New phase equilibrium data at ambient and high pressure for strongly asymmetric mixtures containing menthol

Journal of Molecular Liquids 286 (2019) 110819

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New phase equilibrium data at ambient and high pressure for strongly asymmetric mixtures containing menthol Kamil Paduszyński a,⁎, Mikołaj Więckowski a, Marcin Okuniewski a, Urszula Domańska b a b

Department of Physical Chemistry, Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland Industrial Chemistry Research Institute, Rydygiera 8, 01-793 Warsaw, Poland

a r t i c l e

i n f o

Article history: Received 26 February 2019 Received in revised form 16 April 2019 Accepted 18 April 2019 Available online 30 April 2019 Keywords: Menthol Phase diagrams Liquid-liquid equilibrium High pressure PC-SAFT COSMO-RS

a b s t r a c t New data on phase equilibria in binary and ternary mixtures containing (−)-menthol, n-decane, 1-decanol and water are presented and discussed. In particular, experimental liquid-liquid equilibrium phase diagrams in ternary systems {(−)-menthol + (n-decane, or 1-decanol) + water} are reported along with the predictions by means of leading thermodynamic models, namely, perturbed-chain statistical associating fluid theory (PCSAFT) and conductor-like screening model for real solvents (COSMO-RS). Freezing pressure data for binary systems {(−)-menthol + (n-decane, or 1-decanol)} are reported and the corresponding high-pressure solid-liquid equilibrium phase diagrams are discussed and analyzed by using the Yang equation. The measured data are referred to ambient-pressure phase diagrams published previously. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Terpenes are the most diverse class of natural compounds with broad application in the production of fine chemicals [1]. These floral volatiles are extracted from natural sources like fruits [2], essential oils, or marine plants [3]. Therefore they have found many applications in cosmetic products [4], in food industry [5] and in pharmaceutical sciences [6]. Almost all herbal pharmaceuticals contain terpenes, or their oxygenated forms (terpenoids) derived from the common 5 carbon building block, isoprene [7]. For more than thousand years, terpenes have been extracted from natural sources and essential oils and marine plans. Among others, menthol is used as an additive to cough drops and nasal inhalers as well as is used as a flavor in cigarettes, wines, liqueurs, cosmetics and perfumes [8]. Three monoterpenes, namely, linalyl acetate, (+)-menthol and thymol were used as antimicrobial substances against the gram-positive bacterium Staphylococcus and the gramnegative bacterium Escherichia coli [9]. Despite being widely used in natural products, there is a lack of experimental phase equilibrium data of terpenes, such as solid-liquid equilibria (SLE), or liquid-liquid equilibria (LLE), or vapor-liquid equilibria (VLE) as well as the thermodynamic modeling of the systems containing terpenes. Solubilities, vapor pressures, ternary LLE and other properties to be modeled need physical insight into the behavior observed experimentally. Thus, the large variety of thermodynamic, ⁎ Corresponding author. E-mail address: [email protected] (K. Paduszyński).

https://doi.org/10.1016/j.molliq.2019.04.096 0167-7322/© 2019 Elsevier B.V. All rights reserved.

volumetric and physico-chemical properties are required. On the other hand, thermodynamic models can be used to calculate properties that cannot be measured directly, such as critical properties or activity coefficients. Critical temperatures and pressures provide valuable information for the estimation of vapor pressures and are essential for the description of pure component and mixture behavior by equations of state (EoS) [10]. However, their experimental determination is in many cases impossible, since large components usually decompose before the critical point. Recently, critical properties of terpenes and terpenoids have been estimated using group-contribution methods and EoS [11]. In literature, when critical properties of terpenes are required, most authors use empirical group contribution methods to estimate them [12]. The possibility of using ionic liquids as separation agents for terpenes and terpenoids was evaluated based on the measurements of the activity coefficients at infinite dilution [13]. The solubility in water and physico-chemical properties of few terpenes and terpenoids were presented many years ago [14,15]. The data on SLE have been very recently updated and revised by Martins et al. [16]. The ternary LLE phase behavior was presented for many terpenes and terpenoids with alcohols and water [17–21]. Namely, the βcitronello [17], α-pinene, or β-pinene [18], or α-pinene, or β-pinene and limonene [19] as well as limonene [20] were investigated. Ionic liquids were used for the separation of limonene and linalool [21]. This work is a continuation of our previous studies on the SLE phase diagrams of binary systems {(−)-menthol and thymol + organic solvent} [22,23], or {camphene + organic solvent} [24]. It aims to present both experimental and computational thermodynamic study of high

