J. Phys. Chem. 1992, 96, 8556-8561
8556
approached from the supercritical region along the path of maximum amp.Again, the effect of composition terms would be zero at the critical point where amp +m and h ; , --. Therefore, the effects of stationary-phase composition changes in the chromatographic determinations of q,,and , hy,,, appear minimum just in the region of T and P where such measurements are most interesting. Since accurate determinations of the extremum values of (a In k l / a P ) , and (a In k,/aZ"),are quite difficult, the effects of the composition terms may well be comparable to experimental error along the two paths mentioned above. Third, in contrast to the above considerations concerning (a In k l / a P ) , and (a In k,/aT),, the contribution of composition terms appears to be more significant in the quotient [a In k l l d (1/79Ip (cf. Table I1 and eqs 4-7). This is because, in eq 5, h;,,, and u4;, are coupled in such a way that the near-critical anomalies in the two quantities are o f f ~ e t . ' ~ . ~ ~ Application of the ModeL Since the model contains adjustable binary parameters, it is not predictive, and its applications require some nonchromatographic information; in general, supercritical solubility data are needed to fix bI3and sorption or swelling data are required to fix 623.As there is a general lack of binary data needed to fix 6,*, this parameter may be adjusted using the SFC retention itself after 613 and 623 have been obtained from the respective binary data.
-
-
Conclusion In this paper, expressions developed previously from the random-mixing version of the Panayioutou-Vera lattice model have been tested to evaluate their utility for reducing SFC retention data into thermodynamic quantities. In addition to pure-component parameters, the treatment employs one adjustable parameter per binary. In a typical system encountered in capillary-column SFC (naphtha1ene-PDMS-CO2), the model provides moderately successful reproductions of experimental data on supercritical solubilities, polymer swelling, and solute partition coefficients between the swollen polymer and the supercritical fluid. With the binary parameters fixed by fitting these experimental data, the model yields reasonable predictions of the partial molar
properties of the solute and of the effects of composition on the chemical potential of the solute in the stationary phase. Unlike the previous applications of the Panayiotou-Vera the present treatment does not include the quasichemical approximation. In an application of the model to high-pressure phase equilibria in poly(ethy1eneglyco1)erbon dioxide systems, Daneshvar et al.5 found the correction for nonrandomness to be small. Consequently, there is some indication that the performance of the present treatment would not be largely improved by introducing the quasi-chemical approximation. Any significant improvement in the model's performance near the mobile-phase critical point could only come from relaxing the mean-field approximation.
Acknowledgment. The referees' comments on this paper are gratefully acknowledged. Registry No. Cot, 124-38-9; naphthalene, 91-20-3.
References and Notes (1) Roth, M. J. Phys. Chem., preceding paper in this issue. (2) Panayiotou, C.; Vera, J. H. Polym. J. 1982, 14, 681. (3) Kumar, S. K.; Suter, U. W.; Reid, R. C. Ind. Eng. Chem. Res. 1987, 26, 2532. (4) Ely, J. F.; Haynes, W. M.; Bain, B. C. J. Chem. Thermodyn. 1989, 21, 879. ( 5 ) Daneshvar, M.; Kim, S.;Gulari, E. J . Phys. Chem. 1990, 94, 2124. (6) Tsekhanskaya, Y. V.; Iomtev, M. B.; Mushkina, E. V. Zh. Fir. Khim. 1964, 38, 2166. (7) Shim, J.-J.; Johnston, K. P. AIChE J. 1989, 35, 1097. (8) Shim, J.-J.; Johnston, K. P. AIChE J . 1991, 37, 607. (9) Roth, M. J. Phys. Chem. 1990, 94, 4309. (10) Deknedetti, P. G.; Mohamed, R. S.J . Chem. Phys. 1989,90,4528. (11) Eckert, C. A,; Ziger, D. H.; Johnston, K. P.; Kim, S . J. Phys. Chem. 1986, 90, 2738. (12) Pope, D. S.; Sanchez, I. C.; Koros, W. J.; Fleming, G. K. Macromolecules 1991, 24, 1779. (13) Lauer, H. H.; McManigill, D.; Board, R. D. Anal. Chem. 1983,55, 1370. (14) Martire, D. E.; Boehm, R. E. J . Phys. Chem. 1987, 91, 2433. (15) Roth, M. J . Chromatogr. 1991, 543, 262. (16) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3rd ed.;Butterworths: London, 1982; pp 11-19. (17) Shim, J.-J.; Johnston, K. P. J . Phys. Chem. 1991, 95, 353. (18) Wheeler, J. C. Ber. Bunsen-Ges. Phys. Chem. 1972, 76, 308. (19) Debenedetti, P. G.; Kumar, S.K. AIChE J . 1988, 34, 645.
