Article pubs.acs.org/jced
Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Thermodynamic Modeling of Triglycerides using PC-SAFT Joscha Brinkmann,† Christian Luebbert,† Dzmitry H. Zaitsau,‡ Sergey P. Verevkin,‡,§ and Gabriele Sadowski*,† †
Laboratory of Thermodynamics, TU Dortmund University, Emil-Figge-Strasse 70, D-44227 Dortmund, Germany Department of Physical Chemistry, University of Rostock, 18059, Rostock, Germany § Chemical Department, Samara State Technical University, 443100, Samara, Russia ‡
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S Supporting Information *
ABSTRACT: Vapor pressures for the saturated triglycerides (TGs) tricaprylin, tricaprin, and liquid densities of tricaprylin were experimentally determined. TG purecomponent parameters for the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) were fitted to that data and validated with densities of the binary mixtures octanol/tricaprin and octanol/trilaurin at different temperatures and TG mass fractions. Furthermore, pure-component parameters of the unsaturated TGs triolein and trilinolein were estimated by a group-contribution method. Correctly predicted solid−liquid equilibria of mixtures containing the before-mentioned TGs revealed that intermolecular interactions among TGs are quantitatively described by PC-SAFT.
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pure-component parameters are preferably fitted to purecomponent properties (i.e., vapor pressures and densities. The obtained pure-component parameters were used to predict binary solid−liquid equilibria of TG mixtures. As TGs exist in numerous different conformations, sidechain lengths, and degrees of saturation, we will in this work use a TG nomenclature, which is schematically presented in Figure 1. The TG molecule depicted in Figure 1 contains three hydrocarbon side chains with 10, 12, and 16 carbon atoms. The subscripts represent the number of double bonds in a side chain. The C12 side chain in Figure 1 has one double bond and is thus named 121, the C16 chain has two double bonds and is thus named 162, and the C10 chain is completely saturated (100). The TGs considered in this work are TG808080 (tricaprylin), TG100100100 (tricaprin), TG120120120 (trilaurin), TG140140140 (trimyristin), TG160160160 (tripalmitin), TG180 180 180 (tristearin), TG181181 181 (triolein), and TG182182182 (trilinolein).
INTRODUCTION Triglycerides (TGs) are the main components of fats and oils and possess many applications in the food industry, chemical industry, and pharmaceutical industry. TGs are a highly relevant renewable energy resource, for example, for biodiesel production and moreover are also used for pharmaceutical formulations.1−3 Vapor pressures and liquid densities of TGs are only rarely reported in literature.4,5 This is mainly because their vapor pressures are very low and usually can hardly be determined. Because of the lack of thermo-physical data, so far usually fragment-based approaches were applied to predict TG purecomponent thermodynamic properties relevant for biodiesel production.6,7 These approaches split each TG into four fragments (a glycerol backbone and three fatty acids). Fragment parameters are obtained from fitting to properties of a few TGs for predicting thermo-physical data of the other TGs. Some studies also used group-contribution methods (GCM) to predict the phase behavior of glycerides relevant for biodiesel production.8 Also, the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) turned out to be an appropriative tool for describing phase equilibria of TGs and hydrocarbons.9−12 Thus, PC-SAFT parameters for triolein and a few saturated TGs have been estimated based on different GCMs.9,10,12 However, due to the lack of experimental purecomponent data, neither these parameters nor the obtained modeling results were so far validated for simultaneously describing TG vapor pressures and liquid densities or modeling solid−liquid equilibria of TG systems. In this work, TG vapor pressures and liquid densities were measured and compared to results from literature. PC-SAFT © XXXX American Chemical Society
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MATERIALS AND METHODS Materials. TG808080, TG180180180, and octanol were purchased from Sigma-Aldrich (Steinheim, Germany) with purity greater than 99%. TG100100100 and TG120120120 with a minimal purity better than 98% were obtained from abcr GmbH (Karlsruhe, Germany). Received: November 7, 2018 Accepted: February 25, 2019
A
DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 1. Schematic explanation of the TG abbreviations in this work.
