Infinite-Dilution Binary Diffusion Coefficient, Partition Ratio, and Partial

Moreover, partial molar volumes of CoQ10 in supercritical CO2 were obtained from the k ..... Figure 8 Partial molar volume for CoQ10 in SC CO2 vs pres...
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Ind. Eng. Chem. Res. 2002, 41, 2812-2818

Infinite-Dilution Binary Diffusion Coefficient, Partition Ratio, and Partial Molar Volume for Ubiquinone CoQ10 in Supercritical Carbon Dioxide Toshitaka Funazukuri,*,† Chang Yi Kong,‡ 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 Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan

Infinite-dilution binary diffusion coefficient D12 and partition ratio k for ubiquinone CoQ10 in carbon dioxide were measured by a tracer response technique with a poly(ethylene glycol)-coated capillary column at temperatures from 308.15 to 333.15 K and pressures from 8.5 to 30 MPa. D12 and k values were simultaneously determined from a measured response curve by the curvefitting method. The fitting error between measured and calculated response curves increased with decreasing pressure, as had been the case in our previous studies on various solutes in supercritical CO2 by the Taylor dispersion method. The D12 values were correlated with temperature and CO2 viscosity and the k values with temperature and CO2 density. Moreover, partial molar volumes of CoQ10 in supercritical CO2 were obtained from the k values. Introduction A large number of diffusion data for various organic compounds are available in supercritical fluids, mainly CO2. However, the data1-9 for human-active or antioxidant compounds such as vitamins, unsaturated lipids, and their related compounds are limited. In particular, D12 data for such compounds having high molecular weights are quite few. A measured compound with the maximum molecular weight is glycerol trioleate (molecular weight MW ) 885 g‚mol-1), which was measured with the Taylor dispersion method by Catchpole and King.6 In this study ubiquinone CoQ10 (UQ-10; MW ) 863 g‚mol-1; 2,3-dimethoxy-5-methyl-6-decaprenyl-1,4-benzoquinone) was employed as a solute. This compound is a vitamin-like coenzyme or its precursor, which exists in food or is synthesized in the body. A deficiency of CoQ10 leads to a wide variety of diseases such as heart disease.10 The molecule has a side aliphatic chain with 10 unsaturated double bonds, and this functional group works as an effective antioxidant10 and free-radical scavenger.10 No datum on the binary diffusion coefficient for CoQ10 in supercritical (SC) CO2 so far is available in the literature. In measurements on D12 values for organic compounds in supercritical fluids, most studies employed the Taylor dispersion method. This method is so suitable for a low viscous liquid solute that it can be loaded into a diffusion column with a common injector for highperformance liquid chromatographs. In some initial measurements, however, when a viscous or solid compound, dissolved in an organic solvent, was injected into a diffusion column, there were ambiguities in the measurements due to the presence of the third component. Some workers1,3,5,6,9,11-15 have tried to inject

viscous or solid solutes, dissolved in SC CO2, into SC CO2 flowing in a diffusion column. In this case it is difficult to adjust the amount of solute injected. Recently, Lai and Tan16 and Funazukuri et al.8 employed a polymer-coated capillary column, instead of an uncoated stainless steel column, in the tracer response measurements. This method has an advantage because a solute can be injected into the diffusion column as a solution dissolved in a common organic solvent such as hexane, acetone, benzene, etc. The solute and the solvent are separated chromatographically because of the different values of the partition ratio as they move through the column. The system involves two parameters, an infinite-dilution binary diffusion coefficient and the partition ratio (k) for a solute in the polymer layer to the supercritical phase. The method was originally developed by Golay17 at an ambient pressure. In analyses of the response curves to determine the parameters such as D12 and k, the moment method has been widely employed. However, this method has been claimed to be less accurate in chromatographic adsorption studies at ambient pressures.18 In this study the response curves were analyzed by the curve-fitting method comparing measured and calculated curves. Although partition ratios k for various compounds were measured by supercritical chromatography, as reviewed,19 the binary diffusion coefficient was not measured in most cases. In this study the infinite-dilution binary diffusion coefficient and the partition ratio for CoQ10 in SC CO2 were simultaneously determined from the analysis of the response curve by the curve-fitting method. Moreover, the empirical correlations of both parameters were obtained. Theory

* To whom correspondence should be addressed. E-mail: [email protected]. † Chuo University. ‡ Yokohama National University.

