Thymol+l-menthol eutectic mixtures: Thermophysical properties and possible applications as decontaminants

The substitution of conventional organic solvents for others with less environmental impact is one of the basic premises of green chemistry. To carry this out optimally, tools based on the similarity of thermo-physical behaviour are being developed. Thus, the characterization of new solvents is a key step in any ﬁeld of application. In this work, we studied the eutectic hydrophobic thymol + l-menthol system. The solid–liquid equilibrium of the system and several properties of three of its mixtures close to eutectic composition were measured and discussed. Calculations and correlations were performed to obtain properties of interest such as the internal pressure, critical temperature, and solubility parameter, among others. To predict the system behaviour under any operating conditions, the PC-SAFT equation of state was validated. Considering the problem of the presence of drugs as micro pollutants in the environment, the ability of this eutectic system to both dissolve drugs and remove them from contaminated water was also analysed. The results showed a strong thymol-l-menthol interaction, and a higher thymol ratio made the liquid more compact and structured but less polar and viscous. The difference in densities with respect to that of water and the moderate viscosity values indicated that this system can be an adequate solvent in liquid–liquid extraction processes. The solubilities of quercetin (Q), nitrofurantoin (NF) and tetracycline (TC) were enhanced in the eutectic mixtures; for Q, the solubility was 10000-fold higher than that in water. Finally, this system could be used to remove traces of Q and NF from the water, with an efﬁciency of up to 81 %. (cid:1) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
The goal of directive 1999/13/CE is the prevention of the effects associated with the emissions of volatile organic compounds (VOCs) on people and the environment.For that, limits and conditions of utilization are imposed.Industries can opt for the modification of their facilities or the substitution of VOCs by eco-friendly fluids.The second option is economically advantageous, but the chemical-physical properties of the neoteric solvent must be known and be similar to the one it replaces.Therefore, there must be tools containing a wide database of these properties to optimize the composition of the alternative fluids.The Program for Assisting the Replacement of Industrial Solvents (PARIS III) is the software developed by the United States Environmental Protection Agency (EPA) [1].It uses the following concept: the solvent capacity of a fluid is a consequence of the values of its thermodynamic (activity coefficients, density, surface tension, and critical points) and transport (diffusivity and viscosity) properties.Based on them, each solvent is represented by coefficients, and the application provides a substitute with the closest values.Environmental and safety requirements are also considered.The search for new solvents is essential to the pharmaceutical industry.Several private companies and institutions, such as the ACS Green Chemistry Institute Pharmaceutical Roundtable, have updated solvent selection guides and online tools based on physicochemical affinity [2][3][4].It should be noted that most of the active principles (APIs) are poorly soluble compounds in water [5].Therefore, they present problems such as insufficient bioavailability, the delayed onset of action and erratic absorption [6].Strategies such as the preparation of solid dispersions, formation of cocrystals and salts, emulsions or confinement in mesoporous silica [7] solve some of the problems.The formulations of the APIs in the liquid state could also avoid the inconve-niences associated with their possible polymorphism.They can be obtained by solubilisation using a drug vehicle.For this aim, conventional solvents are not adequate, and eutectic solvents (ESs) can be an alternative [5,8].The ESs are mixtures whose experimental melting temperature T m ð Þ is lower than those of the pure compounds.They are known as deep eutectic solvents (DESs) if the difference between T m and the theoretical temperature assuming ideal behaviour T id m is large, and they are called natural deep eutectic solvents (NADESs) if, in addition, the components are metabolites.The latter are especially interesting due to their low toxicity.Other properties can be mentioned, according to the