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Determination of binary diffusion coefficients in supercritical chlorotrifluoromethane and sulphurhexafluoride with supercritical fluid chromatography (SFC)
Chemical Engineering Science, Vol. 42, No. 9, pp. 2213-2218.
1987. 0
Printed in Great Britain.
ooO9-2509/87 1987 Pergamon
13.00 + 0.00 Journals Ltd.
DETERMINATION OF BINARY DIFFUSION COEFFICIENTS IN SUPERCRITICAL CHLOROTRIFLUOROMETHANE AND SULPHURHEXAFLUORIDE WITH SUPERCRITICAL FLUTD CHROMATOGRAPHY (SFC) A. KOPNER, A. HAMM, J. ELLERT, R. FEIST and G. M. SCHNEIDER Physical Chemistry Laboratory, Department of Chemistry, University of Bochum, D-4630 Bochum, F.R.G. (Received 19 January 1987; accepted for publication 10 March 1987) Abstract-Binary diffusion coefficients D,, have been determined in supercritical chlorotrifluoromethane and in liquid as well as supercritical sulphurhexalluoride with supercritical fluid chromatography (SFC) using the peak broadening method. D,, values of benzene, methylbenzene, 1,4_dimethylbenzene, 1,3,5trimethylbenzene, 1,3-dibromobenzene, 2-propanone and tetrachloromethane are reported at temperatures and pressures from 283 to 338 K apd 3 to 15 MPa respectively; this corresponds to densities from 400 to 1000 kg m-3 for CCIFA and 300 to 1400 kg m m-3for SF+ The binary diffusion coefficients D12 are of the order of 10mR m2 s- ‘. At constant temperature they exhibit a considerable dependence on density whereas the inlhtence of temperature at constant density is relatively small.
1.
diffusion
INTRODUCTION
The Taylor dispersion technique has been introduced some 20 years ago (Giddings and Seager, 1960, Bohemen and Purnell, 1961) and is now widely used for the rapid determination of diffusion coefficients in various media (gases, liquids and supercritical fluids). The method is based on the dispersion analysis first
DIz
presented by Taylor (1953) and later extended by Aris (1956) to more general conditions. These authors have shown that a sharp zone of solute, dissolved in a laminarily flowing solvent, spreads into a Gaussian shaped profile. The local variance of the distribution a’(x) is given by: 02(x)
= 2 K’t
(2) Here D, z is the binary diffusion coefficient, r0 the inner radius of the column and U the mean linear velocity of the mobile phase. In chromatography the height equivalent to a theoretical plate I!Z is defined as: (3)
I
Equations (l)-(3) lead to an expression for H of an unretained compound in a straight, empty column of length 1 and inner radius r,,. HZ----
2012
u
+
L 1 - 4
24D,,
u.
Equation (4) represents the special case of the Golay equation (Golay, 1958) with a vanishing capacity ratio k’ (no retention of the solute). Using eq. (4) the binary ces 42:9-5
can be obtained (Hz-$)“‘],
from (5)
given that K’/ril < 0.01 (Levenspiel and Smith, 1957). The accuracy of the dispersion technique has been discussed in the literature (Cloete er ul., 1976). A more recent paper (Alizadeh et al., 1980) deals with possible deviations from the ideal experiment (finite detector volume etc.) and gives expressions for their correction. 2. EXPERIMENTAL
(1)
CT2(x)
=;[H-
D,2
The experiments have been performed on a selfdesigned fluid chromatograph, which has been used for diffusion measurements earlier and is described in the literature (van Wasen et al., 1980; Wilsch et al.,
with
H=---.
coefficient
1983). The thermostat was modified the available temperature range.
in order to extend
In a typical experimental run the solvent gas is first liquefied and then compressed to the desired pressure by a diaphragm pump. A buffer volume eliminates pressure pulsations of the gas. After thermal and hydrodynamical equilibrium is established, small amounts (typically 1 ~1) of the pure liquid solute are introduced into the carrier fluid by means of a high pressure valve. The time between two subsequent injections is chosen such as to prevent any overlapping of the solute peaks. After the injection a short piece of steel capillary (I = 1.8 m) allows for the development of a symmetrical initial peak shape. The diffusion column consists of an entirely empty stainless capillary (I = 96.66 m, r,, = 2.47 steel x 10m4 m) and is kept in an air thermostat at constant temperature. Two high pressure UV-detectors are used to monitor the distribution of the solute peak when entering
2213
A.