latter is not considered in this work. PC-SAFT considers a molecule as a chain of spherical segments. The three PC-SAFT parameters required to describe TGs are the segment number mseg, the segment diameter σseg, and the dispersion-energy parameter ui/kB and are usually determined by fitting to vaporpressure and liquid-density data.16 The solubility of a crystalline substance (i) in a solvent is calculated using eq 2. The mole-fraction solubility xi of substance i at temperature T is determined using its activity coefficient γi in the liquid phase (calculated via PC-SAFT), and its melting properties (melting temperature TSL oi and melting −1 enthalpy ΔhSL oi ). R is the ideal gas constant (8.314 J mol −1 17 K ). ÅÄÅ ÑÉ ÅÅ Δh0SLi ji 1 T zyzÑÑÑÑ j Å j1 − SL zzÑÑ xi = expÅÅ− ÅÅ RT jj γi T0i z{ÑÑÑÖ (2) k ÅÇ
Table 1 summarizes the commercial sources and purities of all substances used in this work. Table 1. Supplier, CAS Numbers, and Purity of All Utilized Substances Used in This Work component
CAS
source
mass purity
TG808080 TG100100100 TG120120120 TG180180180 octanol
538−23−8 621−71−6 538−24−9 555−43−1 111−87−5
Sigma-Aldrich abcr GmbH abcr GmbH Sigma-Aldrich Sigma-Aldrich
>99% >98% >98% >99% >99%
Experimental Methods. Liquid-density data were obtained using a DMA 4200 M vibrating-tube density meter by Anton Paar Inc. (Saint Laurent, Canada). The pressure in the density meter was adjusted using a manual spindle press by SITEC-Sieber Engineering AG (Zurich, Switzerland) with a relative uncertainty for the pressure of 1% and a relative standard uncertainty of 0.2% for the density. The apparatus was calibrated with water and air. Vapor-pressure data on TG808080 were measured with using the well-established transpiration method.13 In this measurement, a sample is placed in a U-tube being overflown with a constant nitrogen stream at constant temperature. Molecules transported by the nitrogen stream are collected and quantified in a cooling trap. Vapor pressures of TG100100100 were measured applying the quartz-crystal microbalance (QCM) method,14 which was recently developed for studying substances with extremely low vapor pressures. The sample is inserted into an open cavity of a metal block and sealed with the QCM. The changes in quartz-crystal vibrational frequency in the microbalance directly correlate with the mass loss of the sample under vacuum conditions. These measurements can be supported by thermogravimetric analysis.15 PC-SAFT Modeling. PC-SAFT is a model for calculating the residual Helmholtz energy ares, which then allows calculating vapor pressures (pLV), liquid densities (ρ), and activity coefficients (γi). According to PC-SAFT, ares is calculated as the sum of different contributions, which consider different kinds of interactions between molecules as given in eq 1. a res = a hc + adisp + aassoc
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RESULTS Experimental Pure-Component Data of TG808080, TG100100100, and TG120120120. Table 2 contains the measured liquid densities for TG808080. The liquid density for TG808080 at 1 bar decreases with increasing temperature almost linearly from 952.7 kg m−3 at 293.15 K to 907.7 kg m−3 at 353.15 K. The liquid density of Table 2. Experimental Liquid Densities (ρ) and Standard Uncertainties (u) for TG808080 at Different Temperatures (T) and Pressures (p) as Well as the Relative Deviation (RD) of PC-SAFT Calculations Using the Parameters from Table 7a
(1) hc
These contributions are in particular a , which represents the repulsive interactions between molecules, adisp, which accounts for dispersive van der Waals attractions, and aassoc, which describes formation of H-bonds via association. The
a
B
T [K]
p [bar]
u(p) [bar]
ρ [kg m−3]
RD [%]
293.15 298.15 303.15 313.15 333.15 353.15 298.15 298.15 298.15 298.15 298.15 298.15
1.02 1.02 1.02 1.02 1.02 1.02 1.20 98.3 201.0 300.2 400.5 500.4
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.98 2.01 3.00 4.01 5.00
952.7 948.9 944.9 937.4 922.5 907.7 949.9 955.5 961.3 966.6 971.9 977.1
0.63 0.66 0.66 0.71 0.76 0.75 0.44 0.10 0.56 0.98 1.36 1.70
u(T) = 0.03 K; ur(ρ) = 0.002. DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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TG808080 at 298.15 K increases with pressure from 948.9 kg m−3 at 1 bar to 977.1 kg m−3 at 500.4 bar. TG100100100 and TG120120120 are crystalline at ambient conditions and thus, their liquid density could not be determined directly. In order to circumvent this limitation, the densities of TG/octanol mixtures with increasing TG contents were determined and extrapolated to the hypothetical value for the pure TGs. Tables 3 and 4 list the experimental Table 3. Densities (ρ) and Standard Uncertainties (u) for Octanol Solutions of TG100100100 at Different TG Mass Fractions (wTG) and Temperatures (T) as well as Extrapolated (wTG = 1) Pure-TG Densities at Ambient Pressure (p)a
Figure 2. Experimental mixture densities for TG100100100 in octanol (white symbols) at different TG mass fractions as well as extrapolated densities of pure TG100100100 (gray symbols). Mixture densities were determined experimentally at 20 °C (circles), 25 °C (squares), 30 °C (triangles), 40 °C (stars), 60 °C (diamonds), and 80 °C (pentagons).