green chemistry principles, such as their nonflammability and nonvolatility and their easy, cheap and lack of waste preparation; thus, DESs are being used in various applications [9][10][11][12][13][14][15][16][17].Among other factors, the depression in T m is a consequence of the capability of the components to form hydrogen bonds.This network provides the liquid with high stability and facilitates the solubility of species with donor and acceptor groups.Recent studies [8,[18][19][20][21] have reported the increased solubility and improved stability of drugs when they are dissolved in NADESs.For example, the solubility of itraconazole in a choline chloride:glycolic acid mixture is 6700 times greater than that in water, and the hydrolysis of aspirin is 8 times slower in choline chloride:1,2-propanediol.Similarly, there is a second way to obtain liquid pharmacological formulations.Considering that APIs usually contain chemical groups that can act as hydrogen bond donors or acceptors, they can form eutectic mixtures with an excipient or between them.These mixtures have therapeutic characteristics and are called THEDES [22].Their main advantage is that the pharmacological properties of the APIs can be modified without structural changes.The literature reports an improvement in the bioavailability, permeability and therapeutic activity with respect to the solid form [20] of the drug.Bonain's liquid, first prepared in 1889, was the first therapeutic eutectic mixture [23].It is composed of phenol, cocaine hydrochloride and menthol in an equivalent ratio and has anaesthetic effects.In 1992, the U.S. Food and Drug Administration approved the first commercial THEDES, the lidocaine:prilocaine equimolar mixture.It was formulated as an oil-in-water emulsion and exhibited higher efficacy than the compounds applied separately [24,25].Later, mixtures with ibuprofen, aspirin or lidocaine, among others, were evaluated.The high API concentration in the mixture and the presence of permeation enhancers such as menthol or thymol favoured the diffusion of drugs [8].The ever-increasing use of drugs and their high excretion percentage has made their presence in the environment a problem to be addressed by institutions [26].In 2018, the water crisis was classified as one of the 5 main social risks (World Economic Forum's Global Risks Report 2018; https://reports.weforum.org/globalrisks-2018).It is not only a problem of quantity but also of quality.Thus, a specific challenge of the European Green Deal says, 'Towards a zero-pollution ambition for a toxic free environment'.Its aim is focused on the removal of persistent chemicals, highlighting existing deficiencies in scientific knowledge.Eutectic mixtures with hydrophobic character have also been studied since 2015 as extraction solvents of persistent contaminants in aqueous medium [11,[27][28][29][30][31][32][33][34][35].Among them, we highlight those containing thymol (T) and menthol (M) from now called TM system, because both components are considered generally recognized as safe (GRAS) by the Environmental Protection Agency (EPA).Thymol, a phenolic monoterpenoid, is the main component, close to 50 %, of the oil of thyme.It is a powerful fungicide and pesticide that has other uses in the cosmetic, agri-food and pharmaceutical industries.Menthol is a cyclic monoterpenoid alcohol that can be synthesized in the laboratory or extracted from plants in the menthe family.It has eight stereoisomers, with l-menthol being the only one with a natural origin.It also presents the best dermal properties, and has shown several therapeutic properties as an analgesic, antitussive, antiviral or anticancer, among others [36].A synergistic effect of the TM eutectic system as an antimicrobial agent has been observed [37].Despite the similarity of the structures of its components, this system exhibits a nonideal unexpected behaviour [38][39][40][41].Therefore, the study of this THEDES is interesting both from a theoretical point of view and from its applicability.Several authors have analysed the solid-liquid phase transitions [38][39][40][41] and published density and viscosity data at atmospheric pressure [28,[42][43][44][45][46].No density under pressure or other properties were found in the literature; however, there is a greater number of publications about its extraction capacity.The extracts were usually chlorophenols, drugs, pesticides and organic acids, and the matrices were polluted water and biomass [28,43,44,[46][47][48][49][50][51][52].