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K. Paduszyński et al. / Journal of Molecular Liquids 286 (2019) 110819

pressure SLE phase diagrams in binary mixtures {(−)-menthol (1) + ndecane, or 1-decanol (2)} and LLE phase diagrams in the systems {(−)menthol (1) + n-decane, or 1-decanol (2) + water (3)} at T = 318.2 K and ambient pressure p = 0.1 MPa. The main motivation for this study was to check the influence of high pressure on the menthol solubility curves and the eutectic point, hence to provide new information for potential separation processes involving this terpene. The solvents have been chosen to account for the effect of hydrogen bonding on the phase behavior (non-polar n-decane vs. self-associating 1-decanol). Finally, thermodynamic modeling of the investigated systems by means of the Yang equation, perturbed-chain statistical associating fluid theory (PC-SAFT) and conductor-like screening model for real solvents (COSMO-RS) is presented. 2. Experimental methods 2.1. Materials (−)-Menthol (N0.99 mass fraction purity) was purchased from Sigma-Aldrich and dried at 323 K for 24 h prior to the measurements. Solvents, n-decane and 1-decanol (both with N0.99 mass fraction purity), were purchased from Sigma-Aldrich and used as received without any purification, except storing over freshly activated molecular sieves of type 4A (Union Carbide) for several days prior to the measurements. Purity of all the chemicals was checked by gas chromatography (GC) and Karl-Fischer method. The resulting water content was 250 ppm, 100 ppm and 100 ppm in the case of (−)- menthol, n-decane and 1decanol, respectively. The pure water used for the purpose of this study was deionized by a reverse osmosis unit with an ion-exchange system with a specific conductivity b0.05 μS · cm−1 (Cobrabid-Aqua, Poland) and next degassed in an ultrasonic bath at T = 323 K before each measurement. 2.2. Ternary LLE procedure Liquid-liquid phase equilibrium (LLE) diagrams presented in this work were determined following the same procedures as those used in our laboratory since many years, mostly for the systems with ionic liquids, also these involving alcohols and water [25–27]. Herein, we provide a brief description of the methods including some details specific for the systems studied in this work. Heterogeneous samples of binary or ternary mixtures of known overall composition were placed into a thermostatted jacketed glass cells with a volume of 10 cm3, closed tightly in order to avoid any losses by evaporation or moisture absorbing. The samples were prepared by weighing using Mettler Toledo AB 204-S balance, with uncertainty of ±0.0005 g. Then, the mixtures were vigorously stirred using magnetic stirrer for 6 h and rested to for the next 12 h for equilibration. Temperature of the experiments was set to T = 318.2 K in order to prevent (−)menthol from crystallization; as reported in our previous work, melting point of this compound is ≈316 K [22]. The samples, (0.1 – 0.3) cm3 were taken from both phases using syringes with coupled stainless steel needles and placed in an ampules with a septum cap. Finally, they were analyzed using GC/FID-TCD setup (PerkinElmer Clarus 580; more details on the setup can be found in the Supplementary Material, Table S1) following internal standard protocol with 1-butanol applied in this work. Prior to injecting on the chromatographic column, the samples were dissolved in acetone to avoid phase splitting. The uncertainty of the mole fraction was estimated to not exceed ±0.003. 2.3. High pressure SLE procedure The high pressure piston-cylinder device used in this work to measure solid-liquid equilibrium (SLE) phase diagrams was described in detail in our previous papers, including those on the mixtures of simple