When a tracer species is injected as a shot into a fully developed laminar flow in a cylindrical tube, the averaged tracer concentration Ca can be expressed as

10.1021/ie0109096 CCC: $22.00 © 2002 American Chemical Society Published on Web 05/01/2002

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follows:8

Ca(x,t) ≈

( )

((

) )

ua 2 m 1 x exp t /4at 1+k πR2 (1 + k)x4πat (1)

a)

2 2 D12 1 + 6k + 11k2 ua R + 1+k 48D12 (1 + k)3

(2)

where k is the partition ratio, m is the injected amount of the tracer species, R is the tube inner radius, and ua is the average velocity. The root-mean-square error  between the response curves measured (Ca,meas) and calculated (Ca,cal) at x ) L from t1 to t2, as shown in eq 3, is minimized by choosing appropriate values for the two parameters D12 and k, where t1 and t2 are times at the frontal and the

)

[

]

∫tt {Ca,meas(L,t) - Ca,cal(L,t)}2 dt 1/2 ∫tt {Ca,meas(L,t)}2 dt 2

1

2

1

Figure 1. Response curves measured (O) at 270 nm, 313.15 K, and 17.05 MPa and calculated (s) with D12 ) 0.417 × 10-8 m2‚s-1 and k ) 0.3515 for a best fit with  ) 0.0133.

(3)

latter 10% peak heights of the measured response curve, respectively. Note that the fitting was regarded as acceptably good when  < 0.02, the same as that in the case of the fitting criterion in the Taylor dispersion method.20 Experimental Apparatus and Procedures The experimental apparatus and the procedure are almost identical to those employed in the tracer response technique with a poly(ethylene glycol) (PEG) coated capillary column,8 which was coiled in a diameter of 270 mm. In this study the same column (Frontier Laboratories Ltd. UACW-15W-1.0F; bonded PEG, film thickness 1 µm, length 15.86 m) was employed. The tube diameter of the capillary column is a mean value (0.515 ( 0.001 mm) of the two ends measured by an X-ray microanalyzer (model JXA; JEOL, Japan). A solid solute of CoQ10, dissolved in some organic solvents at a concentration of 0.0019 g‚cm-3, mainly benzene and hexane, was loaded through an injector (Rheodyne 7520 with 0.5 µL). The injector was immersed in the water bath in which the coiled diffusion column and a preheating stainless steel uncoated column were horizontally placed to nearly the same plane, whose temperature was maintained at the prescribed value within the fluctuation of (0.01 K. The pressures were measured upstream at the injector and the outlet of the multi-UV detector (MD-1510, Jasco, Japan) by the Heise gauges, and the pressure sensors were equipped with a syringe pump (ISCO 100 DX) and a back-pressure regulator (Jasco model 880-91), respectively. The pressures were continuously monitored with the pressure sensors in the course of the measurements. The pressure fluctuations were found to be less 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 (99.9%), and hexane (95%) were obtained from Aldrich and ubiquinone CoQ10 (98%) from Sigma. These chemicals were used as received without further purification. However, the deterioration of ubiquinone was periodically examined

Figure 2. Contour error map for D12 vs k. The datum is the same as that in Figure 1: +, best fit; ×, by the moment method with D12 ) 0.399 × 10-8 m2‚s-1, k ) 0.3507, and  ) 0.0271.

with a UV-vis detector. Carbon dioxide with a purity higher than 99.995% and a water content < 40 ppm was supplied from Showa Tansan Co., Japan. Results and Discussion Figure 1 shows response curves measured at 270 nm, 313.15 K, and 17.05 MPa and calculated for a best fit. The response curve, calculated with the D12 and k values, was found to be well fitted to the measured response curve. Figure 2 depicts a contour error map for D12 vs k for the datum shown in Figure 1, together with the value obtained by the moment method (marked ×) and the value for the best fit (marked +). It is found that the parameter set of D12 and k can be determined and the value by the moment method is deviated from the best fit. According to this figure, an acceptably good fit criterion, corresponding to  < 0.02, reveals that the uncertainty is 0.2% for k and 3.7% for D12. Figure 3 shows the effects of wavelength on (a) absorbance intensity at maxima of the response curve, (b) root-mean-square (rms) error, (c) D12, and (d) k at 313.15 K and two pressures of 17.05 and 30.02 MPa. At wavelengths from 250 to 280 nm, the values of rms error are low, and D12 values appear to be independent

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Figure 4. Effects of the secondary flow on (a) apparent D′12 and apparent k′ at 313.15 K and 17.05-17.06 MPa.