2214
KOPNER
and leaving the diffusion column. The detector signals are registered on a chart recorder for further analysis. Finally the gas is expanded in a pressure regulation unit, which also controls the flow rate. Measurements have been performed between 283 and 338 K at pressures up to 15 MPa. Due to the low velocities (max. 2 cm s-i) pressure drops along the column as well as coiling effects of the column can be neglected. This had been reconfirmed by test measurements on the apparatus before. 3. DATA
REDUCTION
The temporal variances of the inlet and outlet peak are calculated from the intercept w of the inflection tangents with the base line:
a2(t) = g. The final variance is corrected for the initial width of the peak: a2(r) =
~2(t),,tlet--*(t)inlet.
(7)
From the measured migration time of the peak r, and the known column length 1, the mean flow velocity is obtained: u = l/t,.
(8)
After transforming r2(t) into the local variance via r?(x) = a2(t)ti2
(9)
application of (3) and (5) is straightforward and directly yields the coefficient of binary molecular diffusion D, 2 as known from Fick’s law. 4. RESULTS
AND
DISCUSSION
The diffusion coefficients of various organic substances have been determined in sulphurhexafluoride (SF,)andchlorotrifluoromethane (CClF,, R13) over a considerable range of density. In Fig. 1 D 12 values of benzene, methylbenzene, l,Cdimethylbenzene, 1,3,5trimethylbenzene and tetrachloromethane in SF6 are plotted vs. density at a constant temperature of 328 K. For similar measurements, e.g. in 2,3-dimethylbutane see Sun and Chen (1985). For comparison the selfdiffusion coefficients D1 1 of SF6 at 323 K as reported by Zykov et al. (1980) have been included in Fig. 1. As a whole the density dependence of D,, is considerable; e.g. an increase in density by a factor of four causes a decline of the diffusion coefficient by more than a factor of five. The self-diffusion coefficient D, 1 exhibits a density dependence, which is very similar to that of D1 2. Over the whole density range D, 1 (SF,) lies well above the measured binary diffusion coefficients D1 2 though the investigated substances have molar masses, which are smaller than that of SF6 (M generally = 146.05 g mol-I); in the case of benzene even by a factor of about two. Obviously the more compact shape of the SF6 molecule compensates for its larger mass resulting in an overall higher mobility.
et al.
Determination
2215
of binary diffusion coefficients
Table 2. Binary diffusion coefficients D1 2 in CClF3 (R13) (for densities of CClF3 see Tawfik and Morsy, 1970) Solute
T/K
p/10’
Pa
p/kg m-’
x 108/m2 s-l
l+Dimethylbenzene
318.15
47.3 49.1 52.2 53.8 57.9 64.7 78.7 109.1
400 450 550 600 700 800 900 1000
2.42 2.15 1.62 1.64 1.40 1.26 1.13 1.05
1,3_Dibromobenzene
318.15
47.3 50.7 52.2 53.8 55.7 57.9 60.8 64.7 70.4 78.7 91.0 109.1
400 500 550 600 650 700 750
1.88 1.68 1.32 1.30 1.29 1.25 1.11 1.07 0.87 0.88 0.83 0.70
44.5 45.9 47.0 49. I 50.6 51.9 55.6 58.0 69.0 81.0
398 451 501 600 659 700 779 813 903 956
313.15
2-Propanone
850
At constant decreasing number of
a D12-1’3
m2s-’ 5.0
D,,
-
T =
0:4
328
K
0:s
1:2
p.lO-‘/kg.m-’
Fig. 1. Binary diffusion coeficients D12 of benzene, methylbenzene, 1,4_dimethylbenzene, 1,3,5-trimethylbenzene and tetrachloromethane in SFa vs. density p at T = 328 K (Feist, 1983; Kopner, 1984) [--= self-diffusion coefficient D, I of SF6 at 323 K (Zykov et al., 1980)].
4.02 3.29 3.10 2.45 2.11 2.06 1.86 1.81 1.61 1.45
density
the benzene
diffusion coefficients methyl-groups attached
derivatives
show
with increasing to the aromatic
ring, which reflects the influence of both molar mass and size on the diffusion rate. The D1 2 values of Ccl4 are very close to those of 1,4dimethylbenzene though the molar masses of these are distinctly different (153.8 and compounds 106.2 g mol- 1 respectively). As it has been discussed above for SF6 the advantage of a compact spherical shape becomes evident. In Fig. 2 binary diffusion coefficients D12 of 2propanone (at T = 313 K), 1,4-dimethylbenzene (at T = 318 K) and f,3-dibromobenzene (at T = 318 K) in CC1F3 (R13) are shown as a function of density p. Although the measurements on the system 2propanone/CClF, were performed at a lower temperature, the D12 values are always larger than those found for the two benzene derivatives; this is due to the fact that the size of the 2-propanone molecule is the smallest of the three solutes under investigation, followed by 1,4_dimethylbenzene and 1,3-dibromobenzene. As already demonstrated in Fig. 1 the binary diffusion coefficients D, 2 again show decreasing values for increasing densities.