TG100100100/octanol wTG [gTG g−1 total] T [K]
p [bar]
293.15 298.15 303.15 313.15 333.15 353.15
1.02 1.02 1.02 1.02 1.02 1.02
0.016
0.0385
0.0772
0.1287
1.0000
ρ [kg m−3] 826.5 823.1 819.5 812.6 798.6 783.8
828.7 825.1 821.6 814.7 800.7 785.9
832.5 829.0 825.4 818.5 804.3 789.5
837.4 833.9 830.3 823.3 809.1 794.4
and were found in perfect agreement with data from literature (821.57 kg m−3 at 298.15 K, the overall ARD was 0.03%).18 Vapor-pressure data measured for TG808080 in this work are given in Table 5 together with the experimental uncertainties. The evaluation of the single vapor pressure measurements can be found in the Supporting Information of this work.
921.6 917.9 913.6 906.2 891.0 875.9
a
u(w) = 0.0001; u(p) = 0.01 bar; u(T) = 0.03 K; ur(ρ) = 0.002.
Table 5. Experimental Vapor Pressures (pLV) and Uncertainties (u) for TG808080 at Different Temperatures (T) as Well as Relative Deviations (RD) of PC-SAFT Calculations Using the Parameters from Table 7a
Table 4. Densities (ρ) and Standard Uncertainties (u) for Octanol Solutions of TG120120120 at Different TG Mass Fractions (wTG) and Temperatures (T) as Well as Extrapolated (wTG = 1) Pure-TG Densities at Ambient Pressure (p)a TG120120120/octanol wTG[gTG g−1 total] T [K]
p [bar]
293.15 298.15 303.15 313.15 333.15 353.15
1.02 1.02 1.02 1.02 1.02 1.02
0.019
0.051
0.096
0.149
1.000
ρ [kg m−3] 826.7 823.3 819.7 812.8 798.7 784.0
829.5 826.2 822.5 815.6 801.5 786.8
826.8 819.7 805.6 790.9
831.0 824.0 809.9 795.2
a
905.1 899.6 886.9 870.4
T [K]
105·pLV [bar]
u(105·pLV) [bar]
RD [%]
403.2 408.2 413.2 423.2 433.2 443.2 448.2
0.207 0.313 0.470 1.006 1.977 4.026 5.491
0.01 0.01 0.01 0.03 0.06 0.12 0.16
1.81 1.70 1.88 0.97 4.12 1.59 3.10
u(T) = 0.1 K.
As can be seen from Table 5, the vapor pressures increase exponentially from 2.07 × 10−6 bar at 403.2 K to 5.491 × 10−5 bar at 448.2 K. Further Table 6 lists all measured vapor pressures of TG100100100 determined in this work and their uncertainties together with the corresponding modeled ones as well as the
a
u(w) = 0.0001; u(p) = 0.01 bar; u(T) = 0.03 K; ur(ρ) = 0.002.
