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Ind. Eng. Chem. Res. 2000, 39, 4462-4469
Measurements of Binary Diffusion Coefficients and Partition Ratios for Acetone, Phenol, r-Tocopherol, and β-Carotene in Supercritical Carbon Dioxide with a Poly(ethylene glycol)-Coated Capillary Column Toshitaka Funazukuri,*,† Chang Yi Kong,‡ Nobuhide Murooka,‡ and Seiichiro Kagei‡ Department of Applied Chemistry, Institute of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan, and Department of Information and Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
Binary diffusion coefficients, D12, and partition ratios, k, for the poly(ethylene glycol) (PEG) layer to supercritical carbon dioxide for acetone and some solid solutes such as phenol, R-tocopherol, and β-carotene were measured with a PEG-coated capillary column by a tracer response technique. The D12 values for acetone with the PEG-coated column were consistent with those measured by the Taylor dispersion method in which an uncoated capillary column was employed. The D12 and k values for all of the solutes decrease simply with increasing pressure, and the D12 values were represented by the Schmidt number correlation. Introduction Supercritical fluids have widely been employed not only as an extraction solvent but also as a reaction medium because of their unique physical properties. For designing reactors or predicting mass transfer rates under supercritical conditions, binary diffusion coefficients are significantly important. In fact, many measurements1-40 of binary diffusion coefficients for various solutes in supercritical fluids such as carbon dioxide have been reported. Most4-6,10-12,14-30,32-35,37,40 of these measurements employed the Taylor dispersion technique.41,42 This method is a tracer response technique in which a solute species as a tracer is injected at an upstream point of the diffusion column and the response of the tracer concentration is measured at a downstream position. The diffusion coefficient is obtained from the difference in the variances of the response curves at the two points. This technique is claimed to be moderately accurate (∼1%), less timeconsuming,43 and suitable for liquid and nonpolar or less polar solutes. When the tracer is a liquid, it is convenient to load the tracer through an injector, and the adsorption of the tracer species onto the inner wall of the column is less likely. However, most of the objective compounds for separation and reaction in or with supercritical fluids are those having high boiling points, i.e., viscous liquids or solids under normal conditions. In many previous studies, organic solvents dissolving the objective solutes were injected in the Taylor dispersion measurements. Some workers5,11,17,19,22,24,30,32 injected solutes dissolved in supercritical carbon dioxide. This approach can eliminate the effect of the organic solvent on the binary system, but it is difficult to adjust the tracer concentration. Recently, Lai and Tan31 employed a polymer-coated diffusion column to measure the binary diffusion coefficients and the partition ratios for the polymer layer * Author to whom correspondence should be addressed. E-mail:
[email protected]. † Chuo University. ‡ Yokohama National University.
to the supercritical fluid. This technique was originally developed by Golay44 at ambient pressure. In this study, binary diffusion coefficients and partition ratios were measured with a poly(ethylene glycol)-coated capillary column as in the study of Lai and Tan. However, both values were determined by the method of fitting in the time domain, instead of by the moment method used by Lai and Tan. The accuracy in terms of fitting error and the correlation for predicting D12 values are discussed. Theory When a tracer species is injected as a shot into a fully developed laminar flow in a cylindrical tube, the tracer concentration can be described as follows:41,42
{
}
{
( )}
∂2C ∂C 1 ∂ ∂C r 2 ∂C r + 2 - 2ua 1 ) D12 (1) ∂t r ∂r ∂r R ∂x ∂x
( )
where D12 is the binary diffusion coefficient of the tracer species, R is the tubing radius, ua is the average solvent velocity, t is the time, and r and x are the radial and axial distances, respectively. When a polymer-coated capillary column is employed, the boundary conditions are given by
D12 ∂C ∂C ) -k R ∂r ∂t
2
∂C )0 ∂r C)0
at r ) R
(2)
at r ) 0
(3)
at x ) (∞
(4)
where k is the partition ratio, assuming that the tracer species instantly reaches equilibrium between the polymer layer and the supercritical carbon dioxide contacting the polymer surface and that the concentration of the tracer species in the polymer layer is radially uniform and a function of time and axial distance. The initial condition is
10.1021/ie000201b CCC: $19.00 © 2000 American Chemical Society Published on Web 10/13/2000
Ind. Eng. Chem. Res., Vol. 39, No. 12, 2000 4463
C)
( )
m 1 δ(x) 1 + k πR2
at t ) 0
(5)
where m is the injected amount of the tracer species. In many cases, a Gaussian-like solution can be used as a solution for a shot response. Let Ca be the average concentration on the cross section of the column.
