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J . Phys. Chem. 1987, 91, 4198-4203
enter solution as molecules rather than as microbubbles. We do not know whether membranes could be made which were simultaneously strong enough and permeable enough to function as desired. The above recital makes it clear we believe that this paper opens up the possibility of a major research program which could significantly impact the whole field of nucleation of one phase in another. Although we intend to pursue at least some of the openings suggested, we are in no position to explore all of the possibilities. In any field, it is desirable that there be some duplication in different laboratories to ensure that conclusions can be trusted. It is also true that extensive competitive duplication
is wasteful of scientific manpower. If our work suggests studies which others might wish to undertake, we would appreciate it if we were informed as to their plans. We would be happy to reciprocate.
Acknowledgment. This work was supported in part by Grant No. CHE-8405518 from the National Science Foundation. We are indebted to Professor Peter G. Bowers of Simmons College for making the trace of Figure 3 available to us. Professors Arthur W. Adamson of the University of Southern California and Howard Reiss of UCLA helped to introduce us to a literature with which we were unfamiliar; we accept responsibility for any oversights.
Vapor Pressure Isotope Effects in Liquid Methylene Difluoride Arundhati Kanungo, Takao Oi,+ Anthony Popowicz,*and Takanobu Ishida* Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 1 1 794 (Received: November 7 , 1986)
The vapor pressures of the isotopic methylene difluorides '*H2F2, I3CH2F2,and '%D2F2 have been measured at temperatures between 149.36and 244.82 K by differential manometric techniques in a precision cryostat. Throughout the whole temperature range of the measurement, P(13CHzF2)> P(I2CH2F2)> P("CD2F2). The data are best represented by T In cfc/fg)= -(31.64 f 1.97)/T- (0.4069 f 0.0107) for the I2C/l3C effect and by Tln cf,/f,) = (632.26 f 97.62)/T- (19.175 f 1.016) - (0.0532 f 0.0025)T for the H/D effect. The vapor pressure of the natural abundance methylene difluoride is given by log P(Torr) = 7.1990 - 842.31/[t ("C) + 246.811. The normal H/D vapor pressure isotope effect (VPIE) in liquid methylene difluoride is due to the zero-point energy shift upon condensation of the deuterio species being greater than that of the protio species, a fact which is also found for the H/D VPIEs in liquid methyl fluoride and fluoroform. The H/D effect in methylene difluoride is unusually higher than those found in methyl fluoride and fluoroform due to an enhanced perturbation of the C-H stretching modes by a relatively large intermolecular force in liquid methylene difluoride. Results of the normal-coordinate analyses of the cell model are presented. Temperature dependency of the external-internal interaction force constants is a necessary requirement for the satisfactory reproduction of the observed H/D and l2C/l3CVPIEs and spectroscopic data on the liquid.
+
Introduction Studies of vapor pressure isotope effects (VPIE) have in the past led to elucidations of intermolecular forces and perturbations of internal vibrations in the condensed phases in a wide variety of The rather surprising success of the simple cell model which the analyses of these VPIE data have been based on is mainly due to the fact that all configurational factors of the condensed-phase partition function are independent of isotopic substitutions under the Born-Oppenheimer approximation and, thus, cancel 0ut2324when the isotopic ratio of the reduced partition function (RPFR) is taken. Following an isotope effect convention we define RPFR for an isotopic pair of a chemical species as In (s/s')J and s and s'are the symmetry numbers of the heavier and lighter isotopic species of the pair, respectively, and f is the ratio of partition function of the lighter to that of the heavier divided by the classical limit of the ratio. All quantities with a prime refer to the lighter species and the unprimed counterpart to the heavier one. The method of differential manometry using a cryostat such as the BBJR cryostat,25which is capable of tempetature stability and uniformity better than 0.001 K, provides precise (50.1%)data on the logarithm of the isotopic vapor pressure ratio, In (P'IP). The latter is directly related' to the ratio of the RPFR's of the condensed phase, f,,and the gas phase, fg In WfJ = (1 + P[Bo- (V,/RTIj In ( P ' / P ) (1) where Bo is the second virial coefficient of the gas (PVIRT = 1 t Present address: Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo, Japan 'Present address: Rockefeller University, 1230 York Avenue, New York, NY 10021