molecular compounds [28,29], as well as presenting the data for the systems with complex fluids like ionic liquids [26,30]. The principle of the measurement of freezing pressure of a liquid sample having a known composition is based on volume-pressure curve, recorded with an increasing pressure at constant temperature. Prior to the liquid-solid phase transition, pressure increases smoothly with an increase of density. At the pressure corresponding to crystallization, discontinuity on volume-pressure curve appears. The hand hydraulic press was used to move the mobile piston, whereas its displacement (i.e. the change in the volume) was measured by using mechanical indicator with an uncertainty of ±0.01 mm. The pressure was calculated from electrical resistance of the sample determined with calibrated manganine gauge connected to a digital multimeter Hewlett-Packard 3478A with an accuracy of ±0.001 Ω. Estimated relative uncertainty of the determined freezing pressure (up to 1 GPa) was ±2%. The temperature was controlled by a thermocouple connected with the water thermostat Julabo MA, Seelbach, Germany. The Ptresistance thermometer Delta HD 9215 (Poland) was used for the temperature measurements, with uncertainty of ±0.1 K. 3. Theory 3.1. PC-SAFT method PC-SAFT (perturbed-chain statistical associating fluid theory) is a thermodynamic theory of molecular chains interacting via different types of forces [31,32]. Since almost two decades it has been successfully applied in representing diverse systems differing in chemical nature and complexity. The model is given as a thermodynamic equation of state (EoS), in the form of the expression for residual Helmholtz energy of fluid. Thus, other important thermodynamic properties like pressure and chemical potential can be obtained by using conventional thermodynamic formulae. Details on the model can be found elsewhere [31,32]. In this paper, we briefly summarize the model's parameters as well as the combining rules, which are the key elements for modeling mixtures. Within the PC-SAFT framework, each pure compound i is characterized by three molecular parameters: mi — the formal number of segments; σi — the segment's diameter; ui/kB — square-well depth for disperive interaction potential. In the case of component capable of associating via sites Ai (donor) and Bi (acceptor), the association scheme needs to be defined along with two extra parameters for each association, namely: ϵAiBi/kB — energy of association AiBi; κAiBi — relative volume of association AiBi. The listed parameters are usually determined by means of fitting of model predictions to experimental pure-fluid data like vapor pressure, vaporization enthalpy, or liquid density [22]. In the case of mixtures, the cross-interactions play a fundamental role in governing the macroscopic properties. Since there is not accurate and strict method for obtaining parameters corresponding to interactions between unlike molecules i and j, the following Lorentz-Berthelot (LB) and Wolbach-Sandler (WB) combining rules have been proposed and extensively applied since the original PC-SAFT papers [31,32]: uij ¼ σ ij ¼

 pffiffiffiffiffiffiffiffiffi LB ui u j 1−kij σi þ σ j 2

ð1Þ ð2Þ

ϵ Ai B j ¼

ϵAi Bi þ ϵA j B j WS 1−kij 2

ð3Þ

κ Ai B j ¼

ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pffiffiffiffiffiffiffiffiffiffi σ iσ j 3 κ Ai Bi κ A j B j σi þ σ j

ð4Þ

where kXij (X = LB, or WS) in Eqs. (1) and (3) are so-called binary interaction parameters (or binary corrections) of the respective combining rules.

K. Paduszyński et al. / Journal of Molecular Liquids 286 (2019) 110819 WS Usually, kLB ij and/or kij are fitted to the mixture data of interest, hence the PC-SAFT is applied as a correlative tool only. Alternatively, the binary corrections can be fitted to infinite dilution activity coefficients (either experimental or predicted from UNIFAC group contribution model [33]) and then used to predict other properties like binary phase diagrams [34]. Such approach is basically predictive as it does not require any experimental data, but only the group assignments of the molecules forming the studied mixture. Very recently we have published a paper testing this idea for ternary LLE [35]. Despite the fact that the proposed approach has turned out to be successful of the systems with ionic liquids, it is readily applicable to other molecular systems as well. In this work, it is applied to predict LLE phase diagrams in ternary mixtures {(−)-menthol + ndecane + water} and {(−)-menthol + 1-decanol + water}. It is noteworthy that the PC-SAFT, as an EoS model, is capable of computing high-pressure SLE phase diagrams as well [36]. We have made some preliminary calculations to represent the measured phase diagrams for {(−)-menthol + n-decane} and {(−)-menthol + 1decanol} systems. The results were not so satisfactory to be published. Based on our previous experience we are aware that in many cases the PC-SAFT may fail in modeling phase equilibria in associating systems at ambient pressure, so that the poor results obtained at very high pressure are not surprising.

