Measurements of binary diffusion coefficients for metal complexes in organic solvents by the Taylor dispersion method

Fluid Phase Equilibria 297 (2010) 62–66

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Measurements of binary diffusion coefficients for metal complexes in organic solvents by the Taylor dispersion method Minoru Toriumi a , Ryohei Katooka a , Kazuko Yui a , Toshitaka Funazukuri a,∗ , Chang Yi Kong b , Seiichiro Kagei c a

Department of Applied Chemistry, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan Department of Materials Science and Chemical Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku Naka-ku, Hamamatsu 432-8561, Japan c Faculty of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan b

a r t i c l e

i n f o

Article history: Received 1 December 2009 Received in revised form 29 May 2010 Accepted 7 June 2010 Available online 17 June 2010 Keywords: Diffusion coefficient Taylor dispersion Correlation Ferrocene Metal acetylacetonate complex

a b s t r a c t Infinite dilution binary diffusion coefficients, D12 , of ferrocene, 1,1 -dimethylferrocene and ethylferrocene in hexane, cyclohexane and ethanol at 313.2 K and pressures from 0.2 to 19 MPa, in acetonitrile at 298.2–333.2 K and 0.2 MPa, and various metallic acetylacetonate, acac, complexes such as Co(acac)3 , Ru(acac)3 , Rh(acac)3 , Pd(acac)2 and Pt(acac)2 mainly in ethanol at 313.2 K and 0.2 MPa were measured by the Taylor dispersion method. The D12 values in m2 s−1 for the three ferrocenes in the present study and those of ferrocene and 1,1 -dimethylferrocene in supercritical carbon dioxide in our previous studies were represented by the modified hydrodynamic equation over a wide range of viscosity: M0.5 D12 /T = 1.435 × 10−13 −0.8446 with average absolute relative deviation of 2.40% for 316 data points, where M is the solute molecular weight, T is the temperature in K,  is the solvent viscosity in Pa s. Although the D12 values for the acac complexes were roughly represented by the above hydrodynamic equation, the accuracies were lower because they were dependent on not solute molecular weight but the number of acac ligand in the complex molecules. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Metal complexes are widely used in various fields such as organic syntheses as catalyst or its precursor, and metal deposition on surfaces of films, nanotubes and pores or metal removal from contaminated soils or substances because of drastically enhanced solubilities of metal complexes rather than those of metal itself. Thus, the use of metal complexes has great potential for improving metal-handling in versatile chemical processes. In particular, supercritical chemical deposition using metal complexes in supercritical fluids has considerably drawn attention in metal coating on surfaces of electronic devices in micro-fabrication processes [1–8] as well as metal removal from contaminated soils or materials [9–14] due to its transportability. Thus, the physical properties of metal complexes are required to design reactors and equipments, and to evaluate the processes. As well as for other properties the diffusion coefficients are also needed to estimate mass transfer rates.

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (T. Funazukuri). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.06.003

So far, binary diffusion coefficients of various metal complexes have been mainly reported by the electrochemical methods such as cyclic voltammetry and chronoamperometry [15–21], while using the Taylor dispersion method, Tominaga et al. [22] measured D12 values of cobalt(III) acetylacetonate, Co(acac)3 , in various organic solvents, and Yang and Matthews [23] those of copper(II) trifluoroacetylacetonate in supercritical carbon dioxide. However, the data are still limited, and not well consistent, and the prediction method is not established. Many predictive correlations, based on the Stokes–Einstein equation such as the Wilke–Chang equation, are known to be valid for predicting D12 values of organic solutes in liquid solvents. These correlations involve the parameters related to specific solvent and solute properties [24]. Unfortunately, the estimation of the parameters such as solute molar volume at its normal boiling point and parachor, is difficult or unreliable for metal complexes. An appropriate correlation is required. Recently, our research group has reported infinite dilution binary diffusion coefficients of ferrocenes [25], and palladium(II) acetylacetonate and cobalt(III) acetylacetonate [26] in supercritical carbon dioxide measured by the chromatographic impulse response method and the Taylor dispersion method. Moreover, we have demonstrated the effectiveness of the hydrodynamic (HD) equation, to correlate binary diffusion coefficients of 12 solutes over