Figure 3. Effects of wavelength on (a) absorbance intensity at the peak of the response curve, (b) rms fitting error, (c) D12, and (d) k for CoQ10 in SC CO2 at 313.15 K and two pressures of 17.05 (O) and 30.02 (∆) MPa.

of the wavelength. Although a strong wavelength dependence was found for benzene in SC CO2,21 almost no dependence was observed at wavelengths from 250 to 280 nm. Unless the characteristic absorption peaks are detected like benzene in CO2, the wavelength dependence of D12 values is not seen, except for extremely low absorption intensities. This observation is similar to those of other solutes such as ketones,20,22 R-tocopherol,8 β-carotene,8 and phenol.8 The partition ratio is almost independent of the wavelength over the whole range. The value is directly dependent on the mean residence time of a solute which corresponds to the first-order moment of the response curve, but the D12 value is affected by the variance, which corresponds to the second-order moment. Figure 4 shows the effect of CO2 flow rate on apparent D′12 and k′ values, together with the fitting error. The D′12 values are affected by the velocity due to the secondary flow caused by column coiling at De × Sc1/2 > 9, and the k′ values are scarcely affected over an entire range of De × Sc1/2 values. Note that fitting errors for all of the data are lower than 0.02. The leveled off value is the intrinsic D12 value. Note that Alizadeh et al.23 evaluated the effect to be less than 1% in terms of the value of the moment when De × Sc1/2 < 8. In this study all measurements were made at De × Sc1/2 < 8.

Correspondingly, the Reynolds and Schmidt numbers ranged from 26 to 52 and from 12 to 33, respectively. Table 1 lists D12 and k values measured in this study, together with the fitting error. Figure 5 compares (a) D12, (b) k, and (c) fitting error vs pressure between the curve-fitting method and the moment method at 313.15 K. Note that the fitting error for the moment method was obtained from response curves measured and reproduced with k and D12 values determined by the moment method. The D12 values by the curve fitting method decrease smoothly with increasing pressure, but those by the moment method from the same response curves are somewhat scattered. These evidences agree with observations of adsorption phenomena by chromatographic analysis in packed beds.18 On the other hand, the k values from the curve-fitting method are almost consistent with those from the moment method. This is why the k value is obtained from the mean residence time derived from the first-order moment and the D12 value from the variance calculated from the second-order moment. Fitting errors for the curve-fitting method are lower than those for the moment method, and those for both methods decrease with increasing pressure, as observed for other solutes.22 Figure 6 plots (a) D12/T and (b) D12/T 2.53 vs CO2 viscosity, respectively. Note that the CO2 viscosity was obtained by the equation of Vesovic et al.24 The authors have demonstrated that eq 4 is valid for various solutes in SC CO28,20,21,25 as well as an organic solvent26 and mixture solvents of CO2 and hexane at various compositions.27

D12/T ) Rηβ

(4)

As can be seen in Figure 6a, the plots show a straight line at each temperature with the same slope but with different intercepts. The temperature dependence on the R value was also observed for phenol.8 By modification of eq 4, all D12 data in the present study can be well

Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002 2815 Table 1. Measured Binary Diffusion Coefficients D12, Partition Ratios k, and Fitting Errors E for CoQ10 in SC CO2 at Temperatures from 308.15 to 333.15 K and Pressures from 8.51 to 30.18 MPa T (K)

P (MPa)

D12 (10-8 m2‚s-1)

k



308.15

8.51 8.90 9.12 9.20 9.62 9.79 10.00 10.52 11.47 12.50 13.49 14.55 15.54 16.53 18.00 20.00 22.00 24.00 26.97 30.05 9.90 10.34 10.42 11.38 12.02 13.00 14.02 15.05 16.04 17.05 17.06 18.32 19.02 20.48 21.50 23.00 25.65 28.05 30.02 12.72 13.08 13.50 14.05 14.45 15.04 15.63 16.27 16.95 17.97 18.56 19.20 20.00 21.02 21.95 22.96 24.00 25.03 26.00 26.97 28.00 29.98 30.18 16.02 17.02 17.95 19.93 22.03 23.95 25.97 28.03 30.00