values for the liquid densities of TG10 0 10 0 10 0 and TG120120120 solutions in octanol as well as the extrapolated values for the pure TGs. The densities estimated by this extrapolation below the melting temperatures of the pure TGs are the densities of the subcooled liquid TGs. For TG100100100 and TG120120120, the TG mass fraction in octanol was limited to wTG = 0.15 gTG g‑1 total to prevent TG precipitation in the density meter. The liquid densities of TG10 0 10 0 10 0 /octanol and TG120120120/octanol mixtures show a perfectly linear trend with increasing amount of TG (shown for TG100100100/ octanol in Figure 2) and are thus assumed to be linear in the entire composition range. Accordingly, the extrapolated densities reach their maximum for the pure TGs. Furthermore, the liquid densities decrease with increasing temperature. Densities of TG100100100/octanol solutions were extrapolated to the values of pure octanol (e.g., 821.51 kg m−3 at 298.15 K)
Table 6. Comparison of the Experimental and PC-SAFT Predicted Vapor Pressures (pLV) of TG100100100 with Their Standard Uncertainties (u) and Their Relative Deviation (RD) from PC-SAFT Modeling at Different Temperatures (T)a T [K] 348.5 353.5 358.4 363.2 367.8
a
C
pLV exp [bar] 1.4 2.9 6.0 1.2 2.3
× × × × ×
−10
10 10−10 10−10 10−9 10−9
u(pLV exp) [bar] 9.80 2.03 4.20 8.40 1.61
× × × × ×
−12
10 10−11 10−11 10−11 10−10
pLV PC‑SAFT [bar] −10
1.5 × 10 2.9 × 10−10 5.8 × 10−10 1.1 × 10−9 2.0 × 10−9 ARD [%]
RD [%] 7.57 0.00 2.90 8.81 12.99 6.45
u(T) = 0.02 K. DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 7. PC-SAFT Pure-Component Parametersa component
M [g mol−1]
mseg [-]
σseg [Å]
u kB−1 [K]
ARD pLV [%]
ARD ρ [%]
TG808080 TG100100100 TG120120120 TG140140140 TG160160160 TG180180180 TG181181181 TG182182182
470.69 554.86 639.02 723.16 807.32 891.48 885.43 879.41
9.482 11.283 13.282 15.169 16.952 18.406 23.383 22.607
4.24 4.26 4.24 4.24 4.25 4.27 3.89 3.86
281.62 277.89 272.86 271.46 269.39 266.44 239.04 228.59
2.17 2.79 1.06 3.75 0.51 2.47
0.78 0.99 0.43 0.25 0.18 0.33
Segment number (mseg), segment diameter (σseg), dispersion-energy parameter (u kB−1), and averaged relative deviations (ARD) to experimental data for the TGs considered in this work as well as molar mass (M). a
Figure 3. PC-SAFT pure-component parameters for the homologous series of even, saturated TGs from TG808080 to TG180180180. Symbols represent different PC-SAFT parameters. (a) Dispersion energy u kB−1. (b) Segment diameter σseg.
pure-component parameters of TGs and is therefore appropriate for modeling TGs in this work. Table 7 summarizes the PC-SAFT pure-component parameters estimated in this work together with the deviation of PC-SAFT calculated vapor pressures and liquid densities from the experimental data. ARD values for the unsaturated TGs are not listed due to the lack of experimental data. The PC-SAFT vapor-pressure calculation for TG808080, satisfactorly fits the experimental data: the ARD of 2.17% lies in the same order of magnitude as the uncertainty of the experimental data which is 1−3%.13 Further, the maximum relative deviation (MRD) between the liquid densities of TG808080 from Table 2 and PC-SAFT calculations is 1.70% at 500.4 bar and 298.15 K. The RDs exceed values of 1% only at pressures above 300 bar and are smallest for small pressures and temperatures of 298.15 K. These small deviations indicate the agreement of experimental data with the PC-SAFT modeling proving that the estimated PC-SAFT parameters are appropiate for describing the physicochemical purecomponent properties of TG808080. Deviations for the other saturated TGs are highest for the vapor-pressure data of TG140140140 (3.75%) and for the density data of TG100100100 (0.99%). Thus, it is found that for all components of the TG series, the maximum ARD for both, densities and vapor pressures, does not exceed 4%, which shows the high agreement between calculations and experiments. The vapor-pressure ARD always exceeds the ARD for the liquid density, which can be explained by the extremely low vapor pressures. Further, Table 7 indicates a reasonable trend for the coarsegrained parameters of the homologous series of saturated TGs also known from earlier works:20 the parameter mseg increases linearly with increasing molecular mass from 9.482 to 18.406,
RD values between experiments and the calculations. Moreover, it lists the relative deviations RD (RD = (ycalc − yexp) × y−1 exp) between experimental data and the PCSAFT calculation, which will be discussed later. The evaluation of the single vapor-pressure measurements can be found in the Supporting Information of this work. The experimental vapor pressures of TG100100100 were found to increase from 1.4 × 10−10 bar at 348.5 K to 2.3 × 10−9 bar at 367.8 K. PC-SAFT Modeling of TG Pure-Component Properties. The PC-SAFT pure-component parameters for TG100100100, TG120120120, TG140140140, TG160160160, and TG180180180 were simultaneously fitted to vapor-pressure and liquid-density data from literature.4,5 In case of TG808080, the PC-SAFT parameters were fitted to experimental vapor pressures and liquid densities from this work. Fitting was conducted by minimizing the average relative deviation (ARD) for all data points, calculated by using eq 3 ARD =
