Thermodynamic Properties of Systems Comprising Esters

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Thermodynamics, Transport, and Fluid Mechanics

Thermodynamic Properties of Systems Comprising Esters: Experimental Data and Modeling with PC-SAFT and SAFT-# Mie Niklas Haarmann, Riko Siewert, Artemiy A. Samarov, Sergey P. Verevkin, Christoph Held, and Gabriele Sadowski Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b00714 • Publication Date (Web): 02 Apr 2019 Downloaded from http://pubs.acs.org on April 11, 2019

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Thermodynamic Properties of Systems Comprising Esters: Experimental Data and Modeling with PC-SAFT and SAFT-γ Mie Niklas Haarmanna, Riko Siewertb, Artemiy A. Samarovb, Sergey P. Verevkinb, Christoph Helda,*, Gabriele Sadowskia aLaboratory bDepartment

of Thermodynamics, TU Dortmund, Emil-Figge-Straße 70, D-44227 Dortmund, Germany

of Physical Chemistry, Institute of Chemistry, University of Rostock, Dr-Lorenz-Weg 2, D-18059 Rostock, Germany

*Corresponding author: Phone: +49 231-7552086; E-mail address: [email protected]

Abstract

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In this work, new experimental vaporThermodynamic Modeling PC-SAFT SAFT- Mie pressure data of 14 esters were obtained -4 -4 using the transpiration method. Besides -6 -6 -8 -8 dimethyl fumarate, dimethyl maleate, -10 -10 -12 -12 diethyl maleate, benzyl ethanoate, benzyl -14 -14 propanoate, and benzyl butanoate, eight -16 -16 2.7x10 3.0x10 3.3x10 3.6x10 2.7x10 3.0x10 3.3x10 3.6x10 T /K T /K representatives of the homologous series New experimental vapor-pressure data of ethyl alkanoates of ethyl alkanoates were investigated. The pure-component vapor pressures and liquid densities were modeled by means of PC-SAFT and SAFT-γ Mie. Satisfying modeling results could be achieved with both equations of state. Furthermore, the molar excess enthalpies of 12 binary mixtures benzyl ethanoate + n-alkane were modeled. Only one binary interaction parameter was fitted for PC-SAFT to quantitatively predict the molar excess enthalpies of all binary mixtures under study, while SAFT-γ Mie predicts these properties in qualitative agreement with the experimental data. Finally, the liquid-liquid equilibria of three binary mixtures ester (benzyl ethanoate, dimethyl maleate, diethyl maleate) + water were investigated. These systems show a very low and almost temperature-independent solubility of the ester in the aqueous phase, whereas the moderate solubility of water in the organic phase is temperature-dependent. Promisingly, both PC-SAFT and SAFT-γ Mie predicted broad and unsymmetrical miscibility gaps for these mixtures, which is in qualitative agreement with the experimental data. ln(p /bar)

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Industrial & Engineering Chemistry Research

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1 Introduction Esters play an important role in biochemical and chemical engineering. Applications of esters range from bulk chemicals to polymers and fine chemicals. For instance, dimethyl maleate and diethyl maleate are used as intermediates for the production of plastics. Since benzyl alkanoates (e.g., benzyl ethanoate, benzyl propanaote, and benzyl butanoate) are naturally occurring esters with a fruity odor, they are used as fragrances in cosmetic products. Ethyl alkanoates are broadly applied as biodiesel components 1. Due to these applications, the knowledge of their individual volatility is crucial. Furthermore, esters such as the fragrance benzyl ethanoate often occur in natural or synthetic mixtures 2, 3. For example, benzyl ethanoate is applied as fragrance in, e.g., oily creams and liquid perfumes. Hence, the knowledge of thermodynamic properties of such mixtures, especially mutual solubilities, is also indispensable. Methods for the measurement of thermodynamic properties such as vapor pressures and mutual solubilities are readily available. However, such methods are mostly time-consuming and cost-intensive, which do neither allow for an efficient screening of esters with desired properties nor for process optimization of polymerization processes. Especially the latter might be conducted under high pressure. Predictive thermodynamic models are desirable that allow both characterizing pure esters and screening properties of mixtures comprising esters. Such models should enable the description of pure-component and mixture properties over a wide range of temperature and pressure, and only equations of state (EOSs) are meaningful for this task. Since its development in the late 1980s, the Statistical Associating Fluid Theory (SAFT) 4 and further derivations of SAFT have been applied and have been proven among the most appropriate models fulfilling the specified requirements. Two promising SAFT-based EOSs are the Perturbed-Chain SAFT (PC-SAFT) 5, 6 and the group-contribution EOS SAFT-γ Mie 7, 8. Both have already successfully been applied for modeling esters and mixtures comprising esters. Recently, Haarmann et al. 9 modeled purecomponent vapor pressures and liquid densities of methyl alkanoates and ethyl alkanoates applying two approaches within the PC-SAFT framework. Further, the use of PC-SAFT for the description of molar excess properties of binary mixtures methyl alkanoates + n-alkane as well as mutual solubilities in binary mixtures methyl alkanoates + water were investigated 9. Overall, very promising results could be achieved. Moreover, esters were modeled using PC-SAFT in various other previous works 10-16. Also, SAFT-γ Mie was applied to represent pure-component properties such as vapor pressures and various properties of binary mixtures for a broad range of esters 7, 8. In this work, PC-SAFT and SAFT-γ Mie were used to model pure-component properties of 14 esters in a first step. The pure-component vapor pressures of these esters were required and were thus measured in this work using the transpiration method to have a new reliable data basis for the esters under study. Based on these results, properties of binary mixtures comprising esters were considered. In general, molar excess enthalpies and liquid-liquid equilibria are among the most sensitive properties. Thus, molar excess enthalpies of the binary mixtures benzyl ethanoate + n-alkane and the liquid-liquid equilibria of three binary mixtures ester (benzyl ethanoate, dimethyl maleate, diethyl maleate) + water were used to validate both models.