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Fig. 1. Wavelength dependencies of (a) maximum peak absorbance, (b) normalized absorbance intensity (NAI) at maximum peak height, (c) D12 , and (d) fitting error for 1,1 -dimethylferrocene in cyclohexane at 313.2 K and 0.2 MPa.

a wide range of solvent viscosity, namely in supercritical and liquid states [27]. The D12 /T values can be well expressed with solvent viscosity as a single representative variable, apparently irrespective of temperature, pressure, and solvent state, i.e. supercritical and liquid. To validate the HD equation for metal complexes, the D12 data are also required in liquid phases, or higher viscosity region. Thus, the objectives are to measure D12 values in organic liquids, and develop a correlation based on the HD equation. 2. Theory The measurements were based on the theory described by Taylor [28] and developed by Aris [29]. In this study the D12 value was obtained by fitting the response curve, calculated Ccal (t) at the column exit in Eq. (1) with the assumed D12 value, to that measured experimentally Cexp (t) in the time domain.



m (L − ut)2 exp − Ccal (t) = √ 4Kt R2 4Kt

 (1)

where K = D12 + R2 u2 /48D12 , m is the amount of solute injected, R and L are the diffusion column inner radius and the length, respectively, and u is the average of solvent velocity. The D12 value was determined such that root-mean-square (rms) fitting error, ε, defined by Eq. (2), was minimized by changing D12 value [30–32].

⎡  2 ⎤1/2 t2 C dt − C (t) (t) exp cal t ⎦ ε=⎣ 1    t2

t1

Cexp (t)

2

3. Experimental 3.1. Experimental apparatus and procedures The experimental apparatus and procedures were almost the same as those shown in the previous studies [30,31], but the components were replaced. The apparatus consisted of a syringe pump (260D, ISCO), a preheating column, a diffusion column made of stainless steel tubing (0.817 mm I.D. × 33.71 m long), an injector (Rheodyne 7520), a UV-Vis multi-detector (MD-2010, JASCO), and a back pressure regulator (BP-2080-M, JASCO). A 1 ␮L solution (at concentrations from 0.0006 to 0.034 g mL−1 ) of each solute dissolved in a solvent was loaded through the injector. The response curves were monitored with the multi-detector by scanning from 195 to 600 nm at increments of 1 nm and an interval of 1.6 s. Each D12 value at each wavelength was determined so that the fitting error between the response curves measured experimentally and calculated was minimized. The detection wavelength for each solute was chosen by examining the wavelength dependency of diffusion coefficient values [30–32]. In most measurements the effect of the secondary flow due to column coiling was less than 1% (in terms of the moment) [33] because the values DeSc1/2 were mainly lower than 8 (the maximum value was 10), where De is the Dean number and Sc is the Schmidt number.

3.2. Chemicals (2)

dt

where t1 and t2 are the frontal and rear times, respectively, at 10% peak height of the response curve.

Cobalt(III) acetylacetonate (98%, Wako), palladium(II) acetylacetonate (99%, Aldrich), platinum(II) acetylacetonate (99%, Aldrich), rhodium(III) acetylacetonate (97%, Aldrich), ruthenium(III) acetylacetonate (97%, Aldrich), ferrocene (98%, Aldrich), 1,1 -dimethylferrocene (95%, Aldrich), and ethylferrocene (98%,

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Table 1 Measured diffusion coefficient D12 , 95% confidence range of D12 , ranges of rms error ε and flow rate u, and number of data point n for various metal complexes. Solute

Solvent

T (K)

P (MPa)

D12 (10−10 m2 s−1 )

±D12 a (10−10 m2 s−1 )

Ferrocene

Acetonitrile Acetonitrile Acetonitrile Acetonitrile Acetonitrile Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Ethanol Hexane Hexane Hexane Hexane Acetonitrile + 0.1 M TEAPb Acetonitrile Acetonitrile Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Ethanol Hexane Hexane Hexane Hexane Acetonitrile Acetonitrile Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Ethanol Hexane Hexane Hexane Hexane Cyclohexane Ethanol Hexane Ethanol Ethanol Ethanol Ethanol

