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D. F. Eggers
(4) J. O'M Bockris and P. P. S.Saluja, J. Phys. Chem., 76. 2140 (1972).
(5)J. O'M Bockris and A. K. N. Reddy, "Modern Electrochemistry", Vol. I, (6) (7) (8) (9) (10)
Plenum Press, New York, N.Y., 1970. N. Purdie and M. M. Farrow, Coord. Chem. Rev., 11, 189 (1973). E. Glueckauf, Trans. faraday SOC.,51, 1235 (1955). A. Fratiello, V. Kubo, R . E. Lee, and R. E. Schuster, J. Phys. Chem., 74, 3726 (1970). J. Stuehr and E. Yeager in "Physical Acoustics", Vol. 11. W. P. Mason, Ed., Academic Press, New York and London, 1965. A. J. Rutgers and Y. Hendrikx, Trans. faraday Soc.. 58, 2184 (1962).
(11) A. J. Rutgers. W. Pigole, and Y. Hendrikx, Chem. Weekbl.. 59 33 (1953). (12) J. C. Clemett. J. Chem. SOC.455 (1966); 458, 761 (1969). (13) T. Erdey-Gruz and E. Levay, Acta Chim. Acad. Sci. Hung., 69, 215 (1971). (14) A. M. Shkodin. N. K. Levitskaya. and V. A. Lozhnikov, Zh. Struct. Khim., 38, 1006 (1968). (15) J. I?. Goates and R. J. Sullivan, J. Phys. Chem., 82, 188 (1958). (16) E. R . Nightingale, Jr.. in "Chemical Physics of Ionic Solutions", B. E. Conway and R. C. Barradas. Ed., W h y , New York, N.Y., 1966, D 87.
A Plastic-Crystalline Phase of Ethane D. F. Eggers, Jr. Department of Chemistry, University of Washington, Seattle, Washington 96 195 (ReceivedJune 16, 1975)
Visual and dilatometric observations are reported for the solidification of liquid ethane. A plastic-crystalline phase has been detected, and it is stable from the solidification temperature of the liquid to a temperature 0.45' lower. The melting point of ethane, as reported by the majority of earlier workers, agrees with our transition temperature between the low-temperature solid and the plastic crystal. All crystals of the low-temperature solid observed in polarized light showed sharp extinctions, and this means the crystal cannot be uniaxial as is presently accepted.
Introduction We had done some infrared spectroscopic work on ethane, and found some definite evidence that the crystal structure could not be that which was reported by Mark and Pohland.' In seeking further evidence regarding solid ethane, we observed the slow solidification of the liquid. A new phase, which we believe to be a plastic crystal, was observed; this has apparently not been previously reported. We record here some optical and dilatometric observations on the two solid phases of ethane and briefly discuss the implications concerning the structure of the low-temperature solid. Experimental Section Phillips research grade ethane was used, with stated purity of 99.92%.We were unable to detect any impurities in it by infrared spectroscopy, and the only purification employed was to pump several times on the frozen solid. The dilatometer was made from a Pyrex tube of 1.94 mm i.d. with an attached bulb to permit condensation of about 0.5 ml of liquid. The position of the meniscus was measured with a cathetometer through the walls of a clear glass dewar tkdt contained liquid oxygen or oxygen-nitrogen mixtures. Slow raising of the coolant level around the dilatometer sufficed to freeze the sample. Visual observations were conducted with the ethane condensed in a cell made entirely of fused quartz; the sample thickness was 0.15 mm. This cell was connected through a quartz-Pyrex graded seal to a bulb of about 400 ml volume; a stopcock and ground joint allowed filling of the system. To ensure a more uniform temperature, the quartz cell was enclosed in a split aluminum cylinder of 2.4 cm diameter and 12 cm long; there were holes drilled through both The Journal of Physical Chemistry, Vol. 79, No. 20, 1975
halves of the cylinder in the vicinity of the cell to permit observation of its contents. The halves of the cylinder were held together with bolts, and the mating faces were milled out to fit fairly snugly around the cell. The aluminum cylinder and ethane cell were placed in a special clear glass dewar whose inner diameter was only 0.5 mm larger than the aluminum cylinder. There was also a thermometer well in the cylinder for a silicon diode that was used as the main device for recording temperature and temperature changes. The dewar was provided with a heating coil between the inner and outer walls. This special dewar was immersed in liquid nitrogen contained in a larger, conventional clear glass dewar. The well of the inner dewar contained liquid oxygen to promote thermal contact; the heater was supplied with a small ac voltage from a variac and transformer. Adjustment of the variac permitted the temperature of the sample to be maintained constant to within O.0lo, or it could be very slowly warmed or cooled. The silicon diode was a 1N5614 Semtech unit. A