2


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2 Experiments The vapor pressures of all esters were determined using the method of transpiration in a saturated N2-stream 17-20. After mixing about 0.5 𝑔 of a sample with glass beads, it was placed into a thermostated U-shaped tube with a length of 20 𝑐𝑚 and a diameter of 0.5 𝑐𝑚. To reach a phase equilibration, glass beads with a diameter of 1 𝑚𝑚 are suitable as they provide sufficient surface. At constant temperature (± 0.1 K), a nitrogen stream was passed through the U-shaped saturator and the transported amount of vaporous material was collected in a cooling trap. Measuring the flow rate of the nitrogen stream using a soap-bubble flow meter, it was optimized to reach the saturation equilibrium of the transporting gas at each temperature under study. The amount of condensed sample was determined by gas chromatography using an appropriate n-alkane as an external standard. The vapor pressure 𝑝𝐿𝑉 at each temperature 𝑇 was calculated from the amount of the product collected within a definite time: 𝑚𝑅𝑇

𝑝𝐿𝑉 = 𝑉𝑀𝑤 with 𝑉 =

(𝑛𝑁2 + 𝑛)𝑅𝑇𝑎

(1)

𝑝𝑎

where 𝑚 is the mass of the investigated compound, 𝑅 is the universal gas constant, V is the volume of the vapor phase consisting of 𝑛𝑁2 moles of the carrier gas and 𝑛 moles of the vaporous compound under study at the atmospheric pressure 𝑝𝑎 and the ambient temperature 𝑇𝑎. While the N2 gas flowrate was measured with a HP soap-film flow meter (model 01010113), the amount of the carrier gas 𝑛𝑁2 was determined from the flow rate and the time measurement. For each temperature, the amount 𝑛 of the compound in the carrier gas was estimated applying the ideal gas law. Before the vapor-pressure measurements, the sample was pre-conditioned at 293-300 K (2 hours) in order to withdraw possible water traces. Afterwards, the saturator was kept at 320 K to remove possible traces of volatile compounds. In order to guarantee the completion of the pre-conditioning, three samples were taken consequently in the course of the sample flushing and analyzed by gas chromatography. If the vapor pressure at this temperature was constant, the transpiration experiments were conducted. No additional impurities were detected by the gas-chromatography analysis of the transported material. The absence of impurities and decomposition products was rechecked by gas-chromatography analysis of the saturator content after completing the whole series of experiments. 3 Theoretical background Here, the calculation of phase equilibria and molar excess enthalpies will be explained. Moreover, the two EOSs PC-SAFT and SAFT-γ Mie will briefly be described. 3.1 Calculation of phase equilibria and molar excess enthalpies Both the vapor-liquid equilibria of pure components and the liquid-liquid equilibria of binary mixtures were obtained applying the isofugacity criteria between two phases I and II: 𝐼𝐼 𝐼𝐼 𝐼𝐼 𝑥𝐼𝑖𝜑𝐼𝑖(𝑇,𝜌𝐼,𝑥𝐼𝑖) = 𝑥𝐼𝐼 𝑖 𝜑𝑖 (𝑇,𝜌 ,𝑥𝑖 )

3

(2)



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where 𝑥𝑖 and 𝜑𝑖 are the mole fractions and the fugacity coefficients of component i, respectively. 𝑇 is the temperature in Kelvin and 𝜌 is the number density of the respective phase. The fugacity coefficients in Eq. (2) were obtained from: ∂𝑎𝑟𝑒𝑠 𝑟𝑒𝑠 ( ) 𝑙𝑛 𝜑𝑖 = 𝑎 + ∂𝑥𝑖

𝑁𝐶

( )

―

∑

∂𝑎𝑟𝑒𝑠 𝑥𝑗 ∂𝑥𝑗

𝑗=1

𝜌,𝑇

∂𝑎𝑟𝑒𝑠 +𝜌 ∂𝜌

( ) ( ) 𝜌,𝑇

𝑇,𝑥𝑖

[ ( )]

∂𝑎𝑟𝑒𝑠 ― 𝑙𝑛 1 + 𝜌 ∂𝜌

(3)

𝑇,𝑥𝑖

where 𝑁𝐶 is the number of components in the mixture and 𝑎𝑟𝑒𝑠 denotes the dimensionless residual Helmholtz energy given as: 𝐴𝑟𝑒𝑠 𝑁𝑘𝐵𝑇

𝑎𝑟𝑒𝑠 =

(4)

In Eq. (4), 𝐴𝑟𝑒𝑠 is the residual Helmholtz energy in Joule, 𝑁 is the total number of molecules, and 𝑘𝐵 is the Boltzmann constant. The molar excess enthalpy ℎ𝐸 of a binary mixture was expressed as: 𝑁𝐶

𝐸

𝑟𝑒𝑠

ℎ =ℎ

―

∑𝑥 ℎ

(5)

𝑟𝑒𝑠 𝑖 0𝑖

𝑖=1

where ℎ𝑟𝑒𝑠 and ℎ𝑟𝑒𝑠 0𝑖 are the residual enthalpy of the mixture and the pure component i, respectively. These molar residual enthalpies were calculated by:

[( ) ( ) ]

ℎ𝑟𝑒𝑠 = 𝜌

∂𝑎𝑟𝑒𝑠 ∂𝜌

―𝑇

𝑇,𝑥𝑖

∂𝑎𝑟𝑒𝑠 ∂𝑇

𝑅𝑇

(6)

𝜌,𝑥𝑖

In this work, the residual Helmholtz energy 𝑎𝑟𝑒𝑠 required in Eqs. (3) and (6) was determined using PC-SAFT and SAFT-γ Mie. In order to express deviations between results of these two models (mod) and experimental data (exp), the percentage average relative deviation (%ARD) for an arbitrary thermodynamic property f was calculated as: %𝐴𝑅𝐷 =

1 𝑁𝑑𝑎𝑡𝑎

𝑁𝑑𝑎𝑡𝑎

∑ |1 ― 𝑓

𝑑=1

|

𝑓𝑚𝑜𝑑 𝑑 𝑒𝑥𝑝 𝑑

∙ 100%

(7)

where 𝑁𝑑𝑎𝑡𝑎 is the number of data points. 3.2 PC-SAFT Within PC-SAFT 5, 6, a molecule is modeled as a coarse-grained chain of a number of 𝑚𝑖 tangentially bonded spherical segments of the same diameter 𝜎𝑖. The segments interact via a modified square-well potential, which is expressed by the dispersion energy 𝑢𝑖. In the case of associating compounds, e.g., water, two additional parameters, namely the association energy 𝜀𝐴𝑖𝐵𝑖 and the association volume 𝜅𝐴𝑖𝐵𝑖, are considered in order to describe associative 4