This article will focus on the thermophysical characterization of thymol:l-menthol mixtures to be implemented in industry as alternative solvents.Moreover, its ability to dissolve three APIs (quercetin, nitrofurantoin, and tetracycline) and its capacity to remove them from aqueous medium were evaluated.The manuscript has been organized as follows.In Section 2, the materials, devices, and methods used to obtain the experimental data are briefly described.Section 3 begins with the study of the solid-liquid phase change.The thermal events are described, and the experimental data are shown and thermodynamically modelled.Later, the results of the thermophysical characterization of three mixtures of TM systems are presented, correlated, and discussed.The measured properties are the density (from 0.1 to 65 MPa), speed of sound, refraction index, static permittivity, isobaric molar heat capacity, surface tension, and viscosity.Finally, solubility and extraction studies are reported.The solubility parameters of the solvents are calculated, and the feasibility of these DESs to dissolve poorly water-soluble drugs and remove them from aqueous medium is given.The article ends with Section 4, which includes a summary of the conclusions.The Supplementary Information (S.I.) contains the description of the correlations and models used in the characterization, all of the experimental values of the measured properties, and additional figures to the manuscript.

Materials
The chemicals used as components of the eutectic mixtures were thymol (T) and l-menthol (M).We chose the l-menthol isomer because it is the main menthol form in nature.The active principles studied in the solubility and extraction experiments were quercetin (Q), nitrofurantoin (NF) and tetracycline (TC).All compounds were supplied by Sigma-Aldrich and were used without further treatment.Table 1 and Fig. 1 report the characteristics and structures of the compounds.The studied mixtures were thymol + l-menthol (TM) in the following three molar ratios: 1:2, 1:1, and 2:1.To prepare the mixtures, the pure compounds were weighed in adequate proportions using a PB210S Sartorius balance with an uncertainty of 1Á10 -4 g.Subsequently, simultaneous stirring and heating were used to obtain a stable liquid phase over time.At this stage, the temperature was maintained close to 323 K to avoid the thermal degradation of the components.Table 2 reports the acronyms used in the manuscript for the TM mixtures, composition, molar mass (M w ), and melting temperature (T m ).

Calorimetric characterization
The solid-liquid equilibria (SLE) was obtained with a differential scanning calorimeter (TA Instruments DSC Q2000) with a RCS cooling system.A standard of Indium was used to carry out the temperature and heat flow calibrations by using its melting properties.The differences between the expected values of Indium and those obtained during the calibration showed that the uncertainties in T m and D m H were 0.5 K and 1 kJÁmol À1 , respectively.For each mixture used to build the SLE diagram, a sample (5 to 15 mg) was weighed and introduced into an aluminum pan in liquid state.If the sample was solid at room temperature, once the pan was in the DSC a preheating step was performed up to a temperature higher than the melting point to ensure the crystallization of the mixture within the device.The samples were firstly cooled at 203-213 K at 3 K/min and later heated at the same scanning rate up to 10 above the phase change.The reported temperatures correspond to the maximum peak because of the asymmetric peak shapes and the presence of thermal anomalies which difficult the determination of the onset temperature.
On the other hand, sapphire was used in addition to Indium during the calibration to obtain the isobaric molar heat capacity values.Two different sapphire experiments were carried out, before and after each daily measurement session, to discard any temporal evolution of the heat capacity calibration factor.

Thermophysical properties
The thermophysical properties were measured with several thermostatised devices that are widely used in the literature.Therefore, no full description is given in this paper.Table 3 summarizes the standard uncertainty in the temperature (uðTÞ), the   calculated combined expanded uncertainties (U c ðYÞ) for each property (0.95 level of confidence, k= 2), and the mean relative deviations (MRDðYÞ=%) in the checking of each piece of equipment.