0022-3654/87/2091-4198$01.50/0
+
B f l ...) and V, the molal volume of the condensed phase. Usually, the internal forces of the gaseous molecules are well-
(1) Bigeleisen, J. J . Chem. Phys. 1961, 34, 1485. (2) Bigeleisen, J.; Roth, E. J . Chem. Phys. 1961, 35, 68. (3) Bigeleisen, J.; Ribnikar, S . V.; Van Hook, W. A. J . Am. Chem. SOC. 1961,83, 2956. (4) Bigeleisen, J.; Ribnikar, S.V. J. Chem. Phys. 1961, 35, 1297. (5) Bigeleisen, J.; Ribnikar, S. V.; Van Hook, W. A. J . Chem. Phys. 1963, 38, 489. (6) Bigeleisen, J.; Stern, M. J.; Van Hook, W. A. J . Chem. Phys. 1963, 38, 497. (7) Van Hook, W. A. J . Chem. Phys. 1966, 44, 234. (8) Van Hook, W. A. J . Chem. Phys. 1967, 46, 1907. (9) Bigeleisen, J.; Cragg, C. B.; Jeevanandam, M. J. Chem. Phys. 1967, 47, 4335. (10) Ishida, T.; Bigeleisen, J. J. Chem. Phys. 1968, 49, 5498. (11) Phillips, J. T.; Van Hook, W. A. J . Chem. Phys. 1970, 52, 495. (12) McDaniel, R. L.; Van Hook, W. A. J . Chem. Phys. 1970,52,4027. (13) Lee, M. W.; Fuks, S.; Bigeleisen, J. J. Chem. Phys. 1970, 53, 4066. (14) Lee, M. W.; Eshelman, D. M.; Bigeleisen, J. J. Chem. Phys. 1972, 56, 4585. (15) Jancso, G.; Van Hook, W. A. Chem. Reu. 1974, 74, 689. (16) Bilkadi, Z.; Lee, M.W.; Bigeleisen, J. J. Chem. Phys. 1975,62, 2087. (17) Yato, Y.; Lee, M.W.; Bigeleisen, J. J . Chem. Phys. 1975,63, 1555. (18) Bigeleisen, J.; Fuks, S.; Ribnikar, S. V.; Yato, Y. J. Chem. Phys. 1977, 66, 1689. (19) Jancso, G.; Van Hook, W . A. J . Chem. Phys. 1978, 68, 3191. (20) Borodinsky, L.; Wieck, H. J.; Mayfield, D.; Ishida, T. J . Chem. Phys. 1978, 68, 3219. (21) Popowicz, A.; Oi, T.; Shulman, J.; Ishida, T. J. Chem. Phys. 1982, 76, 3732. (22) Oi, T.; Shulman, J.; Popowicz, A,; Ishida, T. J . Phys. Chem. 1983, 87, 3153. (23) Pollin, J. S.; Ishida, T. J. Chem. Phys. 1977, 66, 4433. (24) Pollin, J. S . ; Ishida, T. J. Chem. Phys. 1977, 66, 4442.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 4199
Vapor Pressures of Isotopic Methylene Difluorides
0.0 I
known, which enables one to calculate the RPFR of the gas phase and, consequently, f, from eq 1 as a function of temperature. On the assumption that translation and rotation in the liquid can be described by a lattice vibration, we have c
where In b(u,) is the contribution of the i-th (internal or external) vibrational mode to the RPFR, and 6 In b(u) = In b(u9 - In b(u) (3)
- 1.0
4.0
I
I
I
I
I
1
I
1
I
1
I
I
4.5
5.0
5.5
6.0
6.5
7.0
IO'/T
( K - ' )
Figure 1. T In&/& vs. 1/T for I2C/l3C VPIE. The solid line has been computed from the F matrices of Tables I1 and V.
Under the harmonic oscillator approximation, In b(u) becomes In b(u) =
-U2 - I n
u
- In (1 - e-U)
(4)
In eq 2, the first sum is taken over the external vibrational modes for the liquid state, and the second sum involves all internal modes in both liquid and gas states;
A6 In b(u) = 6 In b(u),,, - 6 In b ( ~ ) , , ~
(5)
where u' = hcJ/kT and u = hcv/kT are for the lighter and heavier isotopic molecule, respectively. Usually, each sum of eq 2 is positive. Thus, a strong external force tends to make the VPIE normal (P'> P ) , while the internal vibrations tend to contribute negatively to the VPIE. The information on f,.provides a very sensitive clue on the intermolecular force and its effects on the intramolecular vibrations. For example, a data set, ',v = 1000 cm-I, v, = 950 cm-I, vgl = 1010 cm-l, and vg = 955 cm-', corresponds to A6 In b(u) = 0.013 30, while a small change of ',v to 1001 cm-l yields A6 In b(u) = 0.01069, a 20% change. Recently, we investigated the VPIE in the liquid fluoroformm-21 and liquid methyl fluoride.22 In this paper we will report on the results of the differential manometric measurements of the 13C/'2C and D / H VPIE's in liquid methylene difluoride and a comparison of the results with the VPIEs in fluoroform, methyl fluoride, and methane.