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interactions such as hydrogen bonding 6. Hence, the dimensionless residual Helmholtz energy 𝑎𝑟𝑒𝑠 was obtained considering the following contributions: 𝑎𝑟𝑒𝑠 = 𝑎ℎ𝑐 + 𝑎𝑑𝑖𝑠𝑝 + 𝑎𝑎𝑠𝑠𝑜𝑐

(8)

where the hard-chain contribution 𝑎ℎ𝑐 represents the hard-chain reference system in PC-SAFT. This reference system is disturbed by the perturbative energy contributions caused by dispersive (𝑎𝑑𝑖𝑠𝑝) and associative (𝑎𝑎𝑠𝑠𝑜𝑐) interactions. The PC-SAFT pure-component parameters for water as well as for the esters and n-alkanes under investigation are given in Table 1. Those of the esters were determined in this work by adjusting them to experimental vapor-pressure and liquid-density data. Table 1: PC-SAFT pure-component parameters of esters, water, and n-alkanes used within this work. For water, a 2B association scheme was applied. Pure component i dimethyl fumarate dimethyl maleate diethyl maleate benzyl ethanoate benzyl propanoate benzyl butanoate ethyl pentanoate ethyl hexanoate ethyl octanoate ethyl nonanoate ethyl undecanoate ethyl dodecanoate ethyl tetradecanoate ethyl heptadecanoate water (2B) n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane n-tridecane n-tetradecane n-pentadecane n-hexadecane n-heptadecane

𝑚𝑠𝑒𝑔 ― 𝑖

𝜎𝑖 Å

𝑢𝑖 ∙ 𝑘𝐵―1 𝐾

𝜀𝐴𝑖𝐵𝑖 ∙ 𝑘𝐵―1 𝐾

12.249 5.2026 6.5729 4.8994 5.1200 5.3059 4.5306 4.7311 5.4393 5.7426 6.4903 6.8859 7.3241 8.5514 1.0656 3.0576 3.4831 3.8176 4.2079 4.6627 4.9082 5.3060 5.6877 5.9002 6.2855 6.6485 6.9809

2.3416 3.2076 3.3245 3.4341 3.5042 3.5921 3.5222 3.6084 3.6757 3.7147 3.7509 3.7617 3.8448 3.8647 3.0007 3.7983 3.8049 3.8373 3.8448 3.8384 3.8893 3.8959 3.9143 3.9396 3.9531 3.9552 3.9675

173.20 257.86 232.45 268.07 265.73 270.35 235.96 242.09 244.80 247.07 248.77 248.28 254.10 252.72 366.51 236.77 238.40 242.78 244.51 243.87 248.82 249.21 249.78 254.21 254.14 254.70 255.65

― ― ― ― ― ― ― ― ― ― ― ― ― ― 2500.7 ― ― ― ― ― ― ― ― ― ― ― ―

𝜅𝐴𝑖𝐵𝑖 ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― 0.034868 ― ― ― ― ― ― ― ― ― ― ― ―

Ref. this work this work this work this work this work this work this work this work this work this work this work this work this work this work 6 5 5 5 5 5 5 5 5 5 5 5 5

Regarding the homologous series of the ethyl alkanoates, linear correlations for the segment 𝑠𝑒𝑔 3 𝑠𝑒𝑔 ―1 number 𝑚𝑠𝑒𝑔 𝑖 , the molecular volume 𝑚𝑖 𝜎𝑖 , and the molecular dispersion energy 𝑚𝑖 𝑢𝑖𝑘𝐵 on the carbon number 𝐶𝑛 of the acid-based carbon chain of the ethyl alkanoates can be derived and are given in Table 2. 𝑠𝑒𝑔 3 Table 2: Linear correlations for the segment number 𝑚𝑠𝑒𝑔 𝑖 , the molecular volume 𝑚𝑖 𝜎𝑖 , and the molecular 𝑠𝑒𝑔 ―1 dispersion energy 𝑚𝑖 𝑢𝑖𝑘𝐵 on the carbon number 𝐶𝑛 of the acid-based carbon chain of the ethyl alkanoates.

5



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The correlations are given for the ethyl alkanoates and are based on the PC-SAFT pure-component parameters given in Table 1. Quantity 𝑚𝑠𝑒𝑔 ― 𝑖 3 3 𝑚𝑠𝑒𝑔 𝜎 𝑖 𝑖 Å ―1 𝑚𝑠𝑒𝑔 𝑖 𝑢𝑖𝑘𝐵

𝐾

Equation 0.3359𝐶𝑛 + 2.769

Coefficient of determination 0.9964

24.515𝐶𝑛 + 74.183

0.9998

91.078𝐶𝑛 + 605.34

0.9992

For a binary mixture of component i and component j, the unlike dispersion energy 𝑢𝑖𝑗 is obtained applying the Berthelot-Lorenz combining rule as: 𝑢𝑖𝑗 = 𝑢𝑖𝑢𝑗(1 ― 𝑘𝑖𝑗)

(9)

where 𝑘𝑖𝑗 is a binary interaction parameter for the dispersion energy. For the binary mixtures benzyl ethanoate + n-alkane, 𝑘𝑖𝑗 was adjusted to the experimental molar-excess-enthalpy data and set to 𝑘𝑖𝑗 = 0.037 for all considered n-alkanes. 3.3 SAFT-γ Mie Within SAFT-γ Mie 7, 8, molecules are described by subdividing them into distinct functional groups which represent the various chemical moieties. The chemical functional groups are modeled as spherical segments of different diameters 𝜎𝑘. These are assumed to interact via Mie potentials characterized by a repulsive (𝜆𝑟𝑘) and an attractive (𝜆𝑎𝑘) exponent and the dispersion energy 𝜀𝑘. It should also be noted that a functional group can be formed of a number of 𝜈𝑘∗ identical segments. Moreover, each segment is geometrically characterized by the shape factor 𝑆𝑘. Additionally, acceptor (𝑛𝑘,𝐻) and donor (𝑛𝑘,𝑒1) sites may be mounted onto a group in order to mimic association sites. The SAFT-γ Mie group parameters used in this work were taken from the literature 7, 8 and are given in Table 3. Table 3: SAFT-γ Mie group parameters used within this work 7, 8. group k