3.2. COSMO-RS method COSMO-RS (conductor-like screening model for real solvents) [37,38] is a modern thermodynamic modeling approach, which has been recently widely used in modeling of properties of diverse molecular systems, also these containing terpenes [22–24]. Within this approach, the real system is mimicked by a mixture of surface segments differing in screening charge density σ. The feature distinguishing the COSMO-RS from other thermodynamic models (like PC-SAFT) is that σ, i.e. the main molecular descriptor, is computed by means of independent unimolecular quantum chemical “COSMO” calculation, so that the model can be treated as entirely predictive. Distribution of σ values over all the surface of molecule, so-called σ-profile, is adopted to finally compute thermodynamic properties using the methods of statistical mechanics [38]. In particular, computation of chemical potentials and activity coefficients enables to calculate phase equilibria. Therefore, the COSMO-RS can be applied to predict LLE phase diagrams for the systems investigated in this work. High pressure SLE computations are not feasible, because the COSMO-RS fluid is incompressible, so that an effect of pressure on phase behavior is not accounted for. All the results shown in this work were performed by using the COSMOtherm package [39] purchased from COSMOlogic GmbH & Co. KG (Leverkusen, Germany). In particular, parameterization “BP_TZVP_18” of the thermodynamic (“RS”) part was utilized. COSMO-files containing the information on σ-profiles of all the chemicals, were generated from quantum chemical calculations on the density functional theory (DFT) level, utilizing Becke-Perdew (BP) functional [40–42] and a triple-ζ valence polarized basis set (TZVP) [43] implemented in Turbomole program [44]. Relevant conformations of cation and the solutes were generated by using COSMOconf utility of COSMOtherm suite coupled with Turbomole. Chemical structure files with all the BP-TZVP-COSMO optimized geometries can be readily provided upon e-mail request. 3.3. Correlation of high-pressure SLE data In order to provide a possibility of interpolating/extrapolating the high-pressure SLE pressures, the following equation proposed by Yang et al. [45,46] was applied:

ln x1 ¼

t X i¼0

 iþ1 1 1 bi ðpÞ − T T 1 ðpÞ

ð5Þ

3

where x1 stands for the saturated solution mole fraction of compound forming solid phase, b denotes pressure-dependent coefficient bi ðpÞ ¼

d X

Dji p j

ð6Þ

j¼0

while T1 stands for pressure-dependent melting temperature of pure component 1. The latter can be obtained from independent regression of T-p data for pure component using simple polynomial regression: T 1 ¼ T 01 þ α 1 ðp−p0 Þ þ α 2 ðp−p0 Þ2

ð7Þ

where p0 = 0.1 MPa. Alternatively (or where the respective experimental data are not available), coefficients T01 and αi (i = 1, 2) can be fitted to mixture data simultaneously with the parameters Dji. This approach was applied in this work in the case of freezing pressure data of (−)menthol-rich solutions. The degrees of polynomials given in Eqs. (5) and (7) can be tuned to provide the fit as accurate as needed, taking into account statistical significance of the resulting coefficients Dji as well. In this work, the coefficients were regressed by using in-house MATLAB code (MathWorks, Inc., version R2018a, academic licence), in particular by using nlinfit function, minimizing the sum of squared residuals between calculated and experimental mole fractions. 4. Results and discussion 4.1. Ternary LLE phase diagrams All the measured LLE tie lines for ternary systems {(−)-menthol + n-decane + water} and {(−)-menthol + 1-decanol + water} are listed in Table 1 and Table 2, respectively. Experimental LLE phase diagrams are presented in Figs. 1 and 2 along with the results of the PC-SAFT and the COSMO-RS modeling. As seen, both systems under study exhibit phase diagram of type II with broad miscibility gaps in binary subsystems {(−)-menthol + water} and {solvent + water}. The measured solubility of water in 1-decanol x3 = 0.244) agrees very well with the literature data: x3 = 0.2402 at T = 298.2 K [47], x3 = 0.2407 at T = 318.5 K [48], x3 = 0.2467 at T = 328.5 K [48], x3 = 0.2382 at T = Table 1 Experimental liquid-liquid equilibrium tie lines mole fractions (xi) for ternary system {(−)-menthol (1) + n-decane (2) + water (3)} at T = 318.2 K and ambient pressure p = 0.1 MPa.a Organic phase

