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Phase Diagrams in Representative Terpenoid Systems — Measurements and Calculations with Leading Thermodynamic Models Marcin Okuniewski, Kamil Paduszy#ski, and Urszula Maria Domanska Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02207 • Publication Date (Web): 04 Aug 2017 Downloaded from http://pubs.acs.org on August 8, 2017

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Industrial & Engineering Chemistry Research

Phase Diagrams in Representative Terpenoid Systems — Measurements and Calculations with Leading Thermodynamic Models Marcin Okuniewski,† Kamil Paduszyński,∗,† and Urszula Domańska‡, ¶ † 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 ¶ Thermodynamic Research Unit, School of Chemical Engineering University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4001, South Africa E-mail: [email protected]

Phone: +48 (22) 234 56 40

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Abstract New experimental data on solid-liquid equilibrium (SLE) phase diagrams for binary systems {(−)-menthol, or thymol + n-dodecane, or 1-dodecanol, or 2-phenylethanol} are presented. An influence of chemical structure of both terpenoid and solvent on the solubility curves is established and discussed. The new data are addressed and compared to the SLE data with different set of solvents published previously. Modeling of SLE in the investigated mixtures with three modern thermodynamic models, namely, modified UNIFAC (Dortmund), perturbedchain statistical associating fluid theory (PC-SAFT) and conductor-like screening model for real solvents (COSMO-RS), is presented as well. Predictive capacity of the studied approaches is confronted and compared with respect to their physical foundations for representation of components forming the systems as well as relevant intermolecular interactions governing thermodynamic behavior of the mixtures.


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Introduction Terpenes and terpenoids are large class of chemicals widely occured in nature, mainly as constituents of essential oils isolated from diverse animal and plants species. From the chemical point of view, terpenes are derived from several isoprene, CH3 C(−CH2 )CH−CH2 , units that may be linked together “head to tail” to form linear chains, or they may be arranged to form cyclic structures. Terpenoids are the chemically modified and functionalized terpenes (e.g. via oxidation), so that they can belong to different families of chemicals, e.g. hydrocarbons, alcohols, aldehydes and ketones. In particular, more than 50,000 terpenoids have been isolated so far from both terrestrial and marine plants. Due to their abundance and diversity in nature, the various functions of terpene natural products in the production of pharmaceuticals, food, cosmetics, anti-bacteria and fungus, insects, and other environmental stresses have been widely recognized since many years. 1 Menthol is a chiral cyclic terpenoid (alcohol) naturally occurring as the major component of peppermint oils. Thus far, many number of contributions related to isolation of this compound from natural resources have been presented due to a long list of its possible applications in food and pharmaceutical industry. In particular, solubility of menthol in supercritical CO2 has been widely investigated 2–4 . Menthol was also considered in dissolution of drugs poorly soluble in water. For example, it was applied as cosolvent increasing the solubility of some drugs in supercritical CO2 5,6 . Furthermore, binary mixture of menthol with ethanol was used to change the solubility in the skin and interaction with skin for the lipophilic and hydrophilic drugs 7 . Menthol was also used as a solvent for dissolution and stabilizing polystyrene wastes in recycling processes 8 . Very recently, menthol-based deep eutectic solvents have been proposed, characterized and applied in the liquid-liquid extraction processes of several simple biomolecules from aqueous solutions 9. Structurally, thymol is an an aromatic counterpart of menthol, that can be naturally found in essential oil of thyme. It can be obtained from different extracts of Thymus vulgaris and detected/analyzed by using common chromatographic methods 10. The most important feature of thymol is its biological activity. In particular, thymol exhibits strong the antimicrobial efficacy. For example, this has been demonstrated in the study of three monoterpenes (linalyl acetate, menthol, 3 ACS Paragon Plus Environment


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and thymol) against the gram-positive bacterium Staphylococcus aureus and the gram-negative bacterium Escherichia coli 11 . Antibacterial activity of natural compounds as cellulose acetate with thymol was investigated in supercritical CO2 at different working conditions. Samples of impregnated cellulose acetate were tested against selected microorganisms 12. Recently, thymol was used in antimicrobial active films based on poly(lactic acid) (PLA) prepared with poly(εcaprolactone). Thymol acted as plasticizer weakening the intermolecular forces of polymer chains, thus improving the flexibility and extensibility of the films. The presence of thymol decreased the crystallinity of PLA phase, but did not affect the thermal stability of films 13 . The antimicrobial properties of thymol containing films showed a significant activity against Escherichia coli and Listeria monocytogenes 13. The same as for menthol, applications of thymol in pharmacy have also been reported. For instance, the use of eutectic systems formed by ibuprofen and terpenes, including thymol were considered when studying the effects of melting point depression of on drug transdermal delivery system 14. Unfortunately, the physico-chemical properties and phase diagrams of systems composed of terpenes and terpenoids are still very rare and scarce. In particular, the phase diagrams, including solid-liquid equilibria (SLE) and liquid-liquid equilibria (LLE), are essential in many potential applications of terpenes and terpenoinds, e.g. as deep eutectic solvents 14 as well as in development of methods for their isolation and purification 15. Accurate and versatile modeling of the mixtures formed by terpenes and terpenoids using modern thermodynamic tools should also be perceived as an urgent scientific task in order to: (1) get some physical insight into molecular interactions governing thermodynamic behavior of terpenes; (2) perform predictions and/or virtual screening to search for new chemical suitable for a given process/application, i.e. to enable to estimate different thermodynamic properties for systems not characterized experimentally. In our previous contribution, we presented a thermodynamic study SLE phase diagrams of several binary systems formed by representative terpenoids (menthol/thymol) and several organic solvents (n-decane, 1decanol, phenylmethanol and 2-cyclohexylethanol) 16. Furthermore, similar study was carried out in our group for several mixtures of camphene, used as a representative terpene, with organic


