Solubility of Binary and Ternary Systems Containing Vanillin and

Article pubs.acs.org/jced

Solubility of Binary and Ternary Systems Containing Vanillin and Vanillic Acid in Supercritical Carbon Dioxide Adrián Rojas-Á vila,†,‡ Alfredo Pimentel-Rodas,‡ Teresa Rosales-García,†,‡ Gloria Dávila-Ortiz,† and Luis A. Galicia-Luna*,‡ †

Laboratorio de Proteínas Vegetales, Escuela Nacional de Ciencias Biológicas-Instituto Politécnico Nacional, UPALM, Av. Wilfrido Massieu s/n, C.P.07738, Del. Gustavo A. Madero, Ciudad de México, México ‡ Laboratorio de Termodinámica, S.E.P.I.-E.S.I.Q.I.E. Instituto Politécnico Nacional, UPALM, Edif. Z, Secc. 6, 1ER piso Lindavista, C.P. 07738, México D. F., México ABSTRACT: Experimental solubility data of binary and ternary systems containing vanillin and vanillic acid in supercritical carbon dioxide were carried out in equipment based on the static-synthetic method. Compositions of dissolved solids were determined online via high-performance liquid chromatography with a diode array detector. The carbon dioxide + vanillin, carbon dioxide + vanillic acid, and carbon dioxide + vanillin + vanillic acid systems were studied at (315.00, 324.90, and 334.71) K, (314.91, 324.91, and 334.71) K, and (314.13, 323.67, and 333.17) K, respectively. For all systems the measurements were carried out at pressure range between 8.00 and 30.00 MPa. For binary systems the maximum solubilities were 5.215 × 10−3 and 2.911 × 10−5 in mole fraction for vanillin and vanillic acid, respectively. For ternary systems the maximum solubilities were 4.669 × 10−3 and 2.213 × 10−5 for vanillin and vanillic acid, respectively. The expanded uncertainties (k = 2) for the measured properties are estimated to be U(P) = 0.04 MPa, U(T) = 0.04 K, and Ur(y) = 0.0286 mole fraction. Méndez-Santiago and Teja, Bartle et al., Kumar and Johnston, and Chrastil models were used to correlate the experimental data. The results from the correlation confirmed the consistency of the reported data.

1. INTRODUCTION

A supercritical extraction process using a CO2-like solvent is an excellent alternative to extract this kind of compounds given its properties (not toxic, nonflammable, without environmental impact).10 Furthermore, CO2 supercritical properties are easy to reach (Tc = 304.13 K and Pc = 7.38 MPa) therefore it is suitable for processing thermo-labile compounds.13 Supercritical fluids have several advantages over organic solvents about physical properties and information about solubility (y) of solids in supercritical fluids is very important to be determined. Wells et al.14 have previously reported the solubility of vanillin in supercritical CO2 (SC−CO2) for two isotherms, 308.15 and 318.15 K, covering a pressure range from 8.35 to 19.10 MPa; Škerget et al.15 also reported isotherms at 313.20, 308.20, and 318.20 K covering a pressure range from 8.00 to 27.65 MPa. For vanillic acid, Murga et al.16 reported three isotherms (313.00, 323.00, and 333.00) K and a pressure range from 8.50 to 50.00 MPa. Stassi et al.17 measured solubilities at 313.00 and 328.00 K and pressure range between 9.00 and 25.00 MPa. Deviations between the data published by these authors were found, also the experimental uncertainties in these

Vanilla (Vanilla planifolia Andrews) has been valued and required because of flavor and aroma, and actually is considered the most widely used flavoring agent in the food, flavors, fragrances, and cosmetics industries.1 The aroma developed by cured vanilla pods is naturally very complex and more than a hundred volatile compounds are found and belong to various kinds of chemical groups.2−4 Vanillin and vanillic acid are compounds present in vanilla and participate in the global aroma composition which is developed from a natural fermentation process.5 Green vanilla pods are almost odorless. They develop a faint phenolic odor, unlike that of cured beans. During the process called “curing”, vanilla pods develop flavor as a consequence of enzymatic action.6−9 Most of the components that are involved in aroma composition are thermo-labile and volatile. The quality of the final extract depends on the purification and extraction methods of the vanilla extracts.10 Essentially, multistage lixiviation is the principal extraction method for vanilla oleoresin,11 or simple lixiviation at 353.00 K employing ethanol, but if the process lacks temperature control, degradation of vanilla and other aromatic compounds may happen and a decrease of quality in the extract is expected.12 © XXXX American Chemical Society

