8552
J. Phys. Chem. 1992,96,8552-8556
by substitution of eqs 2&22,29-33, and 39-42 into eq 38. The functional forms of In A3(n and d In X3(n/dT in eqs 39 and 40 need not be specified, as these terms cancel out upon substitution into eq 38. Pprtirl Mohr properties In order to evaluate the performance of the model (see the following paper in this issue), it is useful to consider briefly the partial molar properties of components 1 and 3 in both phases. The infinite-dilution partial molar volume of the solute in the stationary phase, may be obtained from
cs,
c,,,
The values of and 03sare given by similar equations. An absolute value for the partial molar enthalpy of component i, hi, cannot be obtained from the model because of the term_ In in eq.14. However, one can compute the difference hi hi', where h, is the molar enthalpy of pure i in an ideal-gas state at the same temperature. For example,
X,(n
Similar relations may be obtained for
hf;,- h; and h3s - hi.
Conclusion Applications of SFC to physicochemical measurements require an intimate knowledge of the thermodynamics of solute retention in SFC. In the present contribution, a mean-field lattice model
has been employed to derive expressions for the composition terms in the classical thermodynamic relationships for the pressure and temperature quotients of solute retention in SFC with a pure (single-component) mobile phase. This model takes into account the praure or tempcratureinduced changes in both volume and composition of the stationary phase. Parametrization and performance of this model will be discussed in the following paper in this issue.
References rad Notes (1) Johnston, K. P.; Eckert, C. A. AIChE J . 1981, 27, 773. (2) Gitterman, R. B.; Procaccia, I. J. Chem. Phys. 1983, 78, 2648. (3) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice; Butterworths: Boston, 1986. (4) Debenedetti, P. G.; Kumar, S.K. AIChE J. 1988, 34, 645. (5) Martire, D.E.; Bahm, R. E. J. Phys. Chem. 1987, 91, 2433. (6) Martire, D. E. J . Chromatop. 1988, 452, 17. (7) Shim, J.-J.; Johnston, K.P. AIChE J . 1989, 35, 1097. (8) Kelley, F. D.; Chimowitz, E. H.AIChE J . 1990, 36, 1163. (9) Roth, M.J . Phys. Chem. 1990, 94,4309.
(IO) Roth, M.J. Supcrcrit. Fluids 1990, 3, 108. ( 1 1 ) Shim, J.-J.; Johnston, K. P. J . Phys. Chem. 1991, 95, 353. (12) Shim, J.-J.; Johnston, K. P. AIChE J. 1991, 37, 607. (13) Roth, M.J . Microcol. Sep. 1991, 3, 173. (14) Fleming, G. K.; Koros, W.J. Macromolecules 1986, 19, 2285. (15) Pope, D. S.; Sanchez, I. C.; Koros, W.J.; Fleming, G. K. Macromolecules 1991, 24, 1779. ( 1 6 ) Tompa, H. Polymer Solutions; Butterworth: London, 1956; Chapter 4. (17) Roth, M.J . Phys. Chem. 1991, 95, 8 . (18) Panayiotou, C.; Vera, J. H. Polym. J . 1982, 14, 681. (19) Kumar, S. K.; Suter, U. W.; Reid, R. C. Ind. Eng. Chem. Res. 1987, 26, 2532. (20) Daneshvar, M.;Kim, S.;Gulari, E. J . Phys. Chem. 1990,94,2124. (21) Guggenheim, E. A. Mixtures; Clarendon Ress: Oxford, U.K., 1954. (22) Panayiotou, C.; Vera, J. H.Can. J. Chem. Eng. 1981, 59, 501. (23) Guggenheim, E. A. Thermodynamics. An Advanced Treatment for Chemists and Physicists, 3rd 4.; North-Holland: Amsterdam, 1957; Chapter 3, pp 83-95.