𝜈𝑘∗ ―

𝑆𝑘 ―

𝜎𝑘 Å

𝜆𝑟𝑘 ―

𝜆𝑎𝑘 ―

CH3 CH2 CH CH= aCH aCCH2 COO H2O

1 1 1 1 1 1 1 1

0.57255 0.22932 0.07210 0.20037 0.32184 0.20859 0.65264 1.00000

4.0773 4.8801 5.2920 4.7488 4.0578 5.2648 3.9939 3.0063

15.050 19.871 8.0000 15.974 14.756 8.5433 31.189 17.020

6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000

𝜀𝑘 ∙ 𝑘𝐵―1 𝐾 𝑛𝑘,𝐻 ― 𝑛𝑘,𝑒1 ― 256.77 473.39 95.621 952.54 371.53 591.56 868.92 266.68

― ― ― ― 0 0 ― 2

― ― ― ― 1 1 ― 2

In order to describe dispersive interactions between two unlike segments k and l, the unlike dispersion energies 𝜀𝑘𝑙 were applied and are given in Table 4. While most unlike repulsive exponents 𝜆𝑟𝑘𝑙 were obtained using the combining rule in Eq. (10), those between the H2O group and the CH3 group (𝜆𝑟𝑘𝑙 = 100), the CH2 group (𝜆𝑟𝑘𝑙 = 100) or the aCH group (𝜆𝑟𝑘𝑙 = 38.64) were taken from the literature 8, 21.

6


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𝜆𝑟𝑘𝑙 = 3 + (𝜆𝑟𝑘 ― 3)(𝜆𝑟𝑙 ― 3)

(10)

Furthermore, the association parameters between a group of type k and a group of type l, 𝐻𝐵 namely the association energy 𝜀𝐻𝐵 𝑘𝑙,𝑎𝑏 and the association volume 𝐾𝑘𝑙,𝑎𝑏, are given in Table 5. Applying SAFT-γ Mie, the expression for the dimensionless residual Helmholtz energy reads as: 𝑎𝑟𝑒𝑠 = 𝑎𝑚𝑜𝑛𝑜 + 𝑎𝑐ℎ𝑎𝑖𝑛 + 𝑎𝑎𝑠𝑠𝑜𝑐

(11)

where 𝑎𝑚𝑜𝑛𝑜 accounts for the dispersive interactions between the Mie segments, 𝑎𝑐ℎ𝑎𝑖𝑛 is the contribution due to the formation of chains from the Mie segments, and 𝑎𝑎𝑠𝑠𝑜𝑐 is the contribution accounting for associative interactions. Table 4: SAFT-γ Mie unlike dispersion energies 𝜀𝑘𝑙 ∙ 𝑘𝐵―1 𝐾 used within this work 7, 8, 21. group k / group l CH3 CH2 CH CH= aCH aCCH2 COO H2O

CH3 256.77 350.77 387.48 252.41 305.81 396.91 402.75 358.18

CH2 350.77 473.39 506.21 459.40 415.64 454.16 498.86 423.63

CH 387.48 506.21 95.621 502.99 441.43 65.410 279.84 101.89

CH= 252.41 459.40 502.99 952.54 589.41 747.67 899.61 466.33

aCH 305.81 415.64 441.43 589.41 371.53 416.69 568.13 357.78

aCCH2 396.91 454.16 65.410 747.67 416.69 591.56 696.78 220.00

COO 402.75 498.86 279.84 899.61 568.13 696.78 868.92 467.08

H2O 358.18 423.63 101.89 466.33 357.78 220.00 467.08 266.68

Table 5: SAFT-γ Mie association parameters used within this work 8. H of group k / e1 of group l H2O / aCH H2O / aCCH2 H2O / H2O

―1 𝜀𝐻𝐵 𝑘𝑙,𝑎𝑏 ∙ 𝑘𝐵 𝐾 563.56 563.56 1985.40

―1 3 𝐾𝐻𝐵 𝑘𝑙,𝑎𝑏 ∙ 𝑘𝐵 Å 339.61 339.61 101.69

4 Results and discussion In this work, new vapor-pressure data of a series of esters were measured using the transpiration method. The experimental pure-component data were modeled using PC-SAFT and SAFT-γ Mie. Furthermore, the molar excess enthalpies of the binary mixtures benzyl ethanoate + n-alkane and the liquid-liquid equilibria of three binary mixtures ester (benzyl ethanoate, dimethyl maleate, diethyl maleate) + water were modeled with both EOSs. 4.1 Pure-component vapor pressures and liquid densities The pure-component vapor pressures of 14 esters were measured applying the transpiration method (cf. chapter 2). While the experimental vapor-pressure data of dimethyl fumarate, dimethyl maleate, diethyl maleate, benzyl ethanoate, benzyl propanoate, and benzyl butanoate are given in Table 6, those of eight representatives of the homologous series of ethyl alkanoates are listed in Table 7. The corresponding enthalpies of vaporization ∆ℎ𝐿𝑉 can be found in SI. For some esters, other experimental vapor-pressure data are available in the literature as can be seen from Table 8 and the experimental vapor-pressure data of benzyl 7



ethanoate depicted in Figure 1(a). The new data obtained in this work were found to be consistent with experimental vapor-pressure data from the literature. For the first time, experimental data were measured at temperatures close to ambient temperatures. For this reason, a comparison with (mostly) ebulliometric results available in the literature for elevated temperatures is hardly possible. Table 6: Experimental vapor pressures 𝑝𝐿𝑉 of some esters measured with the transpiration method in this work.a dimethyl fumarate 𝑇𝐾 𝑝𝐿𝑉 𝑃𝑎 298.4 3.6 301.4 4.9 304.3 7.0 307.3 10.1 310.4 13.5 313.4 19.2 316.3 25.7 318.4 32.4 323.4 53.2 326.2 72.5 328.5 88.3 333.5 137.0 336.4 191.0 338.6 219.6 343.4 339.3 348.6 532.6