Received: April 19, 2016 Accepted: July 19, 2016

A

DOI: 10.1021/acs.jced.6b00322 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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two-position valve with a loop of 5 μL, a high performance liquid chromatograph (HPLC), a syringe pump and a temperature regulator (heating by air). Figure 1 shows the apparatus used in the measurements. Two sapphire windows are coupled to the visual high-pressure cell with the main objective to observe the phase equilibria. This cell can be operated up to 30.00 MPa. The temperature of the visual highpressure cell was regulated with a temperature regulator and measured by two platinum probes (Pt 100 Ω, Specitec) coupled to a digital display (Hart Scientific, Chub-E4). Platinum probes were calibrated against a 25 Ω reference probe (Rosemount, 162CE ± 0.005 K certified uncertainty) coupled to a precision thermometry bridge (Automatic Systems Laboratories, F300). In this work, after calibration of platinum resistance thermometers, a maximum deviation of ±0.009 K was obtained, while the expanded uncertainties with a level of confidence of 95% (k = 2) in temperature for both probes are 0.04 K.23 The system pressure was regulated by injection of CO2 using a syringe pump and recorded by a pressure transducer (Druck, PDCR 910-1756) connected to the top of the visual highpressure cell to a pressure indicator (DPI 145, Druck) with a resolution of ±1 × 10−7 MPa. The pressure transducer was calibrated against a dead-weight balance (Desgranges & Huot, model 5304) with a certified precision of the order of ±0.005% (full scale). For this work, after calibration of pressure transducer, a maximum deviation of the order of ±0.0074 MPa was obtained. The expanded uncertainty (k = 2) in pressure was obtained corresponding to an estimated maximum of the order of 0.04 MPa.23 With the aim to obtain and record the real-time data, an Electronic Acquisition Data (EAD) was programmed. The acquisition program was programmed in Agilent VEE PRO RELEASE 9.32 software. The EAD was used in all measurements. 2.3. Composition Determinations. The procedure to quantify the solid in the fluid phase consisted in performing high performance liquid chromatography methods with a previous calibration. The apparatus used in this work for composition analysis is integrated by a manual injector port with a loop of 5 μL, a degassing module, a quaternary pump, a precolumn of 7.5 mm × 4.6 mm (Grace, Alltima C18), a column of 250 mm × 4.6 mm (Grace, Alltima C18), both of particle size of 5 μm, and a diode array detector (DAD). The analytical method for the calibration and analysis of each solid

works are not reported. Since these systems are of interest in this work, the experimental solubilities and their experimental uncertainties were determined and reported in this research, allowing comparisons between the data obtained in this work and the literature previously mentioned. Furthermore, in order to study the behavior of vanillin and vanillic acid as a function of temperature and pressure in the determination of solubility in supercritical carbon dioxide, a ternary system consisting of the compounds mentioned before was performed. All measurements were carried out using a static-analytic apparatus with online sampling.18 The solubility data of binary and ternary systems were correlated with Méndez-Santiago and Teja,19 Bartle et al.,20 Kumar and Johnston,21 and Chrastil22 models over the entire experimental conditions.

2. EXPERIMENTAL METHOD 2.1. Materials. Carbon dioxide (CAS No. 124-38-9) with purity 99.995% was provided by Infra (México). Capsaicin (CAS No. 404-86-4) with purity 97.0%, vanillin (CAS No. 12133-5) with purity 99.0% and vanillic acid (CAS No. 121-34-6) with purity 98.0% were supplied from Sigma-Aldrich. Except for CO2, all compounds were carefully degassed by agitation under vacuum prior to injection into the system. Table 1 shows the source and purity of the compounds used in this work. The physical properties of vanillin, vanillic acid, and capsaicin are presented in Table 2. Table 1. Samples Information initial mass fraction puritya

purification method

Infra

0.99995

none

GCb

SigmaAldrich SigmaAldrich SigmaAldrich

0.97

none

HPLCc

0.99

none

HPLCc

0.98

none

HPLCc

name carbon dioxide capsaicin vanillin vanillic acid

source

analysis method

a

Provided by the manufacturer. bGas chromatography. cPerformance liquid chromatography.