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solvents. 17 This paper is a continuation of our previous studies 16,17 dealing with thermodynamic behavior of mixtures containing terpenes and terpenoids. First of all, it comprises experimental work and summarized the collected SLE data for the new six binary systems {(−)-menthol, or thymol + n-dodecane, or 1-dodecanol, or 2-phenylethanol}. The data are discussed and analyzed in terms of an impact of different structural characteristics of both terpenoid and solvent on SLE phase behavior. Thermodynamic modeling of the investigated phase diagrams with three modern thermodynamic approaches, namely, modified UNIFAC (Dortmund), perturbed-chain statistical associating fluid theory (PC-SAFT) and conductor-like screening model for real solvents (COSMO-RS), is presented as well. The models under study essentially differ in the way they treat pure compounds. They also use different levels of complexity and theory for calculating thermodynamic properties of the mixtures. Therefore, we believe that comparison of their performance in modeling of SLE in relatively complex systems (like those containing terpenoids) may be seen as interesting.



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Experimental Section Materials Terpenoids under study, i.e. (−)-menthol and thymol, were supplied by Sigma Aldrich. The initial mass fraction purity certified by the supplier was 0.99. In order to remove residual water and other impurities that could affect further SLE phase diagrams determinations, the samples were subjected in molten state to vacuum (approximately 5 mPa) at 343 K for approximately 24 h. The solvents studied, i.e. n-dodecane, 1-dodecanol and 2-phenylethanol, were purchased from Sigma Aldrich as well and their were used as received without any purification steps. In order to preserve their certified purity as long as possible, they were stored over freshly activated molecular sieves of type 4A (Union Carbide) for several days prior to the SLE measurements. Final purity of the solvents was analyzed by GC, whereas the residual water content of all the chemicals were determined by using Karl-Fischer method. Final water mass fractions of the samples of all the chemicals prior the SLE measurements were as follows: 250 ppm for (−)-menthol, 600 ppm for thymol, 100 ppm for n-dodecane, 150 ppm for 1-dodecanol and 130 ppm for 2-phenylethanol.

SLE Phase Diagrams Determination Following our previous contribution 16, the widely recognized and accepted synthetic method was applied in this work to determine SLE phase diagrams in binary systems {terpenoid + solvent}. Details of the procedures can be found elsewhere 18 . The procedure for determination of a single data point on a solubility curve is as follows. Heterogeneous mixture of terpenoid (solid at room temperature) and solvent (liquid at room temperature except 1-dodecanol) were prepared in tight glass cell equipped with Rotaflow valve by accurate weighing with an uncertainty of 0.0001 g. In mole fraction basis, the combined uncertainty in composition of the binary mixture did not exceed 0.0005. Then, the sample was subjected in a thermostating bath and a very slow heating regime (< 2 K · h−1 ) was applied along with the continuous stirring inside the measuring cell. The temperature at which the heterogeneity disappeared was recognized as the solubility curve ordinate, i.e. SLE 6 ACS Paragon Plus Environment

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temperature, for an abscissa equal to the mixture mole fraction. The SLE temperature was detected visually and measured with an electronic thermometer P 775 (DOSTMANN electronic GmbH) with the probe totally immersed in the thermostating liquid in a very close to the measuring cell. For each data point, the SLE temperature measurement was repeated at least three times and the finally presented values correspond to the mean values. The resolution of the thermometer was 0.01 K, however the standard uncertainty of the obtained data (combining the resolution of thermometer as well as the spread of the measured values of heterogeneity disappearance temperature) was estimated to be of the order of 0.2 K.



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Theory Thermodynamics of SLE In this work, SLE phase diagram is modeled as a locus of equilibrium states between pure solid of component denoted by 1 and saturated liquid solution of 1 in solvent denoted by 2. Both phases are in equilibrium state (defined by the value of equilibrium mole fraction in liquid phase x 1 ) if chemical potentials of solid 1 and 1 dissolved in liquid are equal at given temperature T. A simple relationship between x 1 and T can be derived following fundamentals of classical chemical thermodynamics 19, namely

ln x 1 γ1 = −

∆fus H10 RT

*1 − T + , 0 , Tfus,1 -

(1)

0 where R denotes universal gas constant R = 8.3144621 J · K−1 · mol−1 . The symbols Tfus,1 and

∆fus H10 stand for basic pure-component properties of pure solid, i.e. fusion temperature and fusion enthalpy at standard pressure P = 0.1 MPa, whereas γ1 is the activity coefficient of the solute in the saturated solution depending on T, x 1 as well as both solute and solvent characteristics. In the case of eutectic systems, compound 2 can be considered as a solid as well. Then, subscripts 1 in eq (1) should be replaced by 2, keeping in mind that x 2 = 1 − x 1 . In the case when γ1 = γ2 = 1 irrespective of composition and temperature, eq (1) transforms into the ideal solubility equation. The equation allowing to calculate γ1 as a function of temperature and the liquid mixture composition can be obtained from different thermodynamic models. Finally, SLE temperature T for a given x 1 can be obtained by means of numerical solution of eq (1). In the calculations presented in this paper the trust-region dogleg algorithm implemented in fsolve subroutine of MATLAB Optimization Toolbox (ver. 2016a on an academic license; MathWorks, Inc.) was applied. 0 The values of Tfus,1 and ∆fus H10 for terpenoids were measured and discussed in our recent

paper 16 . They were employed in the calculations presented in this work as well. In the case of the solvents, the fusion data were required only for 1-dodecanol. They values used, namely,


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0 Tfus,1 = 297.3 K and ∆fus H10 = 40.31 kJ · mol−1 , were taken from literature 20 .