298.15 303.15 313.15 322.95 333.15 313.15 313.15 313.15 313.15 323.15 313.15 313.15 313.15 313.15 313.15 298.15 313.15 322.95 313.15 313.15 313.15 313.15 323.15 313.15 313.15 313.15 313.15 313.15 313.15 322.95 313.15 313.15 313.15 313.15 313.15 323.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15

0.18 0.18 0.18 0.19 0.19 0.19 11.09 16.03 19.02 16.02 0.20 0.17 10.99 16.02 19.02 0.18 0.18 0.19 0.19 11.09 16.02 19.02 16.00 0.20 0.17 11.03 16.00 19.02 0.18 0.18 0.17 11.02 16.03 19.01 19.02 16.02 0.20 0.16 11.07 16.03 19.01 0.18 0.18 0.16 0.18 0.18 0.18 0.19

26.54 27.97 31.51 35.50 39.85 15.11 13.17 12.48 12.18 14.81 14.63 36.47 32.74 31.31 30.69 25.16 29.44 32.80 13.69 12.03 11.36 11.08 13.58 12.99 33.85 30.55 28.96 28.31 28.93 31.86 13.73 12.08 11.43 11.25 11.22 13.57 13.07 33.50 29.91 28.73 27.89 7.72 7.54 22.48 9.79 9.76 7.44 7.51

0.24 0.24 0.33 0.42 0.39 0.11 0.06 0.02 0.11 0.03 0.15 0.08 0.15 0.14 0.03 0.17 0.41 0.39 0.07 0.04 0.05 0.14 0.01 0.12 0.21 0.03 0.09 0.16 0.39 0.12 0.09 0.03 0.05 0.18 0.03 0.09 0.11 0.24 0.10 0.13 0.17 – 0.03 0.07 0.05 0.10 0.00 0.05

1,1 -Dimethylferrocene

Ethylferrocene

Co(acac)3

Pd(acac)2 Pt(acac)2 Rh(acac)3 Ru(acac)3 a b

102 ε (–) 0.24–0.73 0.21–0.32 0.21–0.74 0.24–0.26 0.22–0.32 0.17–0.22 0.20–0.21 0.20–0.21 0.20–0.25 0.20 0.43–0.59 0.16–0.35 0.14–0.33 0.13–0.33 0.15–0.18 0.21–0.30 0.27–0.75 0.39–0.42 0.20–0.24 0.21–0.22 0.21–0.34 0.22–0.38 0.33–0.39 0.41–0.60 0.29–0.54 0.43–0.48 0.25–0.65 0.22–0.29 0.82–1.16 0.85–1.17 0.24–0.29 0.23–0.25 0.24–0.26 0.24–0.40 0.25–0.27 0.22 0.31–0.56 0.17–0.28 0.15–0.21 0.16–0.18 0.19–0.20 1.47 0.45–0.84 2.15–2.51 0.58–0.78 0.67–1.23 0.62–0.82 0.52–1.61

u (10−3 m s−1 ) 4.93–5.60 5.59–5.60 5.66–6.40 6.43–6.47 6.87–6.91 4.33–6.67 6.63–6.67 6.62–6.65 6.60–6.64 6.68–6.69 6.30–6.31 6.68–6.72 6.64–6.68 6.60–6.68 6.60–6.62 5.56–5.58 5.67–6.38 6.44–6.47 6.65–6.68 6.64–6.65 6.62–6.66 6.61–6.63 6.66–6.71 4.99–6.31 6.69–6.71 6.66 6.64–6.66 6.60–6.61 5.68–6.38 6.44 6.63–6.65 6.61–6.64 6.62–6.63 6.61–6.63 6.59–6.61 6.69–6.70 6.30–6.31 6.63–6.64 6.59–6.63 6.59–6.61 6.60–6.63 6.60 4.93–6.63 6.61–6.64 4.91–4.99 4.95–4.99 4.96–4.97 4.96–6.62

n 3 5 10 3 4 3 3 4 5 2 3 3 4 7 3 4 4 3 3 3 4 5 3 3 4 3 6 2 5 3 3 3 4 3 4 2 3 5 4 3 3 1 5 4 4 4 3 4

95% confidence range. Tetraethylammonium perchlorate.