A. KOPNER
2216
Table 3. Binary diffusion coefficients DIt of 1,4-dimethylbenzene in SF6 at different temperatures (for densities of SF,, see Tawfik and Morsy, 1970)
T/K
p/10* Pa
0.61 0.58 0.56 0.52 0.48
1510 1530 1560 1590 1620 1650
30.0 40.0 60.0 90.0 120.0 150.0
1420 1450 1490 1530 1570 1600
0.45 0.78 0.73 0.67 0.58 0.54 0.51
35.0 40.0 60.0 90.0 120.0
1330 1350 1410 1470 1510
0.93 0.89 0.79 0.69 0.61
313.15
40.0 50.0 60.0 90.0 120.0
1200 1270 1310 1400 1450
1.14 1.00 0.93 0.82 0.73
323.15
40.7 42.0 44.5 45.0 49.5 50.0 60.0 61.0 84.4 90.0 120.0
600 800 1000 990 1100 1100 1190 1200 1300 1320 1390
2.12 1.73 1.44 1.41 1.26 1.26 1.11 1.11 0.97 0.93 0.86
50.4 53.2 55.8 59.5 65.5 76.3 94.7 125.8
600 700 800 900 1000 1100 1200 1300
2.66 2.28 1.99 1.80 1.54 1.33 1.17 1.01
293.15
303.15
338.15
a D12-‘0
0
CJ‘H60
(313K)
rn2 a-’
p/kg me3 D,, x lO*/rn’~-~
30.0 40.0 60.0 90.0 120.0 150.0
283.15
er al.
3.0
_
2.0
-
1 .o
T=
014
0.0
15 MPa. In Fig. 3 the binary diffusion coefficients D1 2 are plotted vs. pressure for six different temperatures. The isotherms below T,(318.7 K) represent subcritical states in the liquid region of SF,. These isotherms end at the borderline of the two-phase region; the endpoints, however, had to be extrapolated, because exact measurements are possible only at some distance from the point of liquid-gas phase separation. At temperatures above T,, only one phase of the carrier gas exists, independent of pressure. The density of these supercritical fluids exhibits a strong pressure dependence and varies over a considerable range. From Fig. 3 it can be derived that with increasing temperature the pressure dependence of D, 2 becomes more pronounced, reaching maximum values in the
nl-=
Fig. 2. Binary diffusion coefficients D12 of l,Cdimethylbenzone ( T = 318 K), 1,3-dibromobenzene ( T = 318 K) and 2propanone (T = 313 K) in CCIFJ (R13) as a function of density p (Hamm, 1985).
D,,.IO= * =
338 323 323
a 0 0 0
313K 303 K 293 K 283 K
l
m2s-’
;
1.5 _
K K K
1,4-dimethylbenzene in SF,
&
0 The diffusion behaviour of 1,4-dimethylhenzene in SF, has been determined between 283 and 338 K up to
1.2
0:s p - 1 o-=/kg.
I’0
1.5 p/MPo
Fig. 3. Binary diffusion coefficients D,, for a given solute (1,4_dimethylbenzene) in SF, as a function of pressure pat six different temperatures (0, V, Kopner, 1984, all other data Ellert, 1986; . . _ = extrapolated values on vapour pressure curve). vicinity of the critical point. This becomes evident from the isotherms at 3 13 K ( = T, - 5.7 K) and 323 K ( = T, + 4.3 K). With decreasing temperature diffusion in liquid SF6 becomes less pressure dependent, as is the normal case for liquids far away from their critical points. In the supercritical region of SF6 the pressure that of normal gases dependence of Di2 approaches predominantly peratures.
at
low
pressures
and
high
tem-
Determination 13,*.10a
M
m’s_’ 2.5
P PE
-
2.01.5
l
l.+-dimethylbenzene
ro 0 .
-
T
K u
l
s
:
1.o 0.5
in SF*
*
v
0.4
W
* “B ---uD.
1:2
0:s
P c2 (t) 1:6
ff2(x)
p -10-3/kg.m-3 Fig. 4. Binary diffusion coefficients D,* for a given solute (1,4_dimethylbenzene) in SF, as a function of density p at six different temperatures (0, v, Kopner, 1984; all other data Ellert, 1986).
It might be interesting to note that no dramatic changes of D, 2 or other “critical effects” are observed, when passing from subcritical to supercritical temperatures, provided that the system is maintained in the single-phase region. For mole fractions of component 2 that approach zero this is always the case for pressures above pe. If, however, the concentration of the diffusing compound exceeds that of tracer amounts, the complete binary phase diagram has to be considered as well as the dependence of D,, on composition. In Fig. 4 the data of Fig. 3 are plotted vs. the density of SF, instead of vs. pressure. It is remarkable that for densities above ca 1.3 gem-’ there is little if any influence of temperature on D,,. In this region D,, seems to be determined by the density of the system only. The relationship is of course not a linear one as the plot might suggest, because linear extrapolation would lead to negative values of D,, at higher densities. Figure 4 makes evident that the “pressure dependence” of D, 2 in Fig. 3 ispredominantly the result of changes in density. The shape of the isotherms reflects the compressibility, which is small in the liquid phase and high in the supercritical fluid with maximum values in the vicinity of the critical point, where the compressibility becomes infinite. The investigations
are continuing.
