Chyi-Feng Shieh and N. W. Gregory
2346
than 5% of the total volume change occurring during the transition. Thus, it seems probable that the gross effects of temperature upon the transition can be elucidated. In the results discussed below the final volume used in the calculations obtained by interpolation of the curve with crosses in Figure 1 was that which would have been attained by crystallizing at the particular temperature. The results of the studies of the isotropic-crystalline transformation are displayed in Figure 5 and Table IV. Figure 5 shows plots of F ( t ) us. In t for crystallizations taking place in the range 60.25-74.70'. These plots have all been normalized to a supercooling of 10.4" (71.1a)3 by shifting along the In t axis. The fact that they are all superposable indicates that here also only one mechanism of transformation is taking place. In concordance with the previous results on the kinetics of crystallization of cholesteryl esters, it seems probable that this is the temperature range in which homogeneous nucleation is predominant. Avrami plots o f these data yield straight lines from which it is possible to derive the values of the n and K constants of the Avrami equation. These results are displayed in Table IV along with comparable results for cholesteryl myristate and acetate. 'The value of the Avrami n of the stearate does not so closely approximate 4.0 as do those for the myristate and the acetate, However, it is close enough to 4.0 to make us believe here again that we have sporadic nucleation of spherically developing transforming regions. A very notable difference in the behavior of the stearate from the other two esters is the small degree of supercooling which is necessary to attain the homogeneous nucleation range. With the stearate, it is less than 10" whereas both the myristate and the acetate required several times that supercooling to attain the region in which homoge-
neous nucleation was dominant and in which heterogeneous nucleation played an inconsequential part. It has been shown for the myristate, nonanoate, and acetate that the spherulitic growth rates in the crystallization range of interest were essentially independent of temperature.? This means that the temperature coefficient of the K s reflects only the temperature coefficient of the nucleation rate. If it i s assumed that the stearate behaves similarly then it is noteworthy that the temperature coefficient of the nucleation rate of spherulites of the stearate and the acetate are about the same, increasing about 40-fold in a 10" interval, whereas the myristate is much more temperature sensitive, increasing almost 3000-fold in a similar temperature range. We do not wish to speculate further upon these differences.
Acknowledgments. The authors wish to express their appreciation to Professors R. S. Porter and R. S. Stein for helpful discussion during the course of this investigation. References and Notes
I
(1) This work supported by Grant No. HL13188 from the National institutes of Health. (2) F. P. Price and J. H. Wendorff, J. Phys. Chem., 75, 2849 (1971). (3) F. P. Price and J. H.Wendorff, J. Pbys. Chem., 76, 276 (1972). (4) F. P. Price and J. H. Wendorff, J. Phys. Chem., 75, 2839 (1971). (5) F. P. Price and J. H. Wendorff, J. Phys. Chem., 76, 2605 (1972). (6) G. W. Gray, "Molecular Structure and Properties of Liquid Crystals," Academic Press, New York, N. Y., 1962. (7) F. P. Price and A. K. Fritzsche, J. Phys. Chem., 77, 396 (19731, ( E ) G. J. Davis, R, S. Porter, and E. M. Barrall, Ill, Mol. Cryst. Liquid Crysf., 10, 1 (1970). (9) G. H. Stout. "X-Ray Structure Determination," Macmiilan, New York. N . Y.. 1968. (10) J.~H.'Wendorffand F. P. Price, Moi. Cryst. Liquid Cryst., in press. (11) N. Avrami, J. Chem. Phys., 7, 1103 (1939); 8, 212 (1940).
Chyi-Feng Shieh and N. W. Gregory* Department of Chemistry, University of Washington, Seattle, Washington 98195 (Received April 18, 1973) Publication costs assisted by the National Science Foundation
Torsion effusion, spectrophotometric, and transpiration experiments have been used to study the equilibria CrIs(s) = CrIa(s) 1/&(g), CrIa(s) = CrIa(g), Crids) f 1/212(g) = CrII(g) in the temperature range 300-600". Thermodynamic properties and bond energies for the chromium iodides have been derived. Extrapolation of effusion data to zero orifice area gives predicted equilibrium pressures in good agreement with spectrophotometric results. The condensation coefficient of iodine on CrI3-CrI2 appears to be ca. 10-2 and to decrease with increasing temperature. Molar absorptivities of iodine vapor between 100 and 525" have been measured in the interval 370-500 mp.
