Infinite Dilution Binary Diffusion Coefficients Research Articles

Measurements of binary diffusion coefficient for platinum(II) acetylacetonate in high temperature supercritical carbon dioxide by the chromatographic impulse response method

Infinite dilution binary diffusion coefficients D12 and retention factors k for platinum(II) acetylacetonate in high temperature supercritical carbon dioxide (scCO2), at temperatures from (323.3–454.2) K and pressures from (11.0–25.0) MPa, were measured by the chromatographic impulse response method. Although diffusion coefficients for various compounds up to 353 K in scCO2 reported in the literature were well represented by the hydrodynamic equation, the present data deviated more from the equation as the CO2 viscosity decreased. The deviating D12 data corresponded to the gas-like scCO2 region whose conditions were situated below the density fluctuation ridge line on the pressure (or density) − temperature phase diagram, as observed for Cr(acac)3 measured in the authors’ previous study. All the present D12 data and those previously measured below 343 K over the entire region from gas-like to liquid-like scCO2 were well represented by the Schmidt number correlation over the temperature range from 308.2 K to 454.2 K with an average relative deviation (ARD) of 6.5% for 109 measurement conditions. The retention factors measured in the present study were correlated with CO2 density, with temperature dependent constants having an ARD of 4.4% for 47 measurement conditions.

Measurements and correlation of infinite dilution binary diffusion coefficients for Cr(acac)3 in high temperature supercritical carbon dioxide

The infinite dilution binary diffusion coefficient (D12) for chromium (III) acetylacetonate (Cr(acac)3) in supercritical carbon dioxide (scCO2) was measured at temperatures from 343 K to 423 K and pressures from 10 MPa to 22 MPa by the chromatographic impulse response (CIR) method. We previously reported D12 data at relatively low temperatures below 343 K; the D12 data were accurately represented by the hydrodynamic equation where the D12/T vs. CO2 viscosity were expressed by a straight line on a logarithmic plot. However, the newly measured D12 values in the present study showed greater deviations at higher temperatures or lower viscosities (lower pressures/densities) from the correlation determined for low – temperature D12 data. The maximum deviation was 68% at the lowest measured CO2 viscosity of 22 μPa s; thus, the hydrodynamic equation could be no longer applied in this region. The D12 data that deviate from the hydrodynamic equation fully correspond to the gas-like scCO2 region, whereas those fitted by the equation correspond to the liquid –like scCO2 region. The gas–like and liquid–like regions can be separated on the basis of density fluctuations and a ridge line in a pressure vs. temperature diagram, claimed by Nishikawa and Morita [Chem. Phys. Lett., 316 (2000) 238]. Compared with the accuracy in predicting the D12 data by the original Schmidt number correlation, the accuracy was improved by the modified Schmidt number correlation, with an average relative deviation of 6.20 % for 136 conditions, including both gas–like and liquid–like scCO2 regions.

Measurements of infinite dilution binary diffusion coefficients of acetylferrocene and 1,1’-diacetylferrocene in supercritical carbon dioxide and in liquid organic solvents

The infinite dilution binary diffusion coefficients (D12) of acetylferrocene and 1,1′-diacetylferrocene were measured in supercritical carbon dioxide (scCO2) at (313, 353, 363 and 373) K and at pressures from (11 to 26) MPa using the chromatographic impulse response method, and in atmospheric-pressure liquid organic solvents such as acetone at 303 K, methanol at (313, 323, and 333) K and ethanol at (323 and 333) K using the Taylor dispersion method. The D12 values for both solutes were approximately consistent under all of the investigated measurement conditions and were well represented by the hydrodynamic equation, in which D12/T is expressed as a function of solvent viscosity, over almost the entire range of investigated viscosities ranging from the viscosities of liquid organic solvents to that of scCO2. At 313 K and 11 MPa, the D12 values for both the organometallic solutes deviated from the correlation of the D12 values with the solute molecular mass for nonmetallic organic compounds reported in the literature.