Ca(x,t) ) Ca(x,t) ≈
2 R2
∫0RC(r,x,t)r dr
(6)
[(
( )
) ]
ua 2 m 1 exp - x t /4at (7) 2 1+k πR (1 + k)x4πat 2
2 D12 1 + 6k + 11k2 uaR + a) 1+k 48D12 (1 + k)3
(8)
In addition, the solution for the Taylor dispersion technique (k ) 0) can be given by eqs 9 and 10.
Ca(x,t) )
( )
m 1 exp[-(x - uat)2/4at] 2 πR x4πat
(9)
2
u2aR a ) D12 + 48D12
(10)
The root-mean-square error for the response curves measured (Ca,meas) and calculated (Ca,cal) at x ) L between t1 and t2, given by eq 11, is minimized by choosing the appropriate values of the two parameters D12 and k.
)
[
]
∫tt {Ca,meas(L, t) - Ca,cal(L, t)}2 dt 1/2 ∫tt {Ca,meas(L, t)}2 dt 2
1
2
1
(11)
where t1 and t2 correspond to the times at the front and latter 10% peak heights, respectively, of the measured response curve. Note that the fitting was regarded as good when < 0.01, similar to the fitting criterion in the Taylor dispersion method.40 Experimental Apparatus and Procedures The experimental apparatus and the procedure are almost identical to those employed in the Taylor disper-
Figure 1. Comparison of (a) measured D12 values and (b) rootmean-square fitting error for acetone in carbon dioxide at 313.15 K between PEG-coated and uncoated capillary columns.
sion measurements reported in the previous study,40 except for replacement of the uncoated capillary column with a PEG-coated column (Frontier Laboratories Ltd., UACW-15W-1.0F, bonded poly(ethylene glycol), film thickness of 1 µm, length of 15.86 m, coil diameter of 215.5 mm). The reported tube diameter of the capillary column is a mean value (0.515 ( 0.001 mm) of the values measured at the two ends by an X-ray microanalyzer (model JXA, JEOL, Japan). Solid solutes dissolved with some organic solvents, mainly benzene and hexane, were loaded through an injector (Rheodyne 7520 with 0.2 and 0.5 µL). The injector was immersed in a water bath in which the capillary column and a preheating column had been horizontally placed along nearly the same plane; the temperature of the water bath was maintained at the
Table 1. Effect of Tracer Dissolving Solvents on Binary Diffusion Coefficients D12 and Partition Ratios k for Phenol in Supercritical Carbon Dioxide at 313.15 K present study P (MPa)
tracer
UV wavelength (nm)
conc (g/mL)
tracer dissolving solvent
ua (10-3m/s)
k
D12 (10-8m2/s)
14.40
phenol
271
0.021 0.02 0.051 0.055 0.055
benzene hexane acetone ethanol chloroform
9.149 9.301 9.117 9.046 9.190
1.856 1.878 1.842 1.847 1.848
1.306 1.303 1.304 1.307 1.306
16.10
phenol
271
0.021 0.02 0.051 0.055 0.055
benzene hexane acetone ethanol chloroform
8.699 8.428 8.381 8.469 8.498
1.645 1.645 1.643 1.656 1.637
1.240 1.241 1.245 1.238 1.239
25.25
phenol
271
0.021 0.02 0.051 0.055 0.055
benzene hexane acetone ethanol chloroform
8.637 8.216 8.672 8.212 8.243
1.157 1.174 1.167 1.165 1.164
1.063 1.065 1.063 1.062 1.068
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Ind. Eng. Chem. Res., Vol. 39, No. 12, 2000
Table 2. Measured Binary Diffusion Coefficients D12 and Partition Ratios k for Phenol in Supercritical Carbon Dioxide at Temperatures from 308.15 to 328.15 K and Pressures from 8.7 to 30 MPa T (K)
P (MPa)
D12 (10-8m2/s)
k
308.15