Acknowledgment-Financial support of the Fonds Chemischen Industrie e.V. is gratefully acknowledged.
NOTATION D 11 D IZ
H K’
self-diffusion coefficient binary diffusion coefficient height equivalent to a theoretical plate symbol defined by eq. (2)
k’ 1
capacity ratio length of the column
2217
of binary diffusion coefficients
der
molar mass pressure criticai pressure inner radius of the column absolute temperature critical absolute temperature mean flow velocity intercept of the inflection tangents with the base line density variance of the concentration profile in time units variance of the concentration profile in length units
REFERENCES Alizadeh, A., Nieto de Castro, C. A. and Wakeham, W. A., 1980, The theory of the Taylor dispersion technique for liquid diffusivity measurements. Inr. J. Thermophys. 1, 243-284. Aris, R., 1956, On the dispersion of a solute in a Ruid flowing through a thbe. Proc. R. Sot. A235, 67-77. Bohemen, J. and Purnell, J. H., 1961, Diffusional band spreading in gas-chromatographic columns. Part I. The elution of unsorbed gases. J. them. Sot. 360, 263&2638. Cloete, C. E., Smuts, T. W. and de Clerk, K., 1976, The chromatographic determination of binary diffusion coefficients. J. Chromat. 120, l-15. Ellert, J., 1986, Bcstimmung von biniiren Diffusionskoeffizienten mit Fluidchromatographie (SFC): D, .-Werte von Benzolderivaten in fluidem CO, und SF, sowie fliissigem Heptan zwischen 283 und 323 K bis 160 bar. Diploma Thesis, University of Bochum, F.R.G. Feist, R., 1983, unpublished results. University of Bochum, F.R.G. Feist, R. and Schneider, G. M., 1982, Determination ofbinary diffusion coeficients of benzene, phenol, naphthalene and caffeine in supercritical CO2 between 308 and 333 K in the pressure range 80 to 160 bar with supercritical fluid chromatography (SFC). Sep. Sci. Techno!. 17, 261-270. Giddings, J. C. and Seager, S. L., 1960, Rapid determination of gaseous diffusion coetlicients by means of gas chromatography apparatus. J. them. Phys. 33, 1579-1580. Golay, M. J. E., 1958, Theory ofchromatography in open and coated tubular columns with round and rectangular crosssections. Proc. Symp. Gas Chromntog. Amsterdam, pp. 3653. Hamm, A., 1985, Bestimmung bintirer Diffusionskoeffizienten in iiberkritischem CCIFa mit Fluidchromatographie (SFC) in Abhgngigkeit von Temperatur und Druck. Diploma Thesis, University of Bochum, F.R.G. Kopner, A., 1984, Bestimmung der binsren Diffusionskoeflizienten von Benzolderivaten und ausgewlihlten Alkoholen in iiberkritischem SF, bzw. CO2 mit Fluidchromatographie (SFC) in Abhiingigkeit von Druck und Tempcratur bis 160 bar und 338.15 K. Diploma Thesis, University of Bochum. F.R.G. Levenspiel, 0. and Smith, W. K., 1957, Notes on the diffusiontype model for longitudinal mixing of fluids in flow. Chem. Engng Sci. 6, 227-233. Sun, C. K. J. and Chen, C. H., 1985, Diffusion of benzene, toluene, naphthalene and phenanthrene in supcrcritical dense 2,3_dimethylbutane. A.1.Ch.E. J. 31, 1904-1910. Tawfik, E. and Morsy, J., 1970, Extended BenedictWebb-Rubin equation of state. J. them. Engng Data 15, 2.5&265. Taylor, G., 1953, Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Sot. A219,186-203. van Wasen, U., Swaid, I. and Schneider, G. M., 1980,
2218
A. KOPNER et al.
Physicochemical principles and applications of supercritical fluid chromatography (SFC). Angew. Chem. Int. Ed. Engl. 19, 575-587. Wilsch, A., Feist, R. and Schneider, G. M., 1983, Capacity ratios and diffusion coefficients of low-volatile organic compounds in supercritical carbon dioxide from super-
critical fluid chromatography (SFC). Fluid Phase Equib. 10. 299-306. Zykov, P. G., Bogdanov, P. 1. and Rasponin, A. S., 1980, NMR study of the self-diffusion coefficient in SF, over a broad density range. Zh. tekh. Fir. 50, 606 (1980 Soviet Phys. tech. Whys. 25, 362-364).
