice” with a dissolved HCI content of about 0.03 mol %. The following experiments ; were performed 0 0to investigate the discrepancy between these measurements. ( a ) Pressure of H20over “Ice”: Raoult’s Law. The partial pressure of a solvent should be lowered upon addition of a solute, according to Raoult’s law. Measurements were performed by depositing a pure ice substrate, noting the vapor pressure, and then ’doping” the sample with HCI and measuring the resultant H 2 0 pressure. Usually very small amounts of ice were used, 1-2 kmol. HCI vapor deposition pressures could be varied between 0.001 and 0.03 mTorr. The sample was maintained at a constant temperature near 200 K. The H 2 0 partial pressure was noted before and after the addition of the HCI, and the composition of the substrate was measured by rapidly warming it and determining the HCI content with the mass spectrometer system. The results of several different ice deposits are presented in Figure 2 as percent difference in H 2 0 pressure vs mol % HCI found in the substrate. The scatter for each point, usually less than *I%, is mainly due to the occasional sensitivity drifts of the gas analysis system over periods of hours, as temperature drift error, h0.02 K (equivalent to f0.3% in pressure), was very small. It was noted that the points below the zero line were obtained when the gas analysis was less stable, and thus the error associated is somewhat larger than for the other data. The dashed lines are expected deviations for dissociated and undissociated solute assuming a partition coefficient of 0.30. These lines would be expected to flatten out for HCI content between 4 and 12.6 mol % because the H 2 0 pressure remains constant when the threephase equilibrium “ice”/liquid( 12.6%)/vapor is established. Although the released content of the substrates show various amounts of HCI to be associated with the ice, no significant decreases in the H 2 0 pressure were observed. ( b ) P us X with Varying Amounts of Substrate. To distinguish surface effects from bulk solubilities in the measurements presented by Hanson and Mauersberger,*I the vapor pressure and composition of HCI in “ice” were studied as a function of substrate mass. These measurements were performed the same way as discussed in subsection 2a and by Hanson and Mauersberger,21 except that the amount of water frozen was varied between 0.1 and 300 pmol. The results are presented in Figure 3, which is a plot of HCI pressure vs composition with the mass of the substrate grouped into five ranges. The data show more scatter than random measurement error. We believe this is due to the nonreproducibility of the vapor deposition process. However, the five aggregates show a clear trend: a lower composition for greater substrate mass, at a given partial pressure of HCI. This can be interpreted two ways: As the mass of the substrate increased (i) the surface effects becomes less important with respect to the bulk ”ice” behavior and/or (ii) equilibrium was not reached for the larger amounts because of longer diffusion times in the bulk.
0.1
0
A
W
1
0.35 mol-%
0
[
100
v
n
1
;
L
z 01 10
10
01
001
0.001
00001
HCI Content, mol-% Figure 4. Data bins from Figure 3, at PHCl= lod Torr, plotted as boxes. The lines labeled 0.1 and 1.5 indicate results for constant amounts of HCI condensed, in nanomoles. The amount of HCI homomolecularly adsorbed on the cold still is less than 0.1 nanomol, while an H 2 0 film, present on the cold glass when the H 2 0 pressure is near the ice pressure, adsorbs 1-2 nmol. The vertical lines in the figure indicate estimates of the bulk solubility of “ice” from two different partition coefficient measurements, Wofsy et and Gross.” The solubility limit (SL) for HCI in ice given by Gross et al.” is 0.0008 mole %. The N’s are symbols for data taken with NAT substrates; the bulk solubility for HCI in NAT for these conditions is shown by the dotted line.
