J . Phys. Chem. 1987, 91, 1645-1648 (ps'
Within this concentration range the value of increases almost linearly with the electrolyte concentration from 0' (f20') to 42' (f8'). For 1 m NiCI, one estimates that p is of the order of 32' (*IO0).
I
t
4olI
*
t
0
I
1645
10
20
I
I
30
LO
B
Figure 4. Physically acceptable correlation times T~~ and T , for cationic hydration water in 1 m MgC12 solutions at T = 25 'C, as a function of the tilting angle fl (a = 90°). The symbols 0 and 0 denote the corre-
lation times T, and T,, respectively. The lines have been drawn as an aid to the eye.
the range of p values is found to lie intermediate between the dipole (a = 90'; ?! , = 0') and the lone pair (a = 90'; /3 = 55') configuration. Applying the conditions for the physical acceptability of a real root ( (section 4.2), only one acceptable root, (, per value of fl is obtained. In Figure 3 the acceptable roots ( and in Figure 4 the corresponding values of the correlation times T, (= 1/6D0,) and T , (= 1/6D,) are presented as a function of the tilting angle fl. As is shown in Figure 3 rather moderate values of ( are found. The value of ( ranges intermediate between 1.6 and 6.0. The value of the correlation time T~~ is found to range between ca. 16 (@ =0 ' ) and 32 ps (for /3 = p(max)). Now additional information concerning the value of T,, may be incorporated. The overall tumbling time T,, can be estimated theoretically by Debye's equation for the rotational diffusion of a sphere with a volume equal to the volume of the hydrated cation. For an infinite dilute solution one obtains T~~ = 38 ps. Experimentally one can estimate T,,,,, e.g., from proton N M R experiments in water solutions containing divalent paramagnetic cations with an ionic radius comparable to Mg2+ ions. For Cu2+-containing solutions one obtains T , = 25 ps.' From Figure 4 it is seen that with the additional condition 25 I~ ~ " ( p5s )38 only a highly restricted range of values apply for the tilting angle 6, with fl = p(max). For 1 m MgCI, one obtains 33O 5 @ I33.7' with T , = 7.4 f 1.0 ps. The value of the tilting angle /3 agrees rather well with the result one can estimate from the neutron diffraction experiments on NiC12 in liquid D,0.9 From these experiments it is concluded that the tilting angle changes with the electrolyte concentration m for 0.1 S m (molal) I1.46.
5. Conclusions In pure water the values of the interaction constants and the correlation times of the 2H, I7O, and 'H (due to I7O) relaxation rates were determined in the temperature range of -10-53 OC. The interaction constants of 2H, " 0 , lH-170 are respectively related to the quadrupolar constants xD and xo and the intramolecular distance rHo. The interaction parameters xD,xo; and rHOwere calculated by using two emperical relations between xD and xo and between xD and rHO,respectively, together with the observed equality of the deuteron and the I70-induced proton correlation times. The interaction constants were found to be temperature-independent. From the observed equality of the , T~~ it is concluded that the isotropic correlation times T ~ * T, ~and model of water reorientation is adequate within the studied temperature range. From the study of the relaxation rates in 1 and 4 m MgC12 solutions it is concluded that in the magnesium hydration shell the values of the interaction parameters are significantly changed. Relative to the pure water results both the xD and xo decrease with ca. 15%, while the value of rHo increases with ca. 1.5%. The values of the parameters xD,xo, and rHOare found to be insensitive to the electrolyte concentration and the temperature. For the water reorientation in the hydration shell the values of the effective correlation times are considerably enlarged and the hydration water is found to reorient anisotropically, with T ~ < + T**+. The value of the ratio ( T ~ + / T ~ * +changes ) with the electrolyte concentration but is insensitive to the temperature. The anisotropic reorientation of the hydration water, as is depicted in the deuteron and oxygen correlation times, has been interpreted in terms of the overall rotation of the hydrated cation and an internal rotation of the water molecule within the hydrated sphere along the cation-oxygen axis. In concordance with the neutron diffraction results, the symmetry axis of the molecular diffusion tensor may be consistently taken to lie in the bisextrix plane of the water molecule, albeit that only a restricted range of values apply for the angle between this axis and the axis bisecting the water plane.