2.2. Apparatus and Procedures. The equipment used in solubility determinations of solids in SC-CO2 is based on the static-analytic method. The main parts of this apparatus are a visual high-pressure cell with inner volume of 50 cm3, a six-port

Table 2. Physical Properties of Vanillin, Vanillic Acid and Capsaicina

a

Reference 26. B



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Figure 1. Experimental apparatus for measuring the solubility of solids in carbon dioxide: AB, air bath; EC, equilibrium cell; P, pressure transducer; SD, stirring device; SP, syringe pump; SPV, six-port valve; T1 and T2, platinum resistance thermometers; HPLC, high-pressure liquid chromatograph.

Table 3. HPLC Conditions for Calibration and Solubility Measurements compound

mobile phase

flow rate mL·min−1

% volume

capsaicin

acetonitrile/water

1

water + 0.1% trifluoroacetic acid (TFA) (A)/acetonitrile + 0.09% TFA (B)

1

70/30 gradient: at 0 min 5% (B) at 12 min 65% (B) at 14 min 90% (B) at 16 min 90% (B) at 16.01 min 5% (B) at 21 min 5% (B) atop at 21 min

vanillin

vanillic acid

wavelength nm

T/K

280

298.00

280

303.00

range (0−50 μg·mL−1) prepared gravimetrically in the laboratory. Two types of experimental uncertainties were associated with the composition measurements:23 (A) repeatability of the HPLC data, determined to be 0.0088 mole fraction; (B) uncertainty regarding the aforementioned calibration determined to be 0.0053 mole fraction. The relative expanded uncertainty (k = 2) for the composition (Ur(y)) measurements was estimated to be 0.0286 mole fraction.23

in the fluid phase depends on the studied system. The conditions of each HPLC method are given in Table 3. 2.4. Solubility Determinations. For all experimental determinations, 2 g of pure solid (capsaicin, vanillin and/or vanillic acid) was employed and placed inside of the visual highpressure cell. The experimental system (sampling circuit, solvent feeding system, and the visual high-pressure cell) was subjected to vacuum for 1 h. Then, the temperature was fixed (within the experimental uncertainty) using an air bath, and carbon dioxide was fed to the visual high-pressure cell using a syringe pump. Subsequently, the binary mixture (carbon dioxide + solid) was vigorously stirred with a magnetic bar located inside the cell. Prior to measurements and while the pressure and temperature were fixed (within the experimental uncertainty), the initial samples were used as purge because solid compositions are generally found either too low or not repeatable. After the desired temperature was reached for at least 5 h with the fluctuation less than ±0.01 K for more than 30 min, the pressure was recorded and the vapor composition was analyzed by HPLC. After equilibrium was reached, samples were sent online to the HPLC through the loop of 5 μL coupled to a six-port two-position valve. The sampling procedure was stopped when the solid solubility in the fluid phase showed repeatability within 1% for at least three consecutive samples. Those measurements were recorded, and the average is reported as the solubility. The relationship between the chromatographic peak areas and the mole fractions were determined based on six calibration points obtained using vanillin and vanillic acid with varying concentrations in the

3. RESULTS AND DISCUSSION 3.1. Binary Systems. The reliability of the equipment used in this work in order to determine solubility data of solids in supercritical carbon dioxide was validated by measuring the solubilities of capsaicin in SC-CO2 and then comparing with literature data.24,25 These measurements were performed at 313.15 and 323.15 K. The comparison between the experimental solubility data for CO2 + capsaicin system with the international literature24,25 is shown in Figure 2. According to the results of these measurements, the data obtained in this work are in good agreement with Elizalde-Solis and GaliciaLuna24 in both isotherms in the entire pressure range with a maximum deviation of 4.9% and with de la Fuente et al.25 at 313.00 K and up to 15.00 MPa with a maximum deviation of 6.01%. The highest deviations are found with de la Fuente et al.25 after 15.00 MPa (maximum deviation of 18.41%). This discrepancy could be ascribed to a systematic or experimental error which was not account for; however, the solubility data of de la Fuente et al. presents the highest deviations (≤15.00%) at 313 K and at high pressures. The experimental solubility data C