To investigate this, the data in Figure 3, at an HCI pressure of 10” Torr, have been plotted as boxes in Figure 4,a plot of substrate mass vs HC1 content. The dashed vertical lines are expected bulk compositions from use of the two different partition coefficients, adjusted to 10” Torr, assuming that PHc! is proportional to x2.21 The solid lines along the diagonal indicate constant amounts of HCI in nanomoles; they will be discussed in more detail below. Assuming diffusive equilibrium, this figure shows that the lower partition coefficient of Gross et al.I7*I8more closely describes the thermodynamic equilibrium HCI-in-ice, and the data suggest that the bulk HC1 content of ice under these conditions is possibly less than that predicted by using this partition coefficient. The arrow at 0.0008 mol 9% indicates the value implied by Gross et al.” for the solubility limit of HCI in single-crystal ice. It is also clear that surface adsorption/absorption of HCI in this experiment is substantial for small amounts of substrate. The substrate usually covered only a small portion of the glass, so effects due to exposed cold glass were investigated. HCI adsorbed on glass would artificially increase the amount of HCI measured to determine the composition of the ice. The HCI
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The Journal of Physical Chemistry, Vol. 94. No. I I 1990
adsorbed on the cold glass, exposed to a given pressure of HCI, was determined by noting the increase in the HCI pressure upon rapidly warming the glass to room temperature. The amount of HCI adsorbed on the cold glass (at a pressure of 10” Torr in the absence of water vapor) was less than a 0.1 nmol; this amount of HCI is indicated by the lower diagonal line in Figure 4. Similarly, heteromolecular adsorption of HCI and H 2 0 would affect the composition measurements. In the presence of 1.2 mTorr of H 2 0 , HCI adsorbed on the surface was found to be between I and 2 nmol for HCI partial pressures near 10” Torr and the amount of adsorbed water was about 60 nmol. The exposed glass has a surface area of 20 cm2 and, assuming uniform coverage, this results in about 2 X lOI5 molecules/cm2 for H20, a reasonable value for a few water layers covering the glass.29 It is clear from the results shown in Figure 4 that the HCI content of the smallest mass ranges is dominated by HCI adsorbed with water on the glass still, indicated by the diagonal line marked 1.5 nmol. As the amount of substrate increases, the HCI associated with the ice will contribute to the amount of HCI found in the still, both in the bulk and to some extent on the ice surface. Since the surface area of the substrates was unknown, we were unable to make a reliable estimate for the amount of HCI residing on the ice surfaces. A few measurements were made with the nitric acid trihydrate (NAT) as the substrate, and the results are plotted as N’s in Figure 4. As demonstrated in the figure, the HCI content vs mass behavior of NAT substrates is very different from that of “ice” substrates. For HCI pressures near 10” Torr, the HCI solubilities in NAT were always greater than the ice solubilities, as demonstrated by Hanson and Mauersberger.21 For small amounts, a possible explanation for the behavior of the data in Figure 4 is that an NAT or amorphous H N 0 , / H 2 0 layer coats the glass and this layer adsorbs HCI to about 0.1 fractional surface coverage, 10 times that of a water layer on glass. As the amount of NAT increases, the HCI content reaches a limiting value of about 0.3 mol %. This suggests that the HCI is not associated with the exposed glass but is dissolving into the bulk of the NAT crystals, and these results show about 0.3 mol 5% HCI contained in NAT substrates at 200 K and an HCI partial pressure of 10” Torr. This work places the HCI content of “ice” at a maximum of 0.01 mol % and that of NAT at 0.3 mol % for an HCI pressure of IO4 Torr and a temperature of 200 K. Assuming that the HCI adsorption behavior on an “ice” surface is similar to that for water layer(s) on glass, the surface coverage of HCI on ”ice” surfaces could be substantial. About 1 HC1 per 100 H 2 0 molecules or approximately l O I 3 HCI molecules/cm2 were found for water layers adsorbed on glass at 200 K and an HCI pressure of IO” Torr. These results also explain the HCI-ice measurements of Hanson and Mauersberger2’ where the HCI partial pressure was found to be proportional to mole fraction x , rather than proportional to the square of x. For isothermal adsorption at low pressures, the surface coverage of a gas is proportional to its partial pressure,29 and thus these measurements were actually representative of the adsorption isotherm of HCI on a water surface.
Discussion A rough estimate of the diffusion time constant for the system can be made using the characteristic times for a layer of thickness d: T = &/D. With the self-diffusion coefficient of ice near 0 OC, IO-1 I cm2/s,29a 1-pm layer would equilibrate on the order of 1000 s. A much higher value of the diffusion coefficient for HCI in ice, cm2/s, was observed by Molina et al.,20resulting in a much shorter time. This value, more characteristic of liquids than solids, was explained by an interstitial diffusion mechanism rather than substitutional. The diffusion coefficient was not rigorously measured, however, and because of the high HCI pressures used, an HCI hydrate of liquid HCI/H20 could have been present. A I-pm layer, spread over I cm2, contains 5 pmol of ice. For the (29) Hobbs, P . V. Ice Physics; Clarendon Press: Oxford, 1973. (30) Orem, M. W.; Adamson, A . W. J . Colloid Interface Sci. 1969, 31, 278.