Acknowledgment. This work has been carried out under the auspices of the Netherlands Organization for the Advancement of Pure Science (Z.W.O.). Registry No. H 2 0 , 7732-18-5; MgCI2, 7786-30-3.
Diffusion of Isomeric Polycyclic Aromatic Hydrocarbons in Compressed Propane Michal Roth; Joette L. Steger,*and Milos V. Novotny* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: June 20, 1986; In Final Form: November 21, 1986)
Limiting interdiffusion coefficients of ten model polycyclic aromatic hydrocarbons in compressed propane (384.35 K, 103.4 bar, 0.3771 g ~ m - were ~ ) measured by the Taylor dispersion technique. The Stokes-Einstein coefficients were further calculated from these interdiffusion coefficients. The temperature dependencies of the interdiffusion coefficients of anthracene and phenanthrene at constant density of propane were investigated within the range of 358.15-393.15 K. The differences between the values for isomeric aromatic hydrocarbons are discussed.
Introduction Various studies of both fundamental and applied nature necessitate knowledge of the interdiffusion coefficients of large 'Present address: Institute of Analytical Chemistry, Czechoslovak Aca-
demy of Sciences, 61 142 Brno, Czechoslovakia.
'Present address: Radian Corp., 3200 East Chapel Hill Rq & Nelson Hwy, Research Triangle Park,NC 27709.
0022-3654/87/209 1- 1645$01.50/0
molecules in supercritical or near-critical fluids. Information on such Parameters is, for example, needed in the design of supercritical fluid extractors and the supercritical fluid chromatographic systems. In spite of a rapidly growing technological importance of such fluids, the literature diffusion data are Scarce and, often, inaccurate' Among various techniques for measuring the interdiffusion 0 1987 American Chemical Society
1646 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Roth et al.
I
I-
MOBILE PHASE TANK
0
1
I
I
ON-COLUMN DETECTOR
I1
F,
1
2
3
4
5
ulcms-'
Figure 2. The H vs. u plot for perdeuteriated pyrene.
TRANSDUCER
TABLE I: Limiting Interdiffusion Coefficients of Polycyclic Aromatic Hydrocarbons (PAH) in Compressed Propane (384.35 K, 103.4 bar, 0.3771 g PAH i04D,,/cm2 s-I 1o6s/cm2 s-l
-7-
Figure 1. Schematic diagram of the apparatus.
coefficients, the band-broadening technique is now well-established. As demonstrated long ago by Taylor'-3 and the injection of a very narrow concentration pulse into a fully developed laminar flow through a straight tube of a circular cross section results in an outlet concentration profile approaching the Gaussian curve. Under certain flow condition^,^ the deviations of the profile from the Gaussian shape can be neglected, and the variance of the concentration profile per unit length of the tube is then given by H = u z / l = 2D12/u
+ r,2~/(24D12)
(1)