Determination and correlation of infinite dilution binary diffusion coefficients for aluminum acetylacetonate in supercritical and liquid fluids

The infinite dilution binary diffusion coefficients D12 for aluminum acetylacetonate in supercritical CO2 were determined at 308.15–333.15 K and at 7.80–40.00 MPa by the chromatographic impulse response (CIR) method. And, the diffusion measurements in liquid ethanol were carried out at 300.15–333.15 K and at 0.10 and 30.00 MPa by the Taylor dispersion method. It was found that the D12 values measured in supercritical CO2 show slowing down in the region of near critical point. The determined activation energies of diffusion were 23.0, 13.7, 12.0, 11.3 kJ/mol at 12.00, 20.00, 25.00, 35.00 MPa in supercritical CO2 and 19.1 kJ/mol at 0.10 MPa in liquid ethanol, respectively. All determined 90 diffusion data in this study can be correlated with the equation of D12 [m2/s] = 1.558 × 10−14 T [K] η [Pa s]−0.761 with average absolute relative deviation (AARD) of 5.6% over a wide fluid viscosity range from 2.462 × 10−5 to 1.258 × 10−3 Pa s.

Measurement of binary diffusion coefficient and solubility estimation for dyes in supercritical carbon dioxide by CIR method

Infinite dilution binary diffusion coefficients (D12) of two dyestuffs, disperse blue 14 (DB14) and disperse orange 11 (DO11), were measured in supercritical CO2 at 310–330 K and up to 35 MPa by the chromatographic impulse response (CIR) method and in liquid methanol and ethanol at 308–328 K and atmospheric pressure by the Taylor dispersion method. The retention factors (k) were also measured by the CIR method. The diffusion coefficients were well represented by a hydrodynamic equation, as a function of temperature and solvent viscosity, over a wide range of solvent viscosity from scCO2 to liquid solvents with average absolute relative deviations (AARDs) of 1.7% and 2.6% for 63 and 93 data points of DB14 and DO11, respectively. The solubility data for the two dyestuffs reported in the literature were well correlated with solute retention factor measured in the present study and solvent density with AARD of 7.05% for DB 14 of 109 data points and that of 15.4% for DO11 of 43 data points.

Measurement and correlation of binary diffusion coefficients of lithium acetylacetonate in supercritical carbon dioxide and in liquid ethanol

The infinite dilution binary diffusion coefficients D12 of lithium acetylacetonate were measured in supercritical carbon dioxide by the chromatographic impulse response (CIR) method at 308.15–333.15K and pressures up to 36.00MPa. The D12 values were also measured in liquid ethanol at 298.15–333.15K, and at 0.10, 10.00 and 30.00MPa by the Taylor dispersion method. The effects of temperature, pressure and density of fluid on D12 values were studied. The D12 data increased from 1.140×10−9m2s−1 in liquid ethanol at 298.15K and 30.00MPa to 2.218×10−8m2s−1 in supercritical carbon dioxide at 333.15K and 14.00MPa. It was observed that the D12 data in supercritical carbon dioxide at 15.00, 20.00 and 30.00MPa can be well correlated as a function of temperature using an Arrhenius type equation, which provided the diffusion activation energies of 17.5, 13.4 and 11.0kJmol−1; that in liquid ethanol at 0.10, 10.00, 30.00MPa gave the diffusion activation energies of 14.0, 14.2 and 13.8kJmol−1, respectively. It was found that the proposed correlation based on hydrodynamic approach can well represent all the measured D12 data of lithium acetylacetonate in supercritical carbon dioxide and in liquid ethanol with the average absolute relative deviation (AARD) of 1.7% for 88 data points.

Infinite Dilution Binary Diffusion Coefficients for Compounds Derived from Biomass in Water at 0.1 MPa and Temperatures from (298.2 to 353.2) K

Infinite dilution binary diffusion coefficients (D12) for compounds derived from biomass such as furan-2-carbaldehyde (furfural), 5-(hydroxymethyl)-2-furaldehyde (5-HMF), 2-methoxyphenol (guaiacol), 4-hydroxy-3-methoxybenzaldehyde (vanillin), and phenol in water were measured over the temperature range from (298.2 to 353.2) K at 0.1 MPa using the Taylor dispersion method. The relative expanded uncertainties with level of confidence 0.95 (the coverage factor, k = 2.78 for 4 degrees of freedom) for the measured diffusion coefficients were less than 5.8 % and typically ca. 2.4 %. The diffusion coefficients were correlated with the hydrodynamic equation, D12/T = αηβ, with an average absolute relative deviation, AARD, less than 1.16 %.