Finally, this is noteworthy that in eq (1) we did not consider an effect of heat capacity change due to fusion. This for two main reasons: 1) in our opinion, uncertainty of the values of this quantity reported in literature may be very high, or difficult to estimate; 2) in our previous paper regarding SLE in terpene/terpenoids-based systems 16 we did not included this term as well, so in further studies we just would like to keep our protocol of calculations uniform to allow us (and the readers) to easily compare of performance of the thermodynamic model rather than eq (1), which is basically a fundamental thermodynamics.

Modified UNIFAC (Dortmund) UNIFAC is the well known (including both academia and industry) semi-empirical framework for calculating activity coefficients in terms of group contributions 21. In this approach, the real mixture is pictured as composed of functional groups rather than molecules. Activity coefficient of a real molecular component is calculated on the basis of differences between activity coefficients of functional groups forming the component in its mixed and pure state. The groups differ is size and the chemical nature (i.e. molecular interactions) and these differences affect the combinatorial and residual contribution of activity coefficients of molecular components, respectively, thus govern thermodynamic behavior of the system. Since the original paper of Fredenslund et al. 21 , many modification of the original model have been proposed. The most successful one is the modified UNIFAC (Dortmund), 22 widely used in different areas of chemical thermodynamics as well as in the industrial process and product design (implementations to many popular process simulators have been added), mainly due to its a broad range of applicability (a large matrix of parameters available) and an improved predictive capacity for temperature-dependent properties. We will not present and discuss the modified UNIFAC (Dortmund) model in detail as all the relevant expressions and their explanation can be found elsewhere. 23 In the calculations presented in this work, in-house MATLAB code (ver. 2016a on an academic license; MathWorks, Inc.) was applied to perform SLE calculations with the modified UNIFAC (Dortmund). 9 ACS Paragon Plus Environment


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PC-SAFT Equation of State PC-SAFT model developed by Gross and Sadowski 24,25 in the beginning of 2000’s pictures the real molecules as model chains composed of tangent spherical segments interacting via different types of molecular potentials. Thermodynamics of a mixture is given not in terms of activity coefficients, but as the residual Helmholtz energy (Ares ) split into contributions corresponding to different kinds of interactions: hard-chain formation, short-range dispersive forces, association, . . . Then, Ares can be easily transformed into other relevant properties, like activity coefficient, by using simple thermodynamic formulas. 24 It is clear that PC-SAFT equations will not be described in detail in this short research paper. An interested reader is referred to the original works of. 24,25 Herein, we will shortly describe shortly the model parameters, but also we will briefly point out how to adopt the model to represent both pure fluids and mixtures. Each non-associating compound of the mixture is described by three PC-SAFT pure fluid parameters: number of segments forming the chain m, the segment hard-sphere diameter σ and square-well potential depth u/kB (where kB denotes the Boltzmann constant). In the case of molecules able to form hydrogen bonds, the association is pictured by the associating sites (denoted by A, B, . . . ) located at the chains. Two additional parameters describing the strength of association between sites of type A and sites of type B are introduced, namely, the association energy ǫ AB /kB and the relative volume κ AB . PC-SAFT pure-fluid parameters are commonly obtained by fitting them to temperature-dependent pure-fluid data, e.g. liquid density and vapor pressure data. Extension of PC-SAFT framework to mixtures is straightforward. However, so-called combining rules for calculation of cross-terms representing interactions between segments forming dislike molecular chains are required. In particular, cross-dispersive interaction energy u12/kB and diameter (σ12 ) between molecules of components 1 and 2 are usually calculated by using the Lorentz-Berthelot (LB) combining rule √ LB u12 = u1u2 1 − k12

(2)


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σ12 =

σ1 + σ2 2

(3)

whereas, the cross-association energy and volume between site A on molecule 1 (A1 ) and site B on molecule 2 (B2 ) are estimated based on self-association parameters corresponding to self association in pure components 1 and 2 (i.e. A1 B1 and A2 B2 , respectively) by using the Wolbach-Sandler (WS) relation 26 ǫ A1 B2 =

κ

A1 B2

=

ǫ A1 B1 + ǫ A2 B2 WS 1 − k12 2 p

κ A1 B1 κ A2 B2

√

σ1 σ2 σ12

(4)

!3

(5)

LB and k WS denote the binary interaction parameters for LB and WS combining The symbols k12 12

rules, respectively, accounting for deviation of the real value of cross-term from its estimate, i.e. the value calculated from eqs (2) and (4) if they are set to zero. X (where X In our previous paper 16 , we proposed several predictive strategies for calculating k12

denotes LB or WS) on the basis of infinite dilution activity coefficients of a terpeneoid in solvent (γ1∞ ) calculated from the modified UNIFAC (Dortmund) model. In this paper, we follow this methodology to check its performance when applied to other systems. However, based on the results we get previously we decided to abandon further study on PC-SAFT modeling strategies involving temperature-dependent γ1∞ data, so that the approaches finally considered in this work X = 0 (PC-SAFT applied in a conventional way, entirely predictive are as follows: strategy 0, k12 LB fitted to γ ∞ at T = T 0 approach for equation-of-state modeling); strategy 1, k12 obtained from 1 fus,1 LB or k WS modified UNIFAC (Dortmund) (the same as strategy 1a in reference 16); strategy 2, k12 12 0 fitted to γ1∞ at T = Tfus,1 obtained from modified UNIFAC (Dortmund) depending on the chemical

family of the solvent, i.e. X = LB for non-associating solvent like n-decane, whereas X = WS in the case of associating solvents like 1-dodecanol or 2-phenylethanol (the same as strategy 2a in reference 16). In the latter case, the cross-association is assumed to have a predominant effect on the phase behavior of the system.