Experimental Section The design of the BBIR-type cryostat, the calibration and control of its temperature and pressure, and its operation have been described p r e v i o ~ s l y The . ~ ~ sample ~ ~ ~ holder of the cryostat has four sample cavities. The reference isotopic specimen, Le., I2CH2F2of the natural isotopic abundance for the present study, was introduced into two of the cavities, and other species (I3CH2F2 and 12CD2F2in the present study) were condensed into the remaining cavities. Temperatures of all specimens were kept within fO.OO1 K of each other and maintained at a constant temperature level to within fO.OO1 K for at least 3 h at a time. The vapor pressure of the reference specimen, P', was read on a quartz spiral gauge with a resolution of 0.0075 Torr, and the differences between P' and the vapor pressures of other isotopic species, P, were measured by using three capacitance gauges with seven full scale ranges from 100 to 0.1 Torr and the precision of 0.01% of each full scale. The second sample of I2CH2F2provided a check for uniformity of the temperature. The isotopically labeled methylene difluorides purchased from commercial sources contained excessive levels of chemical impurities: The natural abundance CH2F2 (Columbia Organic Chemicals) contained C 0 2 (100 ppm), CHF, (800 ppm), and others (0.2%); I2CD2F2specimen ( U S . Services/Prochem) contained C 0 2 (2.2%), CDF, (100 ppm), and CD2FBr (10.5%); and 13CH2F2( U S . Services/Prochem) contained 13C02(1 .O%), I3CHF3 (20.0%), 13CH2FBr (9.2%), and others (1.5%). For the differential manometry, about 300 mL (NTP) of each specimen containing less than 10 ppm of impurities were needed. This was accomplished by using a preparative gas chromatographic column (3/8 in. 0.d. X 10 m) packed with Chromosorb-102 at room tem( 2 5 ) Bigeleisen, J.; Brooks, F. p.; Ishida, T.; Ribnikar, S. V . Rev. Sci. Instrum. 1968, 39, 353.
16
. -9
a12
-c
10
4.0
4.5
5.0
5.5
6.0
6.5
1.0
1 0 ~ 1 ( K~- ' )
Figure 2. T In&/& vs. 1 / T for H/D VPIE. The solid line has been computed from the F matrices of Tables I1 and V.
perature. The design and operating procedure of the purification column have been described earlier.21 The isotopic compositions of the chemically purified specimen were determined by using a Kratos MS 30 dual beam mass spectrometer with DS 50 data base system. The molar compositions thus found are as follows: natural abundance sample (98.3% '2CH2F2, 1.7% I3CH2F2);I2CD2F2sample (95.4% I2CD2F2, 3.7% I2CHDF2, 0.9% I3CD2F2);and I3CH2F2sample (82.8% I3CH2F2, 17.2; "CH2F2).
Results and Discussion The VPIE measurements were carried out at temperatures between 149.34 and 244.86 K. The carbon VPIE data were taken at 138 temperatures, while the hydrogen VPIE measurements were made at 141 temperatures. The vapor pressure data were corrected for the isotopic impurities on the basis of Raoult's law and the rule of the geometric mean of VPIE.26v27 The RPFR of the isotopic pairs, 1TH2F2/13CH2F2 and 12CH2F2/12CD2F2, were then evaluated by using eq 1. The second virial coefficient B ( T ) summarized in ref 28 and the liquid molal volume based on the density data of Tremaine and Robinson,2gd(g/mL) = 1.7602 2.5165 X lO-,T (K), were used for this purpose. The vapor pressure of the natural abundance methylene difluoride a t temperatures between 149 and 245 K is represented by 842.31 log P (Torr) = 7.1990 (6) t ("C)+ 246.81 The variance of the fit is 1.6 X 10" for log P (Torr). The results (26) Bigeleisen, J. J . Chem. Phys. 1955, 23, 2264. (27) Bigeleisen, J. J . Chem. Phys. 1958, 28, 694. (28) Zwolinski, B. J. Selected Values of Properties of Chemical Compounds; American Petroleum Institute of Research Project 44; Thermodynamic Research Center, Texas A&M University: College Station, TX, 1974. (29) Tremaine, P.; Robinson, M. G. Can. J . Chem. 1973, 51, 1497. (30) Armstrong, G. T.; Brickwedde, F. G.; Scott, R. B. J . Res. Nail. Bur. Stand. 55. . 1955. --,- ,-39. (31) Johns, T. F.Proc. I n f . Symp. Isotope Separation, Amsterdam 1957 1958, 74-10],
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The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
Kanungo et al. TABLE I: Some Properties of Liquid Fluoromethanes AH vap dipole normal at nbp, moment polarizability bp, OC kJ/mol (gas). D (gas). A3
CHI CH3F
CH2F2 CHF, CF4
.s I
_-
-15
_ _ - - _- _ _ -C H-F-3 / C D F 3
I
--
-161.5 -78.4 -51.6 -82.0 -128.0
8.4 17.2 19.2 16.7 12.1
0 1.85 1.97 1.65 0
D, =
2.60 2.67 2.74 2.81 2.89 1.3574!