Variable-Temperature and -Pressure Studies of the Vibrational Spectra and Phase Transition in Quadricyclane Nancy T. Kawai, Denis F. R. Gilson,* and Ian S. Butler* Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6 (Received: January 29, 1992; In Final Form: May 6, 1992)
The variable-temperature and -pressure vibrational spectra of the solid phases of quadricyclane have been measured. Factor group analysis has been used to predict possible space group symmetries of the ordered low-temperaturephase, and the pressure dependences of the frequencies have been employed to make partial assignments of the vibrational modes. The order-disorder transition occurs at 9.3 k 0.5 kbar on compression and at about 7.0 kbar on decompression. The differences observed in the transition temperature, pressure, and entropy change for quadricyclane are compared with the data obtained for several other molecules with cycloheptyl skeletons.
Introduction The seven-membered bicyclic cage hydrocarbons norbornane, norbornylene, and norbornadiene are known to have phase transitions from high-temperature disordered phases to low-temperature ordered crystal structures.ly2 The highly strained cage heptane, C7HB, molecule quadricyclane, tetracyclo[ 3.2.0.02*7.0436] was first obtained as the irradiation product of n~rbornadiene,~ and, as a reversible isomerization reaction, this has been extensively investigated for its potential as a solar-tetherma1 energy conversion 0022-3654/92/2096-8556$03.00/0
qurdrlcyclanr
~ y s t e m Very . ~ little is known about the solid-state properties of quadricyclane, but, by analogy with the other members of the series, this compound should also exhibit an order-disorder 0 1992 American Chemical Society
Temperature and Pressure Studies of Quadricyclane
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8557
A
B
1
'I(
,4
,,
3150
3000
2850
1200 1050 800 Wavenumber ( c m - ' )
750
600
Figure 1. Infrared spectra of quadricyclane at (A) 45 and (B) 180 K.
transition. Such a property can also serve as a thermal energy storage mechani~m.~ The transition has been observed by differential scanning calorimetry,6 which revealed the Occurrence of a sharp phase transition at 153 K on cooling, 180 K on heating, with transition entropies of 45.0 and 40.0 J K-' mol-', respectively. The melting transition occurred at 227 K with an entropy change of only 4.5 J K-l mol-', indicating that melting occurs from a disordered (plastically-crystalline) phase. A preliminary study of the low-frequency Raman spectrum6showed at least 13 peaks at 45 K, i.e., discrete lattice vibrations for the low-temperature phase, but only a broadened Rayleigh line above the transition, continning that the transition is indeed of the order-disorder type. Except for a few C-H fundamentals and their overtones,' the complete vibrational spectra of quadricyclane have not been reported. Some vibrational frequencies have been calculated from ab initio force constants.* Following earlier studies of norbomylene and n~rbornadiene,~J~ the vibrational spectra of quadricyclane have now been examined as functions of temperature and pressure in order to determine the structural characteristics of the solid phases and to aid in assigning some of the vibrational modes.
Experimental Section Quadricyclane was purchased from the Aldrich Chemical Co. Gas chromatographicanalysis showed the sample to be 98% pure, but attempted purification by distillation and by preparative scale chromatography led to decomposition. Since the differential scanning calorimetry (DSC) thermograms were sharp and there was no fluorescence observed in the Raman studies, the sample was used as received. Raman spectra were recorded on an Instruments s. A. spectrometer equipped with a Jobin-Yvon Ramanor U-1000 double monochromator and using the 514.5-nm line of a Spectra Physics 5-W argon-ion laser as the excitation source (30-50 mW at the sample). Infrared spectra were measured on a Nicolet 6000 FT-IR spectrometer with an MCT(B) detector. Low-temperature spectra were recorded with the aid of a closed-cycle helium cryostat and a temperature controller. High-pressure spectra were obtained using two different diamond anvil cells (from High Pressure Diamond Optics and Diacell Products, respectively), both equipped with type IIA diamonds. The pressure calibrant used in the IR experiments was NaN03 diluted in a NaBr matrix (0.1-0.3 wt %),'I while the ruby R1 fluorescence band was used as the calibrant in the Raman experiments.'* Typically, spectra were measured at 1-cm-' resolution at variable temperatures and at 4-cm-I resolution under high pressures.