Aldrich) were employed as received without further purification. Hexane and cyclohexane were in spectroscopic grade, and acetonitrile and ethanol in HPLC grade. Tetraethylammonium perchlorate (99%, Nakalai Tesque) was used without further purification. 4. Results and discussion Table 1 shows measured diffusion coefficient D12 , rms error ε, average flow rate u and number of data point n for various metal complexes. The D12 values listed are the mean values with the 95% confidence interval, i.e. D12 ± D12 , where D12 is the difference between the mean value and the 95% confidence limit, √ namely, equal to 1.96/ n;  2 is the variance, n is the number of data point at the same condition. Response curves for the metal complexes employed in this study did not show tailing, and excellent fits (ε < 1%) were obtained. However, some differences in the vicinity of peak top were observed. Fig. 1 shows the effects of wavelength dependencies for 1,1 dimethylferrocene in cyclohexane at 313.2 K and 0.2 MPa on

(a) absorbance at the maximum peak height, (b) normalized absorbance intensity (NAI), defined as the absorbance intensity at the maximum peak height divided by the value of (peak area) × (calculated solvent velocity), (c) D12 value, and (d) rms error. The strong absorbance at 200–220 nm was observed, and the intensities decreased almost linearly with increasing wavelength above 230 nm (Fig. 1(a)). As seen in Fig. 1(b), the values of NAI were nearly constant at wavelengths from 215 to 280 nm. The shoulders were seen in the response curve at 210 nm, and the D12 value determined from the response curve was less reliable. If the detector linearity that the intensity of detector signal is proportional to the solute concentration is held, the NAI value should be constant. In fact, the D12 values were almost constant over a wide range of wavelength from 215 to 280 nm showing NAI values to be constant, and correspondingly, the values of rms error were low. Below 215 nm and above 280 nm, however, the NAI values and D12 values were dependent on wavelength, and fitting errors were not satisfactorily low. The D12 values were not reliable in the wavelength ranges. In this study the D12 values were obtained by averaging D12 values measured at wavelengths from 240 to 260 nm.

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Fig. 3. D12 /T vs. solvent viscosity  for Pd(acac)2 and Co(acac)3 in various organic solvents and supercritical CO2 . Pd(acac)2 ;

: in ethanol (present study),

supercritical CO2 (Kong et al. [26]), Co(acac)3 ; in cyclohexane (present study),

: in ethanol,

: in hexane,

: in supercritical CO2 (Kong et al. [26]),

: in : : in

acetonitrile + TEAP (Ikeuchi et al. [20]), : in various organic solvents (Tominaga et al. [22]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 2. (a) M0.5 D12 /T and (b) AARD vs. solvent viscosity  for ferrocene, 1,1 dimethylferrocene, and ethylferrocene in various solvents. 1,1 -dimethylferrocene,

: ethylferrocene (present study),

: Ferrocene,

:

: ferrocene in super-

critical CO2 (Kong et al. [25]), : 1,1 -dimethylferrocene in supercritical CO2 (Kong et al. [25]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 2 plots (a) M0.5 D12 /T and (b) AARD vs. solvent viscosity  for ferrocene, 1,1 -dimethylferrocene and ethylferrocene in various organic solvents and supercritical carbon dioxide [25], where AARD is the average absolute relative deviation defined by Eq. (4). For various organic compounds in supercritical carbon dioxide, the D12 values were proportional to M−0.5 [34–36]. For the three solutes the plots were represented by a single straight line in the modified hydrodynamic equation of Eq. (3) with AARD = 2.40% for 316 data points, and apparently independent of pressure and solvent species. The difference in D12 values of isomers, 1,1 -dimethylferrocene and ethylferrocene was not observed. M 0.5 D12 = 1.435 × 10−13 −0.8446 T



(3)