100 N
N
∑ j=1
|ycalc − yexp | yexp
(3)
In this equation, ycalc is the calculated value (vapor pressure or liquid density), while yexp denotes the experimental one. The pure-component PC-SAFT parameters for TG181181181 and TG182182182 were estimated using a GCM,19 which was originally proposed to describe thermophysical properties of polymer molecules. It only refers to the number and type of chemical groups. Using this approach enables a direct calculation of mseg, σseg, and u kB−1 from the TGs’ molecular structure. The method was originally developed to describe densities of polymers as polyacrylates or polyolefins. It comprises all necessary group contributions to estimate the D
DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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the value for σseg remains almost constant at values between 4.24 and 4.27 Å and u kB−1 decreases linearly over the entire TG series from 281.62 to 266.44 K (Figure 3). A decreasing value for u kB−1 might be interpreted as the decreasing influence of the three ester groups with increasing carbonchain length. Considering the trends shown in Figure 3, PCSAFT parameters for other TGs can now be estimated a-priori by interpolating the values of mseg and u kB−1, and averaging σseg. This also enables estimating the phase behavior of TGs with uneven fatty acids, for which no vapor-pressure or liquiddensity data are available. Figure 4 illustrates the comparison of modeled and experimental vapor-pressure data for TG808080 (obtained in this work) as well as for the other TGs obtained from literature.
Figure 5. Liquid-density data for the homologous series of saturated TGs at 1 bar. Symbols stand for the experimental density data (circles, TG808080; squares, TG100100100; triangles, TG120120120; stars, TG140140140; diamonds, TG160160160; pentagons:, TG180180180). Data points from literature5 are gray symbols, black symbols are experimental data determined in this work, white symbols denote data obtained in this work by extrapolation from liquid-solution data. PCSAFT calculations are solid black lines.
Moreover, it becomes obvious that the PC-SAFT modeled data agree with the experiments even within experimental uncertainty: the average deviation of the experimental data reported to be 0.73% for the literature data even exceeds the ARD from the modeled data, which is 0.5%. Thus, the density of TGs is perfectly described by PC-SAFT using the parameters from Table 7. Validation of the PC-SAFT Pure-Component Parameters. Vapor-pressure data at high temperatures from Perry et al.4 were used for fitting PC-SAFT parameters and supported by data for TG808080, which are given in Table 5. The parameters for TG100100100 were used to calculate vapor pressures at much lower temperatures and compared to data obtained in this work (Table 6) using the QCM method, which enables measuring extremely low vapor pressures14 (Figure 6).
Figure 4. Vapor pressures of the homologous series of saturated TGs. Symbols represent experimental data (circles, TG808080; squares, TG100100100; triangles, TG120120120; stars, TG140140140; diamonds, TG160160160; pentagons, TG180180180). Gray symbols are data from literature,4 and black symbols are the experimental data determined in this work. Solid lines are PC-SAFT calculated vapor pressures.
As can be seen, the experimental vapor pressures of TG808080 obtained in this work and the vapor pressures from Perry et al.4 perfectly coincide and the ARD (2.17%) is in the same order as for the other TGs (0.51% to 3.75%). Further, Figure 4 shows the vapor pressures for different components of the homologous TG series from TG808080 to TG180180180. components of the homologous TG series from TG808080 to TG180180180. As expected, the vapor pressures decrease with increasing carbon chain length. Figure 4 underlines the fact that modeling results obtained from the fitted pure-component parameters enable for very accurate vapor-pressure descriptions. Figure 5 summarizes the liquid-density data, partly determined in this work and partly obtained from literature.5 It can be seen that TGs with long chains have lower densities than short-chained TGs. The density difference between two short-chained TGs (e.g., between TG808080 and TG100100100) is higher than that between the long-chained TGs (e.g., between TG160160160 and TG180180180). The extrapolated densities for pure TG100100100 from Table 3 perfectly fit to the literature data, which implies the very good accordance of density data obtained in this work with literature data. Further, it could be verified that extrapolating mixing densities from low TG mass fractions to the pure TGs is a reasonable method to determine liquid densities for components being crystalline at ambient conditions.