Aqueous phase

x1

x2

x3

x1

x2

x3

0.000 0.009 0.036 0.058 0.093 0.131 0.166 0.201 0.269 0.336 0.405 0.488 0.549 0.637 0.667 0.696 0.730 0.775 0.796 0.804 0.832

1.000 0.991 0.964 0.939 0.899 0.860 0.821 0.784 0.709 0.637 0.551 0.466 0.378 0.275 0.227 0.183 0.132 0.078 0.050 0.035 0.000

0.000 0.000 0.000 0.003 0.008 0.009 0.013 0.015 0.022 0.027 0.044 0.046 0.073 0.088 0.106 0.121 0.138 0.147 0.154 0.161 0.168

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

a

Standard uncertainties: u(T) = 0.1 K, u(p) = 1 kPa, u(xi) = 0.003.

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K. Paduszyński et al. / Journal of Molecular Liquids 286 (2019) 110819

Table 2 Experimental liquid-liquid equilibrium tie lines mole fractions (xi) for ternary system {(−)menthol (1) + 1-decanol (2) + water (3)} at T = 318.2 K and ambient pressure p = 0.1 MPa.a Organic phase

Aqueous phase

x1

x2

x3

x1

x2

x3

0.000 0.044 0.052 0.229 0.273 0.279 0.320 0.430 0.455 0.460 0.502 0.534 0.577 0.695 0.767 0.788 0.811 0.828 0.832

0.756 0.710 0.703 0.544 0.504 0.499 0.462 0.363 0.340 0.335 0.298 0.269 0.230 0.124 0.059 0.040 0.019 0.004 0.000

0.244 0.246 0.245 0.227 0.223 0.222 0.218 0.207 0.205 0.205 0.200 0.197 0.193 0.181 0.174 0.172 0.170 0.168 0.168

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

a

Standard uncertainties: u(T) = 0.1 K, u(p) = 1 kPa, u(xi) = 0.003.

318.2 K [49]. Concentrations of (−)-menthol and solvents in aqueous phase were below detection limit of the applied analytical method, so that one may assume that this phase is a pure water. For {(−)-menthol + solvent} binaries, complete miscibility was observed, what is in agreement with experimental data published by our group previously [22]. The absence of OH group in n-decane molecules does not result in the phase split, so that dispersive interactions seems to play a key role in governing the phase behavior of the systems with (−)-menthol. Such finding is interesting also from utilitarian point of view, because the lack of miscibility gap enables the studied solvents to be applied in the processes of extracting (−)-menthol from its aqueous solutions. In the case of the PC-SAFT model, the pure-fluid parameters were taken directly from our previous paper [22] without refitting. Binary interaction parameters were fitted to infinite dilution activity coefficients (γ∞; IDAC) predicted from modified UNIFAC (Dortmund) model [33] at

Fig. 1. Ternary liquid-liquid equilibrium phase diagram for the system {(−)-menthol + ndecane + water} at T = 318.2 K and p = 0.1 MPa. Compositions presented in mole fraction basis. Key: circles, experimental data; squares, PC-SAFT calculations; triangles, COSMO-RS calculations.

Fig. 2. Ternary liquid-liquid equilibrium phase diagram for the system {(−)-menthol + 1decanol + water} at T = 318.2 K and p = 0.1 MPa. Key: circles, experimental data; squares, PC-SAFT calculations; triangles, COSMO-RS calculations.