Results and Discussion As expected, no obvious changes were observed upon cooling from the liquid to the disordered phase I. The lack of any discrete lattice modes in the Raman spectrum of this phase suggests that the phase is isotropic, similar to the disordered phases of norbornane,I3 norbornylene, and n~rbornadiene.~J~ At the phasetransition temperature, sudden and dramatic changes Occurred, with many peaks splitting throughout the spectral region. Typical IR and Raman spectra are shown in Figures 1 and 2, and the vibrational frequencies for both solid phases are listed in Table I, together with some general assignments. Infrared and Raman
3100 3000 2900
1400
1300 1200 1100 1000 Wavenumber (cm ')
900
800
700
Figure 2. Raman spectra of quadricyclane at (A) 43 and (B) 185 K.
r
3200
.
3100
3000 2900 Wavenumber (cm-')
2800
Figure 3. Infrared spectra of the C-H stretching region as function of
pressure upon compression. spectra of quadricyclane were also measured with increasing pressure. The sudden line narrowing and peak splitting characteristic of the phase I to phase I1 transition were apparent at 9.3 f 0.5 kbar. Plots of peak frequencies versus pressure showed distinct discontinuities in the pressure dependences of all vibrational bands, e.g., Figures 3 and 4. Factor group splittings are again evident. In general, the band profiles of the high-pressure phase resembled those of the ordered phase obtained at low temperature, confirming that the same phases occur. The many peaks in phase I1 which are split by solid-state effects diverge with the further application of pressure, due to the decreased intermolecular distances. Overall, the pressure dependences (Table 11) of the Vibrational bands of quadricyclane are much higher than those of the norbornane family of molecules, and this can be attributed to the high degree of strain in the cage. The pressure dependences do not decrease on going from phase I to phase 11, which is unusual. Upon decompression,the ordered phase transformed back to the disordered phase at approximately 7.0 kbar. From the known entropy of transition and the temperature and pressure hystereses, the volume change at the tran~ition'~ is estimated to be 4.0 cm3 mol-', which larger than the value of 3.1 cm3 mol-l obtained for norbomylenegand nearly twice the value observed for adamantane, 2.2 cm3 mol-', as an example of another rigid hydrocarbon cage molecule. I The isolated quadricyclane molecule (C,H8) has 39 normal modes, given by I'ZL = 12al + 8al + lobl + 9b2 under C2, symmetry. Due to the high ring strain in the molecule, the C-H = 3a1 + az + 2bl + 2bJ can be assigned stretching bands
Kawai et al.
8558 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
TABLE I: Vibrationrl Data ( c d ) for Quadricychne liquid phase Raman" (295 K)
398 dp
phase I Raman
(185 K)
phase I1 IR (180 K)
Raman (43 K) 31 w 39 w 43 w 49 w 55 m 63 w 69 w 75 w 80 w,sh 82 w 93 w 101 m 1 I6 w,br
A;:{
398 vs, br 534 vw 664 vw 696 w,br
721 PP
721 m
721 w
768 dp
768 m
766 vs
800 dp
801 m,br
797 s, br
; {::; ; 695 w
831 vw 843 w
843 w
894 PP
892 m
892 m
906
905 w
903 m, br
908 dp
909 w
944 p
943 m
927 vw 945 w,sh
948 dp
951 w,sh
950 w
987 p
985 s
985 vw
w { 664 666 vw 699 w 705 w 712 vw
1697 w 707 vw 710 vw ': sh 765 m
(;!:,: sh
(1;: ; {::;; {9 !9 sim
1034 m, br
1032 vw
1059
1046 w w 1062 w w
1077 p
1078 s
1077 w
1164 dp
1163 w
1164 vw 1182 vw
1236 pp
1218 vw 1236 m
1237 s
{ {; 9996 :w
1250 p
1249 m
1250 w
792 m, sh
{E : 823 m {:891:;t, sh s
skeletal stretches
:9( 998w:w
{E;
{;E
1053 w 1063 w 1068 w 1072 m 1075 vs
{\iy;!