Figure 6. Vapor pressures for TG100100100. Gray squares are the correlation values from Perry et al.4 and black squares are experimental data from this work. The solid line is the vapor-pressure calculation using PC-SAFT.
Even though the PC-SAFT parameters (Table 7) were not fitted to the QCM data obtained in this work, the agreement of modeled and experimental data is surprisingly good. Obviously the experimental vapor pressures measured in this work and the vapor pressures from Perry et al. stand in very high accordance to each other. To the best of our knowledge, this is the first time the correlation from Perry et al.4 could be verified by independent measurements. The ARD between experE
DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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and Wesdorp22 summarized the mutual-solubility data of many TGs, also considering different TG polymorphs. In this work, only the usually thermodynamically stable β-polymorphs were considered for the solubility calculations. Figure 8 illustrates the solubility of TG180180180 in TG808080 (a) and in TG120120120 (b). Figure 8c shows the mutual solubilities of TG180180180 and TG160160160. The melting properties of TG180180180 and TG160160160 required for modeling the solid−liquid phase diagram were taken from literature.23 Pure-component PC-SAFT parameters of the TGs were taken from Table 7 and all binary parameters between two TGs were set to zero. As to be seen from Figure 8, all TG systems show a perfect agreement between predicted solubilities and experimental data. In the systems TG180180180/TG808080 (Figure 8a) and TG180180180/TG120120120 (Figure 8b), the eutectic point is far on the left side of the phase diagram. The solubility of TG180180180 in TG808080 (Figure 8a) is predicted to be comparable to that in TG120120120 (Figure 8b), which very well agrees with the experimental results from literature. In contrast, the eutectic point of the TG180180180/TG160160160 mixture (Figure 8c) is located more in the middle of the phase diagram, and thus both branches of the solubility line could be predicted with PC-SAFT. The eutectic phase behavior and even the exact location of the eutectic point was predicted within experimental uncertainty (Figure 8c): predicted eutectic TG mass fraction 0.205 (experimental value 0.19925) and predicted eutectic temperature 337.78 K (experimental value 337.79 K25). Natural oils mostly contain TGs from unsaturated fatty acids. Because of the lack of experimental vapor pressure and density data for those TGs, parameters for the two unsaturated TGs TG181181181 and TG182182182 were estimated using the GCM from Peters et al.19 These parameters are given in Table 7 and were used to predict the solubility of TG160160160 in these two unsaturated TGs. Figure 9 shows the solubility of TG160160160 in TG181181181 (Figure 9a) and Figure 9b compares the solubilities of TG160160160 in TG181181181 and in TG182182182. In Figure 9a, solubility measurements for TG160160160 in TG181181181 originating from three sources are compared.22,26,27 They show very good agreement among each other and also with the PC-SAFT prediction (pure-component parameters were taken from Table 7, whereas binary parameters were again set to zero). Figure 9b shows that the
imental and predicted vapor pressures in Table 6 (6.45%) is higher than the one for the vapor-pressure data from Perry et al.4 (2.79%), to which the PC-SAFT parameters have been fitted (Table 7). However, it lies within the experimental uncertainty for these very low vapor pressures (7%) meaning that the literature data for TG100100100 from Perry et al.4 perfectly agree with the experimental data obtained in this work. For further validation, PC-SAFT was applied to predict mixing densities of TG100100100 in octanol for varying temperatures and TG mass fractions (Figure 7). These values
Figure 7. Density of TG100100100/octanol mixtures. Densities were experimentally determined at 20 °C (circles), 25 °C (squares), 30 °C (triangles), 40 °C (stars), 60 °C (diamonds), 80 °C (pentagons). Mixture-density data are taken from Table 3. Solid lines are PC-SAFT predicted densities.