the temperature of reported LLE data, i.e. T = 318.2 K. For the system {(−)-menthol (1) + n-decane (2) + water (3)} the finally used values ∞ WS ∞ were: kLB 12 = − 0.0076 (γ21 = 3.2517), k13 = 0.0364 (γ31 = 8.0140) 5 LB ∞ ∞ and k23 = − 0.0183 (γ23 = 6.1438 × 10 ); γij denotes IDAC of compound j. In the case of the system {(−)-menthol (1) + 1-decanol (2) ∞ + water (3)}, the corresponding values were: kWS 12 = − 0.0570 (γ21 ∞ WS ∞ = 1.0061), kWS = 0.0364 (γ = 8.0140) and k = 0.0143 (γ = 13 31 23 23 3.5389 × 104). It should be noted that for the latter system, the binary corrections to Wolbach-Sandler combining rules were fitted, see Eq. (3), whereas all those for Lorentz-Berthelot combining rules were fixed as zeros. Furthermore, the results of LLE predictions depicted in Figs. 1 and 2 are also very satisfactory. Root mean square error (RMSE) between calculated and experimental mole fractions was 0.032 and 0.016 for the system with n-decane and 1-decanol, respectively (taking into account organic phases only). Irrespective of the system, the model captures both binary miscibility gaps with a reasonable accuracy. In the case of the system {(−)-menthol + n-decane + water} the shape of ternary LLE region is not properly reproduced by the model. In fact, the experimental phase diagrams is concave, whereas the one predicted by means of the PC-SAFT approach is convex in the entire range of concentrations. It is quite difficult to explain the observed discrepancies between calculated and measured LLE data. In our opinion, they are simply the result of oversimplified molecular scheme adopted to model such complex real mixture. In the case of the system {(−)menthol + 1-decanol + water}, the PC-SAFT predictions are more promising. Although the curvature of the binodal LLE curve seems to be preserved by the model, the accuracy of the predictions significantly deteriorates as the overall concentration of (−)-menthol decreases. The COSMO-RS predictions shown in Figs. 1 and 2 were obtained by using exactly the same σ-profiles as those presented and discussed in detail in our previous paper [22]. For both ternary systems under study, the model provides approximately the same accuracy as returned by the PC-SAFT. The values of RMSE corresponding to the systems with n-decane and 1-decanol are respectively equal to 0.020 and 0.0023. The most noticeable difference is that the COSMO-RS seems to be more precise method in the case of solvent-rich phases, i.e. the phases with low concentration of (−)-menthol. Indeed, as clearly evidenced in Figs. 1 and 2, miscibility gap in {(−)-menthol + water} system is captured more accurately by the PC-SAFT equation of state. On the other hand, immiscibility in the binary system {1-decanol + water} is represented with much better excellent accuracy by the COSMO-RS. Furthermore,

K. Paduszyński et al. / Journal of Molecular Liquids 286 (2019) 110819

the COSMO-RS properly predicts curvature of the phase envelope for {(−)-menthol + n-decane + water}. Summing up, the results of LLE modeling are surprisingly good taking into account extraordinary complexity of the systems under study, i.e. significant asymmetry in size and shape of constituting molecules as well as diversity of molecular interactions between them. 4.2. Binary SLE phase diagrams All the measured binary high-pressure SLE data, i.e. the values of freezing pressure as a function of temperature and mixture composition, are listed in Tables 3 and 4. The corresponding phase diagrams are presented in Fig. 3 for the binary system {(−)-menthol + n-decane} and Fig. 4 for the binary system {(−)-menthol + 1-decanol}, along with the correlations designated the Yang equation [45,46], see Eqs. (5) to (7). As seen from Fig. 3, the phase diagram for {(−)-menthol + n-decane} system was determined only for n-decane rich solutions, mostly due to problems with sample preparation — difficulties in dissolving of (−)-menthol in n-decane at high concentrations (N0.6 mol/mol). At constant temperature, a significant shift towards high freezing pressure was observed upon addition of (−)-menthol to pure n-decane. The pressure increases monotonically with an increase of (−)-menthol content in the mixture, so that one can assume that the compressed mixture exists as a single phase up to crystallization. As seen from Fig. 3, the Yang equation was capable of correlating the measured data with a satisfactory accuracy. RMSE between fitted and experimental mole fractions of (−)-menthol was 0.021 with R2 = 0.984. The parameters of Eq. (7) were regressed to the measured freezing pressures of pure n-decane and they are equal: T01 = 240.88 K, α1 = 0.2544 K·MPa−1, α2 = 0. The value of coefficient T01 corresponds to the melting point of pure n-decane at normal pressure. A good agreement between the regressed and the experimental value of this temperature (243.51 K [49]) confirms reliability of the apparatus used and the procedures followed in this work. Single term (t = 0) of the polynomial expansion from Eq. (5) has turned out to be sufficient to reproduce the measured SLE data. Finally, the optimized parameters for the Eq. (6) were: d = 1,D00 = − 3325.1 K and D10 = 3.7634 K·MPa−1. In the case of the binary system {(−)-menthol + 1-decanol}, similar phase behavior was detected. However, dissolving (−)-menthol in 1decanol did not cause the problem, so that we were able to determine the freezing pressures in much wider range of composition. As seen from Fig. 4a, both liquidus curves of the SLE phase diagrams were detected, so that determination eutectic point was possible. It is worth mentioning that the same kind of phase diagrams was observed in our previous works on high-pressure SLE, mainly in the case of systems composed of hydrocarbons [50–52]. It can be noticed from Fig. 4a that the concentration of the eutectic point is very close to equimolar composition and does not vary significantly when temperature increases. In fact, similar result was obtained from ambient pressure SLE data for {(−)-menthol + 1-decanol} system published previously [22], so that one can surely state that our high-pressure data are consistent with