do = 1.0934 A
ad = 1 1 3 . 6 6 7
8; =
108.317
= ‘08.683
4
5
1
1
6
7
8
9
IO
1 o 3 / ~(K-’) Figure 3. Comparison of VPIE’s in liquid fluoromethanes and liquid methane: solid lines, 12C/13Ceffects; dashed lines, effects of perdeuteriosubstitutions. Data are methylene difluoride (present work), methyl fluoride (ref 22), fluoroform (ref 21), CH4/CD4 (ref 30), ’2CH,/’3CH4(ref 31).
on the RPFR have been plotted in Figures 1 and 2. The same data can be summarized by
T In If,/fg(12C/13C)] = -
*
632‘26 97*62 T (K)
31.64 f 1.97 - (0.4069 f 0.0107) T (K) (7)
+ (19.175 f 1.016) - (0.0532 f 0.0025)T
(8) The variances of the fit for In (f,/f,) are 1.7 X for 12C/13C and 5.3 X for H/D. A tabulation of the individual data points on P’, P, andjJf, has been deposited as supplementary material (see Supplementary Material Available paragraph at the end of the text). Comparison with Other Fluoromethanes and Methane. The carbon VPIE in methylene difluoride is inverse (P’CP ) while the hydrogen VPIE is normal (P’>P ) , both of which had been expected from the similar behaviors of the VPIE’s in liquid methylene fluoride and liquid fluoroform. However, such a high H / D effect in methylene difluoride was not expected. Referring to Figure 3, the magnitude of the H / D VPIE per deuterium in methyl fluoride is similar to that in fluoroform. However, the magnitude of the per-deuterium H / D effect in methylene difluoride is roughly twice as large as those for the other two fluoromethanes. On the bases of Born-Oppenheimer approximation and the first-quantum correction for In (s/s?f, one would expect the substituent additivity32of isotope effects to be valid to the extent that the molecular force parameters are transferrable amont different chemical species. It seems to be approximately the case between methyl fluoride and fluoroform but not so with methylene difluoride. We will come back to discuss this problem later in this paper. In Figure 3 we also note that a distinct difference exists between methane and its fluoro derivatives: For methane the hydrogen isotope effect is inverse and its carbon VPIE is normal while, for the fluoromethanes, the H / D effects are normal and the carbon effects are inverse. The difference is due to those in the molecular (32) Bigeleisen, J. In Isotopes and Chemical Principles; Rock, P.A,, Ed.; ACS Symp. Ser. No. 11; American Chemical Society: Washington, DC, 1975; pp 7-28.
Figure 4. Equilibrium geometry and valence coordinates of methylene difluoride.
symmetry and the relative magnitudes of the intermolecular forces between methanes and fluoromethanes. Thus, in methane, the carbon atom does not move in all but an F2normal mode, resulting in an insignificant negative contribution of the internal vibrations to the carbon VPIE. The dominant term of the carbon VPIE in methane is the one due to the translational lattice mode, which always contributes positively to In (fJf,). On the other hand, the peripheral hydrogen substitutions in methane lead to a large positive shift in the vibrational zero-point energy (ZPE), which contributes negatively to the RPFR and dominates the effects of the external modes. In contrast, for the fluoromethanes of the lower molecular symmetry, the carbon atom participates actively in all internal modes, many interactions between internal vibrations and lattice modes are symmetry-allowed, and the intermolecular forces are larger than for methane. The consequently higher internal contributions must have resulted in the inverse carbon VPIE’s in the liquid fluoromethanes, while the larger intermolecular force must have caused the normal hydrogen VPIE’s. Furthermore, the unexpectedly high H / D effect in methylene difluoride must be due to a relatively large intermolecular force in the liquid. That liquid methylene difluoride must have a higher intermolecular force than other fluoromethanes is illustrated in Table I. Then, a question arises. How did it happen that the H / D VPIEs in the fluoromethanes are not inverse? Since contributions of internal vibrations to the VPIE’s in a fluoromethane, i.e., the second sum in eq 2, are presumably more significant for the H / D substitutions than for the carbon isotope substitutions in the same fluoromethane, one would have expected a more negative In Cfc/fK)HID than In cfc/fK)12/13. Another aspect of this question is: Why do not the intermolecular forces of the fluoromethanes, which are presumably larger than that in methane, lead to a more positive 12C/’3CVPIE than the l2C/I3C effect in methane? To answer these questions a normal vibrational analysis based on the liquid cell model has been carried out. Normal Vibrational Analysis. As mentioned in the Introduction, a VPIE data can be reduced to a set of data on f, as a function of temperature through calculation of fg based on the ideal gas statistical mechanics. Using a cell model, a liquid force field can, in principle, be deduced such that it reproducesf,( T ) and all known vibrational and lattice frequencies of isotopic liquids. Suzuki and S h i m a n o ~ c h obtained i~~ an F matrix of gaseous methylene difluoride in symmetry coordinates based on their data on CH2F2and CD2F2. We have fitted a new F matrix for the gaseous molecule using additional experimental data that have since become available. The valence coordinates used are Adl (no. l), Ad, (no. 2), AD,(no. 3), A& (no. 4), A a = doAa’ (no. 5 ) , A@ = doApl (no. 6), and As,, = doAqf0where An‘[, is dis( 33) Suzuki, I.; Shimanouchi, T. J . Mol. Spectrosc. 1973, 46, 130.