8.72 8.89 9.08 9.30 9.50 9.68 9.86 10.10 10.60 11.60 12.55 13.54 14.98 16.10 17.40 19.61 20.20 22.63 25.25 28.47 30.28
1.614 1.578 1.538 1.492 1.460 1.450 1.417 1.389 1.350 1.291 1.245 1.202 1.162 1.142 1.104 1.067 1.056 1.010 0.983 0.952 0.944
4.372 3.997 3.645 3.440 3.285 3.122 3.019 2.875 2.654 2.342 2.179 2.043 1.823 1.713 1.636 1.510 1.445 1.380 1.294 1.189 1.154
6.23E-03 7.91E-03 8.58E-03 8.03E-03 8.15E-03 4.81E-03 7.41E-03 6.92E-03 6.78E-03 5.42E-03 5.81E-03 1.07E-02 5.96E-03 3.26E-03 5.51E-03 4.79E-03 7.26E-03 5.81E-03 7.17E-03 2.97E-03 4.10E-03
313.15
10.10 10.60 11.60 12.55 13.54 13.54 14.40 14.98 16.10 17.40 19.61 20.06 22.63 25.25 28.47 30.28
1.688 1.601 1.490 1.408 1.352 1.354 1.306 1.285 1.240 1.217 1.158 1.150 1.107 1.063 1.033 1.018
3.517 3.109 2.537 2.237 2.016 2.012 1.856 1.803 1.645 1.566 1.401 1.380 1.257 1.157 1.085 1.053
7.85E-03 4.01E-03 3.94E-03 4.90E-03 2.76E-03 8.17E-03 3.85E-03 3.23E-03 3.40E-03 4.18E-03 6.21E-03 2.19E-03 3.11E-03 1.98E-03 3.05E-03 2.64E-03
318.15
11.60 12.55 13.54 14.98 16.10 17.40 19.61 22.63 25.25 28.47 30.28
1.751 1.613 1.533 1.448 1.385 1.341 1.268 1.199 1.147 1.102 1.082
3.063 2.461 2.095 1.813 1.655 1.507 1.345 1.172 1.093 0.997 0.966
9.57E-03 6.06E-03 3.42E-03 9.24E-03 4.35E-03 5.45E-03 5.34E-03 4.32E-03 5.55E-03 3.12E-03 3.75E-03
323.15
12.55 13.54 14.98 16.10 17.40 19.61 22.63 25.25 28.47 30.28
1.909 1.757 1.621 1.546 1.486 1.405 1.315 1.252 1.195 1.181
2.783 2.275 1.847 1.639 1.464 1.284 1.107 1.019 0.914 0.891
7.66E-03 5.99E-03 3.78E-03 5.21E-03 4.28E-03 3.92E-03 4.75E-03 5.02E-03 1.91E-03 1.14E-03
328.15
17.40 19.61 22.63 25.25 28.47 30.28
1.664 1.547 1.440 1.375 1.314 1.278
1.550 1.256 1.079 0.958 0.866 0.839
1.08E-02 4.16E-03 4.39E-03 2.27E-03 3.18E-03 2.14E-03
prescribed temperature within a fluctuation of (0.01 K. The pressures were measured upstream at the injector and the outlet of a multi UV detector (MD-1510, JASCO, Japan) by Heise gauges and pressure sensors equipped with a syringe pump (ISCO 100 DM) and a
Figure 2. Effects of (a) D12 value, (b) partition ratio k, and (c) root-mean-square fitting error at 308.15 and 313.15 K for phenol.
Figure 3. D12 value vs CO2 density for phenol at all temperatures, together with literature data of Feist and Schneider5 and Lai and Tan.31
back-pressure regulator (JASCO, model 880-91), respectively. The pressure sensors were calibrated with two Heise gauges with pressure ranges up to 10 and 50 MPa. The pressures were continuously monitored with the pressure sensors during the course of the measurements. The pressure fluctuations were found to be less
Ind. Eng. Chem. Res., Vol. 39, No. 12, 2000 4465
Figure 4. D12/T vs CO2 viscosity for phenol at all temperatures.
than 2 kPa, and the pressure drop between the inlet and the outlet of the column was estimated to be less than 10 kPa. Acetone (purity, 99.5%), benzene (99.5%), hexane (96%), and phenol (99%) were obtained from Junsei Chemical Co. Ltd., Japan, and R-tocopherol (98.0%) and β-carotene (80.0%) from Wako Pure Chemical Industries, Japan. These chemicals were used as received without further purification. Carbon dioxide with a purity higher than 99.995% and a water content