5

Table 4 Experimental freezing pressures (p) for binary mixture {(−)-menthol (1) + n-decane (2)} as a function of mole fraction (x1) and temperature (T).a x1

p/MPa 0.0000 0.1013 0.2190 0.2823 0.4244 0.5255 0.5372 0.6624 0.7422 0.8345 a

T/K 298.2

303.2

308.2

313.2

318.2

323.2

328.15

333.15

86.9 94.7 112.6 117.1 157.3 193.6 187.6 100.0

115.3 125.4 141.3 145.7 182.6 210.6 208.8 124.8

138.3 150.7 174.2 180.6 212.4 262.0 247.6 162.1 111.8

170.3 185.0 210.1 224.3 248.0 297.2 288.0 188.0 143.0 100.0

204.9 220.1 247.5 258.6 278.6 334.2 330.3 232.0 181.1 143.8

235.4 251.2 280.6 296.6 322.0 361.1 357.5 274.5 227.2 186.7

262.1 283.3 310.8 328.3 363.0 415.0 409.0 301.0 257.0 208.9

290.6 319.5 341.2 355.2 401.8 442.4 429.6 350.8 299.2 257.0

Standard uncertainties: u(x1) = 0.0005, u(T) = 0.1 K, ur(p) = 2%.

the previous measurements. We were not able to measure the T-p curve for pure (−)-menthol, what hindered the correlation of the binary data. In order to circumvent this problem, the parameters T01 and α1 from Eq. (7) were fitted to mixture data along with the coefficients Dji, see Eq. (6). Furthermore, it was not possible to represent the measured data using a single set of parameters. Separate sets were used to represent both liquidus lines of the phase diagrams. The finally optimized parameters of Eqs. (5) and (7) are as follows: (−)-menthol forming the solid phase, T01 = 311.41 K, α1 = 0.1355 K·MPa−1, α2 = 0, t = 0, d = 2, D00 = − 1385.4 K, D10 = − 1.7757 K·MPa−1, D20 = 6.0435 · 10−4 K·MPa−2 (RMSE = 0.012, R2 = 0.991) – note that the value of T01 is very close to the normal melting point of pure (−)-menthol [22], thus high-pressure data seem to be consistent with those at ambient pressure; 1-decanol forming the solid phase, T01 = 280.58 K, α1 = 0.2076 K·MPa−1, α2 = − 9.375 × 10−5 K·MPa−1 (fitted to pure-fluid p-T data, including the value at normal pressure [22]), t = 0, d = 1, D00 = − 4800.5 K, D10 = 2.3628 K·MPa−1 (RMSE = 0.028, R2 = 0.965). Using the listed values of coefficient, the Yang equation can be utilized to calculate “conventional” isobaric SLE phase diagrams to study an effect of pressure on solubility and eutectic point. Exemplary