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COSMO-RS Approach Conductor-like screening model for real solvents (COSMO-RS) 27–29 is a modern and progressive hybrid thermodynamic approach employing methods from quantum chemistry and statistical thermodynamics to predict diverse properties of fluid mixtures. As in the case of two models presented above, we will not discuss all COSMO-RS equations in detail as well. For a description and derivation of theoretical foundations of COSMO-RS the reader is referred to a comprehensive monography of Klamt. 29 In terms of the model, a liquid mixture is formed by an incompressible ensemble of ideally screened molecules. The molecular interactions are represented by the interactions between segments forming the surface around the molecules. The segments differ in screening charge density (σ), which is obtained beforehand from quantum chemical single-molecule calculation coupled with continuum solvation model (COSMO). The spatial distribution of σ is converted into a histogram, so-called σ-profile, which is further processed by statistical thermodynamic formulas to obtain chemical potentials and activity coefficients. All the SLE calculations presented in this paper were carried out by using the commercial COSMOtherm program 30 purchased from COSMOlogic GmbH & Co. KG (Leverkusen, Germany). Parameterization BP_TZVP_C30_1601 has been used. The molecular input files (socalled COSMO-files) containing the information on the compound optimized geometry and σ) were extracted directly from the databases COSMObase utility which was also supplied by the COSMOlogic 30 . The files represent the results of the quantum chemical COSMO calculations performed with TURBOMOLE program 31 on the density functional theory (DFT) level, utilizing Becke-Perdew (BP) functional 32–34 and a triple-ζ valence polarized basis set (TZVP) 35 .


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Results and Discussion Experimental data Detailed lists of experimental SLE temperature of terpeneoid dissolved in n-dodecane, 1-dodecanol and 2-phenylethanol are given in Supporting Information Tables S1 and S2 for (−)-menthol and thymol, respectively, as a function of terpeneoid mole fraction. The corresponding SLE phase diagrams are plotted in Figure 1 and Figure 2, where the results measured in this work were additionally confronted to the SLE data for binary systems {(−)-menthol, or thymol + n-decane, or 1-decanol, or 2-cyclohexylethanol} reported by us previously 16. Such comparison allows to discuss an impact alkyl chain length of the solvent (n-decane vs n-dodecane and 1-decanol vs 1-dodecanol) and its aromacity (2-cyclohexylethanol vs 2-phenylethanol) on SLE phase diagram. Ideal solubility curve was also plotted in Figure 1 and Figure 2 in order to demonstrate the deviations of the investigated mixtures from the ideal behavior. It can be noticed that in the case of binary systems with n-alkanes, the solubility curves are shifted towards slightly higher temperatures (especially at low terpeneoid mole fraction), when the solvent is changed from n-decane to n-dodecane. This statement regards both (−)-menthol and its thymol, thus the observed effect is not affected by the aromacity of the terpeneoid. Therefore, the observed trend in solubility may be related to higher contribution of van der Waals dispersive interactions in longer n-alkanes, hence overall weakening of terpeneoid-solvent molecular interactions. Besides, the systems {terpeneoid + n-alkane} exhibit strongly positive deviations from ideal solubility equation, so that one may speculate that difference in size and shape of the molecules forming the mixtures predominate in governing their phase behavior. In the case of systems with 1-alcohols, the phase diagrams were determined in the entire range of terpeneoid concentration and simple SLE phase diagrams with eutectic point were detected. An impact of alkyl chain length of 1-alcohol on liquidus curves of terpeneoids is similar to that observed for n-alkanes and this can be explained on the basis on the same reasoning. In turn, the impact on solubility curves of 1-alcohol in terpeneoid is related to a significant difference in melting 13 ACS Paragon Plus Environment


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points of 1-decanol and 1-dodecanol, i.e. the higher melting point, the lower solubility (or higher SLE temperature). This also explains a shift of eutectic composition when replacing 1-decanol by 1-dodecanol. The deviations of the systems {terpeneoid + 1-alcohol} are, however, negative in contrast to the systems with n-alkanes, although the alkyl chain length are the same. We believe that this is related to somewhat compensation of the combinatorial and energetic contributions of activity coefficients due to possible hydrogen bonding between OH groups located at the molecules of terpeneoid and 1-alcohol. An influence of aromacity of the solvent can be deduced by comparing SLE curves of ethanol substituted with cyclohexyl and phenyl groups. In the case of (−)-menthol (i.e. the non-aromatic terpeneoid), the values of SLE temperature for systems with 2-phenylethanol are higher compared to 2-cyclohexylethanol. This means that (−)-menthol is better soluble in 2-cyclohexylethanol. This result follows the well-known general and heuristic rule similia similibus solventur (“like dissolves like”). In the case of thymol (the aromatic terpeneoid), one could expect reverse trend, i.e. that 2-phenylethanol should pose as a better solvent for this terpeneoid. However, the measurements presented in this work revealed that the trend observed for (−)-menthol is preserved. Nevertheless, the difference between solubility of thymol in non-aromatic and aromatic solvent is significantly lower compared with (−)-menthol. This can be seen as an evidence that aromacity of solvent promotes indeed stronger thymol-solvent interactions, thus higher solubility of terpeneoid. An importance of aromaticity of terpeneoids on their solubility can be also highlighted when the magnitude of the deviations of their mixtures with non-polar and polar solvents from ideal behavior are compared. In the case of mixtures with n-alkanes, the (positive) deviations are much stronger in the case of thymol. Thus, terpeneoid’s aromacity deteriorates solubility of non-polar compounds. Reverse trend was evidenced for alcohols: in spite of the fact that both terpeneoids disclose negative deviations from ideal behavior, these observed for thymol are significantly lower compared to (−)-menthol. Finally, it is interesting to note that the mixtures of (−)-menthol with 2-phenylethanol exhibit positive deviations from ideal behavior, whereas in the case of mixtures with 2-cyclohexylethanol the deviations are negative. In the case of systems with thymol, the


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deviations are negative regardless of the solvent. This another observation confirms a significant impact of aromacity of terpeneoids on their solubility in associating solvents.