simple circuit was constructed for supplying the diode with a small dc current of 0.4 mA that was carefully regulated. The resulting voltage drop across the diode near 90 K was only slightly less than the voltage of a standard cell; this difference voltage was balanced against the voltage across some precision resistors carrying a known current. The net voltage was directly recorded on a 10-mV strip-chart recorder. Since the diode voltage under these conditions changes by 2.14 mVldeg, it is easily possible to see a change of 0.01'. The nonlinearity of the voltage as a function of temperature is negligible over the small temperature range of interest here. The calibration of the diode was carried out by comparing it with a platinum resistance thermometer that
A
Plastic-Crystalline Phase of Ethane
was supplied by Leeds and Northrup and certified by the National Bureau of Standards. One problem with the use of the diode is sensitivity to light. In earlier exploratory work the diode was not enclosed in a thermometer well; simply turning on and off the observation light bulb produced voltage changes equivalent to temperature changes of several tenths of a degree. With proper shielding from light the diode has been found to be remarkably stable and reproducible as a thermometer. Only enough ethane was used to half-fill the quartz cell, and it was tilted with the long axis almost horizontal during the cool-down and freezing process. Upon returning the cell to the vertical position, we had the solid ethane confined to one side of the cell. The melting could then be readily observed since the liquid as formed would flow to the bottom of the cell. Pieces of sheet Polaroid were placed in back and in front of the outer clear glass dewar; the ethane in the cell was viewed through the polaroids with the aid of a light bulb in back of the assembly. The polaroids were kept in the crossed position by rotating them simultaneously.
Results Careful cooling of the liquid invariably first produced a solid that appeared uniformly dark for all rotations of the (crossed) polaroids; the liquid phase yielded similar results. Further cooling transformed the solid to another form that produced definite directions of sharp extinctions in small areas as the polaroids were rotated. By a careful adjustment of the temperature, regions of single crystal with areas of several mm2 could be produced; they displayed striking first-order interference colors. This anisotropic solid is presumed to be the familiar solid form. Careful warming of the anisotropic solid invariably produced the isotropic solid before the liquid phase was formed. The isotropic solid phase must therefore be thermodynamically stable and not a metastable phase formed only under certain special conditions. The dilatometer showed a decrease in volume accompanying the change from liquid to isotropic solid of about 2.7 f 0.2%. We also attempted a direct measurement of the volume decrease from liquid to anisotropic solid, but on repeated attempts these solids displayed numerous large cracks. The value that we obtained, about 9%, is thus a lower limit to the true magnitude. This may be compared with a value of 11.1%deduced from the measured values for the heat of fusion, the change of melting temperature with pressure, and use of the Clapeyron equation.233 It is interesting that we have never, in the course of many solidifications of ethane, either in the quartz cell, in quartz tubes of several millimeter diameter, or in Pyrex tubes, observed fractures of any type in the isotropic solid. Very careful observation of the solidification in the quartz cell showed some faint needles at the liquid-isotropic solid interface; however, after the entire sample had solidified, only the perfectly clear solid could be seen. These observations, together with the absence of any rotation of planepolarized light, strongly suggest that this form is a plastic crystal. The temperature of the solid-solid transition was found to be 89.82 f 0.02 K; the melting point of the isotropic solid was found to be 90.27 f 0.02 K. The indicated uncertainties reflect mainly the difficulty of telling exactly when the sample was entirely transformed to isotropic solid or to liquid upon warming, rather than uncertainty in measured
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temperature. It is interesting to note that Witt and Kemp2 gave 89.87 K as the melting point; more recently Burnett and Muller4 reported 89.82 K based on an NMR method. Both of these values agree quite well with our temperature of the solidTsolid transition. On the other hand, Clusius and Weigand reported a melting point of 90.35 K; our value is in essential agreement.