The Journal of Physical Chemistry, Voi. 91, No. 15, 1987
Vapor Pressures of Isotopic Methylene Difluorides
4201
TABLE II: F Matrix of Gaseous Methylene Fluoride in Valence Coordinates' off-diagonals diagonals value, value, mdyn mdyn description notation .&-I notation A-1 0.130 fdd C-H, C-H C-H stretch fd 4.829 0.106 C-F stretch fD 6.020 fdD C-H, C-F fda C-H, HCH 0.105 HCH bend fa 0.462 FCF bend fs 1.000 fdp C-H, FCF -0.136 fd, C-H, H C F -0.063 H C F bend f, 0.635 f'd, C-H, HCF 0.073 fDD C-F, C-F 0.996 fD, C-F, HCH -0.305 fDp C-F, FCF 0.346 0.249 fh C-F, HCH f'h C-F, H C F -0.253 fa@ HCH, FCF -0.286 fa, HCH, H C F -0.053 fs, FCF, H C F -0.160 HCF, H C F -0.048 HCF, H C F -0.161 f',,, HCF, H C F -0.222
TABLE Ilk Observed and Calculated Frequencies of Gaseous Methylene Fluoride' experimental molecule mode Suzukib KondoC Andrewsd Plylere calcd 2949 2946.997 2948.0 2958 ul(Al) 2948.0 12CH,F, _ _ u;(AI) 1508.0 1508.0 1507 1507.089 YJ(AI) 1113.2 1 1 I I .2 1 107.0 1070 1 107.293 ~q(A1) 528.5 528.5 533.5 529 532.280 ~s(A2) 1262.0 1260.568 Yg(B1) 3014.3 3014.0 3032 3015 3014.194 UT(BI) 1177.9 1178.3 1178.5 1165 1183.340 ~g(B2) 1435.0 1435.0 1436.5 1430 1436.908 ~g(B2) 1090.1 1090.1 1079.5 1090 1081.203
'All bending coordinates are weighted by the equilibrium C-H bond length. An F matrix element with one subscript is a diagonal element. When two off-diagonal elements are listed to a similar interaction, e.g., f'd, and fd,, the one without a prime refers to the interaction between two coordinates which share a common C-H bond, while the one with a prime refers to the interaction between two coordinates which do not share a common bond. 'For f,,d and f,nD they share a C-H bond and a C-F bond, respectively.