Solubility and extraction
The thermodynamic solubilities (W) of Q , NF, and TC were measured in the three TM mixtures with the shake-flask method at a constant temperature of 298.15 K.The method is based on the addition of a solid solute until supersaturation is reached and subsequent analysis of the liquid phase.We used an ultrasonic bath with temperature control to facilitate solute-solvent mixing.For each result, five samples were prepared and mixed, and two aliquots of each sample were centrifuged and filtered (PES syringe filter, 0.22 lm).Then, every solubility result was the average value of ten analyses.The measurement had to correspond to the system in equilibrium, and thus, several analyses were performed at different mixing times (30 to 120 min).The value that remained constant was given as the thermodynamic solubility.The API concentration was measured by VIS-UVA spectrophotometry with VWR 6300 PC double-beam equipment (uðk)=±0.2nm).In the Supplementary Information (S.I.), Table S1 lists the equations of the calibration curves and their limits of detection and quantification.
The extraction efficiency, EE, was determined by liquid-liquid extraction taking advantage of the hydrophobic nature of this system.To do this, stock solutions of contaminated water were prepared and analysed to determine the API pre-extraction concentration, C i .The values were Similar volumes of stock solution and eutectic solvent were mixed over 12 h in a double wall thermostatic flask at 298.15 K.After deposition and centrifugation, the postextraction concentration, C f , was obtained.Each data point is the average of the analyses that reached thermodynamic solubility.The efficiency was calculated with the following equation:

Results and discussion
Knowing the thermophysical behaviour of fluids under different pressure and temperature conditions is essential for their use in industry.If experimental values are not available, having prediction tools can be a good substitute, although they must first be validated.We report herein a comprehensive characterization of the thymol + l-menthol (TM) system.It includes the measurement and analysis of both the change in the solid-liquid phase of the system and the thermophysical properties of three mixtures of molar ratio compositions (1:2), (1:1), and (2:1).Additionally, several correlations and models were validated using the experimental values.A brief description of them is given in the S.I.

Solid-liquid equilibria
Table 1 lists the melting temperatures values and enthalpy of the pure thymol and l-menthol.The experimental values agreed with those of the literature considering the experimental uncertainties.For these mixtures, the thermograms had two main features.First, the enthalpy peaks were very small even at compositions far from the eutectic composition (Fig. 2).This could be due to the presence of micro heterogeneities formed by clusters of different sizes, which would result in the crystallization of only a small fraction of the sample [41,59].On the other hand, no melting of the eutectic fraction (T E exp ) was detected in any of the experiments.Instead, glass transition temperatures (T g ) have been obtained (Fig. 3).For the equimolar mixture, there was no peak upon heating.The strong interactions between thymol and lmenthol provoke kinetic constraints on the formation of crystalline phases because the hydrogen bonds hinder the molecular rearrangement necessary for crystallization.The system transitions from a subcooled metastable state to a vitreous state [39].As we move away from the eutectic composition, the kinetic restrictions decrease, and the molecules that are not part of the eutectic manage to rearrange themselves by crystallizing and subsequently melting.Alhadid et al. [39,40] only detected T E exp , with a value of 241.45 K, if the sample was stored at 193 K for one month.
Table S2 lists the melting and glass temperatures determined in this work during the heating step.Mixtures of compositions within the range 0.16 < x Thy < 0.78 were liquids at T > 298.15 K.This wide liquid window allows tuning the mixture with the most suitable thermophysical properties for each application.Our data of solid-liquid phase equilibria (SLE) and those from the literature are displayed in Fig. 4. The diagrams were similar, and the largest deviations were found in the interval 0.6 < x Thy < 0.8, in which T m barely changed with x Thy .This fact is related to the presence of metastable solid-states [40].The figure also includes T g points.Our average value of 213.76 K was only 0.6 % higher than that reported by Abranches [38].
A eutectic mixture can be named deep (DES) if its melting temperature is much lower than it would be if it were ideal.Therefore, it is convenient to estimate the ideal phase diagram of the system and to compare it with the experimental diagram.To do this, the thermodynamic equation that provides the solubility of a solid in the liquid phase is used.Neglecting the term corresponding to the variation in the heat capacity, the expression is: where c l i is the activity coefficient in the liquid phase of component i at composition x i ;T m;i and D m H i are the melting temperature and melting enthalpy of component i; and T m is the melting temperature of the mixture.For c l i = 1, the calculated solubilities are those assuming ideal behaviour.Although we were unable to measure T E exp , Fig. 4 shows a clear negative deviation from ideality, with a (T E exp À T E id ) of approximately 40 K.Then, the TM system could be named a DES.