Modeling: Pure Compounds The modified UNIFAC (Dortmund) group assignments of all the compounds considered in this are as follows (original Dortmund numbering of groups 22 is given in parentheses): (−)-menthol, 3 × CY-CH2 (main group no. 42 / subgroup no. 78), 3 × CY-CH (42 / 79), 3 × CH3 (1 / 1), 1 × CH (1 / 3), 1 × OH(s) (5 / 81); thymol, 3 × ACH (3 / 9), 1 × ACCH3 (4 / 11), 1 × ACCH (4 / 13), 2 × CH3 (1 / 1), 1 × ACOH (8 / 17); n-dodecane, 2 × CH3 (1 / 1), 10 × CH2 (1 / 2); 1-dodecanol, 1 × CH3 (1 / 1), 11 × CH2 (1 / 2), 1 × OH(p) (5 / 14); 2-phenylethanol, 5 × ACH (3 / 9), 1 × ACCH2 (4 / 12), 1 × CH2 (1 / 2), 1 × OH(p) (5 / 14). PC-SAFT parameterization of (−)-menthol and thymol used in this work was transferred from our previous paper on these terpeneoids 16 . In the case of the solvent, the parameters were taken from literature 25,36 , except 2-phenylethanol for which the parameters were determined in this work based on fitting them to liquid density data correlation presented in DIPPR 801 database 37 and normal boiling point, T = 492.65 K reported in literature. 38 The optimized values of PC-SAFT parameters for 2-phenylethanol are as follows: m = 3.0567, σ = 3.8646 Å, u/kB = 336.767 K, ǫ AB /kB = 2380.72 K and κ AB = 0.00675 (with 2B association scheme applied). Screening charge distributions (calculated at BP-TZVP-COSMO quantum chemical level) for all the compounds investigated in this work and their corresponding distributions (σ-profiles) finally used in the SLE calculations are summarized in Figure 3. Each compound has been considered as a combination of several conformers differing to some extent in the optimized molecular geometries and COSMO energies, because averaging of conformers due to Boltzmann distribution of the conformers total free energies is feasible in the used of version COSMOtherm package. 30



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Modeling: SLE Phase Diagrams The quality of the prediction of the SLE phase diagrams under consideration will be discussed in terms of average absolute deviation (AAD) between calculated and experimental SLE temperature, defined as N 1 X calcd exptl Ti − Ti AAD(T ) = N i=1

(6)

where N denotes the number of data points measured for a given system. The values of AAD obtained with modified UNIFAC (Dortmund), PC-SAFT and COSMO-RS for each binary system are summarized in Table 1, where the deviations obtained from ideal solubility law were additionally listed as well. In the case of PC-SAFT model, it has been turned out that the performance of strategies 1 or 2 for binary interaction parameter determination is better or worse depending on the system. Detailed list of AAD values obtained for each PC-SAFT strategy is presented in Table 2 X along with other relevant information regarding application of this model, namely, the values of k12

and the respective values of γ1∞ used to adjust the binary corrections. In general, strategy 2 yielded in a little bit better overall (i.e. calculated based on all the collected data points) AAD compared to strategy 1 (2.5 K vs 2.7 K), and that is why this strategy is used in comparison of PC-SAFT with other models in Table 1. The experimental vs calculated SLE phase diagrams are plotted in Figures 4 to 6. In the case of binary systems {terpeneoid + n-dodecane} (see Figure 4), COSMO-RS discloses the best predictive capacity of the solubility curve representation. This is particularly evident for the system with (−)-menthol, whereas in the case of the mixture with thymol COSMO-RS AAD is indeed the lowest one, however, only slightly lower than the values obtained from the modified UNIFAC (Dortmund) and PC-SAFT. It is noteworthy that for the mixture {(−)-menthol + n-dodecane}, the AAD values obtained from the modified UNIFAC (Dortmund) and PC-SAFT are comparable with the AAD obtained from ideal solubility law. However, only the absolute values of the deviations are approximately the same for this system, whereas the actual values differ in sign. In fact, it is


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clearly seen in Figure 1 and Figure 4 that ideal solubility law underestimates the SLE temperature, whereas all the applied models capture the positive deviations from ideal behavior indeed, but they unfortunately significantly overestimate the SLE temperature over the entire range of terpeneoid’s concentration. For the binary system {(−)-menthol + 1-dodecanol} (see Figure 5), modified UNIFAC (Dortmund) and COSMO-RS (including the ideal solubility law) exhibit basically the same accuracy of prediction of solubility (−)-menthol in 1-dodecanol. In the case of PC-SAFT model the observed AAD is a little bit higher. This is due to the fact that PC-SAFT predicted SLE temperatures at solubility curve of 1-dodecanol in (−)-menthol are considerably lower than the experimental values as well as the values predicted by the two competitive models. Moreover, the deviations become larger when approaching the eutectic point. The quality of predictions obtained for the system in thymol is roughly the same as for (−)-menthol. This time, however, PC-SAFT turned out to be the most successful model, while COSMO-RS calculations resulted in highest overall AAD and the worst estimation of eutectic temperature. In the case of PC-SAFT, both of solubility curves were represented with a reasonable accuracy, whereas the remaining models were capable of reproducing a single solubility curve of the phase diagram only: thymol in 1-dodecanol in the case of modified UNIFAC (Dortmund) and 1-dodecanol in thymol in the case of COSMO-RS. The results obtained for the binary systems {terpeneoid + 2-phenylethanol} confirm that COSMO-RS fails against PC-SAFT when applied as a predictive tool for the SLE calculations of cross-associating mixtures. In fact, as can be seen in Figure 6 the latter approach nicely reproduces the solubility curves in the entire range of composition under study. In particular, in the case of the system with (−)-menthol, the SLE temperatures predicted by modified UNIFAC (Dortmund) and COSMO-RS are substantially higher than the experimental data and the quality of predictions downgrades with a decrease of terpeneoid mole fraction. On the other hand, for the system {thymol + 2-phenylethanol} the SLE temperatures predicted by the modified UNIFAC (Dortmund) and COSMO-RS are lower than these obtained experimentally.