+
The thermal decomposition of chromium(II1) iodide was CrI,(s) = CrI,(s)
+
'/z12(g)
studied in this laboratory some time ago by measurement of the quantity of iodine vapor leaving effusion cells over relatively long periods of time.1 Recent studies using the The Journai of Physicai Chemistry, Vo!. 77, No. 19, 1973
torsion effusion method, which gives steady-state pressures over short time intervals, have shown that vapor concentrations generated by solid-state reactions frequently show a significant fall-off with time as the reaction becomes diffusion controlled.2 In such a case apparent equilibrium pressures based on collectibn o f total effu-
2347
The Chromium-Iodine System
sate over periods of many hours would reflect only an average of diminishing steady-state pressures and be unsuitable as a basis for derivation of equilibrium characteristics. Indeed in the earlier work1 apparent equilibrium pressures of iodine based on effusion were found to be somewhat lower than those indicated by a diaphragm gauge experiment in which total pressure in a sealed system was measured a t higher temperatures. In the latter, however, a question arises about possible contribution of volatile iodides. To clarify these matters and to seek evidence concerning the molecular nature and properties of volatile compounds of chromium in iodine atmospheres we have undertaken a reexamination of the chromium-iodine system. Steady-state iodine pressures have been measured by the torsion effusion method, and predicted equilibrium behavior for reaction 1 verified by determination of the equilibrium iodine vapor concentration by a spectrophotometric absorption technique. The dependence of the concentration of volatile iodides of chromium on iodine pressure has also been determined by transpiration experiments in which argon-iodine mixtures were used as a carrier gas. When iodine partial pressures are significant evidence is found for the formation of CrIc(g). Thermodynamic constants for the various vaporization processes in the system and bond energies for CrI3(g) and CrIAg) have been evaluated. Experimental Section The torsion effusion apparatus and the cells used have been described earlier.3 Cr13 was prepared by reaction of iodine with chromium powder (Fisher) in an evacuated and sealed Pyrex tube at 500O.4 A black, shiny crystalline product of relatively small particle size was obtained. This material is not appreciably hygroscopic when pure and was quickly transferred to the various cells without the use of a drybox. The torsion effusion apparatus was flushed with dry nitrogen prior to and while mouniing the cells. About half the volume of the effusion cells was initially filled with Cr13. Reproducible results a t various temperatures over a total period of about 10 hr were obtained except for the largest orifice area cell (no. 2) for which a decrease in steady-state pressure was noticeable after about 3 hr (time dependent on temperature) of heating. Only those results which showed no measurable time dependence were used to derive thermodynamic constants. The molar absorptivity of iodine vapor was studied between 370 and 500 mp in the temperature interval 100525", using a Cary 14H recording spectrophotometer. The quartz absorption cells, furnace, and general technique have also been described previously.3J Samples A, B, D, and E, obtained from resublimed iodine (Allied), were sublimed into absorption cells, previously pumped to 10-6 Torr and baked for 10 hr a t 500". Sample C was prepared by decomposition of CrI3. A, B, and C, which ranged in concentration from 0.588 to 2.06 mM (as determined by subsequent titration with standard Na~S203),were used to measure the molar absorptivity. D and E were used to verify these results by measurement of the apparent concentration of the saturated vapor of iodine and subsequent comparison with reported vapor pressure data. The concentration of iodine vapor established by equilibrium 1, using five independent samples, was then de-
termined from absorbance measurements and iodine molar absorptivities over the temperature range 482-539". The samples studied were prepared in different ways to check for possible solid solution effects. Two samples (of the formation reaction product) were placed directly in absorbance cells, which were then evacuated at 10-6 Torr and heated at 200" for several hours before sealing off. The next two samples were heated a t 350 and 400" for 0.5 and 1 hr, respectively, to partially decompose the crI3. After cooling the cells were sealed off from the vacuum system and small amounts of the solid weremmechanically transferred from a side arm into the cell by tilting the apparatus. The remaining excess in the side arm was then sealed off. In the fifth sample a small excess of iodine was introduced along with Cr13 by heating some excess Cr13 left in the transfer side arm; the residual matter was then sealed off. Within experimental error all samples gave the same temperature dependent apparent iodine concentrations for equilibrium 1; hence solid solutions of appreciable concentration were assumed not to form. The transpiration apparatus used to study the volatilization of chromium iodides in argon-iodine mixtures in the temperature range 500-600" was basically the same as that described by Zaugg.6 An argon-iodine gas mixture was passed over heated samples of CrI3 and/or Cr12 formed by decomposition of Cr13 a t flow rates between 20 and 59 ml min-1, calculated a t the reaction temperature and pressure; the apparent equilibrium characteristics in the vapor phase were independent of flow rate in this range. As the gas mixture left the equilibrium vessel, the chromium iodide vapors condensed in the exit tube in the cooler regions adjacent to the main