Statistical Thermodynamic Treatment of HigkPressure Phase Equillbria in Supercritical Fluid Chromatography. 2. Parametrization and Testing of the Model Michal Roth Institute of Analytical Chemistry, Czechoslovak Academy of Sciences, 61142 Brno, Czechoslovakia (Received: February 6, 1992)
In a typical capillary-columnsupercritical fluid chromatography (SFC)system [naphthalentpoly(dimethylsiloxane)-carbon dioxide], the random-mixing version of the Panayiotou-Vera lattice model is shown to yield moderately successful reproductions of experimental data on supercritical solubility, polymer swelling, and solute partition coefficients with a unique set of purecomponent parameters and one adjustable parameter per binary. With the parameters fixed by fitting the above data, the treatment described in part 1 of this series (preceding paper in this issue) provides reasonable predictions for the partial molar properties of the solute and for the effect of compositionon the chemical potential of the solute in the stationary phase. In the present system, swelling of the stationary phase by the supercritical fluid is predicted to make a positive contribution to (a In kl/aP)Tand a negative contribution to (a In kl/a7')p It appears that relative contributions of the stationary-phase composition changes t o (a In k,/aP),and (a In k,/aT), generally decrease with increasing isothermal compressibility and isobaric expansivity of the mobile-phase fluid, respectively.
Introduction In part 1 of this series,' the random-mixing version of the Panayioutou-Vera lattice model2 has been used to derive expressions for the effect of swelling on the presure and temperature derivatives of solute mention in supercritical fluid chromatography (SFC).In the present part, an example of parametrization of the model will be given in order to evaluate the performance of the model. It will be shown how the complicated effect of mobilephase sorption into the stationaryphase on the solute retention in SFC may be addressed by employing information on the re-
spective binary subsystems involved. The system to test the theoretical treatment will be naphthalene (1)-poly(dimethylsiloxane) (PDMS)(2)-carbon dioxide (3). For this particular system, nearly all necessary experimental data are available. This (second) part of the series may roughly be divided into two sections. In the first section, the sour- and calculations of the purecomponent and unlike interaction-energy parameters will be described. At the same time, this section will illustrate the capability of the model to reproduce the experimental data used
0022-3654/92/2096-8552S03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8553
Parametrization and Testing of the Model
TABLE I: Pun-Compooent Parameters for Carbon Dioxide vi, cm3 set source eIJkR,K mol-' a ref 3 82.026 38.72 15.498 43.54 b T,,pC P,. and (aP/av)T= 01, 40.21 c T,,pc P,,and (@P/av2),= 01, 18.652 d (aP/aV)T = 01, and (@P/av2), = Olc 16.944 31.11 "The critical data for C02 were taken from ref 4.
--
-6
0
I
1
0.2
0.4
-8
I 0.6
0.8
p I p "3 Figure 1. Pressure-density isotherms for C02 at 308.15 K. The solid curve results from the high-accuracy EOS of Ely et al? Curves a and b are lattice isotherms calculated with parameter sets a and b (cf. Table
I), respectively.
to obtain the parameters. In the second section, the model will be employed to predict several properties that were not used to obtain the parameters, the quality of predictions will be assessed, and some implications of the predicted trends will be discussed.
hue-Component Parameters The parameters for naphthalene (denoted as 1 in the subscripts) will be those reported previously by Kumar et al.,3 Le., ell/ke = 146.9K and uI* = 106.07cm3mol-'. For poly(dimethylsi1oxane) (denoted as 2 in the subscripts), the parameters given by Panayiotou and Vera2 will be employed; c22 is treated as a temperature-dependent parameter, cz2/kB= (67.038 + 7.3015 X 10-2T)K, and the specific hard-core volume of PDMS is = 0,8911 cm3 g-I. The effect of cross-links on c22 and u2,sp*wlll be neglected. For supercritical carbon dioxide (denoted as 3 in the subscripts), Kumar et aL3 obtained the parameters by fitting the lattice equation of state (EOS, see eq 13 in part 1) to experimental isotherms. The pressure-density isotherm for C 0 2 at 308.15K calculated from the lattice EOS with the parameters of Kumar et al. is shown by curve a in Figure 1. The shape of this curve does not compare well with the solid curve showing the isotherm computed from an accurate EOS of Ely et a1.4 