Owing partly to the rapid development of chromatographic instrumentation, the Taylor dispersion technique had been used for diffusion studies of a number of g a ~ , liquid ~ - ~ 5,'&23 and compressed fluid2e28systems, with considerable effort being spent
(1) Taylor, G. Proc. R. SOC.London, Ser. A 1953, 219, 186. (2) Taylor, G. Proc. R. SOC.London, Ser. A 1954, 223, 446. (3) Taylor, G . Proc. R. SOC.London, Ser. A 1954, 225, 473. (4) Aris, R. Proc. R. SOC.London, Ser. A 1956, 235, 67. (5) Tyrrell, H. J. V.; Harris, K. R. Diffusion in Liquids; Butterworths: London, 1984; pp 193-199. (6) Giddings, J. C.; Seager, S . L. J. Chem. Phys. 1960, 33, 1579. (7) Balenovic, Z.; Myers, M. N.; Giddings, J. C. J. Chem. Phys. 1970, 52, 915. (8) Grushka, E.; Maynard, V. R. J. Phys. Chem. 1973, 77, 1437. (9) Grushka, E.; Schnipelsky, P. J. Phys. Chem. 1974, 78, 1428. (10) Ouano, A. C. Ind. Eng. Chem. Fundam. 1972, 11, 268. (11) Komiyama, H.; Smith, J. M. J. Chem. Eng. Data 1974, 19, 384. (12) Pratt, K. C.; Wakeham, W. A. Proc. R. SOC.London, Ser. A 1974, 336, 393. (13) Grushka, E.; Kikta, E. J. Phys. Chem. 1974, 78, 2297. (14) Pratt, K. C.; Wakeham, W. A. Proc. R. SOC.London, Ser. A 1975, 342, 401. (15) Ouano, A. C.; Carothers, J. A. J . Phys. Chem. 1975, 79, 1314. (16) Pratt, K. C.; Wakeham, W. A. J . Phys. Chem. 1975, 79, 2198. (17) Grushka, E.; Kikta, E. J. Phys. Chem. 1975, 79, 2199. (18) Grushka, E.; Kikta, E. J. Am. Chem. SOC.1976, 98, 643. (19) Evans, D. F.; Chan, C.; Lamartine, B. C. J . Am. Chem. SOC.1977, 99, 6492. (20) Evans, D. F.; Tominaga, T.; Chan, C. J . Solurion Chem. 1979,8,461. (21) Evans, D. F.; Tominaga, T.; Davis, H. T. J . Chem. Phys. 1981, 74, 1298. (22) Tominaga, T.; Yamamoto, S.; Takanaka, J.-I. J. Chem. SOC.,Faraday Trans. 1 1984, 80, 941. (23) Tominaga, T.; Matsumoto, S.; Ishii, T. J.Phys. Chem. 1986, 90, 139. (24) Swaid, I.; Schneider, G. M. Ber. Bunsen-Ges. Phys. Chem. 1979,83, 969. (25) Feist, R.; Schneider, G. M. Sep. Sci. Technol. 1982, 17, 261. (26) Wilsch, A.; Feist, R.; Schneider, G. M. Fluid Phase Equilib. 1983, 10, 299.
phenanthrene phenanthrene-dlo anthracene anthracene-dlo
1.70 1.67 1.74 1.71
2.8 2.0 7.4
pyrene pyrene-dlo
1.67 1.65
2.0 1.4
chrysene chrysene-d, triphenylene 1,2-benzanthracene
1.57 1S O 1.54 1.56
2.3 8.0 2.1 1.6
3.3
to negotiate numerous error sources.29 We have recently designed a chromatographic apparatus30 for precise kinetic and thermodynamic measurements in supercritical fluids. In this communication, we report the high-precision measurements obtained with the system on the interdiffusion coefficients of isomeric 3- and 4-ring polycyclic aromatic hydrocarbons in compressed propane using the Taylor dispersion technique. To our knowledge, this is the first study where the data precision permits correlation of diffusional characteristics with relatively minor structural changes.