Discussion The apparent absence of earlier observations of the plastic-crystalline phase is puzzling. Witt and Kemp2 found a substantial increase in the heat capacity of solid ethane from about 67 K up to the melting point, and they ascribed the increase to a premelting phenomenon due to about 0.5% impurity. Apparently no analysis of the sample was done to verify the existence of the impurity. It is possible that their sample was actually more pure, and that the rising heat capacity is associated with increased motions of the molecules as the solid-solid transition temperature is approached. It is also noteworthy that the heat capacity of the solid was always measured by Witt and Kemp with sufficient heat input to raise the temperature by approximately 2 or 3O. The initial temperature of the highest such measurement on the solid was 86.73 K; the final temperature was 88.63 K. Thus the sample would not have reached the solid-solid transition temperature. Many years ago Wah16 reported his observations on the freezing of ethane to form the anisotropic solid. He deduced that it was uniaxial since he found some crystal sections that remained dark as the crossed Nicol prisms of his polarizing microscope were rotated. We have tried to repeat this observation numerous times, omitting the microscope, and had no success. That is, in a sample completely converted to the low-temperature phase, all parts were observed to have definite extinction directions. We attempted to convert a large part of the sample to one single crystal but were never successful; however, the presence of a number of different single crystals a t the same time provided more opportunity to verify the uniaxial nature of the solid, if indeed it were. We can only report the consistent failure to observe even one small crystal that did not rotate polarized light. We suggest that Wahl might very well have had part of his sample transformed into the isotropic solid, and this would of course lead to the erroneous conclusion that the (single) solid phase was uniaxial. It should be noted that Mark and Pohland’ used Wahl’s result, together with their X-ray powder pattern from solid ethane, to deduce the crystal symmetry of space group D6h4. However, if the crystal is not uniaxial, a space group of such high symmetry can no longer be a possibility. Mark and Pohland’s work was done at a time when the true symmetry of the isolated ethane molecule was not firmly established. Thus the site symmetry for ethane molecules in the D6h4 space group is &;.we now know that the molecular symmetry is D3d. The infrared-active fundamentals of pure solid ethane show splittings in the spectrum near 60 Ke6We have also studied isotopic mixtures and found that most of the degenerate fundamentals are still split even when the molecule of interest, e.g., C2D6, is isolated in a large excess of C2H6. This observation conclusively rules out the existence of a threefold rotation symmetry axis that passes through the ethane molecule in the crystal; it is in agreement with our failure to observe evidence of uniaxial crystals in the anisotropic solid. The Journal of Physical Chemistry, Vol. 79, No. 20, 1975
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P. Ripa and 0. Zgrablich
We have made some attempts to observe the infrared and Raman spectra of the isotropic solid; thus far we were not successful. In the infrared there is a problem arising from the nonzero vapor pressure of the ethane; it sublimes to a slightly colder region of the conventional lpw-temperature cell. We have designed a special infrared cell that incorporates two cold windows with provision for introducing ethane between them and isolating the sample from the insulating vacuum. For Raman work the sample was contained in a quartz tube connected to an expansion bulb; cooling was done by a stream of cold nitrogen gas. It was not possible to hold the sample temperature in the 0.4O range of stability for the isotropic phase for more than a few minutes. A different cell, with provision for much better temperature control, has been designed; we plan to report the infrared and Raman spectra of the isotropic solid phase in a separate paper. In some work on condensed phases of ethane at high pressures, Webster and Hoch' reported a solid-solid phase transition; solid I, which lies between the liquid and solid 11, has a range of stability of about 5' at a pressure of 1 kbar. These workers suggested that there must be a solid I-solid 11-liquid triple point between 0 and 1 kbar; they were unable to conduct measurements in this region. We believe that the isotropic solid phase that we have observed
is the same as their solid I phase, and that there is no triple point involving these phases in the range of pressures from 0 to 5 kbars, the upper limit of their measurements. It would be most interesting to have additional measurements of the heat capacity of highly purified ethane in the vicinity of the solid-solid transition temperature as well as near the melting point. We suspect that the enthalpy change of the solid-solid transition may be substantially larger than the enthalpy change of melting.