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Table 5. Experimental Solubilities of Vanillin in Supercritical Carbon Dioxidea T/K

P/MPa

vanillin y(103)

ρCO2/kg·m−3

315.00

8.61 10.56 14.97 20.43 23.81 30.81 8.10 10.15 15.10 20.24 25.29 30.36 10.28 14.84 19.17 25.54 30.10

0.063 1.015 1.994 2.996 3.318 3.783 0.090 0.563 2.010 3.426 4.358 4.784 2.075 2.642 3.342 4.787 5.215

334.95 632.13 766.32 834.32 862.78 907.36 218.38 374.84 686.73 777.14 828.57 865.77 297.61 581.30 699.05 784.25 823.84

324.90

Figure 2. Solubility of capsaicin in SC-CO2; (○) Elizalde-Solis and Galicia-Luna24 at 312.86 K; (△) Elizalde-Solis and Galicia-Luna24 at 322.91 K; (■) de la Fuente et al.25 at 313.00 K; (●) this work at 313.15 K; (▲) this work at 323.15 K.

334.71

Table 4. Experimental Mole Fraction Solubilities of Capsaicin in Supercritical Carbon Dioxidea

a

T/K

P/MPa

capsaicin y(10 )

313.15

10.78 12.56 15.08 17.53 20.02 25.09 30.09 10.76 12.50 15.10 17.53 20.02 25.09 30.09

5.74 7.82 9.95 12.77 17.84 21.54 25.75 5.92 8.05 13.08 16.95 21.23 25.70 29.10

323.15

Expanded uncertainties (k = 2) for the measured properties are estimated to be U(P) = 0.04 MPa, U(T) = 0.04 K, and Ur(y) = 0.0286 mole fraction. ρCO2 is the density of pure CO2 from the correlation of ref 27.

5

Table 6. Experimental Solubilities of Vanillic Acid in Supercritical Carbon Dioxidea T/K

P/MPa

vanillic acid y(107)

ρCO2/kg·m−3

314.91

8.57 10.56 14.67 20.25 23.81 30.81 8.42 9.63 15.10 20.24 30.36 8.41 10.28 14.84 19.17 25.54 30.10

9.601 23.457 68.072 112.293 129.076 145.056 21.912 40.919 101.924 148.740 202.763 3.538 72.291 162.161 197.486 259.998 291.108

328.56 632.13 760.92 832.53 862.78 907.36 236.08 323.81 686.73 777.14 865.77 204.45 297.61 581.30 699.05 784.09 823.84

324.91

a

Expanded uncertainties (k = 2) for the measured properties are estimated to be U(P) = 0.04 MPa, U(T) = 0.04 K, and Ur(y) = 0.0286 mole fraction. 334.71

for capsaicin in SC-CO2 are given in Table 4. Once the method was validated, the systems containing SC-CO2, vanillin, and vanillic acid were measured. The solubilities of vanillin and vanillic acid in carbon dioxide were measured at 315.00, 324.90, and 334.71 K for vanillin and 314.91, 324.91, and 334.71 K for vanillic acid. The pressure range was 8−30 MPa for each isotherm in both systems. The solubility of the vanillin and vanillic acid was measured based on the mole fraction (y), of the solute in supercritical CO2. Tables 5 and 6 show the experimental results for CO2 + vanillin and CO2 + vanillic acid systems, respectively. Over the entire experimental conditions, the mole fraction of vanillin and vanillic acid are in range of (6.300 × 10−5 to 5.215 × 10−3) and (3.538 × 10−7 to 2.911 × 10−5), respectively. Figure 3 shows the comparison between the solubility data for CO2 + vanillin system from the international literature14,15 with the experimental solubilities obtained in this work. According to the results of these measurements, the data obtained in this work are in good agreement with Wells et al.14 at 308.15 K at all pressures in the range and with Škerget et al.15 at 313.20 K and up to 14.00 MPa. Deviations are found with Škerget et al.15

a

Expanded uncertainties (k = 2) for the measured properties are estimated to be U(P) = 0.04 MPa, U(T) = 0.04 K, and Ur(y) = 0.0286 mole fraction. ρCO2 is the density of pure CO2.27

after 14.00 MPa, perhaps due to the difference between experimental methods; however, the trend of the data of this study is in good agreement with Wells et al.14 It is worth mentioning, there is a small difference between the experimental temperature of this work and the references temperatures. Figure 4 shows the comparison between the solubility data for CO2 + vanillic acid system from the international literature16,17 with the experimental solubilities obtained in this work. According to the results, the solubility data obtained in this work are in good agreement with the international literature considering that there are differences D