{
fw 1050 w 1053 vw
1075 m 1159 w
1162 vw {1181 m
1181 vw 1186 w
1185 w 1190 w
w { 1215 1221 w
i,
{ 1245 m
1238 m, sh
{z;:
skeletal deformations
930 w 941 w 950 s
943 s 949 m 953 m
{E;:
1047 w 1063 w
{Z;
(!; Ei 1001 m 1006 vw
1030 dp
assignment
531 vw
821 w 828 841 dp
IR (45 K)
sh
{z:: 1232 s 11236 s
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8559
Temperature and Pressure Studies of Quadricyclane TABLE I (Continued) liquid phase Raman" (295 K)
phase I1
phase I
IR
Raman (185 K)
(180
Raman (43 K)
K)
1254 dp
1258 w
1256 m
1330 p
1331 s
1330 m
1365 w 1441 m
1439 vw
1454 dp
1454 m
1452 vw
2861 p
2858 m
2859 s
2932 p
2929 m
2931 s
2938 pp
2942 m, sh
2938 m, sh
1438 w (1443 w 1451 w (1454 w 2858 vs 2905 m
1451 m (1455 m 2856 m 2904 w 2907 w
{
3059 m, br 3071 s 3080 s
al, methylene C-H str bz, methylene C-H str
2918 vs 2926 vs 2944 m 2949 m 3047 s 3050 s 3053 s 3056 s 3063 m 3067 s 3074 m 3079 m
3050 m, br
3083 p
1341 m (1343 m
1344 w
2910 w, sh
3055 dp
assignment
1257 w, sh
1348 vw 1360
IR (45 K)
a l r Cz(4)-H str
3054 m 3057 m 3064 s
, cyclobutane C-H
str
3097 w
3096 s "dp = depolarized, pp = partially polarized, and p = polarized.
TABLE II: presclure Depcadeaces of Vibntiod Peaks of oUrdricvcl.nea phase I dvlQ d In v/dp , v (cm-I) (cm-l kbar-I) (kbar-I X lo4) v (cm-I) 5 767 766 0.4 797 0.4 5 798 804 843 892 903
0.27 0.20 -0.5
2.2 -6
(903)
0.67
7.4
(E
950
0.56
5.9
922 94 1 950
985
0.53
5.4
891
{E 998 1025
1032
0.2
2
1077 1164
0.55 -0.3
5.1 -3
1237 1256 1330 2859 293 1
0.11 0.30 0.29 0.62 0.76
0.89 2.4 2.2 2.2 2.6
307 1
1.2
4.0
1075 (1079 (R) 1159 1214 1236 1253 1327 2858 2926 3069
phase I1 dVldP (cm-' kbar-I) 0.2 -0.04 0.67 0.6 0.17 0.34 0.26
d In v/dp (kbar-1 X lo4) 3 -0.6 8.3
a
C C str C C str
2.0 4.0 2.9
0.60 0.92 0.41 0.28 0.66 -0.004 0.1 0.52 0.2 1
6.5 9.9 4.4 3.0 6.9 -0.04 1 5.2 2.0
0.63 0.76 0.29 0.35 0.36 0.25 0.2 0.96 1.37 1.52 1.69
5.8 7.0 2.5 2.9 2.9 I1.9 1 3.3 4.7 5.1 5.7 2.4
0.79
assignment
C - C str
C C str C C str C C str, a l
CHI str, a1 CZ(4)-H str, a l CZ(4)-H str, bl cyclobutane C-H str
"All peaks are from the IR spectrum, except for that marked with an R (Raman).
more definitively. The three polarized Raman bands at 2858, 2929, and 3080 an-'all have a1 symmetry, and can be attributed to the methylene, the C2-H and C4-H, and the four cyclobutane C-H (C,-H, Cs-H, C6-H, and C r H ) stretches, respectively. The three other higher frequency bands, at 3050,3059, and 3071 an-I, are also C-H stretching modes of the cyclobutane ring, while the band at 2942 cm-I can be assigned to the antisymmetric C,,,,-H
stretch, and the remaining band is the antisymmetric methylene stretch, at 2910 cm-I. The ab initio force field for quadricyclane gave calculated frequencies that were often too far from the observed band positions to permit vibrational assignments.* However, in combination with the d In u / d P values, the computed frequencies can be used to assign some of the observed vibrations. Stretching
Kawai et al.