Acknowledgment. We are grateful to Professor B. J. Zwolinski for suggestions concerning the literature on ethane. We are also grateful to Mr. J. Van Zee for suggesting the use of a certain silicon diode for measurement of temperature, and to Mr. D. Hinman for assistance in comparing our diode with the platinum resistance thermometer. References and Notes (1) H.Mark and E. Pohland. 2.Krlstallogr.,82, 103 (1925). (2)R. K. Witt and J. D. Kemp, J. Am. Chem. Soc., 59,273(1937). (3)K. Clusius and K. Weigand, 2.Phys. Chem., 846, 1 (1940). (4) L. J. Burnett and E. H. Muller, J. Chem. Eng. Data, 15, 154 (1970). ( 5 ) W. Wahl, 2.Phys. Chem., 88, 133 (1914).
( 6 ) S.B. Tejada and D. F. Eggers, Jr., to be submitted for publication. (7) D. S.Webster and M. J. R. Hoch, J. Phys. Chem. Solids, 32, 2663 (1971). We are grateful to Professor W. A. Steele for pointing out the relation of this work to ours.
Effect of the Potential Correlation Function on the Physical Adsorption on Heterogeneous Substrates P. Rlpa and 0. Zgrabllch* Departamento de Fhica, Universidad de San Luis, San Luis, Argentina (Received April 2 1, 1975)
A model for heterogeneous substrates with a multivariate gaussian distribution for the adsorption potential is proposed. The evaluation of second and third virial coefficients shows a considerable dependence on the correlation length, in the range of the other parameters where heterogeneity plays an important role. The model has as limiting cases the homogeneous and large patches models; but the behavior at finite correlation lengths is by no means intermediate between that corresponding to those extremes.
1. Introduction
The most commonly used model for the adsorption of gases on heterogeneous substrates depicts the adsorption potential ( Uad) as being constant through large 2atches of the surface.1 Another model was also proposed in which the surface is partitioned in an infinity of single adsorbing sites and U,d is randomly distributed on them with no correlation between the values of Uad for neighboring sites.2 For both mdels, the best distribution for the values of Uad was found to be g a ~ s s i a n . ~ . ~ We propose here a model in which Uad is considered to have a chaotic (stochastic) structure with a finite correlation length. The potential has a multivariate gaussian distribution and, therefore, all its statistical properties are given in terms of its mean value and covariance function. The usual formulae for the evaluation of the two-dimensional virial coefficients (reviewed in section 2) are used in The Journal of Physical Chemistry, Vol. 79, No. 20, 1975
section 3 with the distribution of the present model to obtain a general expression for the nth coefficient. The second and third coefficients are evaluated in section 4 for a square well parametrization of the interparticle potential, while the conclusions are discussed in section 5. We include an Appendix with the deduction of the multivariate gaussian distribution for the sake of completeness. 2. Virial Expansion of the Adsorption-Isotherm Equation We are interested in those adsorption processes that can be pictured in terms of an ideal nonadsorbed phase (NAP), a two-dimensional adsorbed phase (AP), and an inert solid substrate, responsible for the adsorption force. For simplicity we take both phases to have one component. The NAP is macroscopically described by means of its absolute temperature T, the volume particle density PO,