1987. 0
Printed in Great Britain.
ooO9-2509/87 1987 Pergamon
13.00 + 0.00 Journals Ltd.
DETERMINATION OF BINARY DIFFUSION COEFFICIENTS IN SUPERCRITICAL CHLOROTRIFLUOROMETHANE AND SULPHURHEXAFLUORIDE WITH SUPERCRITICAL FLUTD CHROMATOGRAPHY (SFC) A. KOPNER, A. HAMM, J. ELLERT, R. FEIST and G. M. SCHNEIDER Physical Chemistry Laboratory, Department of Chemistry, University of Bochum, D-4630 Bochum, F.R.G. (Received 19 January 1987; accepted for publication 10 March 1987) Abstract-Binary diffusion coefficients D,, have been determined in supercritical chlorotrifluoromethane and in liquid as well as supercritical sulphurhexalluoride with supercritical fluid chromatography (SFC) using the peak broadening method. D,, values of benzene, methylbenzene, 1,4_dimethylbenzene, 1,3,5trimethylbenzene, 1,3-dibromobenzene, 2-propanone and tetrachloromethane are reported at temperatures and pressures from 283 to 338 K apd 3 to 15 MPa respectively; this corresponds to densities from 400 to 1000 kg m-3 for CCIFA and 300 to 1400 kg m m-3for SF+ The binary diffusion coefficients D12 are of the order of 10mR m2 s- ‘. At constant temperature they exhibit a considerable dependence on density whereas the inlhtence of temperature at constant density is relatively small.
1.
diffusion
INTRODUCTION
The Taylor dispersion technique has been introduced some 20 years ago (Giddings and Seager, 1960, Bohemen and Purnell, 1961) and is now widely used for the rapid determination of diffusion coefficients in various media (gases, liquids and supercritical fluids). The method is based on the dispersion analysis first
DIz
presented by Taylor (1953) and later extended by Aris (1956) to more general conditions. These authors have shown that a sharp zone of solute, dissolved in a laminarily flowing solvent, spreads into a Gaussian shaped profile. The local variance of the distribution a’(x) is given by: 02(x)
= 2 K’t
(2) Here D, z is the binary diffusion coefficient, r0 the inner radius of the column and U the mean linear velocity of the mobile phase. In chromatography the height equivalent to a theoretical plate I!Z is defined as: (3)
I
Equations (l)-(3) lead to an expression for H of an unretained compound in a straight, empty column of length 1 and inner radius r,,. HZ----
2012
u
+
L 1 - 4
24D,,
u.
Equation (4) represents the special case of the Golay equation (Golay, 1958) with a vanishing capacity ratio k’ (no retention of the solute). Using eq. (4) the binary ces 42:9-5
can be obtained (Hz-$)“‘],
from (5)
given that K’/ril < 0.01 (Levenspiel and Smith, 1957). The accuracy of the dispersion technique has been discussed in the literature (Cloete er ul., 1976). A more recent paper (Alizadeh et al., 1980) deals with possible deviations from the ideal experiment (finite detector volume etc.) and gives expressions for their correction. 2. EXPERIMENTAL
(1)
CT2(x)
=;[H-
D,2
The experiments have been performed on a selfdesigned fluid chromatograph, which has been used for diffusion measurements earlier and is described in the literature (van Wasen et al., 1980; Wilsch et al.,
with
H=---.
coefficient
1983). The thermostat was modified the available temperature range.
in order to extend
In a typical experimental run the solvent gas is first liquefied and then compressed to the desired pressure by a diaphragm pump. A buffer volume eliminates pressure pulsations of the gas. After thermal and hydrodynamical equilibrium is established, small amounts (typically 1 ~1) of the pure liquid solute are introduced into the carrier fluid by means of a high pressure valve. The time between two subsequent injections is chosen such as to prevent any overlapping of the solute peaks. After the injection a short piece of steel capillary (I = 1.8 m) allows for the development of a symmetrical initial peak shape. The diffusion column consists of an entirely empty stainless capillary (I = 96.66 m, r,, = 2.47 steel x 10m4 m) and is kept in an air thermostat at constant temperature. Two high pressure UV-detectors are used to monitor the distribution of the solute peak when entering
2213
A.
2214
KOPNER
and leaving the diffusion column. The detector signals are registered on a chart recorder for further analysis. Finally the gas is expanded in a pressure regulation unit, which also controls the flow rate. Measurements have been performed between 283 and 338 K at pressures up to 15 MPa. Due to the low velocities (max. 2 cm s-i) pressure drops along the column as well as coiling effects of the column can be neglected. This had been reconfirmed by test measurements on the apparatus before. 3. DATA
REDUCTION
The temporal variances of the inlet and outlet peak are calculated from the intercept w of the inflection tangents with the base line:
a2(t) = g. The final variance is corrected for the initial width of the peak: a2(r) =
~2(t),,tlet--*(t)inlet.