8560 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 A
TABLE IIk P b Transitions in Seven-Membered Cage Hydrocarbons
3100
molecule norbornane 3050
-
norbornylene
'E
norbornadiene
2 3000 c.
quadricyclane
n
$
129/130 305/3 13 360" 114/127 320'' 175/201 254d 153/180 227d
entrop? 3 1.7/31.5 0.3 12.7 35.8/35.9 10.9 40.4/42.8
5.8 40.0/45.0 4.5
transition pressureC 16.4/ 16.1
14.9/13.3 6.4/10.7/9.3
"In kelvin, for cooling and heating directions, respectively. joules per kelvin per mole. 'In kilobar, for comprwsion and decom-
2950
pression, respectively. For fusion.
k
2900
2850
5
0
10
15
Pressure (kbar)
B 1100
I
1095
1090
E
v
L.
z
transition temperature"
1085 0
f
1080
1075
1070 0
5
10
15
Pressure (kbar)
Figure 4. Pressure dependences of various quadricyclanevibrations in
the (A) infrared and (B) Raman spectra.
modes generally have higher pressure dependences than do deformation modes, and, of the bands measured in the high-pressure phase, the peaks at 804,823,911,998, and 1075 cm-' all have higher pressure dependences than do the remaining bands and can be attributed to skeletal stretching modes. The frequencies correspond relatively well with the calculated band positions of 81 1 (partial contribution), 901 (partial contribution), 937 (partial contribution), 975, 1008, and 1034 cm-I. Extending the assignments to the skeletal, CH2, and C-C-H deformations is not possible at this time since only general trends in their pressure dependences have been observed. For the various C-H stretches, the cyclobutane C-H stretch should have the highest pressure dependence, followed by the two CZo-H, and the methylene C-H stretch should have the lowest. Unfortunately, pressure broadening in the diamond-anvil cells obscured the measurement for all but a few of the C-H modes. In phase I, the three broad peaks do follow the expected trend, as do the methylene and C,,4,-H stretches in phase 11. The highest energy peak, at 3069 c m - I , had
a lower than expected pressure dependence, but this peak is actually the pressure broadened average of eight single bands and its behavior might not be typical of any of its components. In phase I, the quadricyclane molecules reorient extensively and no structural information can be deduced simply from the vibrational spectra. The lattice may have hexagonal symmetry, in common with the other members of the norbornyl series, or it may be cubic, which is usual for most disordered cage compounds. In phase 11, many IR peaks were observed to split into two, and several Raman bands into doublets or triplets; for example, the peak at 768 an-'(at 185 K in phase I) splits into peaks at 765,767, and 770 an-l in the Raman spectrum at 43 K. Since there is a large degree of coincidence between the IR and Raman peaks throughout the spectral region, it can be concluded that the unit cell is noncentrosymmetric. The correlation method can be used to deduce the site and factor group symmetriesof phase 11. The site symmetry of the molecules in the lattice can be C, C,, C,, or CI,and correlation with passible crystal symmetries leads to three combinations of site and factor group: (1) Dzcrystal with a Czsite, or C, crystal with either a C2or C, site; (2) DU crystal with a C, site; or (3) S4or C, crystal with a C1site. The first possibility should result in some IR peaks splitting into doublets and a doubling of all Raman peaks. The second combination would cause some IR peaks to double and the Raman peaks to split into two or three, and the final set would lead to all IR peaks doubling and all Raman peaks to triple. Since some, but not all, of the Raman peaks were split into triplets, the third set of site and factor group combinations is unlikely and the probable factor groups of this ordered phase are monoclinic (C,) with Z = 2, orthorhombic (D2or C,") also with Z = 2, or tetragonal (DZd) with Z = 4. The transition temperatures, pressures, and entropy changes are now known for four