Table 3 Experimental freezing pressures (p) for binary mixture {(−)-menthol (1) + n-decane (2)} as a function of mole fraction (x1) and temperature (T).a x1

p/MPa 0.0000 0.1098 0.2088 0.3001 0.4001 0.5109 a

T/K 293.2

298.2

303.2

308.2

313.2

318.2

323.2

205.2 222.1 236.8 256.8 281.9 315.1

225.3 244.7 264.7 285.8 308.6 344.6

245.5 265.1 285.4 308.0 339.2 386.0

265.8 290.3 310.3 338.5 375.3 425.0

285.0 310.0 336.8 371.8 411.0 467.5

302.1 330.0 360.1 395.4 445.8

324.2 353.6 390.4 428.5 484.3

Standard uncertainties: u(x1) = 0.0005, u(T) = 0.1 K, ur(p) = 2%.

Fig. 3. High-pressure solid-liquid equilibrium phase diagram (isotherms of freezing pressure p versus mole fraction x1) for binary system {(−)-menthol (1) + n-decane (2)}. Key: circles, T = 293.2 K; squares, T = 298.2 K; upward-pointing triangles, T = 303.2 K; diamonds, T = 308.2 K; right-pointing triangles, T = 313.2 K; left-pointing triangle, T = 318.15 K; downward-pointing triangle, T = 323.15 K; solid lines, Yang equation; L, liquid phase; S2 solid phase of component no. 2.

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K. Paduszyński et al. / Journal of Molecular Liquids 286 (2019) 110819

state. On the other hand, an increase of pressure does not noticeably change the composition of eutectic point. 5. Conclusions New sets of phase equilibrium data for binary and ternary systems composed of (−)-menthol, n-decane, 1-decanol and water were measured, discussed and analyzed in by using empirical and thermodynamic equations. Ternary LLE data for systems {(−)-menthol + (ndecane + 1-decanol) + water} indicate that both n-decane and 1decanol can be considered as extractants of (−)-menthol from its aqueous solutions. From the measured high-pressure SLE data, one may estimate an effect of pressure on the phase behavior, e.g., a shift in eutectic point, what is a key information when any applications involving (−)menthol (or any other terpenoid compound) at elevated pressures, e.g. when designing working conditions for processes where crystallization is an adverse effect. Both thermodynamic modeling approaches utilized in this work (i.e., PC-SAFT and COSMO-RS) are capable of correct capturing the type of LLE phase diagram in the studied ternary systems, regardless of the solvent. Therefore, they are recommended to be used in modeling of similar systems. Finally, the Yang equation has been shown to be a very powerful correlative tool for reproducing SLE data at both high pressures, resulting in the fits consistent with ambient pressure SLE phase diagrams within an excellent accuracy. Supplementary data to this article can be found online at https://doi. org/10.1016/j.molliq.2019.04.096. Acknowledgements Funding for this research was provided by the National Science Centre, Poland, UMO-2016/23/B/ST5/00145. References

Fig. 4. (a) High-pressure solid-liquid equilibrium phase diagram (isotherms of freezing pressure p versus mole fraction x1) for binary system {(−)-menthol (1) + 1-decanol (2)}. Key: circles, T = 298.2 K; squares, T = 303.2 K; upward-pointing triangles, T = 308.2 K; diamonds, T = 313.2 K; right-pointing triangles, T = 318.2 K; left-pointing triangle, T = 323.15 K; downward-pointing triangle, T = 328.15 K; plus signs, T = 333.2 K. (b) High-pressure solid-liquid equilibriumphase diagram (isobars of melting temperature T versus mole fraction x1) estimated from the regression of freezing pressure data. Key: markers, experimental data at p = 0.1 MPa [22]. In panels a and b: solid lines, Yang equation (details in text); dashed line, eutectic point locus; L, liquid phase; Si solid phase of component i.

results of such calculations are shown in Fig. 4b, where the T − x1 phase diagrams are presented at (0.1, 100, 200 and 500) MPa. First of all it should be emphasized that the data reported herein has turned once again to be in an excellent agreement with the data measured at low pressure [22]. The highest deviations appear in the region of (−)-menthol solubility, what can be explained by small discrepancy between its modeled and experimental melting point. Moreover it can be noticed that an impact of pressure on the solubility curves, thus eutectic point temperature, is quite significant and cannot be neglected when considering the phase behavior of the system under study in a compressed

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