Experimental Procedure The main features of the apparatus used for the measurements reported here are outlined in Figure 1, while the design details and performance characteristics will be reported elsewhere.30 A sample of the measured substance is deposited in a dry state into the extraction cell. To introduce a concentration pulse into the diffusion column of a representative mixture of compressed propane and a respective aromatic hydrocarbon, an air-actuated Valco injection valve with inlet splitter (1:2 to 1 :4 splitting ratio) was employed. The flow restrictors, controlling the mean linear flow velocity in the column and the splitting ratio, were smalldiameter (50 bm, i.d.) glass capillaries of various lengths. For the measurements reported in this paper, a fused-silica capillary tube (16.84 f 0.02 m in length, and 0.262 & 0.005 mm, i.d.) was employed. The sample volumes metered into the system were 0.1 pL. The sample concentration profiles were monitored near the end of the capillary tube (on-column detection) with a modified fluorometric detector (FS 950 Fluoromat, Kratos Analytical Instruments, Ramsey, NJ). The detector signal was fed into an IBM personal computer for digitization and subsequent calculation of the statistical moments of the resulting concentration profiles. The software used for the data collection and processing was developed previously in this laboratory. (27) Lauer, H. H.; McManigill, D.; Board, R. D. Anal. Chem. 1983,55, 1370. (28) Springston, S. R.; Novotny, M. Anal. Chem. 1984, 56, 1762. (29) Alizadeh, A.; Nieto de Castro, C. A,; Wakeham, W. A. Int. J. Thermophys. 1980, I , 243. (30) Olesik, S . V.; Steger, J. L.; Roth, M.; Novotny, M. J . Chromatogr., in press.
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 1647
PAH Diffusion in Compressed Propane 18
TABLE II: Relevant Values of Hydrodynamic Groups Re and D e s c
u/cm s-'
I
20
1 2 4 5
VI
De2Sc 6
40
23 52 92 144
60 81
3
%.
Re 20
101
2 8
TABLE 111: Stokes-Einstein Coefficients and van der Waals Radii for Polycyclic Aromatic Hydrocarbons (PAH) PAH f12 1o8r2/cm phenanthrene 5.96 3.41 anthracene 5.81 3.41 190
210
230
250
s, icmz Figure 3. The DI2vs. S2plot: 1, phenanthrene; 2, anthracene; 3, pyrene; 4, triphenylene; 5, chrysene; 6, 1,2-benzanthracene. 10"
Instrument grade propane (99.5% purity, Air Products and Chemicals, Inc., Allentown, PA) was used throughout the study. The samples of the polycyclic aromatic hydrocarbons were obtained from two different suppliers (Aldrich Chemical Co., Inc., Milwaukee, WI, and Sigma Chemical Co., St. Louis, MO); their minimum purity was 95%. The mixture to be injected and the detector cell were kept at the same temperature and pressure as the diffusion tube itself. The concentration of an aromatic hydrocarbon in the mixture did not exceed 30 mg ~ m - ~The . temperature of the diffusion tube was controlled by an oil bath, and a computer-controlled syringe pump was used to keep the tube inlet pressure at the preset value. For sufficiently high flow velocities, the first term on the right-hand side of eq 1 can be neglected, so that the interdiffusion coefficient DI2can be evaluated from the slope of a linear plot of H vs. u. A typical experimental run to determine a single value of DI2comprised measurements at 4-5 different flow velocities, with 4-5 injections being made at each velocity. As an example, the resulting plot of H vs. u for perdeuteriated pyrene is shown in Figure 2.
Results and Discussion The resulting values of limiting interdiffusion coefficients of aromatic hydrocarbons in compressed propane (384.35 K, 103.4 bar, 0.3771 g ~ m - are ~ ) listed in Table I together with the standard deviations as given by the least-squares analysis of the H vs. u plots. Relatively high standard deviations noted with perdeuteriated anthracene and perdeuteriated chrysene reflect the fact that only very small amounts of these compounds (9 and 3 mg, respectively) were available for the study. As a deuterium atom is more bulky than a hydrogen atom, the interdiffusion coefficients of deuteriated hydrocarbons are generally lower than those of the corresponding nondeuteriated compounds. Figure 3 shows an approximate correlation between the interdiffusion coefficients and molecular surface aread' of the hydrocarbons studied. Small differences among the interdiffusion coefficients of isomers are noticed; however, such differences are becoming less noticeable with increasing molecular weight. In general, the determination of diffusion coefficients by the Taylor dispersion technique is subject to errors caused by several different effects, namely (a) nonzero width of the pulse at the tube inlet; (b) nonzero extra-tube volume of the system; (e) density change due to the pressure drop across the tube; (d) sample adsorption on the column inner wall; and (e) secondary flow due to column coiling. As discussed by Levenspiel and Smith,32the effect of nonzero pulse width at the inlet of the diffusion tube can be considered negligible if the volume of the injected sample does not exceed 1% of the volume of the tube. Moreover, it can be estimated that, with the measurements reported in this paper, the ratio of the (31) Yalkowsky, S.H.; Valvani, S. C . J . Chem. Eng. Data 1979, 24, (32) Levenspiel, 0.; Smith, K. Chem. Eng. Sci. 1957, 6, 227.