are compared to the experimental data as shown in Figure 2 and Table 3. It should be noted that none of the mixturedensity data have been used for parameter fitting and the binary interaction parameter was set to zero. PC-SAFT parameters for octanol were taken from literature.21 As can be seen, the accordance of predictions and experimental data is very high for the entire range of compositions and temperatures. A slightly increasing deviation is found toward higher temperatures, but even at the highest temperature of 80 °C the ARD is still only 0.34%. Predicting Solid−Liquid Equilibria of TG Mixtures. The TG PC-SAFT parameters determined above were used to predict the solid−liquid equilibria of TG mixtures. Marangoni
Figure 8. (a) Solid−liquid equilibrium of TG808080 and TG180180180,24 (b) TG120120120 and TG180180180,25 and (c) TG160160160 and TG180180180.25 The symbols are experimental data points and the solid lines represent the PC-SAFT predictions. F
DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 9. (a) Solubility of TG160160160 in TG181181181. Different literature data are indicated by different symbols (circles,26 triangles,22 stars27). (b) Comparison of the TG160160160 solubility in TG181181181 (gray stars) and TG182182182 (white circles)27 The solid lines in panels a and b represent PC-SAFT calculations for the solubility in TG181181181 (gray line) and in TG182182182 (black line).
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solubilities of TG160160160 in the two unsaturated TGs TG181181181 and TG182182182 do not differ significantly. This is again supported by the PC-SAFT predictions, which also lead to indistinguishable results for the two solubility lines. It can thus be concluded that unsaturation of the TGs does have a great impact on the solubility of other TG components. However, complete saturation of the TG carbon side chain has a huge influence on the crystallization properties of TGs. Compared to TG180180180 (TSL TG180180180 = 345.7 K), the two unsaturated TGs TG181181181 and TG182182182 are liquid at room temperature, although all three TGs have the same carbon-chain length (18 carbon atoms) and almost the same molecular weight.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b01046. Additional tables (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Joscha Brinkmann: 0000-0001-8446-4344 Christian Luebbert: 0000-0001-5555-4965 Dzmitry H. Zaitsau: 0000-0002-4002-7019 Sergey P. Verevkin: 0000-0002-0957-5594 Gabriele Sadowski: 0000-0002-5038-9152
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CONCLUSION In this work, a systematic approach was applied to describe the thermodynamic phase behavior of pure triglycerides (TGs) and TG mixtures. Vapor pressures and liquid-density data for saturated and unsaturated TGs with an even carbon number in the TG side chains were collected from literature and complemented by new experimental data. For the very first time, difficult-to-determine very low vapor pressures (down to 1.5 × 10−5 Pa) of TG808080 and TG100100100 were determined and agreed very well with the vapor pressures measured by Perry et al.4 at higher temperatures. The whole variety of available density data (literature values, extrapolations, and own measurements) fully agree with each other thus providing a complete picture of pure-component TG densities and vapor pressures. The before-mentioned thermodynamic TG properties could be exactly described via PC-SAFT in the entire range of temperatures and pressures. The determined PC-SAFT parameter sets now also enable interpolating PC-SAFT parameters for TGs with uneven number of carbon atoms in the TG side chains, for which vapor pressures and liquid densities are not available. PC-SAFT parameter estimation for two unsaturated TGs (TG181181181 and TG182182182) was performed using a group contribution method proposed by Peters et al.19 The parameters determined in this work allowed predicting the mutual solubilities of two TGs which were found in an even quantitative agreement with literature data. PC-SAFT is thus a powerful tool for describing the phase behavior of pure TGs and of TG-containing mixtures.
Funding
This work has been supported by Deutsche Forschungsgemeinschaft (DFG) with Grant SA700/20 (Gottfried Wilhelm Leibniz Prize awarded to Gabriele Sadowski) and the Government of Russian Federation (decree no. 220 of 9 April 2010), agreement no. 14.Z50.31.0038. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors would like to acknowledge Susanne Richter from the Laboratory of Thermodynamics at TU Dortmund University for performing the density measurements.
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NOMENCLATURE a, Helmholtz energy [J mol−1] ARD, average relative deviation [%] h, specific enthalpy [J mol−1] kB, Boltzmann constant [J K−1] M, molar mass [g mol−1] m, segment number [-] N, number of data points [-] RD, relative deviation [%] R, ideal gas constant [J mol−1K−1] p, pressure bar T, temperature [K] u, uncertainty [-] u kB−1, dispersion energy [K]
G
DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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w, mass fraction [gi g−1 total] x, mole fraction [-] y, property [-]
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GREEK CHARACTERS γ, activity coefficient [-] σ, segment diameter [Å] ρ, density [kg m−3] Δ, difference [-]
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SUBSCRIPTS calc, calculated exp, experimental i, component r, relative 0, pure component
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SUPERSCRIPTS assoc, associating disp, dispersion hc, hard chain L, liquid res, residual S, solid V, vapor
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DOI: 10.1021/acs.jced.8b01046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