I3CH2F2 vl(Al) Y2(AI)
~
2:;'
I2CD2F2 ul(Al) u~(AI) u~(AI) ~q(A1) ~5(A2) ~g(B1) Y,(B~) ~g(B2) vg(B2)
v3(Al)
YdAd 442) v6(B1) Y7(BI) YdBZ) Vg(B2)
2128.9 1170.3 1026.5 521.7 907.3 2283.9 962.1 1158.3 1002.4
2128.9 1172.0 1029.0 521.7
2130 1165 1028 526
2283.9 961.6 1158.0 1003.2
2294 960 1151 1001 295 1 1503 1084.5 530.3 3020 1165.5 1430.2 1055.0
2131.640 1171.781 1024.293 521.702 907.260 2277.749 950.499 1148.386 998.109 2942.458 1501.263 1085.975 529.232 1260.568 2998.531 1170.766 1430.602 1056.194
placement of the angle between Hi and Fj (cf. Figure 4); AvI1 (no. "All frequencies are in cm-I. 'Reference 33. cReference 36. 7), AvI2 (no. 8), Av2, (no. 9), and A722 (no. 10). The equilibrium dReference 37. 'Reference 35. /This work, computed from the gas F matrix of Table 11. geometry shown in Figure 4 is that of hi rota'^.^^ Starting with i ~ ~working with the the F matrix of Suzuki and S h i m a n ~ u c h and symmetry coordinates by the same authors, we refitted the F TABLE IV: F Matrix for Liquid Methylene Fluoride matrix to a data base consisting of those on protio and deuterdiagonals off-diagonals iospecies of gaseous methylene d i f l ~ o r i d e ~and ~ *those ~ ~ *obtained ~~ notation value," mdyn A-' notation value,a mdvn A-' from an argon-matrix of '*CH2F2, I2CD2F2,and "CH2F2. 4.882 0.131 The final gas F matrix, transformed back to the valence coordinate fd 5.959 0.106 fD system, is given in Table 11, and the calculated frequencies are 0.462 0.105 f, compared to the experimental results in Table 111. 0.983 -0.136 fs For liquid methylene difluoride only two sets of spectroscopic 0.630 -0.063 f, data, i.e., an IR and a Raman study of 12CH2F2,are a ~ a i l a b l e . ~ * - ~ ~ 0.073 However, the VPIE data set rather strict limiations on the liquid 0.869 F matrix, the most restrictive of which is the very steep positive 0.300 -0.314 vs. 1 / T plot for the H / D VPIE (Figure slope of the T In U,/f,) 0.200 0.398 0.300 0.239 2) and the negative slope for the 12C/13Ceffect (Figure 1). Any 0.200 -0.263 set of large external diagonal elements which yields a sufficiently 0.070 -0.283 large slope for the H / D effect also leads to a positive slope and/or -0.053 0.300 a normal VPIE for the carbon isotope effect. Changes in F matrix -0.157 elements for the internal motions would shift the plots vertically -0.055 without significantly affecting the slopes. -0.156 Fourteen symmetry-allowed external-internal interaction force -0.217 constants in the symmetry coordinate system were tested. Most of these Fi,'s were too ineffective in changing the slope and/or magnitude of the H / D plot. Some moved the plot effectively at the expense of affecting the vibrational frequencies of liquid 'TH2F2too much in undesirable combinations. The only elements 'All elements are in mdyn .k', exceptf,, and& which are in mdyn found acceptable on these accounts were FSR, and F 7 R ,where Ss A and mdyn, respectively. A = T - 190. = ( h i - A912 - A721 + A122)/2 and S7 = (A711 + 8712- A121 - Av22)/2. decreasing temperature. The external force which usually inA negative curvature in a plot of T In U,/f,) vs. 1 / T such as creases with decreasing temperature tends t o force a positive Figure 2 is an indication of a changing vibrational ZPE shift due curvature. A negative curvature would thus imply a relatively to a variation in the extent of internal-external interactions with strong temperature dependence of the external-internal interacand F 7 R were fitted to reproduce the observed tions. Thus, FSR, VPIEs at T = 160, 175, 190,205, and 220 K, and the resultant (34) Hirota, E.; Tanaka, T.; Sakakibara, K.; Ohishi, Y.;Morino, Y.J. Mol. Spectrosc. 1970, 34, 222. numerical values were least-squares fitted, FSR, to a quadratic (35) Plyler, E. K.; Benedict, W. S.J. Res. Natl. Bur. Srand. 1951, 47,202. function of T and F7R,as a linear function of T. Table IV sum(36) Kondo, S.;Nakanaga, T.; Saeki, S. J . Chem. Phys. 1980, 73, 5409. marizes the best liquid F matrix thus obtained and expressed in (37) Andrew, L.;Prochaska, F. T. J . Chem. Phys. 1979, 70, 4714. the valence coordinate system, in which the temperature depen(38) Glockler, G.; Leader, G. R. J. Chem. Phys. 1939, 7, 382. (39) Rank, D. H.; Shull, E. R.; Pace, E. L. J . Chem. Phys. 1950,18,885. dence off,Ry and fnR, have been expressed in terms of A T (K)
4202
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
TABLE V: Internal and External Frequencies (cm-I) for Liquid Methylene Fluoride 12CH2F2 12CD2F2, I3CH2F2, mode exptl" calcdb calcdb calcdb 2963.031 2963 2142.293 2958.510 1508.039 1508 1156.494 1502.601 1078.898 1078 1012.746 1058.217 531.188 527.960 532 520.448 1263.205 1262 960.207 1263.205 3030.018 2287.900 3030 3014.412 1170.264 1170 934.787 1158.436 1437.258 1435 1153.927 1430.831 1089.115 1000.937 1089 1064.015 102.987 80.809 89.494 80.157 80.809 80.197 98.028 98.970 97.100 78.558 78.894 76.206 80.005 104.526 78.291 100.360 100.360 98.952 "References 38 and 39. bCalculated by using the liquid F matrix at T = 190 K.
Kanungo et al.