compounds based on the bicycloheptyl s k e l e t ~ n ~ (see ~ ~ -Table ~ * ' ~111). As expected, low-temperature transitions require higher applied pressures, and there is a good correlation between the transition temperature and transition p m u r e for these compounds. The compounds with high transition entropy have low fusion entropy, but the sum of the two is almost constant. The entropies of transition in rigid hydrocarbons are always significantly higher than the value calculated from the GuthrieMcCullough equation, AS = R In ( N I / N 2 )where , N1 and N2 are the number of distinguishable positions in the disordered and ordered lattices, respectively. Norbornylene, which has the lowest symmetry, should, therefore, have the largest configurational entropy contribution, and the remaining three compounds should have the same values, assuming the disordered phases have similar structures. However, the observed transition entropies vary over a wide range, and the quadricyclane transition entropy is among the highest observed for order-disorder transitions in rigid compounds. The *excess entropy" has been correlated for a series of five rigid cage compounds, including norbornane, with both the temperature range of the disordered phase and the molecular dimension^.'^*'^ Quadricyclane does not follow this trend. In interpreting these entropy changes, the volume change that occurs at the transition may lead to a significant contribution to
J. Phys. Chem. 1992,96, 8561-8568 the total entropy change. The requirement of nucleation and growth of a new lattice within the old leads to strain in the crystal and is responsible for the hysteresis in the transition temperature and pressure. This strain contribution increases as the difference in volume increases. In this series of compounds, there is a direct correlation between the largest hysteresis, for quadricyclane and norbornadiene, and the highest entropy, whereas norbornane, which has the lowest entropy change, has almost no hysteresis.
Acknowledgment. This work was supported by operating and equipment grants from the NSERC (Canada) and the FCAR (Quebec). N.T.K. gratefully acknowledges the award of a postgraduate scholarship from the NSERC. Registry No. Quadricyclane, 278-06-8.
References .ad Notes (1) Parsonage, N. G.; Staveley, L. A. K., Disorder in Crysrals; Clarendon Press: Oxford, U.K.,1978. (2) Westrum, E. F. In Molecular Dynamics and d e Srructure of Solids; Carter, R. S., Rush, J. J., Eds.; National Bureau of Standards: Washington, D.C., 1969. (3) Dauben, W. G.;Cargill, R. L. Tetrahedron 1951, 15, 197.
8561
(4) Hammond, G.S.; Turro, N. J.; Fischer, A. J . Am. Chem. Soc. 1961, 83, 4614. (5) See,for example: (a) Canas, L. R.; Grecnbcrg, D. B. Solar Energy 1985, 34, 93. (b) Arai, T.; Oguchi, T.; Wahbayashi, T.; Tsucbiya, M.; Nishimura, Y.;Oishi, S.;Sakuragi, H.; Tokumaru. K. Bull. Chem. Sm. Jpn. 1987, 60, 2937, and references cited therein. (6) Kawai, N. T.; Gilson, D. F. R.; Butler, I. S . Mol. Crysr. Liq. Crysr.
-. ---.
1992. 21 I . 59. ~
(7) Lishman, D. G.; Rcddy, K. V.; Hammond, G.S.; Leonard, J. E.1. Phys. Chem. 1988, 92,656. (8) Doms, L.; Geise, H. J.; Van Alsenoy, C.; Van den Elden, L.; Safer, L. J. Mol. Srrwr. 1985, 129, 299. (9) Kawai, N. T.; Butler, I. S.;Gilson, D. F. R. J . Phys. Chem. 1991, 95, 634. (IO) Kawai, N. T.; Gilson, D. F. R.; Butler, I. S. J. Phys. Chem. 1990,94, 5129. (11) Klug, D. D.; Whalley, E. Rev. Sci. Instrum. 1983, 54, 1205. (12) Piemarini, G. J.; Block, S.; Barnett, J. D.; Forman, R. A. J . Appl. Phys. 1975,46, 2774. (13) Kawai, N. T. Ph.D. Thesis, McGill University, 1991. (14) Smith, E.B. J. Phys. Chem. Solids 1959, 9, 182. (15) Hara, K.; Katou, Y . ;Osugi, J. Bull. Chem. Soc. Jpn. 1981,54687. (16) Clark,T.; McKmey, M. A.; Mackie, H.; Rooney, J. J. J . Chem. Soc., Faraday Trans. 1 1974, 70, 1279. (17) Clark, T.; b o x , T. Mc. 0.;Mackle. H.; McKervey, M. A. J . Chem. Soc., Faraday Trans. 1 1977, 73, 1224.