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Sensitivity Analysis of the PC-SAFT Predictions In contrary to the COSMO-RS and the modified UNIFAC (Dortmund), PC-SAFT calculations may be sensitive towards the quality of the predicted values of γ1∞ used in binary interaction parameter fitting. Indeed, one has to keep in mind that significant discrepancies between the UNIFACpredicted and experimental γ1∞ data may occur, in particular in the case of such complex systems, like these under study presented in this work. In order to estimate an impact of uncertainty of γ1∞ on the SLE phase diagrams, they were recalculated following strategy 2 using, however, the values of γ1∞ differing from the “exact” values estimated by the UNIFAC by ±10%. As a measure of sensitivity of the model, differences between the obtained AADs and these reported in Table 2 were employed. The differences observed for all the investigated systems are presented graphically in Figure 7. As can be noticed, all the differences are within ±2 K. The systems with a noticeable impact of γ1∞ on AAD were {(−)-menthol + n-dodecane, or 2-phenylethanol}, see Figure 7a. For the mixture with n-dodecane, an artificial increase and decrease of γ1∞ by 10% resulted in a deterioration and an improvement of accuracy, respectively; it is noteworthy, this particular system was the one described by the PC-SAFT with the worst accuracy, so that the observed change in AAD does not significantly affect the overall performance of the model. For the remaining systems, accuracy of the SLE predictions did not vary outside the range ±0.5 K. Based on these results, we conclude that, in general, one may rely on the γ1∞ -supported SLE predictions with the PC-SAFT model. Nevertheless, accurate experimental data of γ1∞ are strongly recommended (if available) to be used in this kind of modeling as using modified UNIFAC (Dortmund) leads to some extra uncertainty in phase equilibrium data associated directly with the estimated γ1∞ .


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Conclusions New experimental data on SLE in six binary systems {(−)-menthol or thymol + n-dodecane, or 1-dodecanol, or 2-phenylethanol} were presented and discussed in terms of an impact of different molecular features of both terpeneoid and solvent on the sign and magnitude of deviations of the observed phase behavior from ideal solubility law. In particular, it was demonstrated that introducing aromatic in place of aliphatic ring into terpeneoid’s structure hinders dissolution in non-polar solvents and enhances dissolution in associating solvents. It was demonstrated that all the three presented methodologies for thermodynamic modeling can serve as promising predictive tools when used to estimate SLE phase diagrams of the systems composed of terpeneoids. Performance of a particular approach varies when changing from system to system. This is therefore not a trivial task to state whether a given model is better or worse and what is the reason for that. The values of overall AAD calculated over all the 133 data points collected in this study may be helpful in drawing some conclusions. They are as follows: 6.2 K for ideal solubility law, 2.9 K for modified UNIFAC (Dortmund), 2.7 K for PC-SAFT (strategy 1), 2.5 K for PC-SAFT (strategy 2), 3.0 K for COSMO-RS. Thus, PC-SAFT seems to be the most promising model. This is particularly interesting result, taking into account simplicity of SAFT-like molecular picture vs complexity of the modeled mixtures, especially these where cross-association occurs. Nevertheless, it should be pointed out that the successful strategy for PC-SAFT modeling was not purely predictive. Indeed, it involves some auxiliar data generated by means of modified UNIFAC (Dortmund). Modified UNIFAC (Dortmund) calculations themselves can be perceived as pure predictions, because the systems under study were not used by the UNIFAC consortium in the model parameterization. In the case of the COSMO-RS, the calculations are based solely on molecular 3D structure and quantum chemical input and several global parameters hidden in the model. Therefore, similar degree of accuracy of this model compared to PC-SAFT should be appreciated, although its performance in predicting phase behavior of the most of cross-associating systems was noticeably worse.



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Supporting Information Available Table S1, experimental SLE data for the systems {(−)-menthol + solvent} investigated; Table S2, experimental SLE data for the systems {thymol + solvent} investigated. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement Funding for this research was provided by the National Science Centre based on decision number DEC-2013/11/N/ST5/01930.