dimethyl diethyl maleate maleate 𝑇𝐾 𝑇𝐾 𝑝𝐿𝑉 𝑃𝑎 𝑝𝐿𝑉 𝑃𝑎 293.5 13.6 295.6 5.1 296.4 17.4 298.5 7.0 298.4 20.5 301.5 9.0 301.3 26.6 303.4 10.3 303.4 31.7 306.3 13.9 308.4 47.3 308.4 16.8 311.4 57.3 311.3 20.4 316.5 83.5 313.4 24.6 318.4 99.8 316.3 30.7 321.3 121.2 318.4 37.0 323.4 141.4 321.3 47.1 328.5 190.6 323.5 55.5 333.5 269.4 326.4 67.8 336.3 325.5 328.5 78.4 338.4 380.9 331.4 95.7 341.4 441.9 333.5 111.8 343.5 514.3 336.5 139.9 348.4 676.2 338.8 165.4 351.4 804.5 353.5 908.1 benzyl benzyl benzyl ethanoate propanoate butanoate 𝑇𝐾 𝑇𝐾 𝑇𝐾 𝑝𝐿𝑉 𝑃𝑎 𝑝𝐿𝑉 𝑃𝑎 𝑝𝐿𝑉 𝑃𝑎 295.3 12.68 287.2 3.53 303.3 5.07 298.3 16.54 290.3 4.59 306.6 6.76 300.2 19.42 293.2 6.43 309.2 8.39 303.2 24.7 296.2 7.97 312.6 11.18 306.2 31.37 299.3 10.53 315.6 14.12 307.2 33.42 302.2 13.31 318.5 17.78 308.3 36.95 305.2 17.28 321.4 22.33 309.2 39.92 308.3 21.28 324.2 28.25 312.2 50.38 311.3 28.20 327.5 36.11 315.2 61.52 314.3 35.35 330.6 44.59 318.2 77.14 317.2 43.69 321.2 92.86 320.3 57.28 324.2 116.25 323.3 70.28 a𝑢 = 0.1 K; absolute vapor pressures 𝑝𝐿𝑉 were measured with expanded uncertainties of 𝑢 𝐿𝑉 = 0.005 +0.025( 𝑇 𝑝 𝐿𝑉 𝐿𝑉 𝐿𝑉 𝑝 / 𝑃𝑎) for pressures below 5 𝑃𝑎 and with 𝑢𝑝 = 0.025 + 0.025(𝑝 / 𝑃𝑎) for pressures from 5 to 3000 𝑃𝑎. The uncertainties of vapor pressures are expanded uncertainties (0.95 level of confidence, k = 2) calculated according to a procedure described elsewhere 19. It includes uncertainties from the transpiration experimental conditions (temperature measurements, flow-rate measurements, and the gas-chromatographic method for the mass determination).

8


Page 8 of 18

Page 9 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 7: Experimental vapor pressures 𝑝𝐿𝑉 of ethyl alkanoates measured with the transpiration method in this work.a ethyl pentanoate 𝑇𝐾 𝑝𝐿𝑉 𝑃𝑎 273.1 106.5 274.1 115.6 275.0 124.3 277.9 148.5 283.2 218.0 288.2 308.5 293.2 439.4 298.1 605.8 303.2 839.4 304.3 891.9 305.2 960.1 308.2 1168.5 310.2 1341.3 312.2 1509.1 313.2 1609.0

ethyl ethyl octanoate nonanoate 𝑇𝐾 𝑇𝐾 𝑝𝐿𝑉 𝑃𝑎 𝑝𝐿𝑉 𝑃𝑎 285.6 8.1 293.3 5.43 288.4 10.3 298.3 8.30 290.4 12.3 303.4 12.74 292.4 15.0 308.1 19.61 293.4 16.5 313.1 28.46 295.2 19.2 318.1 42.23 296.4 21.6 323.0 58.43 297.2 22.8 328.0 83.71 298.2 24.8 333.0 121.69 299.2 26.6 338.0 164.43 301.1 31.3 343.0 220.77 303.2 36.5 348.0 296.55 306.3 47.7 352.9 395.65 308.2 55.6 311.3 69.6 313.2 80.1 316.1 98.3 318.2 113.9 ethyl ethyl ethyl ethyl undecanoate dodecanoate tetradecanoate heptadecanoate 𝑇𝐾 𝑇𝐾 𝑇𝐾 𝑇𝐾 𝑝𝐿𝑉 𝑃𝑎 𝑝𝐿𝑉 𝑃𝑎 𝑝𝐿𝑉 𝑃𝑎 𝑝𝐿𝑉 𝑃𝑎 297.2 0.73 303.6 0.52 308.2 0.11 328.0 0.06 297.3 0.76 305.8 0.63 313.8 0.20 333.0 0.10 300.0 1.00 307.5 0.75 318.9 0.32 338.0 0.16 303.7 1.46 310.4 1.07 323.8 0.50 343.0 0.27 305.0 1.68 312.0 1.22 328.8 0.86 347.9 0.43 305.2 1.70 314.0 1.47 333.7 1.34 352.9 0.68 310.3 2.72 316.4 1.79 338.9 2.08 353.9 0.72 313.3 3.68 319.1 2.38 343.8 3.23 357.9 1.07 316.3 4.77 321.0 2.65 348.6 4.88 362.9 1.60 318.2 5.54 322.1 3.14 351.0 5.82 365.9 2.14 321.3 7.15 324.1 3.61 353.4 6.99 371.8 3.33 323.2 8.64 326.6 4.33 355.6 8.61 326.3 11.07 328.1 5.08 358.6 10.65 328.2 12.56 329.4 5.37 360.2 12.44 331.1 16.21 331.1 6.56 363.3 15.17 333.2 19.30 333.2 7.59 364.5 16.46 336.2 24.49 335.2 9.00 365.5 18.75 338.1 28.73 337.2 10.34 369.2 23.45 340.1 33.36 370.4 26.23 343.2 42.88 373.2 31.27 a𝑢 = 0.1 K; absolute vapor pressures 𝑝𝐿𝑉 were measured with expanded uncertainties of 𝑢 𝐿𝑉 = 0.005 +0.025( 𝑇 𝑝 𝐿𝑉 𝐿𝑉 𝐿𝑉 𝐿𝑉 𝑝 / 𝑃𝑎) for pressures below 5 𝑃𝑎 and with U(𝑝 ) = 𝑢𝑝 = 0.025 +0.025(𝑝 / 𝑃𝑎) for pressures from 5 to 3000 𝑃𝑎. The uncertainties of vapor pressures are expanded uncertainties (0.95 level of confidence, k = 2) calculated according to a procedure described elsewhere 19. It includes uncertainties from the transpiration experimental conditions (temperature measurements, flow-rate measurements, and the gas-chromatographic method for the mass determination).b Experimental vapor pressures for ethyl hexanoate published earlier 22 were recalculated in this work according to Eq. (1) taking into account the amount of the vaporous compound under study present in the gas stream.