The two-phase region in the lattice isotherms obtained with the parameters of Kumar et al. still persists up to about 323 K. Although a mean-field lattice EOS should not be used in the vicinity of the critical point, an attempt may be made to parametrize the lattice EOS by employing the conditions prevailing at the critical point. The parameters z33 and u3* may then be obtained from fitting the E o 5 to any two of the following three conditions: (1) reproduction of the critical pressure from the critical temperature and density; (2)(aP/aV)T= 0 at the critical point, u being the molar volume; and (3) ( a * P / a ~=~0) at ~ the critical point. The three resultant pairs of tj3 and u3* are listed in Table I together with the parameters given by Kumar et al.3 Curve b in Figure 1 shows the 308.15 K isotherm calculated with the parameters from conditions l and 2 above. As compared to isotherm a, isotherm b presents an improvement in the low- and mediumdensity regions at the expense of larger deviations in the highdensity region. This trend continues at higher temperatures.. The isotherms resulting from parameter sets c and d are not shown in Figure 1. At 308.15 K, set c produces a two-phase region the extent of which is intermediate between those seen in isotherms a and b. Set d correctly produces a single-phase isotherm; however, the inflection point of the isotherm is shifted to a pressure of about
100
200
P I bar
300
Figure 2. Solubilityof naphthalene in C02 as a function of pressure at 3 18.1 5 K. Circles show the experimental data of Tsekhanskaya et a1.6 Curve a: C02parameter set a (cf. Table I), 613 = 0.10. Curve b: C02 parameter set b, 613 = 0.06.
112 bar, while the correct value is close to 80 bar (cf. the solid curve in Figure 1). For all three pure components, the other purecomponent parameters are obtained from eqs 4,8,and l l in part l. Since r2 a,it follows from eq 4 in part 1 that q2/r2= 0.8.
-
Unlike Interaction-Energy Parameters Following Daneshvar et al.,5 the unlike interaction-energy parameters will be expressed by a modified geometric-mean rule
= (eiicjj)1/2(1 - ai,) for i+ j (1) where the deviation parameters 6, may be obtained from fitting the model to available experimental data on the respective i-j system. Supercritical Solubility (til3). Figure 2 shows a comparison of lattice model predictions with the experimental solubilities6 (mole fractions, yI)of naphthalene in C 0 2 at 318.15 K. The calculated curves result from equating the chemical potential of naphthalene in a mixture with C 0 2 to that of pure (crystalline) naphthalene. It is wen from Figure 2 that, as compared to C02parameter set a (cf. Table I), set b presents a better overall reproduction of the shape of the solubility-pressure isotherm at the expense of a worse reproduction of the slope of this isotherm. To do so,set b requires a value of 613 which is lower than that needed in set a (cf. caption to Figure 1). At 308.15 and 328.15 K,set b with SI3 = 0.06 still yields a reasonable reproduction of the shapes of the experimental isotherms: although the lattice isotherm at 308.15 K already shows a discontinuity. Polymer Swelling (&). At present, no information is available on the solubility of supercritical C 0 2 in PDMS. In order to evaluate 623, the model may be fitted to experimental isotherms7** for the swelling of cross-linked PDMS rubber by supercritical C02, Figure 3 shows the relative change in the volume of the polymer phase as a function of pressure at 308.15 K. The parameters 623 in the calculated isotherms have been adjusted to give a correct value of AV/V,, at the upper limit of the experimental pressure range. C 0 2parameter set b provides a better overall reproduction of the experimental dilation isotherm. This conclusion also applies to the 323.15 and 343.15 K isotherms. For C02parameter set b, the temperature dependence of 623may be expressed by 623= 0.1603 - 5.346 X 104T + 9.524 X lO-'P (2) Partition Coefficients (tilz). No suitable experimentaldata on the naphthalene-PDMS binary system have been found in the literature. Therefore, SI,will be evaluated from fitting the model q,
8554 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
Roth
0.8 Av -
"0 0.4
0
Figure 3. Swelling of PDMS rubber by absorption of C02at 308.15 K. Circles show the experimental data of Shim and J o h n s t ~ n .Curve ~ ~ ~ a: C02parameter set a, 623 = 0.11. Curve b: C02parameter set b, 623 = 0.086.
50
100
P/hr
Figure 5. Quotient ( l / R T ) ( a ~ ( t / d s 3 , ) as ~ ~a ,function ~ , , ~ ~of pressure at 308.15 K.