D12,prd 100  AARD (%) = × 1 − D12,exp N N

(4)

i=1

where D12 [m2 s−1 ] is the binary diffusion coefficient, M is the solute molecular weight, T [K] is the temperature, and  [Pa s] is the solvent viscosity, N is the number of total data point, and subscripts exp and prd are designated experimental and predicted, respectively. We have already demonstrated that the similar equation to Eq. (3), with different constants, is effective for var-

ious solute and solvent systems in liquid and supercritical states [35]. Most literature data of metal complexes such as ferrocene were mainly measured by two electrochemical methods such as cyclic voltammetry and chronoamperometry. In both methods an electrolyte was added to a non-electrolytic solvent at a concentration from 0.1 to 0.2 M to decrease the electrical resistance [20], and the effect of the presence is not clear. Thus, to compare between the Taylor dispersion and electrochemical methods, a mixture of acetonitrile and 0.1 M tetraethylammonium perchlorate (TEAP) was used as a solvent at 298.15 K and ambient pressure in the Taylor dispersion measurement. As a result, diffusion coefficients were (2.516 ± 0.017) × 10−9 and 2.53 × 10−9 m2 s−1 by the Taylor dispersion method and cyclic voltammetry method reported by Ikeuchi et al. [20], respectively. In the absence of the electrolyte the value of (2.654 ± 0.024) × 10−9 m2 s−1 , and was slightly higher than that with TEAP. The difference was not large, but was clearly observed. Fig. 3 plots D12 /T vs. solvent viscosity for Pd(acac)2 and Co(acac)3 in organic solvents such as hexane, cyclohexane and ethanol in the present study, together with those in various organic solvents [20,22] and supercritical CO2 [26] reported in the literature. As observed for various solute–solvent systems [27,32,34–36] and ferrocenes in Fig. 2, D12 /T values for Pd(acac)2 and Co(acac)3 were well represented by each straight line, and the slope and the intercept were dependent on the solute, irrespective of solvent species. The absolute values of the slopes for both solutes were less than unity. Although the D12 values for the metallic acac complexes studied are roughly correlated by Eq. (3), the average absolute relative deviations AARD from Eq. (3) are high: 3.7, 8.4, 24.8, 19.0, and 18.3% for Pd(acac)2 , Pt(acac)2 , Co(acac)3 , Rh(acac)3 and Ru(acac)3 , in ethanol at 298.2 K and 0.2 MPa, respectively. Since the D12 values for various organic compounds decreased with increasing M0.5 [34–36], the solute molecular weight dependency of D12 value for various metallic acetylacetonate complexes were examined in Fig. 4. The D12 values for metallic acac complexes with two acac ligands such as Pd(acac)2 (M = 304.2) and Pt(acac)2 (M = 393.2) were almost consistent, and those with three such as Co(acac)3 (M = 356.2), Ru(acac)3 (M = 398.4) and Rh(acac)3 (M = 400.2) also agreed with each other. Thus, the D12 values depend not on solute molecular weight but on the number of acac ligands. It can be considered that the agreement on D12 values for various metal complexes having different

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T u ε 

temperature solvent velocity root-mean-square error defined as Eq. (2) solvent viscosity

Acknowledgements The authors are grateful to the Ministry of Education, Sports, Culture, Science and Technology of Japan for financial support through grant-in-aid of #22360325. References

Fig. 4. D12 vs. solute molecular weight M for metallic acac complexes in ethanol at 313.2 K and 0.2 MPa. : Pd(acac)2 , : Pt(acac)2 , : Co(acac)3 , : Rh(acac)3 , : Ru(acac)3 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

molecular weights is caused by the nearly same atomic size of these centered metals, whereas the atomic masses are quite different. In this case solute molecular size, not the molecular weight, should be taken into account. 5. Conclusions Infinite dilution binary diffusion coefficients of various metal complexes were measured by the Taylor dispersion method. As seen for organic compounds, the modified hydrodynamic equation in Eq. (3) was effective for predicting binary diffusion coefficients for the three ferrocenes. However, the D12 values for metallic acetylacetonate complexes were not well represented by Eq. (3) because they were almost the same values for the metal complexes having the same number of the acac ligand, irrespective of molecular weights. This suggests that the solute molecular sizes should be considered for the correlation. List of symbols AARD average absolute relative deviation defined by Eq. (4) D12 infinite dilution binary diffusion coefficient ±D12 difference between the mean value and the 95% confidence limit M molecular weight NAI normalized absorbance intensity N number of total data point n number of data point at the same condition P pressure

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