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Figure 5. New experimental data for the systems: (●) SC-CO2 + vanillin at 315.00 K; (▲) SC-CO2 + vanillic acid at 314.9 K; (○) vanillin in ternary system (SC-CO2 + vanillin + vanillic acid) at 314.13 K; (△) vanillic acid in ternary system (SC-CO2 + vanillin + vanillic acid) at 314.13 K.

Figure 3. Solubility of vanillin in SC-CO2: (■) Wells et al.14 at 308.15 K; (●) Škerget et al.15 at 313.2 K; (▲) this work at 315.00 K.

Figure 4. Solubility of vanillic acid in SC-CO2: (●) Murga et al.16 at 313.00 K; (■) Stassi et al.17 at 313.00 K; (▲) this work at 314.91 K. Figure 6. Comparison of the correlated results from the MendezSantiago and Teja19 model with the experimental data for the binary systems: (●) SC-CO2 + vanillin and (▲) SC-CO2 + vanillic acid; (○) vanillin in ternary system (SC-CO2 + vanillin + vanillic acid) and (△) vanillic acid in ternary system (SC-CO2 + vanillin + vanillic acid). The solid line represents the calculated data using the MST model for all temperatures and up to 30 MPa.

Table 7. Acid in Supercritical Carbon DioxideExperimental Solubilities of Vanillin and Vanillic in a Ternary Systema T/K

P/MPa

vanillic acid y2(107)

vanillin y3(103)

ρCO2/kg · m−3

314.13

9.51 11.23 14.61 19.99 23.99 28.77 10.06 15.27 19.98 24.80 29.99 10.69 12.74 19.53 23.82 29.63

8.282 8.495 9.344 1.255 20.079 25.567 4.217 19.350 40.792 68.655 86.693 6.460 39.796 132.138 180.137 221.307

0.187 0.246 0.308 0.674 1.113 1.349 0.172 0.506 0.940 1.794 2.230 0.303 0.511 3.076 4.046 4.669

550.80 679.63 766.65 834.56 867.98 899.13 382.82 701.76 781.10 830.08 868.28 335.44 488.37 715.97 774.05 826.86

323.67

333.17

From the data given in Tables 5 and 6 it can be observed that for all temperatures an increase in pressure causes an increment in solubility of vanillin and vanillic acid in SC-CO2. This can be explained as being due to the increment on SC-CO2 density by effect of an increment in pressure at fixed temperature. This density enhancement is due to a lower intermolecular distance which causes a higher solubility strength. Consequently, if the system pressure increases, the solubility of vanilla and vanillic acid increases. This effect is more significant at higher temperatures. Under the same conditions of temperature and pressure, vanillin shows higher solubility than vanillic acid. This behavior can be explained since both compounds contain hydroxyl and methoxy functional groups in an adjacent position, which cannot form an intramolecular hydrogen bond between the two substituents.15 For this reason, the solubility of the compounds is not affected by these interactions. However, both compounds contain a third functional group, aldehyde for vanillin and

a

Expanded uncertainties (k = 2) for the measured properties are estimated to be U(P) = 0.04 MPa, U(T) = 0.04 K, and Ur(y2) = Ur(y3) = 0.0286 mole fraction. ρCO2 is the density of pure CO2.27

between the experimental temperature reported in this work and that reported in the international literature. E



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Figure 7. Comparison of the correlated results from the Bartle et al.20 model with the experimental data for the binary systems: (●) SC-CO2 + vanillin and (▲) SC-CO2 + vanillic acid; (○) vanillin in ternary system (SC-CO2 + vanillin + vanillic acid) and (△) vanillic acid in ternary system (SC-CO2 + vanillin + vanillic acid). The solid line represents the calculated data using the Bartle et al.20 model for all temperatures and up to 30 MPa.