0.560 0.523 0.511 0.506 0.490 0.486 0.476 0.461 0.441 0.422 0.411 0.400 0.391 0.383 0.375 0.366 0.351 0.340 0.331 0.322 0.570 0.546 0.539 0.502 0.486 0.460 0.453 0.432 0.422 0.417 0.416 0.406 0.416 0.387 0.392 0.371 0.356 0.347 0.339 0.614 0.588 0.576 0.558 0.546 0.544 0.522 0.510 0.499 0.485 0.477 0.468 0.465 0.451 0.441 0.434 0.432 0.429 0.423 0.411 0.406 0.401 0.395 0.645 0.612 0.597 0.558 0.530 0.529 0.498 0.479 0.461

13.580 5.917 4.532 4.130 2.813 2.319 2.026 1.553 0.986 0.693 0.533 0.428 0.356 0.295 0.239 0.201 0.177 0.153 0.118 0.098 9.503 5.272 4.881 2.181 1.499 0.976 0.698 0.518 0.414 0.352 0.360 0.277 0.260 0.215 0.201 0.171 0.139 0.121 0.103 6.255 4.613 3.253 2.294 1.821 1.368 1.102 0.878 0.692 0.530 0.472 0.411 0.365 0.299 0.267 0.232 0.210 0.195 0.181 0.167 0.152 0.152 0.135 3.051 1.776 1.242 0.639 0.414 0.323 0.244 0.199 0.166

2.26 × 10-2 5.12 × 10-2 3.00 × 10-2 4.91 × 10-2 4.14 × 10-2 2.58 × 10-2 4.28 × 10-2 3.46 × 10-2 2.64 × 10-2 2.23 × 10-2 1.78 × 10-2 1.58 × 10-2 9.96 × 10-3 4.13 × 10-3 1.01 × 10-2 5.66 × 10-3 5.24 × 10-3 6.62 × 10-3 7.57 × 10-3 6.36 × 10-3 6.46 × 10-2 2.27 × 10-2 6.67 × 10-2 4.72 × 10-2 2.11 × 10-2 3.91 × 10-2 1.74 × 10-2 2.56 × 10-2 2.07 × 10-2 1.33 × 10-2 8.69 × 10-3 1.50 × 10-2 4.40 × 10-3 1.28 × 10-2 5.79 × 10-3 7.79 × 10-3 5.91 × 10-3 7.52 × 10-3 4.15 × 10-3 3.24 × 10-2 3.80 × 10-2 3.55 × 10-2 1.85 × 10-2 1.77 × 10-2 1.28 × 10-2 1.81 × 10-2 1.90 × 10-2 1.77 × 10-2 1.19 × 10-2 1.79 × 10-2 8.13 × 10-3 1.34 × 10-2 5.76 × 10-3 1.05 × 10-2 3.63 × 10-3 5.28 × 10-3 5.51 × 10-3 9.46 × 10-3 5.13 × 10-3 7.38 × 10-3 5.71 × 10-3 4.52 × 10-3 1.82 × 10-2 1.13 × 10-2 8.75 × 10-3 9.47 × 10-3 6.85 × 10-3 4.58 × 10-3 3.17 × 10-3 1.22 × 10-2 1.65 × 10-3

313.15

323.15

333.15

Figure 5. Comparison of (a) D12, (b) k, and (c) fitting error between the curve-fitting method (O) and the moment method (×) at 313.15 K.

correlated with eq 5, as can be shown in Figure 6b,

D12 [m2‚s-1] 2.53

(T [K])

) 1.978 × 10-18(η [Pa‚s])-0.727

(5)

where AAD % ) 0.87% for N ) 71. Note that AAD % ) 3.33% for eq 5a.