(7)
From the measured migration time of the peak r, and the known column length 1, the mean flow velocity is obtained: u = l/t,.
(8)
After transforming r2(t) into the local variance via r?(x) = a2(t)ti2
(9)
application of (3) and (5) is straightforward and directly yields the coefficient of binary molecular diffusion D, 2 as known from Fick’s law. 4. RESULTS
AND
DISCUSSION
The diffusion coefficients of various organic substances have been determined in sulphurhexafluoride (SF,)andchlorotrifluoromethane (CClF,, R13) over a considerable range of density. In Fig. 1 D 12 values of benzene, methylbenzene, l,Cdimethylbenzene, 1,3,5trimethylbenzene and tetrachloromethane in SF6 are plotted vs. density at a constant temperature of 328 K. For similar measurements, e.g. in 2,3-dimethylbutane see Sun and Chen (1985). For comparison the selfdiffusion coefficients D1 1 of SF6 at 323 K as reported by Zykov et al. (1980) have been included in Fig. 1. As a whole the density dependence of D,, is considerable; e.g. an increase in density by a factor of four causes a decline of the diffusion coefficient by more than a factor of five. The self-diffusion coefficient D, 1 exhibits a density dependence, which is very similar to that of D1 2. Over the whole density range D, 1 (SF,) lies well above the measured binary diffusion coefficients D1 2 though the investigated substances have molar masses, which are smaller than that of SF6 (M generally = 146.05 g mol-I); in the case of benzene even by a factor of about two. Obviously the more compact shape of the SF6 molecule compensates for its larger mass resulting in an overall higher mobility.
et al.
Determination
2215
of binary diffusion coefficients
Table 2. Binary diffusion coefficients D1 2 in CClF3 (R13) (for densities of CClF3 see Tawfik and Morsy, 1970) Solute
T/K
p/10’
Pa
p/kg m-’
x 108/m2 s-l
l+Dimethylbenzene
318.15
47.3 49.1 52.2 53.8 57.9 64.7 78.7 109.1
400 450 550 600 700 800 900 1000
2.42 2.15 1.62 1.64 1.40 1.26 1.13 1.05
1,3_Dibromobenzene
318.15
47.3 50.7 52.2 53.8 55.7 57.9 60.8 64.7 70.4 78.7 91.0 109.1
400 500 550 600 650 700 750
1.88 1.68 1.32 1.30 1.29 1.25 1.11 1.07 0.87 0.88 0.83 0.70
44.5 45.9 47.0 49. I 50.6 51.9 55.6 58.0 69.0 81.0
398 451 501 600 659 700 779 813 903 956
313.15
2-Propanone
850
At constant decreasing number of
a D12-1’3
m2s-’ 5.0
D,,
-
T =
0:4
328
K
0:s
1:2
p.lO-‘/kg.m-’
Fig. 1. Binary diffusion coeficients D12 of benzene, methylbenzene, 1,4_dimethylbenzene, 1,3,5-trimethylbenzene and tetrachloromethane in SFa vs. density p at T = 328 K (Feist, 1983; Kopner, 1984) [--= self-diffusion coefficient D, I of SF6 at 323 K (Zykov et al., 1980)].
4.02 3.29 3.10 2.45 2.11 2.06 1.86 1.81 1.61 1.45
density
the benzene
diffusion coefficients methyl-groups attached
derivatives
show
with increasing to the aromatic
ring, which reflects the influence of both molar mass and size on the diffusion rate. The D1 2 values of Ccl4 are very close to those of 1,4dimethylbenzene though the molar masses of these are distinctly different (153.8 and compounds 106.2 g mol- 1 respectively). As it has been discussed above for SF6 the advantage of a compact spherical shape becomes evident. In Fig. 2 binary diffusion coefficients D12 of 2propanone (at T = 313 K), 1,4-dimethylbenzene (at T = 318 K) and f,3-dibromobenzene (at T = 318 K) in CC1F3 (R13) are shown as a function of density p. Although the measurements on the system 2propanone/CClF, were performed at a lower temperature, the D12 values are always larger than those found for the two benzene derivatives; this is due to the fact that the size of the 2-propanone molecule is the smallest of the three solutes under investigation, followed by 1,4_dimethylbenzene and 1,3-dibromobenzene. As already demonstrated in Fig. 1 the binary diffusion coefficients D, 2 again show decreasing values for increasing densities.