9

ethyl hexanoateb 𝑇𝐾 𝑝𝐿𝑉 𝑃𝑎 274.3 32.0 276.3 39.1 279.4 50.0 282.4 61.2 285.4 77.1 288.4 99.9 291.4 123.0 294.4 153.4 297.4 184.9 300.4 234.5 303.2 280.5 306.8 348.5 309.2 425.0 312.2 511.5 314.2 587.9



In this work, the vapor pressures and the corresponding liquid densities of all 14 esters under study were modeled using PC-SAFT and SAFT-γ Mie. Although the esters investigated in this work show moderate dipole moments, no polar interactions were taken into account within PC-SAFT since SAFT-γ Mie does not incorporate an explicit dipole contribution 7, 8. For the pure-component vapor pressure and liquid density of benzyl ethanoate, very good agreement between the modeling results of PC-SAFT and the experimental data can be observed in Figure 1 and from the %ARDs in Table 8. This can mainly be attributed to the fact, that the PC-SAFT pure-component parameters were adjusted to the respective experimental pure-component vapor-pressure data and saturated-liquid-density data. Considering the fact that the modeling results of SAFT-γ Mie are predictions, the agreement with the experimental data is still very satisfying. 800 700

0

600

T/K

LV

ln(p /bar)

5

-5

500 400

-10

300

-15 -3 1.0x10

-3

2.0x10

-3

3.0x10 -1 -1 T /K

200

-3

4.0x10

0

1

2

3

4

5

6

7

8

-3

/mol·dm

(a) (b) Figure 1: Vapor pressure 𝑝𝐿𝑉 (a) and saturated liquid density 𝜌𝐿 (b) of benzyl ethanoate. The symbols represent the experimental data taken from this work (squares) and reference 23 (triangles). The modeling results of PC-SAFT and SAFT-γ Mie are shown as solid and dashed lines, respectively.

-6 C5

-8

C6

-10

C8 C9

-12 -14

C17

C14

C C12 11

-16 -3 -3 -3 -3 2.7x10 3.0x10 3.3x10 3.6x10 -1 -1 T /K

LV

LV

-4 ln(p /bar)

-4 ln(p /bar)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 18

-6 C5 C6

-8 -10

C8 C9

-12 -14 C17

C14

C C12 11

-16 -3 -3 -3 -3 2.7x10 3.0x10 3.3x10 3.6x10 -1 -1 T /K

(a) (b) Figure 2: Vapor pressures 𝑝𝐿𝑉 of ethyl alkanoates (ethyl pentanoate (𝐶5), ethyl hexanoate (𝐶6), ethyl octanoate ( 𝐶8), ethyl nonanoate (𝐶9), ethyl undecanoate (𝐶11), ethyl dodecanoate (𝐶12), ethyl tetradecanoate (𝐶14), ethyl heptadecanoate (𝐶17)) (a+b). The symbols represent the experimental data obtained in this work. The modeling results of PC-SAFT (a) and SAFT-γ Mie (b) are shown as solid and dashed lines, respectively.

In Figure 2, the vapor pressures of the eight ethyl alkanoates under study in this work are shown. Regarding the new experimental vapor-pressure data, a decrease of the vapor pressure can be seen with increasing chain length of the ethyl alkanoate. This is an expected result. It 10


Page 11 of 18


1 2 3 can be seen that the modeling results obtained with PC-SAFT are in quantitative agreement 4 with the experimental data [Figure 2(a); Table 8]. The full predictions of SAFT-γ Mie slightly 5 underestimate the vapor pressures of the ethyl alkanoates leading to higher %ARDs. 6 7 8 While the PC-SAFT pure-component parameters of all esters were adjusted to the pure9 component vapor-pressure data and liquid-density data of the respective esters, the 10 SAFT-γ Mie parameters were not fitted to the data shown. Hence, very low %ARDs can be 11 12 observed for the PC-SAFT modeling results given in Table 8, whereas the predictive results 13 of SAFT-γ Mie show overall higher %ARDs. 14 15 Table 8: %ARDs for the PC-SAFT (PC) and SAFT-γ Mie (Mie) modeling results of pure-component vapor 16 pressures and liquid densities of esters. Besides the references of the experimental data, the number of data 17 points and the temperature range are listed for each pure component. 18 19 Vapor pressure 𝑝𝐿𝑉 Liquid density 𝜌𝐿 20 %ARD %ARD 21 Pure component 𝑁𝑑𝑎𝑡𝑎 ― 𝑇 range/𝐾 𝑁𝑑𝑎𝑡𝑎 ― 𝑇 range/𝐾 Ref. Ref. PC Mie PC Mie 22 23 23dimethyl maleate 23 294 - 354 this work 1.27 67.99 23 294 - 354 0.05 7.85 24 24dimethyl fumarate 16 298 - 349 this work 11.72 27.59 2 240 - 293 7.65 14.58 25diethyl maleate 23 18 296 - 339 this work 1.52 70.17 18 296 - 339 0.13 18.63 26 23 benzyl ethanoate 13 295 - 324 this work 0.89 64.78 13 295 - 324 0.12 2.30 27 24 benzyl propanoate 13 287 - 323 this work 1.58 73.83 8 288 - 358 0.07 1.46 28 24 benzyl butanoate 10 303 331 this work 0.68 66.19 2 291 293 0.15 1.12 29 25 26 ethyl pentanoate 15 273 418 this work, 1.39 17.37 15 298 393 0.25 0.59 30 28, 29 27 14 279 - 462 this work, 0.63 15.11 7 288 - 368 0.09 0.42 31ethyl hexanoate 29, 31 15 286 - 480 this work, 27, 29, 30 1.35 17.34 15 278 - 368 0.04 0.24 32ethyl octanoate 30 33ethyl nonanoate 14 293 - 498 this work, 32 2.15 24.24 2 293 - 298 0.03 0.26 33, 34 34ethyl undecanoate 12 297 - 340 this work 2.39 24.94 4 290 - 316 0.13 0.24 31 35ethyl dodecanoate 12 352 - 548 this work, 27, 30 1.61 18.62 15 283 - 353 0.03 0.20 36ethyl tetradecanoate 29, 31 15 333 - 582 this work, 27, 30, 35 1.35 23.72 15 283 - 368 0.03 0.16 37 30 30 ethyl heptadecanoate 13 338 - 473 this work, 2.58 37.40 2 303 -308 0.19 0.20 38 39 40 4.2 Binary mixtures comprising benzyl ethanoate 41 Regarding the binary mixtures benzyl ethanoate + n-alkane, the molar excess enthalpies at 42 43 temperature 𝑇 = 298.15 K and pressure 𝑝 = 1.013 bar were investigated for 12 n-alkanes, 44 namely from n-hexane (𝐶6) to n-heptadecane (𝐶17). The experimental data in Figure 3 show 45 46 an increase of the molar excess enthalpy and a shift of the maximal value with respect to the 47 molar composition with increasing chain length of the n-alkane 9. Applying one binary 48 interaction parameter 𝑘𝑖𝑗 = 0.037 for all considered mixtures independent of the chain length 49 50 of the n-alkane, PC-SAFT qualitatively represents both experimental findings [Figure 3(a)]. 51 While the increase of the molar excess enthalpy with increasing chain length of the n-alkane 52 is in good agreement with the experimental data, the shift of the maximal value of the molar 53 54 excess enthalpy is overestimated for increasing chain length of the n-alkane. This leads to 55 higher deviations to the experimental data as can also be seen from the increasing %ARDs in 56 Table 9. This also holds for the predictions of SAFT-γ Mie [Figure 3(b); Table 9]. 57 58 Furthermore, SAFT-γ Mie predicts an increase of the molar excess enthalpy with increasing 59 chain length of the n-alkane. However, SAFT-γ Mie overestimates the molar excess 60