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

Infinite dilution binary diffusion coefficients, D 12, 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 D 12 values in m 2 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: M 0.5 D 12/ T = 1.435 × 10 −13 η −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, η is the solvent viscosity in Pa s. Although the D 12 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.

Infinite Dilution Binary Diffusion Coefficients of Hydrotreating Compounds in Tetradecane in the Temperature Range from (310 to 475) K

Infinite dilution diffusion coefficients of benzothiophene, dibenzothiophene, acridine, naphthalene, and anthracene in tetradecane have been measured in a temperature range from (313.2 to 473.2) K using the Taylor dispersion technique. Predicted values based on the correlations of Wilke−Chang and Tyn−Calus deviate up to 35 %. An Arrhenius type of equation was used to describe the temperature dependence of the diffusion coefficients with an accuracy on average of less than 5 %.

Infinite Dilution Binary Diffusion Coefficients for Six Sugars at 0.1 MPa and Temperatures from (273.2 to 353.2) K

Infinite dilution binary diffusion coefficients D12 for arabinose, xylose, glucose, mannose, galactose, and sucrose in water were measured over the temperature range from (273.2 to 353.2) K at 0.1 MPa with the Taylor dispersion method. The values of D12/T were well correlated with water viscosity for each solute with average absolute deviation AAD < 1.7 %. The accuracies for various predictive correlations were also examined.

Simultaneous determination of binary diffusion coefficients from multiple response curves by chromatographic measurements

The chromatographic impulse response technique with a polymer coated capillary column was applied to measurements of infinite dilution binary diffusion coefficients D and retention factors k in supercritical carbon dioxide by injecting a hexane solution dissolving a mixture of three unsaturated fatty acids such as α-linolenic acid, eicosapentaenoic acid, and docosahexaenoic acid. The coefficients were simultaneously estimated by the curve fitting analysis even from partially overlapping response curves with the resolution of 0.8. The D and k values for each solute were able to be so obtained as accurately as those determined by individually injecting a single component solution. Almost no effect of the interaction among the components in the mixture was found from various approaching ways for curve fitting and the consecutive injection of the mixture at a certain interval.

Infinite Dilution Binary Diffusion Coefficients of Several α-Amino Acids in Water over a Temperature Range from (293.2 to 333.2) K with the Taylor Dispersion Technique

Infinite dilution binary diffusion coefficients (D12) were determined for 10 α-amino acids, glycine, alanine, α-amino-n-butyric acid, norvaline, valine, norleucine, leucine, isoleucine, alloisoleucine, and tert-leucine in water over a temperature range from (293.2 to 333.2) K with the Taylor dispersion technique. At 298.2 K, the literature data for the two α-amino acids alloisoleucine and tert-leucine are not available, whereas the determined D12 values of the others are in good agreement with the data reported previously within the experimental errors of ± 2.0 %. The D12 values for all α-amino acids studied were well-represented by two simple correlations, and the accuracies for the correlations were examined for each α-amino acid.

Binary diffusion coefficients and retention factors for γ-linolenic acid and its methyl and ethyl esters in supercritical carbon dioxide

Infinite dilution binary diffusion coefficients D 12 and retention factors k for γ-linolenic acid were measured by chromatographic impulse response technique in supercritical carbon dioxide over the ranges of temperature from 308 to 343 K and pressure from 9 to 30 MPa, together with those for the methyl and ethyl esters at 313 and 343 K and pressures from 8 to 16 MPa. In comparison with literature values for C18 free fatty acids and the esters, the differences in D 12 data were almost indiscernible for each isomer group: α- and γ-linolenic acid, oleic and elaidic acids, oleic and elaidic acid methyl esters, and their ethyl esters. The number of carbon double bonds did not affect the D 12 values significantly. Moreover, the differences in the values between free fatty acid and the ester forms were also small, whereas the D 12 values increased in order of acid to ethyl ester to methyl ester. The validities of the predictive correlations we had proposed such as the D 12/ T–CO 2 viscosity and the Schmidt number correlation were verified. The retention factor k values for the acid form were much higher than those for the methyl and ethyl esters. The k values were correlated with temperature and CO 2 density for each compound, and the solute partial molar volumes were determined from the k–CO 2 density correlation.