Figure 9. Comparison of the correlated results from the Chrastil22 model with the experimental data for the binary systems: (●) SC− CO2 + vanillin and (▲) SC−CO2 + vanillic acid; (○) vanillin in ternary system (SC−CO2 + vanillin + vanillic acid) and (△) vanillic acid in ternary system (SC−CO2 + vanillin + vanillic acid). The solid line represents the calculated data using the Chrastil22 model for all temperatures and up to 30 MPa.

in SC-CO2, which causes a decrease in the solubility of both compounds compared with solubility in binary systems. Figure 5 shows experimental solubility data of ternary systems compared with binary systems. 3.3. Correlation of Experimental Solubility Data. In this work the experimental solubilities data of vanillin and vanillic acid in binary and ternary systems were correlated by four density-based semiempirical models proposed by MéndezSantiago and Teja,19 Bartle et al.,20 Kumar and Johnston,21 and Chrastil.22 These models were developed from theory of dilute solutions, which involves the expansion of the Helmholtz energy around the solvent critical point in order to describe properties of infinite dilute solutions. The equation proposed by Mendez-Santiago and Teja (MST)19 was the first one tested. This equation was derived considering a classical expansion of the Helmholtz energy near the critical point of solvent to represent the mixture properties at infinite dilution. It is considered a correlation with three fitting parameters with the assist of a Clausius−Clapeyron expression for the sublimation pressure. The consistency of the reported data are considered as well, if all isotherms collapse to a single straight line on a graph of the left-hand side of the equation versus the density of the solvent. For details about this model the reader is referred to the original literature source.19 With the aim to represent and/or modeling the experimental results, the measured solubilities data were used to fit parameters of the Mendez-Santiago and the Teja and Chrastil models. Comparison of the correlated results from the MST model with experimental values for the systems CO2 + vanillin, CO2 + vanillic acid and CO2 + vanillin + vanillic acid are presented in Figure 6. Since all isotherms, for each system performed, collapse to a single straight line on a graph of the left-hand side of the equation versus the density of the solvent, we considered that the experimental solubility data have a good consistency, with a maximum absolute average relative deviation (AARD) of 4.64%.

Figure 8. Comparison of the correlated results from the Kumar and Johnston21 model with the experimental data for the binary systems: (●) SC-CO2 + vanillin (▲) SC−CO2 + vanillic acid; (○) vanillin in ternary system (SC-CO2 + vanillin + vanillic acid) and (△) vanillic acid in ternary system (SC−CO2 + vanillin + vanillic acid). The solid line represents the calculated data using the Kumar and Johnston21 model for all temperatures and up to 30 MPa.

carboxyl for vanillic acid. Therefore, the aldehyde group of vanillin interacts with SC-CO2, providing more solubilization power than provided by the carboxyl group present in the vanillic acid. 3.2. Ternary System. The solubility data for the ternary systems, containing CO2, vanillin and vanillic acid, were determined at the same pressure and temperature adopted for the binary systems. For ternary systems solubility determination, 1 g of each pure solid (vanillin and vanillic acid) was placed in the equilibrium cell to ensure a sufficient amount of these components. Experimental solubility data for the ternary systems are listed in Table 7. Just as mentioned in the binary systems, vanillin has greater solubility than the vanillic acid. However, because there are two compounds in the ternary system, competition between them exists to solubilize F



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Table 8. Correlation Parameters for Experimental Solubility Data of Vanillin and Vanillic Acid in SC-CO2 in Binary and Ternary Systems and AARD of Different Modelsa correlation parameters name

equation

solute vanillin

MST

T ln(y2 P) = a0 + a1ρ + a 2T vanillic acid

Bartle

Kumar and Johnston

Chrastil a

vanillin

⎛ y P⎞ a ln⎜ 2 ⎟ = a0 + a1(ρ − ρref ) + 2 T ⎝ Pref ⎠

ln y2 = a0 + a1ρ +

vanillic acid vanillin

a2 T

ln y2 = a0 + a1 ln ρ +

vanillic acid vanillin

a2 T

ρ is the density of pure CO2 obtained from the reference.

vanillic acid

system

a0

binary ternary binary ternary binary ternary binary ternary binary ternary binary ternary binary ternary binary ternary

−2402.520 −3020.870 −3696.790 −3087.000 −3.953 −3.747 −3.194 −5.262 −9.947 −17.469 −9.735 −17.546 0.999 5.727 1.964 −2.176