The measured T m values were correlated with the nonrandom two-liquid model (NRTL) (S.I.) [60].The model parameters were A 12 ¼ À 3363.16JÁmol À1 and A 21 ¼ À 5820.78JÁmol À1 , and the estimated eutectic points were x E Thy;NRTL ¼0.4651 and T E Thy;NRTL ¼ 232:65K.The activity coefficients (c i ) were also calculated and are listed in Table S2.From them, a deviation from ideal-ity more pronounced at higher x Thy was observed.These results can be explained by the resonant effects of thymol when delocalizing the free pair of electrons from oxygen.For Eq. ( 1), c l i can be calculated with a thermodynamic model as the ratio between the fugacity coefficients of component i in the mixture and in the pure state.Herein, we used the PC-SAFT equation of state (EoS) (S.I.) [61,62].The parameters necessary for the calculation are given in Table S3, and the estimated curve is included in Fig. 4. The mean relative deviation calculated between the experimental and predicted melting temperatures for the three characterized mixtures was lower than 1 % (Table S4), and the average value for the SLE was MRDðT m Þ = 1.5 %.

Thermophysical study of TM mixtures
The studied properties were density  4 to ease the follow-up of the discussion.
Standard uncertainties are: u T ð Þ=0.005K for density and speed of sound and 0.01 K for the rest of properties; u p ð Þ=0.5 kPa.The combined expanded uncertainties (0.95 level of confidence, k=2) The densities at 0.1 MPa ranged (Fig. S1) from 890.67 kgÁm À3 for TM12 at 338.15 K to 953.12 kgÁm À3 for TM21 at 288.15 K.At the same compositions and temperatures and 65 MPa, they were 928.82 and 985.50 kgÁm À3 , respectively.On average, q was 6.5 % lower than that of water at similar p and T, which can ensure an adequate phase separation in the liquid-liquid processes [28].The density increased with increasing thymol molar ratio (x Thy ), which is logical since thymol is a flatter molecule than l-menthol due to the presence of the aromatic ring.Several authors [28,[42][43][44][45] have published densities of the TM system at atmospheric pressure.The values were in agreement with ours, with an average mean relative deviation of 0.12 %.The graphic comparison is shown in Fig. S2a.No pqT data were found in the literature.As usual, q decreased with increasing temperature and decreasing pressure.Thermal agitation weakens the interactions in the mixture, while decreasing the free volume increases the number of  molecules per unit volume.At 0.1 MPa, this behaviour is shown in Fig. S1a.The behaviour under pressure is displayed in Fig. 5a for the TM11 mixture and Fig. S3 for the rest of the mixtures.The equations of the relationships are summarized in S.I.Table 5 reports the parameters of the qT relationship at 0.1 MPa, and Table 6 lists those of pqT.