I
0.00s
-
1
- 0.010
I
5
-
V-
.OD05
1
1
100
P I bar
200
x 1.
Figure 4. Infinite-dilution partition coefficient of naphthalene between
supercritical C02and swollen PDMS rubber. Experimental data of Shim and Johnstonsrefer to 307.35 K (O), 322.25K (a),and 342.15 K (0). Parameters of the lattice isotherms are given in the text. to infinite-dilution partition coefficients of naphthalene between supercritical COz and swollen PDMS rubber.8 Naturally, this can only be done after 613 and 823 have been obtained from solubility and dilation data as described above. In Figure 4, the experimental partition coefficients of naphthalene are compared with the lattice model results obtained by using C02parameter set b, b I 3 = 0.06, 623 given by eq 2, and 612 calculated from 612 = 0.1883 - 2.874 X 10-4T
0
50
100
150
PIbar
Fipw 6. Quotients ( a s 3 , / a P ) , ,and (as,,/aT),, as functions of pressure at 308.15 K.
(3)
Except for the near-critical region, agreement between experimental and calculated partition coefficients is satisfactory. In the naphthalene-PDMS-C02 system, the random-mixing version of the Panayiotou-Vera lattice model appears to yield reasonable reproductions of experimental data on the supercritical solubility, polymer swelling, and partition coefficientswith a unique set of purecomponent parameters and one temperature-dependent parameter per binary. Magnitudes of the deviation parameters, 6, are similar to those found previously in similar system?J In general, the sensitivity of model predictions to the values of 6, increases with increasing pressure.
Results and Discussion Model predictions within this section will employ C02parameter set b and the values of 6, given above. Composition Terms. Figure 5 illustrates the pressure dependence of the isobaric composition derivative of pTs (cf. eqs 15-23 in part 1) at 308.15 K. This quotient is negative, and as expected, its absolute value is maximum at zero pressure where 83s= 0. By employing the Scatchard-Hildebrand-Flory-Huggins theory combined with the pertinent data, the value of (l/RT)(Bp,,"/ I38,), in the same system at 308.15 K and 74.6 bar has previously been estimatedg at about 60% of the value read from Figure 5. Figure 6 shows the pressure course^ of the quotients (&/aP)T,. and (1383,/13T)p,, at 308.15 K. Except for the breaks in the calculated isotherms (cf. Figure l), the plots agree qualitatively with what may be expected. Experimental dilation data7-*suggest that the model predictions of (1393s/13P)T,u are likely to be underestimated at pressures above the break in the calculated isotherm (cf. Figure 3). The results displayed in Figures 5 and 6 indicate that, in the present system, the composition terms make a positive contribution
100
200
300
P I bar
Figure 7. Infinite-dilution partial molar volume of naphthalene in C02 at 308.38 K. Circle show the experimental data of Eckert et a1.I'
to (I3 In kllI3P)Tand a negative contributionto (I3 In kl/13T), (cf. eqs 1 and 2 in part 1). putirl Molar Voluws. The infinite-dilution partial molar volume of a solute is known to divergeloas the temperature and pressure approach the critical point of the solvent. In Figure 7, the lattice isotherm for the infinitdilution partial molar volume of naphthalene in C 0 2at 308.38 K is shown together with the experimental values of Eckert et al." Compared to the experimental data, the calculated curve' is shifted toward higher pressures. In part, the shift results from errors in the isothermal compressibility of C02 calculated from the lattice model (cf. the s l o p of curve b and the solid curve in Figure 1). The partial molar volume of the dissolved C02 in PDMS at 308.15 K is predicted to vary between 61 and 65 cm3mol-' within the pressure range 0-200 bar. The experimental value for the zero-pressure limit of B3* at 308.15 K is 46.1 cm3 mol-', and 0 , increases with increasing pressure.l2 The pnsent parametrization of the model should not be expected to perform well in the lowpressure region because it has been derived from experimental data measured at supercritical pressures. In the PDMS-C02 system, no experimental values of D3, are available at pressures
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8555
Parametrization and Testing of the Model
TABLE n: Cbmcteri#tiw of the Temperature Dep"w of In k , 1 for Napbthakac in the PDMSCO, S y 3 W temp, OC
-*
-
35 40 45 50 55 60 65 70 0.5
K 3680 3340 3100 2910 2770 2650 2540 2450
the terms in % b, 5% 61.5 -0.1 66.2 -0.1 69.8 -0.1 72.7 4 . 1 75.2 -0.1 77.2 -0.1 79.0 -0.1 80.6 -0.2 (I,
c,
5%
38.6 33.9 30.3,. 27.4 24.9 22.9 21.1 19.6
'COz density pm = 0.3 g cm-3;phase-volume ratio at 35 OC and zero pressure V,/V, = 0.016. bAH, = if,- A;,,,.