4 t -0.2
Y2
Y
a
TABLE VI: Comparison of Frequency Shifts in Fluoromethanes, CF.H,. (II= 0-3)" fluoroformb at 165 K ~l(A1) u~(AI) u3(A1) u4(E) %(E) u6(E)
12CHF3 u,'(gas) Avi' 3036.2 1138.9 701.4 1381.0 1151.8 507.7
totals
methyld fluoride at 153 K ul(A1) u2(A1) u3(Al) u403
us(E) U6(E) totals
-26.3 20.4 4.6 5.4 -7.9 -0.2 -6.7
12CDF3 Au; 6Aui -18.3 22.6 3.0 -6.1 1.7 0.0 -1.5
-8.0 -2.2 1.6 11.5 -9.6 -0.2 -5.2
I3CHF3 6Au;
Aui
-26.2 18.8 4.3 5.8 -8.1 -0.2 -8.1
-0.1 1.6 0.3 -0.4 0.2 0.0 1.4
I2CH2F2 u,'(gas) Au,' 2947.0 -16.0 -0.1 1507.1 28.4 1107.3 1.1 532.3 -2.2 1260.6 -15.8 3014.2 13.0 1183.3 1436.9 -0.4 -7.9 1081.2 0.1
I2CD2F2 Aui 6Aui -10.7 -5.3 15.3 -15.4 11.5 16.9 1.3 -0.2 1.1 -3.3 -10.2 -5.6 15.7 -2.7 -5.5 5.1 -2.8 -5.1 15.7 -15.6
I3CH2F2 Auj 6A~i -16.1 0.1 -1.3 1.2 27.8 0.6 1.2 -0.1 0.4 -2.6 -15.9 0.1 0.7 12.3 -0.2 -0.2 -7.8 -0.1 2.7 -2.6
I2CH3F vi'(gas) Aui' -5.3 2909.8 5.6 1462.6 61.7 1056.8 -23.6 3006.7 1479.3 -1.0 1183.0 1.3 15.4
12CD3F 6Aui 3.5 -8.8 18.8 -13.2 28.9 32.8 -12.8 -10.8 -3.1 2.1 0.9 0.4 21.2 -5.8
I3CH3F Aut ~Au, 0.7 -6.0 6.1 -0.5 0.2 61.5 0.4 -24.0 -0.3 -0.7 1.3 0.0 14.8 0.6
I2CH4 ui'kas) Aui'
I2CD4 Au, 6Au;
Aui
5.0
6.0 7.0 1 0 ~ (1 K - '~ ) Figure 5. Contributions of individual normal modes and external motions to T In (fJf,) for I2C/l3CVPIE; all calculated contributions were obtained by using the liquid F matrix of Table V at 190 K. 4.0
Yg
Y3
methanec U~(AI) u~(E) ~3(F2) ~4(F2) totals
3143.7 1574.2 3154.1 1357.4
11.5 3.9 13.8 4.9 75.4
8.2 2.8 11.5 3.0 57.3
3.3 1.1 2.3 1.9 18.1
13CH4 Aui 6Au, 11.5 3.9 13.6 4.9 74.8
0.0 0.0 0.2 0.0 0.6
"All values are calculated and in the unit of cm-I. Aui = u,(gas) ui(liq). 6Aui = Au,' - Aui = &,(gas) - 6ui(liq) where 6ui = P,' - vi. bTaken from ref 21. cPresent work; computed by using F matrix of Table V. dTaken from ref 22. CTaken from ref 9, which is consistent with the experimental data of ref 30 and 31.
- 190. The frequencies calculated by using this F matrix a t T = 190 K a r e compared with the experimental results in Table V.
4.0
5.0
6.0
7.0
1 0 3 / T (K-')
Figure 6. Contributions of individual normal modes and external motions to T In cfc/fg)for H / D VPIE; all calculated contributions were obtained by using the liquid F matrix of Table V at 190 K.
The solid lines in Figures 1 and 2 also have been obtained from this T-dependent F matrix. Table VI is a summary of the frequency shifts in the fluoromethanes and methane due to condensation and the H/D and l2C/I3C substitutions, in which Aui) = ui)(gas) - v/(liq), Avi = vi(gas) - v,(liq), and 6Avi = Aui) - Aui = [vi)(gas) - .&as)] [vi)(liq) - vi(liq)] = A b i . The sum of 6Avi, Le., C,8Avi,is proportional to the isotope effect in the ZPE shift upon condensation.
J. Phys. Chem. 1987, 91, 4203-4206
4203
produce the positive slope of the experimental H / D VPIE by an addition of these contributions (Figure 6) and it is equally impossible to obtain the negative slope of the I2C/l3C VPIE as a linear combination of these contributions (Figure 5 ) .