Hanson and Mauersberger data in Figures 3 and 4, the HCI content of a 5 pnol substrate is 10 times less than that of a 0.2 pmol substrate, and times as long as 2 h were allowed for settling. The large substrates covered more area, 10-20 cm2. In addition, a few points were taken by co-depositing the water and HCI: there seemed to be no difference between these two techniques. These considerations indicate equilibrium is sufficiently attained for these measurements. The results obtained from the experiment applying Raoult’s law to “ice” support these conclusions. If “ice” acts as an ideal solution and obeys Raoult’s law, then the null result of the depression of the H 2 0 pressure over HCI-doped ice also indicates that very little HCI is incorporated into the ice crystals at thermodynamic equilibrium. At a temperature of 200 K, the HCI resides at 12.6 mol % liquid solution in equilibrium with “ice” for HCI pressures of Torr, and the H 2 0 pressure is very close to that over pure ice. For HCI pressures that are found within the “ice” stability region, much less HCI would be found in the “ice” substrate. This being the case, the HCl/H20 measurements of Wofsy et a1.,I0 Molina et al.,*O and Hanson and Mauersbergerzl would not apply to the thermodynamic equilibrium HCI-in-single-crystal ice solid solution. Previous r e s e a r c h e r ~ ’ have ~ - ~ ~noted that ice grown at low temperatures in concentrated solutionsI0 is very difficult to keep free of occluded liquid, which skews partition coefficient measurements. Likewise, when vapor deposit experiments are performed with relatively high HCI partial pressures,’0,20other phases of the HCI/H20 system can be formed. Even when the HCI partial pressure is characteristic of the stratosphere, HCI shows a large affinity for adsorbed water on glass, and this effect was misinterpreted in previous work2’ as representing the HCIin-ice system. The results presented here confirm studies recently published by Wolff et a1.,I9 who measured a very low solubility of HCI in ice and gave an upper limit for the partition coefficient of 0.002. In addition, the measurements presented here confirm that the NAT crystal absorbs considerably more HCI than the ice crystal under stratospheric conditions.2’ The observation that NAT can absorb much more HCI than ice at low HCI pressures indicates that the ternary system HCI/HN0,/H20 is more important for the stratosphere than the binary system HCI/H,O. One explanation for the enhanced affinity of HCI for NAT is that the NAT crystal appears to have an excess of water and thus has HNO, vacancies: its composition under stratospheric conditions is near 0.20 mole fraction.2 This might allow for HCI to occupy sites, forming an HCI hydratein-NAT solid solution. Assuming this approximation is valid for small amounts of HCI in NAT, HCI would have a unique relationship for partial pressure vs composition at a given temperature and H 2 0 p r e s s ~ r e . ~ ’Hanson ? ~ ~ and Mauersberger2’ noted that the ability of the NAT crystal to absorb HCI was strongly dependent upon the H 2 0 pressure; this was also noticed in these experiments. The HNO, content of NAT has been observed2 to vary with H 2 0 pressure, and this would presumably affect the HCI solubility. For this reason, it was necessary to keep the NAT crystal within 2 OC of the ice frost point, or much less HCI could dissolve into the crystal. These are the approximate conditions in the polar stratosphere as well. The variation of the HCI content of “ice” was shown by Hanson and Mauersberger*’ to depend upon the ratio of the partial pressure of HCI to the HCI pressure at the upper boundary of the ‘ice” stability region at that temperature. For dissolution of electrolytes, the HCI content would decrease in proportion to the square root of this ratio, and for physical adsorption it would decrease in proportion to this ratio. The proportionality factor for dissolution is determined by the HCI content of “ice” at its phase boundary, and for NAT must be determined by pressure vs composition measurements. Similarly, the adsorption behavior on either surface must be determined by measurement. ( 3 I ) Kroeger, F A The Chemistry ojlmperfect Crystals; North-Holland. Amsterdam, 1982, Chapter 2 (32) Findlay, A , Campbell, A N , Smith, N 0. Phose Rule and Its Applicarion, 9th ed , Dover Publrcatrons New York, 1951, Chapter 2 and 3
J . Phys. Chem. 1990, 94, 4105-4712 Stratospheric partial pressures, shown by the dotted line in Figure 1, are a factor of 10-20 below the HCI pressure along the “ice”/hexahydrate coexistence curve, given as log (Pi/),(Torr)) = 10.00 - 2970/T (where subscript i/h denotes the value along the “ice”/hexahydrate coexistence). Assuming that a solubility limit for HCI-in-ice is not reached and that the composition of “ice” coexisting with the hexahydrate does not vary much and its value is that at the eutectic, we have xi/h = 0.0027(0.1285) x(pHCI) = xi/h(pHCI/pi/h)o’s and the HCI content of ”ice” for stratospheric conditions is about 0.009 mol %. The data in Figure 4 for NAT were taken at an HCI pressure a factor of I O below the HCI pressure at the phase boundary, and thus, assuming that the temperature variation of the HCI in NAT solubility is similar to HCI in “ice”, the HCI content of NAT in the stratosphere would be about 0.3 mol %. The bulk solubility of HCI in ice presented here suggests a very slow HCI content of ice particles in the stratosphere. According to Leu,33the heterogeneous reactions of C10N02 and N 2 0 Son ice with very low HCI content is primarily with water, and thus HCI reactions on NAT become very important for activating the chlorine that is contained in the HCI reservoir. The heterogeneous reactions have not as of yet been studied on NAT surfaces; however, Tolbert et reported reactions on sulfuric acid solutions at stratospheric temperatures and noted that dissolved HCI (33) Leu, M. T. Geophys. Res. Leu. 1988, I S , 8 5 5 . (34) Tolbert, M. A.; Rossi, M . J.; Golden, D. M. Geophys. Res. Lett. 1988, I S , 847.