11



enthalpies of all binary mixtures benzyl ethanoate + n-alkane as can be seen in Figure 3(b) and from the %ARDs in Table 9.

1000

E

E

·

C16

1500 C6

500 0 0.0

0.2

0.4 0.6 xbenzyl ethanoate/-

0.8

1.0

4000 3500 3000 2500 · 2000 1500 1000 500 0 0.0

C16

h /J mol

-1

2000

-1

2500

h /J mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 18

C6

0.2

0.4 0.6 xbenzyl ethanoate/-

0.8

1.0

(a) (b) Figure 3: Molar excess enthalpies ℎ𝐸 of the binary mixtures benzyl ethanoate + n-alkane (n-hexane (𝐶6), n-octane, n-decane, n-dodecane, n-tetradecane, n-hexadecane (𝐶16)) at temperature 𝑇 = 298.15 K and pressure 𝑝 = 1.013 bar (a+b). The symbols represent experimental data from reference 36. The modeling results of PC-SAFT (a; 𝑘𝑖𝑗 = 0.037) and SAFT-γ Mie (b) are shown as solid and dashed lines, respectively. Table 9: %ARDs of the PC-SAFT (𝑘𝑖𝑗 = 0.037) and SAFT-γ Mie modeling results of the molar excess enthalpies ℎ𝐸 for a series of binary mixtures benzyl ethanoate (1) + n-alkane (2) at temperature 𝑇 = 298.15 K and pressure 𝑝 = 1.013 bar.

Binary mixture benzyl ethanoate + n-hexane benzyl ethanoate + n-heptane benzyl ethanoate + n-octane benzyl ethanoate + n-nonane benzyl ethanoate + n-decane benzyl ethanoate + n-undecane benzyl ethanoate + n-dodecane benzyl ethanoate + n-tridecane benzyl ethanoate + n-tetradecane benzyl ethanoate + n-pentadecane benzyl ethanoate + n-hexadecane benzyl ethanoate + n-heptadecane

Ref. 36 36 36 36 36 36 36 36 36 36 36 36

Excess enthalpy ℎ𝐸 %ARD PC-SAFT SAFT-γ Mie 3.61 44.18 3.58 48.95 3.03 52.25 3.98 54.75 4.87 56.58 4.84 57.63 7.02 60.06 6.74 60.33 7.62 58.29 7.70 63.49 7.94 59.15 7.77 60.16

Furthermore, the liquid-liquid equilibrium of the binary mixture benzyl ethanoate + water was modeled using both PC-SAFT and SAFT-γ Mie. The phase behavior is shown in Figure 4. The mixture exhibits a very unsymmetrical miscibility gap, i.e. a virtual insolubility of benzyl ethanoate in the aqueous phase but a much higher solubility of water in the organic phase. Both PC-SAFT and SAFT-γ Mie predict a very broad miscibility gap and a much lower solubility of benzyl ethanoate in the aqueous phase than vice versa. Further, Figure 4 illustrates that the experimentally observed low mutual solubilities increase with increasing temperature, which can be represented applying both EOSs. Using PC-SAFT, a 2B association scheme was applied for water as it was found to be superior to a 4C association scheme regarding the binary mixtures ester + water 9. While no binary interaction parameter 𝑘𝑖𝑗 was used, the induced association between the ester and water was explicitly taken into 12


Page 13 of 18

account for PC-SAFT 37. Applying this approach, PC-SAFT yields slightly underpredicted mutual solubilities. Considering the predictive character of this approach, this modeling result is very satisfying. In contrast, SAFT-γ Mie underpredicts the mutual solubilities in both phases leading to a broader miscibility gab compared to the experimental data. It should be emphasized that no association is taken into account between the COO group and water according to the original version of SAFT-γ Mie. The same conclusions can be drawn for the binary mixtures dimethyl maleate + water and diethyl maleate + water. 380 360 340

T/K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


320 300 280 260 0.0

0.1

0.2 0.999 xwater/-

1.0

Figure 4: Liquid-liquid equilibrium of the binary mixture benzyl ethanoate + water at pressure 𝑝 = 1.013 bar. The symbols represent the experimental data from reference 38. The predictions of PC-SAFT (𝑘𝑖𝑗 = 0) and SAFT-γ Mie are shown as solid and dashed lines, respectively.