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References (1) Gershenzon, A.; Dudareva, N. The Function of Terpene Natural Products in the Natural World. Nature Chem. Biol. 2007, 3, 408. (2) Sovova, H.; Jez, J. Solubility of Menthol in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1994, 39, 840. (3) Sovova, H.; Stateva, R. P.; Galushko, A. A. High-Pressure Equilibrium of Menthol + CO2 . J. Supercrit. Fluids 2007, 41, 1. (4) Goto, M.; Sato, M.; Hirose, T. Extraction of Peppermint Oil by Supercritical Carbon Dioxide. J. Chem. Eng. Jpn. 1993, 26, 401. (5) Thakur, R.; Gupta, R. B. Formation of Phenytoin Nanoparticles using Rapid Expansion of Supercritical Solution with Solid Cosolvent (RESS-SC) Process. Int. J. Pharm. 2006, 308, 190. (6) Hosseini, M. H.; Alizadeh, N.; Khanchi, A. R. Effect of Menthol as Solid Cosolvent on the Solubility Enhancement of Clozapine and Lamorigine in Supercritical CO2 . J. Supercrit. Fluids 2010, 55, 14. (7) Kobayashi, D.; Matsuzawa, T.; Sugibayashi, K.; Morimoto, Y.; Kobayashi, M.; Kimurad, M. Feasibility of Use of Several Cardiovascular Agents in Transdermal Therapeutic Systems with L-Menthol-Ethanol System on Hairless Rat and Human Skin. Biol. Pharm, Bull. 1993, 16, 254. (8) García, M. T.; Gracia, I.; Duque, G.; de Lucas, A.; Rodríguez, J. F. Study of the Solubility and Stability of Polystyrene Wastes in a Dissolution Recycling Process. Waste Manag. 2009, 29, 1814. (9) Ribeiro, B. D.; Florindo, C.; Iff, L. C.; Coelho, M. A. Z.; Marrucho, I. M. Menthol-Based



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Eutectic Mixtures: Hydrophobic Low Viscosity Solvents. ACS Sustainable Chem. 2015, 3, 2469. (10) Zeković, Z.; Lepojeviíc, Z.; Vujić, D. Supercritical Extraction of Thyme (Thymus vulgaris L.). Chromatographia 2000, 51, 175. (11) Trobetta, D.; Castelli, F.; Sarpietro, M. G.; Ventui, V.; Critani, M.; Daniele, C.; Saija, A.; Mazzanti, G.; Bisignanol, G. Mechanisms of Antibacterial Action of Three Monoterpenes. Antymicrobial Agents and Chemoth. 2005, 49, 2474. (12) Milovanovic, S.; Stamenic, M.; Markovic, D.; Ivanovic, J.; Zizovic, I. Supercritical Impregnation of Cellulose Acetate with Thymol. J. Supercrit. Fluids 2015, 97, 107. (13) Wu, Y.; Qin, Y.; Yuan, M.; Li, L.; Chen, H.; Cao, J.; Yang, J. Characterization of an Antimicrobial Poly(Lactic Acid) Film Prepared with Poly(ε-caprolactone) and Thymol for Active Packaging. Polym. Adv. Technol. 2014, 25, 948. (14) Stott, P. W.; Williams, A. C.; Barry, B. W. Transdermal Delivery from Eutectic Systems: Enhanced Permeation of a Model Drug, Ibuprofen. J. Controlled Release 1998, 50, 297. (15) Martins, M. A. R.; Domańska, U.; Schröder, B.; Coutinho, J. A. P.; Pinho, S. P. Selection of Ionic Liquids to be Used as Separation Agents for Terpenes and Terpenoids. ACS Sustainable Chem. Eng. 2016, 4, 548. (16) Okuniewski, M.; Paduszyński, K.; Domańska, U. (Solid + Liquid) Equilibrium Phase Diagrams in Binary Mixtures Containing Terpenes: New Experimental Data and Analysis of Several Modelling Strategies with Modified UNIFAC (Dortmund) and PC-SAFT Equation of State. Fluid Phase Equilib. 2016, 422, 66. (17) Okuniewski, M.; Paduszyński, K.; Domańska, U. Thermodynamic Study of Molecular Interactions in Eutectic Mixtures Containing Camphene. J. Phys. Chem. B 2016, 120, 12928.


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(18) Domańska, U. Vapour-Liquid-Solid Equilibrium of Eicosanoic Acid in One- and TwoComponent Solvents. Fluid Phase Equilib. 1986, 26, 201. (19) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice Hall: New Jersey, 1999. (20) van Miltenburg, J. C.; van den Berg, M., G. J. K.; Ramirez Heat Capacities and Derived Thermodynamic Functions of 1-Dodecanol and 1-Tridecanol Between 10 K and 370 K and Heat Capacities of 1-Pentadecanol and 1-Heptadecanol Between 300 K and 380 K and Correlations for the Heat Capacity and the Entropy of Liquid n-Alcohols. J. Chem. Eng. Data 2003, 48, 36. (21) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21, 1086. (22) Gmehling, J.; Li, J.; Schiller, M. A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178. (23) Constantinescu, D.; Gmehling, J. Further Development of Modified UNIFAC (Dortmund): Revision and Extension 6. J. Chem. Eng. Data 2016, 61, 2738. (24) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244. (25) Gross, J.; Sadowski, G. Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res. 2002, 41, 5510. (26) Wolbach, J.; Sandler, S. Using Molecular Orbital Calculations to Describe the Phase Behavior of Cross-Associating Mixtures. Ind. Eng. Chem. Res. 1998, 37, 2917. (27) Klamt, A. Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224.



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(28) Klamt, A.; Eckert, F. COSMO-RS: A Novel and Efficient Method for the A Priori Prediction of Thermophysical Data of Liquids. Fluid Phase Equilib. 2000, 172, 43. (29) Klamt, A. COSMO-RS: From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design; Elsevier: Amsterdam, 2005. (30) Eckert, F.; Klamt, A. COSMOtherm, Version C3.0, Release 16.01; COSMOlogic GmbH & Co. KG, Leverkusen, Germany. 2015. (31) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Electronic Structure Calculations on Workstation Computers: The Program System TURBOMOLE. Chem. Phys. Lett. 1989, 162, 165. (32) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098. (33) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Can. J. Phys. 1980, 58, 1200. (34) Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B 1986, 33, 8822. (35) Schäfer, A.; Huber, C.; Ahlrichs, R. Fully Optimized Contracted Gaussian Basis Sets of Triple-ζ Valence Quality for Atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829. (36) Grenner, A.; Kontogeorgis, G. M.; von Solms, N.; Michelsen, M. L. Modeling Phase Equilibria of Alkanols with the Simplified PC-SAFT Equation of State and Generalized Pure Compound Parameters. Fluid Phase Equilib. 2007, 258, 83. (37) Design Institute for Physical Property Research (DIPPR)/AIChE, DIPPR Project 801. https://app.knovel.com/web/toc.v/cid:kpDIPPRPF7 (accessed May 26, 2017).