4705
was readily available for reaction at concentrations as low as 0.02 mol % HCI. It is not clear that the reactions involving HCI in ice have been measured under conditions that would ensure that only “ice” were present. Coexisting liquid or HCI hydrate could be present if the HCI pressure is outside the “ice” stability region. In addition, Turco et al.” discussed the requirements imposed upon heterogeneous reactions by the dechlorinating effects of the sedimentation of ice particles in the cold, polar stratosphere. This concern arose because of the recent measurements’0,20suggesting high HCI solubilities in ice. Hanson and Mauersberger2I estimated that 60% of the HCI reservoir could be absorbed on ice clouds with a frozen water content of 2 ppmv. A new estimate for the amount of HCI condensed in ice particles can be made assuming a maximum of 0.01 mol % HCI content. The amount of HCI dissolved in 2 ppmv of ice is then about 0.2 ppbv out of a total HCl content of 2 ppbv. This is a small fraction of the chlorine reservoir, and the requirement that chlorine become activated before sedimentation occurs can be relaxed. The conclusion by Turco, however, that heterogeneous reactions on NAT are the major source of active chlorine is supported by the measurements reported here. More study of heterogeneous reactions on NAT and ice at low HCI pressures are needed to determine how heterogeneous mechanisms might be responsible for the release of active chlorine.’ This is now one of the most important aspects concerning the polar ozone holes. In addition, the HCI adsorption/absorption behavior on sulfuric acid mixtures is needed to determine the HCI affinity for stratospheric aerosols present globally. (35) Turco, R. F.; Toon, 0. 9.; Hamill, P. J . Geophys. Res., in press.
Simulation of Polymer Chain Dynamics with Small Organic Molecules and Their Mixtures S . Havriliak, Jr. Modifiers Research Department, Rohm and Haas Co., Bristol, Pennsylvania 19007 (Received: September 5, 1989)
Experimental simulation of polymer properties or structure with small organic molecules is a well-known technique that appears not to have been applied to the study of polymer chain dynamics. In this work we apply this simulation methodology by examining the dielectric relaxation data on isoamyl bromide and its mixtures with 2-methylpentane reported by Denney et al. These molecules form an interesting pair for study because they are isometric, they form solutions over their entire composition range, and one of them is a simple polar molecule while the other is nonpolar. They also tend to form glasses rather than crystallize when cooled to low temperatures. Denney’s relaxation data are represented in terms of a function proposed by Havriliak and Negami for polymers. The parameters of this function as well as their dependence on temperature were determined by using the multiresponse techniques developed by Havriliak and Watts. The dynamic parameters for the mixtures in the 50-75 mol % range of isoamyl bromide are similar to the parameters for the a-relaxation process of many polymers previously reported. The parameters are discussed in terms of the general Kirkwood-Cole theory of polar liquid relaxation and Mansfield’s specific model for polymer chain dynamics. The experimental results described in this work support the results derived from Mansfield‘s model for polymer chain dynamics, Le., the shape of the dielectric relaxation process when viewed in a complex plane is not due to molecular weight but is due to the nature and relative magnitudes of the intramolecular and intermolecular interactions.
Introduction This paper is another in a series of papers directed at a better understanding of the dynamics of polymer chains above and below their glass transition region. Simulation of polymer properties with small (organic) molecules is a time-honored pursuit in the study of polymer structure property relationships. For example, Liang et a1.I were among the first to examine the idea that polymer ( I ) Liang, C. Y.;Krimm, S.; Sutherland, G. B. B. M.J . Chem. Phys. 1956, 25(3), 543.
chain vibrations in the infrared region may actually be understood by studying a series of linear hydrocarbons of differing molecular weight. More recently Paul2 initiated an understanding of compatibility of polymer blends by measuring the heats of mixing of small molecule solutions. Still more recently, Paul and CruzRamo3 simulated the compatibility of poly(viny1chloride) blends (2) Paul, D. R.; Newman, S.Polymer Blends; Academic Press: New York, 1978; Chapter 1. (3) Cruz-Ramos, C. A.; Paul, D. R. Mocromolecules, in press.
0 I990 American Chemical Society