5 Conclusions In this work, new experimental vapor-pressure data of 14 esters were measured applying the transpiration method. The new experimental data were found to be consistent with partially available literature data. The two EOSs PC-SAFT and SAFT-γ Mie were applied to model the pure-component vapor pressures and liquid densities of all esters under study. In general, good agreement between modeling results and experimental data was obtained using both EOSs. While PC-SAFT relies on experimental pure-component data to adjust the model parameters for each compound, the group-contribution character of SAFT-γ Mie allows for a predictive description of vapor pressures and liquid densities. Based on the overall satisfying modeling of pure-component properties, binary mixtures were considered with the focus on modeling the molar excess enthalpies of the binary mixtures benzyl ethanoate + n-alkane and the liquid-liquid equilibrium of the binary mixture benzyl ethanoate + water. Both EOSs require binary interaction parameters. While PC-SAFT makes use of mixture-dependent binary interaction parameters, those of SAFT-γ Mie are group-specific and independent of the mixture. Abbreviations %ARD

percentage average relative deviation

EOS

equation of state

PC-SAFT

Perturbed-Chain Statistical Associating Fluid Theory

13



SAFT

Statistical Associating Fluid Theory

List of symbols Roman symbols 𝑎

dimensionless Helmholtz energy per number of molecules ( ― )

𝐶𝑛

carbon number ( ― )

𝑓

arbitrary thermodynamic property ( ― )

ℎ

molar enthalpy (𝐽 ∙ 𝑚𝑜𝑙 ―1)

𝑘

binary interaction parameter (PC-SAFT) ( ― )

𝑘𝐵

Boltzmann constant (𝐽 ∙ 𝐾 ―1)

𝐾𝐻𝐵 𝑘𝑙,𝑎𝑏

association volume (SAFT-γ Mie) (Å3)

𝑚

mass (𝑘𝑔)

𝑚𝑠𝑒𝑔

number of segments ( ― )

𝑀𝑤

molar mass (𝑘𝑔 ∙ 𝑘𝑚𝑜𝑙 ―1)

𝑛

amount of moles (𝑚𝑜𝑙)

𝑛𝑘,𝐻

number of acceptor sites ( ― )

𝑛𝑘,𝑒1

number of donor sites ( ― )

𝑁𝐶

number of components ( ― )

𝑁𝑑𝑎𝑡𝑎

number of data points ( ― )

𝑝

pressure (𝑏𝑎𝑟)

𝑅

universal gas constant (𝐽 ∙ 𝑚𝑜𝑙 ―1 ∙ 𝐾

𝑆

shape factor ( ― )

𝑇

temperature (𝐾)

𝑢

dispersion energy (PC-SAFT) (𝐽)

𝑣

molar volume (𝑐𝑚3 ∙ 𝑚𝑜𝑙 ―1)

𝑉

volume (𝑚3)

𝑥

mole fraction ( ― )

14

―1

)


Page 14 of 18

Page 15 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Greek symbols 𝜀

dispersion energy (SAFT-γ Mie) (𝐽)

𝜀𝐻𝐵 𝑘𝑙,𝑎𝑏

association energy (SAFT-γ Mie) (𝐽)

𝜀𝐴𝑖𝐵𝑖

association energy (PC-SAFT) (𝐽)

𝜅𝐴𝑖𝐵𝑖

association volume (PC-SAFT) ( ― )

𝜆𝑎

attractive exponent of Mie potential ( ― )

𝜆𝑟

repulsive exponent of Mie potential ( ― )

𝜇

dipole moment (𝐷)

𝜈∗

number of identical segments per group ( ― )

𝜌

number density (𝑚 ―3)

𝜎

segment diameter (Å)

𝜑

fugacity coefficient ( ― )

Subscript 0i

pure-component index

a

atmospheric

i,j

component index

k,l

type of segment

Superscript I, II

phase index

assoc

association

chain

chain

disp

dispersion

dipol

dipole

E

excess

exp

experimental

hc

hard chain

LV

liquid-vapor

15



mod

modeled

mono

Mie segment - Mie segment interaction

res

residual

Acknowledgement A special gratitude is expressed to George Jackson and co-workers for helping us to validate our implementation of SAFT-γ Mie. Moreover, this work was performed as part of the Collaborative Research Center Transregio 63 “Integrated Chemical Processes in Liquid Multiphase Systems” (subproject A9). Financial support by the Deutsche Forschungsgemeinschaft (DFG: German Research Foundation) is gratefully acknowledged (TRR 63). Furthermore, this work has been partly supported by the German Science Foundation (DFG) in the frame of the priority program SPP 1708 “Material Synthesis Near Room Temperature”. Artemiy A. Samarov gratefully acknowledges a research scholarship from the DAAD and his current address is Department of Chemical Thermodynamics and Kinetics, Saint Petersburg State University, Russia. References 1. Knothe, G., "Designer" biodiesel: Optimizing fatty ester (composition to improve fuel properties. Energ Fuel 2008, 22, (2), 1358-1364. 2. Numanoglu, U.; Sen, T.; Tarimci, N.; Kartal, M.; Koo, O. M. Y.; Onyuksel, H., Use of cyclodextrins as a cosmetic delivery system for fragrance materials: Linalool and benzyl acetate. Aaps Pharmscitech 2007, 8, (4). 3. Rastogi, S. C.; Johansen, J. D.; Frosch, P.; Menne, T.; Bruze, M.; Lepoittevin, J. P.; Dreier, B.; Andersen, K. E.; White, I. R., Deodorants on the European market: quantitative chemical analysis of 21 fragrances. Contact Dermatitis 1998, 38, (1), 29-35. 4. Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M., SAFT: Equation-of-State Solution Model for Associating Fluids. Fluid Phase Equilibria 1989, 52, 31-38. 5. Gross, J.; Sadowski, G., Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Industrial & Engineering Chemistry Research 2001, 40, (4), 1244-1260. 6. Gross, J.; Sadowski, G., Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Industrial & Engineering Chemistry Research 2002, 41, (22), 55105515. 7. Papaioannou, V.; Lafitte, T.; Avendano, C.; Adjiman, C. S.; Jackson, G.; Muller, E. A.; Galindo, A., Group Contribution Methodology Based on the Statistical Associating Fluid Theory for Heteronuclear Molecules Formed from Mie Segments. The Journal of chemical physics 2014, 140, (5), 054107. 8. Dufal, S.; Papaioannou, V.; Sadeqzadeh, M.; Pogiatzis, T.; Chremos, A.; Adjiman, C. S.; Jackson, G.; Galindo, A., Prediction of Thermodynamic Properties and Phase Behavior of Fluids and Mixtures with the SAFT-γ Mie Group-Contribution Equation of State. Journal of Chemical & Engineering Data 2014, 59, (10), 3272-3288. 9. Haarmann, N.; Enders, S.; Sadowski, G., Heterosegmental Modeling of Long-Chain Molecules and Related Mixtures using PC-SAFT: 1. Polar Compounds. Industrial & Engineering Chemistry Research 2018.

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Thermodynamic Properties of Systems Comprising Esters

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