A. KOPNER
2216
Table 3. Binary diffusion coefficients DIt of 1,4-dimethylbenzene in SF6 at different temperatures (for densities of SF,, see Tawfik and Morsy, 1970)
T/K
p/10* Pa
0.61 0.58 0.56 0.52 0.48
1510 1530 1560 1590 1620 1650
30.0 40.0 60.0 90.0 120.0 150.0
1420 1450 1490 1530 1570 1600
0.45 0.78 0.73 0.67 0.58 0.54 0.51
35.0 40.0 60.0 90.0 120.0
1330 1350 1410 1470 1510
0.93 0.89 0.79 0.69 0.61
313.15
40.0 50.0 60.0 90.0 120.0
1200 1270 1310 1400 1450
1.14 1.00 0.93 0.82 0.73
323.15
40.7 42.0 44.5 45.0 49.5 50.0 60.0 61.0 84.4 90.0 120.0
600 800 1000 990 1100 1100 1190 1200 1300 1320 1390
2.12 1.73 1.44 1.41 1.26 1.26 1.11 1.11 0.97 0.93 0.86
50.4 53.2 55.8 59.5 65.5 76.3 94.7 125.8
600 700 800 900 1000 1100 1200 1300
2.66 2.28 1.99 1.80 1.54 1.33 1.17 1.01
293.15
303.15
338.15
a D12-‘0
0
CJ‘H60
(313K)
rn2 a-’
p/kg me3 D,, x lO*/rn’~-~
30.0 40.0 60.0 90.0 120.0 150.0
283.15
er al.
3.0
_
2.0
-
1 .o
T=
014
0.0
15 MPa. In Fig. 3 the binary diffusion coefficients D1 2 are plotted vs. pressure for six different temperatures. The isotherms below T,(318.7 K) represent subcritical states in the liquid region of SF,. These isotherms end at the borderline of the two-phase region; the endpoints, however, had to be extrapolated, because exact measurements are possible only at some distance from the point of liquid-gas phase separation. At temperatures above T,, only one phase of the carrier gas exists, independent of pressure. The density of these supercritical fluids exhibits a strong pressure dependence and varies over a considerable range. From Fig. 3 it can be derived that with increasing temperature the pressure dependence of D, 2 becomes more pronounced, reaching maximum values in the
nl-=
Fig. 2. Binary diffusion coefficients D12 of l,Cdimethylbenzone ( T = 318 K), 1,3-dibromobenzene ( T = 318 K) and 2propanone (T = 313 K) in CCIFJ (R13) as a function of density p (Hamm, 1985).
D,,.IO= * =
338 323 323
a 0 0 0
313K 303 K 293 K 283 K
l
m2s-’
;
1.5 _
K K K
1,4-dimethylbenzene in SF,
&
0 The diffusion behaviour of 1,4-dimethylhenzene in SF, has been determined between 283 and 338 K up to
1.2
0:s p - 1 o-=/kg.
I’0
1.5 p/MPo
Fig. 3. Binary diffusion coefficients D,, for a given solute (1,4_dimethylbenzene) in SF, as a function of pressure pat six different temperatures (0, V, Kopner, 1984, all other data Ellert, 1986; . . _ = extrapolated values on vapour pressure curve). vicinity of the critical point. This becomes evident from the isotherms at 3 13 K ( = T, - 5.7 K) and 323 K ( = T, + 4.3 K). With decreasing temperature diffusion in liquid SF6 becomes less pressure dependent, as is the normal case for liquids far away from their critical points. In the supercritical region of SF6 the pressure that of normal gases dependence of Di2 approaches predominantly peratures.
at
low
pressures
and
high
tem-
Determination 13,*.10a
M
m’s_’ 2.5
P PE
-
2.01.5
l
l.+-dimethylbenzene
ro 0 .
-
T
K u
l
s
:
1.o 0.5
in SF*
*
v
0.4
W
* “B ---uD.
1:2
0:s
P c2 (t) 1:6
ff2(x)
p -10-3/kg.m-3 Fig. 4. Binary diffusion coefficients D,* for a given solute (1,4_dimethylbenzene) in SF, as a function of density p at six different temperatures (0, v, Kopner, 1984; all other data Ellert, 1986).
It might be interesting to note that no dramatic changes of D, 2 or other “critical effects” are observed, when passing from subcritical to supercritical temperatures, provided that the system is maintained in the single-phase region. For mole fractions of component 2 that approach zero this is always the case for pressures above pe. If, however, the concentration of the diffusing compound exceeds that of tracer amounts, the complete binary phase diagram has to be considered as well as the dependence of D,, on composition. In Fig. 4 the data of Fig. 3 are plotted vs. the density of SF, instead of vs. pressure. It is remarkable that for densities above ca 1.3 gem-’ there is little if any influence of temperature on D,,. In this region D,, seems to be determined by the density of the system only. The relationship is of course not a linear one as the plot might suggest, because linear extrapolation would lead to negative values of D,, at higher densities. Figure 4 makes evident that the “pressure dependence” of D, 2 in Fig. 3 ispredominantly the result of changes in density. The shape of the isotherms reflects the compressibility, which is small in the liquid phase and high in the supercritical fluid with maximum values in the vicinity of the critical point, where the compressibility becomes infinite. The investigations
are continuing.