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(38) Stull, D. R. Vapor Pressure of Pure Substances. Organic and Inorganic Compounds. Ind. Eng. Chem. 1947, 517.



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Table 1. Average Absolute Deviations (AAD) between SLE Temperatures Calculated by Using the Investigated Thermodynamic Models and the Experimentally Determined Values, see eq (6). terpenoid

solvent

(−)-menthol n-dodecane

thymol

overall: a

ideal UNIFAC PC-SAFTa

COSMO-RS

7.2

7.4

6.9

3.4

1-dodecanol

1.0

1.0

2.2

1.0

2-phenylethanol

0.9

3.2

1.1

4.3

n-dodecane

18.9

2.1

2.1

1.7

1-dodecanol

2.5

1.6

1.1

3.1

2-phenylethanol

3.1

2.5

1.4

6.5

6.2

2.9

2.5

3.0

The results shown correspond to the strategy 2 applied.


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Table 2. Summary of Thermodynamic Modeling of the Investigated Binary Systems in Terms of PC-SAFT Equation of State: Infinite Dilution Activity Coefficients of Terpene in Solvent (γ1∞ ) Predicted by the Modified UNIFAC (Dortmund) Model, Binary Interaction Parameters X ) Adjusted to γ ∞ and the Corresponding Average Absolute Deviations (AAD) between (k12 1

Calculated and Experimental SLE Temperature. terpene

solvent

strategy 0

γ1∞

LB k12

AAD(T) / K menthol

n-dodecane 1-dodecanol 2-phenylethanol

menthol

a

13 6.5 12

strategy 1

strategy 2 AAD(T) / K

X

X k12

AAD(T) / K

3.723

−0.0105

6.6

LB

−0.0105

6.9

1.018

−0.0269

1.1

WS

−0.0605

2.2

1.472

−0.0476

2.9

WS

−0.0797

1.1

n-dodecane

2.7

4.780

0.0030

2.1

LB

0.0030

2.1

1-dodecanol

3.7

0.4060 −0.0310

1.6

WS

−0.0783

1.1

2-phenylethanol

6.4

0.3849 −0.0664

0.94

WS

−0.1221

1.4

Details given in the text.



320

300

T/K

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280

260

240 0

0.2

0.4

0.6

0.8

1

x1

Figure 1. Experimental SLE phase diagrams for binary systems {(−)-menthol (1) + solvent (2)}. Open symbols (this work): circles, n-dodecane; squares, 1-dodecanol; triangles, 2-phenylethanol. Filled symbols (see reference 16):

circles, n-decane; squares, 1-decanol; triangles, 2-

cyclohexylethanol. Solid line designated by ideal solubility equation.


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330

310

T/K

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290

270

250 0

0.2

0.4

0.6

0.8

1

x1

Figure 2. Experimental SLE phase diagrams for binary systems {thymol (1) + solvent (2)}. Open symbols (this work): circles, n-dodecane; squares, 1-dodecanol; triangles, 2-phenylethanol. Filled symbols (see reference 16):

circles, n-decane; squares, 1-decanol; triangles, 2-

cyclohexylethanol. Solid line designated by ideal solubility equation.



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Figure 3. Screening charge distributions (BP-TZVP-COSMO level) and COSMO-RS σ-profiles of the compounds investigated in this work: (a) terpeneoids: (−)-menthol and thymol; (b) solvents: n-dodecane, 1-dodecanol and 2-phenylethanol. Thicker lines correspond to lowest-energy conformers.


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Figure 4. Experimental vs calculated SLE phase diagrams for binary systems {terpeneoid (1) + n-dodecane (2)} investigated in this work. Symbols: circles, (−)-menthol; squares, thymol. Lines designated by the models: solid lines, modified UNIFAC (Dortmund); dashed lines, PC-SAFT (strategy 2); dash-dot line, COSMO-RS.



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Figure 5. Experimental vs calculated SLE phase diagrams for binary systems {terpeneoid (1) + 1-dodecanol (2)} investigated in this work. Symbols: circles, (−)-menthol; squares, thymol. Lines designated by the models: solid lines, modified UNIFAC (Dortmund); dashed lines, PC-SAFT (strategy 2); dash-dot line, COSMO-RS.


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Figure 6. Experimental vs calculated SLE phase diagrams for binary systems {terpeneoid (1) + 2-phenylethanol (2)} investigated in this work. Symbols: circles, (−)-menthol; squares, thymol. Lines designated by the models: solid lines, modified UNIFAC (Dortmund); dashed lines, PCSAFT (strategy 2); dash-dot line, COSMO-RS.



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Figure 7. Sensitivity analysis of the PC-SAFT calculations (strategy 2) expressed in terms of difference in average absolute deviation (AAD) of SLE temperature obtained from binary corrections fitted to infinite dilution activity coefficient differing by ±10% from the value predicted by modified UNIFAC (Dortmund): (a) systems with (−)-menthol; (b) systems with thymol.


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TOC Graphic


Phase Diagrams in Representative Terpenoid ... - ACS Publications

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