0.6
-:;
(a In kl/a(l/7'))h,
AifI/R,b K 33300 16200 10300 7 260 5 430 4 220 3 350 2700
-
the present system. This claim may also be supported by a model-independent thermodynamic argument. In a binary, two-phase system (2 3) in which heavy component 2 is insoluble in component 3 (see part l ) , the chemical potential of component 3 in the mobile phase is a function of T and P, while the chemical potential of component 3 in the stationary phase is a function of Then it may be shown that T,P, and
+
where s! and u! are the molar entropy and molar volume of pure mobile-phase fluid 3 and 35, is the partial molar entropy of the mobile-phase fluid in the stationary phase, all at T and P. In general, the coefficient of proportionality between the two derivatives in eq 8 does not equal -ymv [=-(8&8~$)~]. Consequently, the c term (eq 7) is different from zero. Implications of the Predicted Treads. It is apparent from the generul eqs 15, 27, 28, 37,and 38 in part 1 that the quotients (a~:~aa~.),,~(a3,,/ap),,,and (a3,,/a~)~,,are always finite, even at T and P corresponding to the critical point of the moand h;,,,, the bilephase fluid. Unlike the quantities p,,,= amp,q,, three quotients do not diverge as T and P approach the critical point. First, let us consider the calculation of from (a In k l / a P ) , via eq 1 in part 1 . As pointed out by Shim and Johnston," it is convenient to regress In kl against In p,,, and use the identity (a In k 1 / a P ) ,= BmT (a In k l / a In P , , , ) ~ To a first approximation, the effect of the product (acr:I/a~,,)T,,(ab,,/aP)T,, on the resultant value of qmis minimum at the pressure, p,,,,,, at which BmT is maximum for the given temperature. If the pressure is changed from P,, in either direction at a constant T,the relative contribution of the composition terms to (a In k l / d P ) , decreases because the change in ( a ~ ~ / ~ 3 s ) , d aisSs ~ /d a compared ~),,u to the concomitant drops in magnitudes of BmT and cm. Using the treatment described above and the experimental data of Shim and Johnston? one finds that, in the present system at 34.2 OC, the contribution of composition terms to (a In k l / l J P ) Tis -16% at 75.3 bar, -3.6% at 79.4 bar, and -29% at 126.2bar. For C 0 2 at 34.2 OC, the maximum in the isothermal compressibilityBmT occurs at PmX= 78.8 bar, as computed from the high-accuracy EOS of Ely et a1.4 Thus, one arrives at the conclusion that the effect of composition terms on the resultant is minimum if the mobilephase critical point is approached from the supercritical region along the path of maximum BmT. Hypothetically, at the mobile-phase critical point itself, the composition terms would have no effect since BmT and a;, -a. Second, let us briefly discuss the calculation of &, from (a In k l / a T ) pvia eq 2 in part 1. Here, to a first approximation, the effect of ( ~ ~ ~ I / ~ 8 , , ) , ( ~ 3 3 on ,/~ ther )resultant p , , value of h;,,, is minimum at the temperature, T,,,,,, at which ampis maximum for the given pressure. If the temperature is changed from T, in either direction at a constant P,the relative contribution of the composition terms to (a In k 1 / a r ) , decreases because the change in (a~:,/a3,),das,,/aT),, is small compared to the concomitant drops in magnitudes of ampand h;,. The effect of composition terms on the resultant &, is minimum if the critical point is
c,,,
c,,,
- +-
-
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 molecule quadricyclane, tetracyclo[ 3.2.0.02*7.0436] heptane, C7HB, 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