Multiple Equilibrium States in Effusion Cells. Catastrophic Phase Transitions Jimmie G. Edwards* and Richard S.Uram Department of Chemistry, University of Toledo, Toledo, Ohio 43606 (Received: February 21, 1992; In Final Form: June 8, 1992)
The thermodynamic state function of a chemical system at equilibrium in an effusion cell can be discontinuous, with multiple values of vapor pressure, partial pressures, and condensed-phase composition within incremental neighborhoods of certain temperatures and of vanishing area of effusion orifice. Transformation between such multiple states requires discrete changes in commition and other properties while the system is in a transition state, Le., a nonequilibrium, activated condition. Such transformations are classifiable as topological fold catastrophes. With vapor species of significantlydifferent molecular weights, any phase transition in or near the temperature range of an effusion experiment might induce an observable discontinuity in equilibrium state within an effusion cell. Every phase transition in an effusion cell involves phases of differing compositions; effusion methods have been used to acquire much of the existing information on materials at high temperatures; attention to the possibility of multiple states in any such study is suggested. These effects were deduced from striking phenomena exhibited during vaporization of gallium seaquisulfide; their influence in other systems, including Ga-Se, In-Se, K-S,Li-S, and MnS-Ga2S3,is discussed.
Introduction This paper explains a class of anomalous observations in chemical effusion experimentsreported independently from several laboratoriesduring the past two decades. Perhaps the first of this class was that by Roberts and Searcy’ (RS) from Knudsen-cell mass spectrometry on the effusing vapor of gallium sulfide with compositions near that of G a s 3 . (Here, the terms “Knudsen cell” and “effusion cell” will be used interchangeably; in other applications, it is sometimes better to distinguish them.) Among the anomalous effects reported by RS was an increase in a partial vapor pressure when the temperature was decreased. Gates and Edwards2and Starzynski and Edwards3observed the total vapor pressure to increase with decreasing temperature and vice versa, over the systems MnS-Ga2S3and Ga2S-S2, respectively. More recent work in this laboratory on the effusion of gallium sulfide from a Knudsen cellc6 has led to the discovery and demonstration reported here, that the equilibrium state function of any system in an effusion cell can be discontinuous in temperature. At a temperature of discontinuity, an incremental temperature change causa a discrete change in the thermodynamic equilibrium state defined by the composition, pressure, and temperature of the system. While it is in transition between equilibrium states, gallium sulfide in an effusion cell exhibits anomalous, counterintuitive properties such as the one in the previous paragraph. The effect arises from concert between the general physical properties
of an effusion cell and the chemical properties of the substance in the cell. Such a transition can be classified as a topological fold catastrophe,7.*and the transition can be called catastrophic. The term “multiple equilibrium states” (MES) in effusion cells will be used in reference to the discontinuity. The intended meaning of this term is that more than one quilibrium state of a system, defined by the state variables composition, X,pressure, P, and temperature, T, exist within an arbitrarily small neighborhood of a given T. In particular, it will be seen that lim P # lim P (1) T-T‘
TI-T
lim X # lim X
T-T‘
T‘-T
(2)
where arrows of opposite directions imply approach to a limit, T’, from opposite directions. Not only does this new effect account for anomalous phenornem in the gallium-sulfur system, but it clarifies previous reports of apparent variations from established phase diagrams in effusion studies of the InSegJoand K-SI’systems. Anomalous results like those on Ga-S have been reported for the GaSelz and systems and can be explained in terms of MES. It is likely that this effect is a general one and has affected many effusion studies. Much that is known about chemical systems at high temperatures comes from effusion studies, and the effects of MES may be important in interpreting such studies.
0022-3654/92/2096-8S61$03.00/00 1992 American Chemical Society