Acknowledgment-Financial support of the Fonds Chemischen Industrie e.V. is gratefully acknowledged.
NOTATION D 11 D IZ
H K’
self-diffusion coefficient binary diffusion coefficient height equivalent to a theoretical plate symbol defined by eq. (2)
k’ 1
capacity ratio length of the column
2217
of binary diffusion coefficients
der
molar mass pressure criticai pressure inner radius of the column absolute temperature critical absolute temperature mean flow velocity intercept of the inflection tangents with the base line density variance of the concentration profile in time units variance of the concentration profile in length units
REFERENCES Alizadeh, A., Nieto de Castro, C. A. and Wakeham, W. A., 1980, The theory of the Taylor dispersion technique for liquid diffusivity measurements. Inr. J. Thermophys. 1, 243-284. Aris, R., 1956, On the dispersion of a solute in a Ruid flowing through a thbe. Proc. R. Sot. A235, 67-77. Bohemen, J. and Purnell, J. H., 1961, Diffusional band spreading in gas-chromatographic columns. Part I. The elution of unsorbed gases. J. them. Sot. 360, 263&2638. Cloete, C. E., Smuts, T. W. and de Clerk, K., 1976, The chromatographic determination of binary diffusion coefficients. J. Chromat. 120, l-15. Ellert, J., 1986, Bcstimmung von biniiren Diffusionskoeffizienten mit Fluidchromatographie (SFC): D, .-Werte von Benzolderivaten in fluidem CO, und SF, sowie fliissigem Heptan zwischen 283 und 323 K bis 160 bar. Diploma Thesis, University of Bochum, F.R.G. Feist, R., 1983, unpublished results. University of Bochum, F.R.G. Feist, R. and Schneider, G. M., 1982, Determination ofbinary diffusion coeficients of benzene, phenol, naphthalene and caffeine in supercritical CO2 between 308 and 333 K in the pressure range 80 to 160 bar with supercritical fluid chromatography (SFC). Sep. Sci. Techno!. 17, 261-270. Giddings, J. C. and Seager, S. L., 1960, Rapid determination of gaseous diffusion coetlicients by means of gas chromatography apparatus. J. them. Phys. 33, 1579-1580. Golay, M. J. E., 1958, Theory ofchromatography in open and coated tubular columns with round and rectangular crosssections. Proc. Symp. Gas Chromntog. Amsterdam, pp. 3653. Hamm, A., 1985, Bestimmung bintirer Diffusionskoeffizienten in iiberkritischem CCIFa mit Fluidchromatographie (SFC) in Abhgngigkeit von Temperatur und Druck. Diploma Thesis, University of Bochum, F.R.G. Kopner, A., 1984, Bestimmung der binsren Diffusionskoeflizienten von Benzolderivaten und ausgewlihlten Alkoholen in iiberkritischem SF, bzw. CO2 mit Fluidchromatographie (SFC) in Abhiingigkeit von Druck und Tempcratur bis 160 bar und 338.15 K. Diploma Thesis, University of Bochum. F.R.G. Levenspiel, 0. and Smith, W. K., 1957, Notes on the diffusiontype model for longitudinal mixing of fluids in flow. Chem. Engng Sci. 6, 227-233. Sun, C. K. J. and Chen, C. H., 1985, Diffusion of benzene, toluene, naphthalene and phenanthrene in supcrcritical dense 2,3_dimethylbutane. A.1.Ch.E. J. 31, 1904-1910. Tawfik, E. and Morsy, J., 1970, Extended BenedictWebb-Rubin equation of state. J. them. Engng Data 15, 2.5&265. Taylor, G., 1953, Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Sot. A219,186-203. van Wasen, U., Swaid, I. and Schneider, G. M., 1980,
2218
A. KOPNER et al.
Physicochemical principles and applications of supercritical fluid chromatography (SFC). Angew. Chem. Int. Ed. Engl. 19, 575-587. Wilsch, A., Feist, R. and Schneider, G. M., 1983, Capacity ratios and diffusion coefficients of low-volatile organic compounds in supercritical carbon dioxide from super-
critical fluid chromatography (SFC). Fluid Phase Equib. 10. 299-306. Zykov, P. G., Bogdanov, P. 1. and Rasponin, A. S., 1980, NMR study of the self-diffusion coefficient in SF, over a broad density range. Zh. tekh. Fir. 50, 606 (1980 Soviet Phys. tech. Whys. 25, 362-364).