We note that, in every chemical species, the magnitude of C6Aui for the hydrogen isotope substitution is significantly greater than that for the carbon isotope substitution and that C6Aui(H/D) in the fluoromethanes are negative while that in methane is positive. The negative C6Aui(H/D) is an anomaly, caused mainly by the large blue shifts in the C-H stretching frequencies upon condensation. These facts explain the qualitative differences between the VPIEs in the fluoromethanes and those in methane pointed out earlier in this paper. Also noted in Table VI is the fact that CBAu,(H/D) in methylene difluoride is considerably more negative than those in other fluoromethanes, which is the reason for the unexpectedly large H / D VPIE in methylene difluoride. One usually expects a red shift in the ZPE upon condensation and, consequently, a positive C6Aui. The negative C6Av, in every fluoromethane is mostly due to the blue shifts upon condensation in the C-H stretching frequencies, Le., u1 in fluoroform, v 1 and u6 in methylene difluoride, and ul and u4 in methyl fluoride. The blue shift upon condensation of fluoroform has been explained on a basis of hydrogen bondingS2' The necessity for the temperature-dependent liquid F matrix that we deduced earlier is illustrated by Figures 5 and 6, in which are plotted the contributions of the individual modes to T In vs. against 1 / T and compared with the experimental T In 1 / T plot. The individual contribution is given by T 6[ln b(uic) - In b(uig)]and these have been computed by using the liquid F matrix of Table V at 190 K. It is seen to be impossible to re-
Conclusion In liquid methylene difluoride the H / D VPIE is normal, while the I2C/l3C VPIE is inverse. The normal H / D VPIEs in liquid methyl fluoride, methylene difluoride, and fluoroform are due to the ZPE shift upon condensation of the deuteriospecies being larger than that of the protio species. Compared to methyl fluoride and fluoroform, the H / D VPIE in methylene difluoride is unusually high because the perturbation of the C-H stretch modes in it is abnormally extensive, being enhanced by the large intermolecular force. Acknowledgment. This research was supported by the Office of Basic Energy Sciences, US.Department of Energy, under Contract No. DE-AC02-80ER10612. Supplementary Material Available: Data on the individual experimental points on P H , Po, and fc/f,for the H / D vapor pressure isotope effect and data on the individual experimental points on P('*C), P(13C), and&/& for the lZC/l3Cvapor pressure isotope effect (14 pages). Ordering information is given on any current masthead page.
uc/f,) uC/fg)
Osmotic and Activity Coefflcients of Amphiphilic Drugs in Aqueous Solution D. Attwood,* N. A. Dickinson, Department of Pharmacy, University of Manchester, Manchester MI 3 9PL, U.K.
V. Mosquera, and V. PBrez Villar Departmento de Fisica de la Materia Condensada, Facultad de Fisica, Universidad de Santiago, Santiago de Compostela, Spain (Received: February 13, 1987)
Osmotic and activity coefficients have been derived from vapor-pressure measurements on aqueous solutions of the amphiphilic drugs promethazine, chlorpromazine, clomipramine, and imipramine hydrochloride. A mass action model of association, based on the Guggenheim equations for the activity coefficients of mixed electrolyte solutions as proposed by Burchfield and Woolley (J. Phys. Chem. 1984,88, 2149), quantitatively described the concentration dependence of the osmotic coefficient for molalities up to 0.25 mol kg-'.
In this paper we report determinations of osmotic and activity coefficients of the phenothiazine tranquillizing drugs promethazine hydrochloride (I) and chlorpromazine hydrochloride (11) and the antidepressant drugs imipramine hydrochloride (111) and clomipramine hydrochloride (IV). Previous studies of the association
Introduction Studies on the association of amphiphilic drugs in aqueous solution have been concerned mainly with the association characteristics of these compounds.' Particular attention has been paid to the elucidation of the structural factors which determine whether association is micellar or follows a continuous association pattern. A calorimetric investigation of the aggregation of amphiphilic drugs undergoing continuous association has recently been reported.* No similar direct measurements of the thermodynamic properties of those drugs which are thought to form micelles have been published. In the limited number of publications in which thermodynamic properties of micellar drugs are presented, these have invariably been derived from measurements of the critical micelle concentration (cmc) a method which is of limited value in view of the often ill-defined nature of the cmc in systems such as these with low aggregation numbers.
R
I
(1) A t t w d , D.; Florence, A. T. Surfucrunr Systems; Chapman and Hall: London, 1983; Chapter 4. (2) Attwood, D.; Fletcher, P.; Boitard, E.; Dub&, J. P.; Tachoire, H. J . Phys. Chem. 1987, 91, 2970.
0022-3654187 , ,I209 1-4203%01SO10 I
Q 1987 American Chemical Societv -