127.
pyrene
5.88
chrysene triphenylene 1.2-benzanthracene
5.91
3.68
6.01
3.68
6.00
3.68
3.52
variance of the input pulse to the variance of the outlet concentration profile did not exceed 0.0025. The extratube volume of the system was made as low as possible by employing the oncolumn detection and by carefully connecting the tube to the injection valve. In our experiments, the maximum mean linear flow velocity of propane in the tube was always less than 5 cm s-I. The viscosity of propane at the above conditions was estimated33to be 4.9 X lo4 g em-' s-I. Using these viscosity and velocity values, one can show from the Poiseuille equation that the required pressure drop across the used capillary was less than 0.2 bar. At 384.35 K and 103.4 bar, the change in the density of propane corresponding to the pressure change of 0.2 bar is less than 0.05%, as it can be calculated from the Strobridge equation of state with the parameters given by Kratzke and M ~ e 1 l e r . j ~Consequently, the effect of pressure drop on the results given in Table I appears negligible. Sample adsorption onto the column wall did not seem to interfere with the measurements, as the peaks were symmetric and there were no systematic differences in retention times of different hydrocarbons with the same flow restrictor. The typical values of the skew and excess of the resulting concentration profile were on the order of and lO-I, respectively, indicating relatively small deviations from the Gaussian curve. In the theoretical model, a symmetrical parabolic flow pattern in the tube was assumed. This assumption holds strictly for straight tubes only. In any curved tube, centrifugal forces cause the development of a double-helical secondary flow pattern. However, the effect of the secondary flow can be considered to be negligible i p s De2Sc < 100
(2)
where
(4) The values of Re and De2Sc relevant to the measurements presented in this paper are listed in Table 11. The mean linear velocities of propane in the tube ranged between 1.5 and 5 cm s-'. Even at the highest flow velocities, we did not observe any deviations from linearity of the H vs. u plots. Since De2Sc values are close to or even higher than 100 at the highest velocities employed, a downward curvature of the plot would be expected. Therefore, the secondary flow does not have a significant influence on the data given in Table I. As demonstrated by the Reynolds numbers given in Table 11, the flow pattern is well within the (33) Vargaftik, N. B. Tables on the Thermophysical Properties of Liquids and Gases, 2nd ed.;Wiley: New York, 1975; p 244. (34) Kratzke, H.; Mueller, S. J . Chem. Thermodyn. 1984, 16, 1157. (35) Moulijn, J. A,; Spijker, R.; Kolk, J. F. M. J . Chromatogr. 1977, 142, 155.
1648 The Journal of Physical Chemistry, Vol. 91, No. 6,1987 -””
I
Roth et ai. TABLE I V Temperature Dependencies of the Stokes-Einstein Coefficients for Anthracene and Phenanthrene at Constant Density of Propane (0.3771 g c d ) fi2
T IK 357.75 362.75 373.15 384.35 393.15
-_.