furnace; iodine vapor was collected in a following trap, cooled with liquid oxygen (most collected in the tubing just preceding the trap), and argon was collected in a second trap, cooled with liquid nitrogen. Iodine was initially introduced into the argon carrier gas by permitting the latter to flow through a trap containing crystalline iodine immediately preceding the main furnace and heated to various temperatures to introduce the desired partial pressure of iodine. The quantities of material condensed from the effluent gas stream were determined by titration of iodine with NazSz03, measurement of the pressure of the evaporated sample of argon in a standard volume, and oxidation of chromium to chromate followed by complexation with diphenylcarbazide and comparison of absorbance against standards with a Beckman DU spectrophotometer as described by Sandell.? Dalton's law was then used to relate the relative numbers of moles of the various species to the total pressure, measured manometrically, and the respective partial pressures. Results and Discussion
Torsion Effusion. Total steady-state pressures in the effusion cells were evaluated from observed angles of rotation and apparatus constants determined by calibration, with the vapor pressure of zinc in the range 286-351" used as a reference standard.3 The transpiration experiments to be discussed confirm that chromium iodide species do not contribute significantly in the temperature range of the effusion measurements, 300-350". However the dissociation of 12 into iodine atoms must be considered; the relative contributions of the two species were evaluated using equilibrium constants for the dissociation provided in the JANAF The Journal of Physical Chemistry, Vol. 77, No. 19, 1973
2348
Chyi-Feng Shieh and N. W. Gregory tables.8 Partial pressures of IZwere used to derive equilibrium constants for (1). Data from each cell were fitted to the form log P(torr) = A - BT-l by a least-squares treatment; the linear correlation and actual data points are displayed in Figure 1. It is clear that steady-state pressures depend markedly on cell orifice area. The dashed line indicates the apparent equilibrium pressures derived from a plot of the reciprocal of the steady-state pressures us. the orifice area and extrapolation to zero orifice area. It was necessary in some cases to extrapolate the leastsquares lines for the various cells to a common temperature range to facilitate the comparison. An apparent condensation coefficient was estimated using the equation P, = P,(l a o / a A ) where the surface area A was taken as the cross sectional area of the cell, a0 represents the orifice area, and 01 is the apparent condensation coefficient for the reaction.88 The Freeman-Searcy orifice factors are included in the calibration constants. (Torsion effusion data for reaction 1 are listed in Table I.) As illustrated on Figure 1, apparent pressures from the Knudsen studies are substantially lower than the torsion data and the derived equilibrium values; the slope for the latter is fortuitously close t o that of the Knudsen data. The lower steady-state pressures apparently result from a combination of the effect of a low condensation coefficient and a time-dependent fall-off of the Knudsen data. The figure also shows that the deviation of the torsion steadystate pressures from the projected equilibrium value increases as the temperature is increased. This indicates an apparent enthalpy of activation (27 kcal mol-1 of 12) smaller than the enthalpy of vaporization (40 kcal mol-1),9 a behavior similar to that observed for the sublimation of elementary iodine.1° The condensation coefficient for (1) also appears to have a similar magnitude to that of crystalline iodine. Projected thermodynamic constants for (1) will be discussed after consideration of spectrophotometric data. Absorbance Measurements. A number of investigators have used the absorbance in the region around 480 mp, which is fairly insensitive to temperature variation between 60 and 120" and to the presence of foreign gases, as a measure of the concentration of iodine vapor.11 There is some disagreement as to the correct value of the molar absorptivity; a value around 350 M - I cm-I at loo", somewhat lower than the value (365) of Sulzer and Wieland,l2 has been used in recent work.11 Molar absorptivities determined in the present study are shown graphically in Figure 2 . 3 Data from the three samples were averaged. At 150 and 300" our values are also somewhat lower than those of Sulzer and Wieland,l2 especially between 450 and 490 mp; a t 500 mp, however, our results correspond well with theirs. We confirm that the molar absorptivity in the region near 480 mH is relatively insensitive to temperatures as high as 250" and find the value 350 f 2 M - I cm-1 at 480 mp acceptable. A comparison of the vapor pressure of iodine derived from our absorbance data (samples D and E) with the early transpiration work of Baxter, et al.,13 and Ramsay and Young14 is shown in Figure 3. These workers are considered most reliable by the authors of the JANAF tables.8 The molar absorptivities of iodine at 5-mp intervals between 460 and 500 mp were then used to determine the iodine vapor concentration in equilibrium with CrI,(s) and CrIz(s). At a given temperature the apparent value of the concentration was evaluated at each wavelength and
+
4.0
, \ 1.60
1.70 1000/T"K
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I75
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Figure 1. Steady-state effusion pressures of 12 established by reaction 1: 0 , cell 1; 0 cell 2; 0, cell 4; A , cell 5; 0 , equilibrium pressure predicted by extrapolation: Knudsen effusion data' (--).
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