Binary Diffusion Coefficients and Retention Factors for Long-Chain Triglycerides in Supercritical Carbon Dioxide by the Chromatographic Impulse Response Method

Infinite dilution binary diffusion coefficients D12 and retention factors k have been measured in supercritical carbon dioxide for the long-chain triglyceride triarachidonin at 313.2 K at (10 to 30...

Effects of molecular weight and degree of unsaturation on binary diffusion coefficients for lipids in supercritical carbon dioxide

Infinite dilution binary diffusion coefficients and retention factors for the oleic acid family such as oleic acid, methyl- and ethyl esters, and mono-, di-, and triglycerides at 313.21 K and 8–30 MPa, and for other 13 lipids consisting of C18–C22 unsaturated fatty acid constituents at 313.21 K and 11 MPa were measured in carbon dioxide by a chromatographic impulse response method with a polymer coated capillary column. The binary diffusion coefficients and the retention factors for each compound decreased with increasing pressure. The binary diffusion coefficients could be represented by a Schmidt number correlation and by an empirical equation written in terms of temperature and CO 2 viscosity. The retention factors for each solute could be expressed in terms of CO 2 density. While the binary diffusion coefficients at 313.21 K and 11 MPa decreased with solute molecular weight, those for compounds having the same carbon numbers in each group, such as methyl ester, ethyl ester, and triglyceride, decreased with increasing the number of C–C double bonds.

Infinite dilution binary diffusion coefficients of benzene in carbon dioxide by the Taylor dispersion technique at temperatures from 308.15 to 328.15 K and pressures from 6 to 30 MPa

Infinite dilution binary diffusion coefficients, D12, of benzene in carbon dioxide were measured by the Taylor dispersion technique at temperatures from 308.15 to 328.15 K and pressures from 6 to 30 MPa. The diffusion coefficients were obtained by the method of fitting in the time domain from the response curves measured with a UV–vis multidetector by scanning from 220 to 280 nm at increments of 1 or 4 nm. The wavelength dependences on the binary diffusion coefficient and the uncertainty were examined. The detector linearity, in terms of the relationship between the absorbance intensity and the product of the peak area of the response curve and CO2 velocity, was found to fail at some characteristic absorption wavelengths such as 243, 248, 253, and 259 nm, even when the maximum absorbance intensities of the response curves were less than 0.5 and the fits were good. Although the D12 values obtained from the response curves measured at 253 nm were almost consistent with some literature data, the D12 values measured at wavelengths showing the detector linearity to be satisfactory, i.e., at 239 nm, were higher than those at 253 nm. The present D12 data at 239 nm were well represented by the Schmidt number correlation, except for those showing the anomalous decrease in a plot of D12 vs density in the density range from 250 to 500 kg·m−3.

Infinite-Dilution Binary Diffusion Coefficients of 2-Propanone, 2-Butanone, 2-Pentanone, and 3-Pentanone in CO2 by the Taylor Dispersion Technique from 308.15 to 328.15 K in the Pressure Range from 8 to 35 MPa

Infinite-dilution binary diffusion coefficients of 2-propanone, 2-butanone, 2-pentanone, and 3-pentanone in carbon dioxide were measured by the Taylor dispersion method at temperatures from 308.15 to 328.15 K and pressures from 7.60 to 34.57 MPa. The D 12 values were obtained from the response curves by the method of fitting in the time domain. The accuracy in the fitting error was examined for each measurement. The measured D 12 data were found to be well correlated by the Schmidt number correlation, with AAD%=3.74% for all solutes.

Infinite Dilution Binary Diffusion Coefficients of C5-Monoalcohols in Water in the Temperature Range from 273.2 K to 353.2 K at 0.1 MPa

Infinite dilution binary diffusion coefficients of C5-monoalcohols in water were measured by the Taylor dispersion method at 273.2 K to 353.2 K and 0.1 MPa. At each temperature it was found that the D12 values for the isomers increase with the boiling point of the pure alcohols. The D12 values were correlated with temperature, water viscosity, and solute boiling point. The accuracy in the correlation was superior to the various correlations reported in the literature.