We quantified the effect of the temperature and pressure on the density with the calculation of the isobaric thermal expansibility (a p ) and the isothermal compressibility (j T ): For each p and T, a p hardly changes as the molar ratio of thymol increases.On the other hand, the expansion capacity of the mixtures increased with increasing temperature or decreasing pressure according to the weakening of the forces between the components (Fig. 5b and S4).The effect of T on a p was more pronounced at lower pressure, and the effect of p on a p was more pronounced at higher temperature.For example, for TM12 at 0.1 MPa, a p ranged from 0.730 kÁK À1 at 283.15 K to 0.911 kÁK À1 at 338.15 K.At 65 MPa, the values were 0.620 and 0.704 kÁK À1 , respectively.The j T calculated values showed that the more compact the mixture was, the higher the thymol ratio.Thus, TM21 was, on average, 4 % less compressible under isothermal conditions than TM12.This property increased when the temperature increased, especially at lower pressures, and with higher pressure decreased mostly at higher temperatures (Fig. 5c and S5).The internal pressure (p T ) is defined as the change in internal energy of a system when the volume changes at constant temperature.The p T sign indicates the type of intermolecular forces prevailing in the system.The more positive the internal pressure is, the greater the attractive forces.It can be calculated from a p and j T data: For the studied mixtures, Table 4 collects the values at 298.15 K, which increased with increasing thymol ratio.This result highlights the importance of the pÀ interactions.To validate the PC-SAFT EoS for the volumetric behaviour, we calculated the densities in the p and T working ranges of this work and compared them with the experimental densities.The model slightly overestimated the pqT data with an average deviation of 1.21 % for the TM system.No trends were observed with composition and temperature, but the higher the pressure was, the greater the deviation.The maxima deviations were 0.83 and 2.00 % at 0.1 and 65 MPa, respectively.Table S4 lists the deviation values, and Fig. S6a shows the graphic comparison for the TM11 mixture; the remaining compositions were similar.
The compactness of a fluid can also be evaluated in terms of the free intermolecular length (L f ) and the free volume (f m ).These properties can be calculated from q; u and n D experimental data with the following expressions: where K ¼ f ðTÞ is Jacobson's constant [63]; j s is the isentropic compressibility; and V m and R m are the molar volume and refraction, respectively.The more compact the fluid is, the higher the speed of sound and the refraction index and, consequently, the lower the values of j s , L f ; R m ; and f m .In fact, the effect of the composition and temperature on these properties (Table 4, Fig. S1b, S1c, S7) was similar to that obtained for the volumetric properties.
The linear fit parameters of the u À T and n D À T equations are found in Table 5.For L f and f m , the calculated values ranged from 0.422 to 0.567 Å and 112.48 to 125.56 cm 3 Ámol À1 , respectively.Considering V m , the percentage of free volume (f m =V m ) of each mixture was within 71.3-72.5 % for TM12, 70.8-72.0% for TM11, and 70.4-71.5% for TM21.It is known that the PC-SAFT EoS does not adequately predict the values of the speed of sound, and the way to improve this prediction entails the modification of the universal constants of the model.For that, a deeper study of the question must be carried out in the future.In this work, the calculated u values were less than those measured with an average MRD u ð Þ ¼ 15 %.The deviations increased with decreasing T and x Thy , and the maximum deviation was 18 % (Table S4).The static permittivity allows the polarity of nonionic fluids to be analysed.For that,e; q and n D data under the same conditions are necessary, and the Fröhlich equation [64] is used: where e 0 is the vacuum static permittivity and l is the dipole moment of the mixture estimated from those of the pure compo- . The g factor is the Kirkwood-Fröhlich correlation parameter and is related to the orientation of the neighbouring dipoles.Therefore, g > 1 for fluids with parallel preferential disposal and <1g for those with antiparallel dipoles.Taking the l i data found in the literature (Table 1), we calculated the g parameter for each TM mixture.The values ranged from 1.33 to 1.69, were higher at lower x Thy , and barely changed with T. This result indicated a parallel preferred orientation between dipoles for all mixtures.The polarisation is also evaluated with the orientational dipolar parameter gl 2 À Á .Bouteloup et al. [65] published gl 2 data for pure thymol and l-menthol.The calculated values for the TM mixtures (Table 4) were much higher than those, which indicates that this parameter is not additive.Taking into account Eq. ( 7), similar trends of e and gl 2 with T must be expected.The e À T fit coefficients are listed in Table 5.Nevertheless, the opposite is observed, as shown in Fig. S1d and S8.This fact was already observed for other liquids, such as eutectic mixtures containing thymol or l-menthol and carboxylic acids [34,35].This is related to the increase in the effective dipole of the system caused by thermal agitation favouring the linear form of the aggregates over the cyclic form.