252
256
26
264
268
272
276
28
1000K/T
Figure 4. The plot of In D I 2vs. O lO O r / 0,anthracene; 0,phenanthrene.
laminar flow region even at the highest linear velocities in the diffusion tube. From the interdiffusion coefficients given in Table I, the corresponding Stokes-Einstein coefficients were calculated36by using the following equation
h2 = kT/(D127mr2)
(5)
The resulting values off,, are listed in Table I11 together with the values of van der Waals molecular radii employed in these calculations. For any aromatic hydrocarbon, the r2 value is the radius of a sphere the volume of which is equal to the van der Waals volume of a respective hydrocarbon molecule. The van der Waals volumes of the molecules can easily be calculated from tabulated atomic increment^.^^ No corrections for molecular nonsphericity were applied. All Stokes-Einstein coefficients given in Table I11 are close to 6. Assuming that deviations from sphericity of the diffusing molecules can be neglected36gives very little or no “slip” between a diffusing molecule and the surrounding propane In the second part of this work, the temperature dependencies of limiting interdiffusion coefficients for anthracene and phenanthrene were studied at a constant density of propane ( p l = 0.3771 g ~ m - ~ The ) . results are shown in Figure 4. From the slope of a constant-density plot of In D,2 vs. 1 / T , the activation energy of diffusion can be calculated: For anthracene and phenanthrene, the activation energies of diffusion are 2.4 and 5.0 kJ mol-’, respectively. This difference is surprisingly large and under no circumstances explicable by measurement uncertainties (*10%). This difference may, at least partly, be related to the disparities in the geometry of the two molecules. The anthracene molecule is planar, whereas the phenanthrene molecule is probably somewhat distorted due to the nonbonding interaction of the hydrogen atoms in the positions 4 and 5 . (36) Edward, J. T. J . Chem. Educ. 1970, 47, 261 (37) Reference 5, p 259.
anthracene 5.71 5.72 5.70 5.81 5.81
phenanthrene 6.13 6.13 6.02 5.93 5.78
The Stokes-Einstein coefficients of anthracene and phenanthrene are listed as functions of temperature in Table IV. During calculation of thefiz values, the viscosity of propane was assumed to be constant (4.9 X lo4 g cm-’ s-]). Thefi2 values suggest that an increasing temperature may render the anthracene molecule to become more “sticky”, while the phenanthrene molecule tends to become more “slippery”.
Conclusion At a constant temperature and pressure, the limiting interdiffusion coefficients of polycyclic aromatic hydrocarbons in compressed propane decrease with increasing molecular weight. The deuteriated hydrocarbons diffuse more slowly than the corresponding nondeuteriated compounds. As far as the differences among the diffusion rates of isomers are concerned, the results suggest that the more stretched molecules tend to diffuse faster,24 i.e., that the hydrocarbon molecules tend to diffuse in the direction of the least resistance. This view is also supported by the difference between the activation energies of diffusion for anthracene and phenanthrene. Acknowledgment. This work was supported by a grant from the Office of Naval Research. Glossary limiting interdiffusion coefficient, cm2 s-l Dean number E A activation energy of diffusion, kJ mo1-I h2 Stokes-Einstein coefficient H variance of the outlet concentration profile per unit length of the diffusion tube, cm k Boltzmann constant, g cm2 s - ~K-’ 1 length of the diffusion tube, cm r C coil radius of the diffusion tube, cm Ti radius of the diffusion tube, cm r2 van der Waals radius of an aromatic molecule, cm R gas constant, kJ mol-] K-I Re Reynolds number S standard deviation of the diffusion coefficient, cm2 SKI s 2 surface area of an aromatic molecule, cm2 sc Schmidt number T temperature, K U mean linear flow velocity, cm SC’ Greek Letters ?I propane viscosity, g cm-’ s-] PI propane density, g L72 variance of the outlet concentration profile, cm2 Registry No. Propane, 74-98-6; phenanthrene, 85-01-8; anthracene, 120-12-7; pyrene, 129-00-0; chrysene, 218-01-9; triphenylene, 217-59-4; benzanthracene, 56-55-3. Dl2
De