D12 [m2‚s-1] (T [K])

) 1.004 × 10-14(η [Pa‚s])-0.756

(5a)

We have demonstrated the validity of the Schmidt number correlation for predicting infinite-dilution binary diffusion coefficients for various solutes in SC CO2.8,20-22 However, it is found that the correlation does not well represent the measured D12 data (AAD % ) 17.2% for N ) 71). The reason is not clarified, but it partly results from an uncertainty of the hard sphere or the van der Waals diameter of ubiquinone and/or a mixing rule of solute and solvent molecular diameters. Figure 7 shows logarithmic plots for k values: (a) k vs pressure and (b) k vs CO2 density. Note that the values of the CO2 density were obtained by the equation of Pitzer and Schreiber28 and the lines at each temper-

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Figure 6. (a) D12/T and (b) D12/T 2.53 vs CO2 viscosity for all present data: ∆, 308.15 K; O, 313.15 K; 0, 323.15 K; ), 333.15 K.

ature were predicted from the correlation in eq 7. The k values decrease simply with increasing pressure with nonstraight lines, and the plot shows the temperature dependence. k values can be represented by eq 6,29

(

)

∂(ln k) ∂(ln F)

) T

v∞m - v∞s -1 RgTβT

(6)

where v∞m, v∞s , and βT are the solute partial molar volume (PMV), PMV for the stationary phase, and isothermal compressibility, respectively. At a nearcritical point, v∞s can be reduced to zero.29 If PMV v∞m is obtained, the partition ratio k is represented by eq 6. Unfortunately, the value of PMV cannot be accurately predicted because the estimated values of the acentric factor and the critical properties are less reliable for such a high molecular weight compound. Thus, as can be seen in Figure 7b, the partition ratios k are correlated with temperatures and densities in eq 7 (AAD % ) 7.32% for N ) 71), where a1 ) -11.6475, a2 ) -0.0346,

ln k ) a1 ln F + a2T + a3

Figure 7. Logarithmic plots of (a) k vs pressure and (b) k vs CO2 density. The lines were obtained by eq 7. The key is the same as that in Figure 6.

(7)

and a3 ) 87.893. Figure 8 plots PMV vs pressure. The PMV values were obtained through eq 6, assuming v∞s to be negligible. At lower temperatures or closer to the critical temperature of CO2, PMV values decrease with pressure. At pressure, showing the minimum PMV value, clusters consisting of solute and solvent molecules could be formed. Thus, the D12 values seem to be less accurate at lower pressures and lower temperatures studied, as

Figure 8. Partial molar volume for CoQ10 in SC CO2 vs pressure. The plots, obtained from eq 6, correspond to the measurement pressures. The key is the same as that in Figure 6. The lines were obtained by eq 6, with k values from eq 7.

compared with those at higher pressures. This evidence corresponds to the pressure dependence of the fitting error. Conclusions The infinite-dilution binary diffusion coefficient and the partition ratio for CoQ10 in SC CO2 at 308.15333.15 K and 8.51-30.18 MPa were measured with a polymer-coated capillary column by a tracer response

Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002 2817

technique. The curve-fitting method gave accurate D12 values, while the moment method sometimes led to inaccurate values. Nevertheless, both methods produced almost the same k values. The correlations in eqs 5 and 7 well represented the D12 and k values, respectively. Furthermore, solute partial molar volumes of CoQ10 in carbon dioxide were obtained from the partition ratio k. Acknowledgment The authors express their thanks to the Takahashi Industrial and Economic Research Foundation and to the Promotion and Mutual Aid Corp. for Private Schools of Japan for their financial support. Thanks are also due to the Ministry of Education, Culture, Sports and Technology for a Grant-in-Aid. Nomenclature AAD % ) average absolute deviation Ca ) average concentration D12 ) binary diffusion coefficient D′12 ) apparent binary diffusion coefficient De ) Dean number ) (Fuadtube/η)(dtube/dcoil)1/2 dcoil ) coil diameter of the diffusion column dtube ) inner diameter of the diffusion column k ) partition ratio of the solute in the polymer layer to the supercritical phase k′ ) apparent partition ratio L ) distance between the injection point and the detection point m ) injected amount of the tracer N ) number of data points P ) pressure R ) tube radius Rg ) gas constant Sc ) Schmidt number T ) temperature t ) time ua ) average velocity v∞ ) partial molar volume x ) axial distance βT ) isothermal compressibility  ) fitting error defined by eq 3 η ) viscosity F ) density Subscripts cal ) calculated m ) mobile phase meas ) measured s ) stationary phase

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Received for review November 8, 2001 Revised manuscript received March 12, 2002 Accepted March 14, 2002 IE0109096