2.190 2.418 1.539 1.418 6.747 7.436 4.728 4.361 4.866 5.146 2.802 2.070 3.613 4.244 2.747 4.450

a1

a2

AARD%

× × × × × × × ×

1.661 2.258 −0.333 −2.183 −950.562 −1332.360 −2693.450 −2071.360 854.230 826.660 1149.380 87.741 −7423.310 −10573.900 −7583.530 −10327.300

3.472 4.640 3.649 2.892 3.030 3.898 3.013 2.409 2.348 3.457 2.447 2.432 2.759 4.568 2.909 3.464

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

27

The second model used was that proposed by Bartle et al.20 This model takes a correlation of the so-called enhancement factor and fits it to a function of density. However, vapor pressures, needed to calculate the enhancement factor, are not known for many compounds, particularly the solids. Therefore, the first approach was based on a reference pressure and density. Finally, Bartle et al. modified this equation using a reference density. For details about this model the reader is referred to the original literature source.20 The resulting modeling data (binary and ternary systems) using the Bartle et al. model are show in Figure 7. Through the correlation results it can be seen that the model is in good agreement with the experimental data with a maximum AARD of 3.90%. The Kumar and Johnston21 model was the third equation used. In this model, it is considered that the chemical potential of the solute is the same in the condensed and supercritical phases. In the first instance, the chemical potential is referred to in terms of fugacities. Kumar and Johnston reformulated the expression in terms of the density of the supercritical fluid as an independent variable. For details about this model the reader is referred to the original literature source.21 The experimental data and correlating data results (binary and ternary systems) using the Kumar and Johnston model are shown in Figure 8. The correlation results show that the model is in good agreement with the experimental data with a maximum AARD of 3.46%. The last density-based model tested was the one proposed by Chrastil,22 which was developed on the basis of the solute with solvent complex formation in the gas phase. The Chrastil model is linear in a log−log graph of solubility versus density. For details about this model the reader is referred to the original literature source.22 Comparison of the correlated results from the Chrastil model with experimental values for the systems CO2 + vanillin, CO2 + vanillic acid, and CO2 + vanillin + vanillic acid are shown in Figure 9. According to the correlation results, it can be seen that the model used has a good agreement with the data obtained in this work with a maximum AARD of 4.57%. The absolute average relative deviation AARD (%) was calculated as follows:

AARD(%) =

100 N

N

∑ i=1

y exp − y cal y exp

(1)

where N is the number of data points, yexp is the experimental solubility, ycal is the solubility obtained from the correlation. The optimal parameters and the AARD(%) from the semiempirical models proposed by Méndez-Santiago and Teja,19 Bartle et al.,20 Kumar and Johnston,21 and Chrastil22 using the experimental data of this work (over the entire range of pressure and temperature) are reported in Table 8.

■

CONCLUSIONS The solubility data of the vanillin and vanillic acid in supercritical carbon dioxide at temperature and pressure range of 308.15 to 338.15 K and 16.00 to 30.00 MPa, respectively, were experimentally determined using a staticanalytic method. The obtained results in this work show that vanillin and vanillic acid have solubility in carbon dioxide (binary mixture) over the mole fraction range of (6.300 × 10−5 to 5.215 × 10−3) and (9.601 × 10−7 to 2.911 × 10−5), respectively. For ternary mixtures as it was expected, the solubilities of both compounds are smaller than that obtained in binary systems; however, the solubility of vanillin is still greater than that of vanillic acid. For all systems measured, the reported solubilities data show that an increase in the pressure leads to an increase in the solubilities with a higher impact of pressure on the solubility enhancement at the higher temperatures. The correlation results show that the calculated data from the models used have a good agreement with the experimental data obtained in this work with a maximum absolute average relative deviation (AARD) of 4.64% obtained from the MST model. The minimum AARD was 3.46% obtained from the Kumar and Johnston model. The results of this study are useful to help determine the optimal conditions for performing vanilla extractions by using supercritical fluid extraction. G



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AUTHOR INFORMATION

Corresponding Author

*Tel.: +52 55 5729 6000 ext. 55133. Fax: +52 55 5586-2728. Email: [email protected]. Funding

The authors would like to thank the Instituto Politécnico Nacional and CONACyT for the financial support of this research. Notes

The authors declare no competing financial interest.

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REFERENCES

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Solubility of Binary and Ternary Systems Containing Vanillin and

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