To characterize variable temperature processes, it is necessary to know the thermal behaviour of solvents.This includes knowing both its phase diagram and its ability to store heat.The measured values of the isobaric molar heat capacity were within 298 and 357 JÁmol À1 ÁK À1 .They were similar for all TM mixtures, which can be explained by their similarity of nature and molar mass.The C p;m value is related to the accessible vibration modes of the molecules, and its number increases with T. Therefore, unlike the rest of the thermophysical properties studied here, the slope of the C p;m À T equation was positive (Table 5, Fig. S1e).Taherzadeh et al. [66] have proposed a correlation to estimate the C p;m of deep eutectic solvents from the molar mass and critical properties (S.I.).The average deviation between our experimental and correlated values was 7.3 %, increasing with x Thy , and it was slightly higher than the predictive capacity of the model, 5.3 %, published by the authors.Moreover, we used the PC-SAFT EoS to calculate C p;m .Similar to u, the model underestimated the values, although to a lesser extent.The average and maximum deviations were 5.64 and 8.73 %, respectively.Unlike for u, the trends were opposite.MRDðC p;m Þ increased with increasing T and x Thy , as shown in Fig. S6b.
The surface tension of a liquid is a measure of the cohesive forces in the bulk.The more structured the system is, the higher the c value.It is an essential property in processes including solvent atomization.The experimental values for the TM system varied from 27.35 to 31.18 mNÁm À1 .In agreement with the above results, TM21 presented the highest values.The rise of energy favours chaos in the fluids, and thus, the slope of the equation is negative (Table 5), as shown in Fig. 6a.The obtained values of the thermodynamic properties of the surface per unit surface area at 298.15 K are found in Table 4.The entropy (DS Parameters of the Tait equation and the corresponding standard deviations, MRD q ð Þ a , of the [TM]ESs.

TM12 TM11 TM21
A 0 =kg Á m À3 1028:23 1033:09 1084:32  was similar for the three mixtures, and the enthalpy (DH S ¼ c À T @c=@T ð Þ p ) increased with the thymol ratio.The authors have proposed equations that relate the surface tension to the critical temperature (T c ) of fluids.This is interesting because knowing the T c value is imperative for the application of thermodynamic models, but its measurement is sometimes not possible.In this work, we applied the Guggenheim and Eötvos correlations (S.I.) [67,68] as well as the PC-SAFT EoS.The calculated data are reported in Table S7.Assuming that the latter is an adequate model for the TM system, the average deviations for the two correlations were less than 3 %.Fig. S9 displays the predicted critical locus, T c À x Thy and p c À x Thy curves, for the system.
Finally, we analysed the fluidity of the TM hydrophobic mixtures.They presented moderately high values at low temperatures, reaching 347 mPaÁs for TM12.The literature suggests that 100 mPaÁs can be the maximum viscosity value to ensure a proper mass transfer process [28].According to that, the operating temperature with the TM mixtures must be higher than 288 K to achieve their best functionality.In Fig. S2, a comparison with the literature [28,42,45] is shown.The values were different between the authors, and our results were in agreement with those of Martins et al. [42] with a deviation of 6.4 %.The change in temperature has an important effect on this property, as seen in picture g À T (Fig. 6b), which fits an exponential mathematic function whose coefficients are listed in Table 5.The pre-exponential factor A Y ð Þ is the viscosity of the fluid at T ¼ 1, that is, without molecular interactions, and the rest of coefficients B Y ; C Y ð Þallow us to calculate the energy of the viscous flow (E a;g ); that is, the barrier that must be overcome for a molecule to move around others: Fig. S10 shows the polynomial decay of E a;g with T. The E a;g values were higher for TM12, and thus, we can say that this mixture has greater interactions between layers.We used the Pelofsky and Murkerjee equations [69] to correlate the viscosity and surface tension properties.The expressions and coefficients are collected in the S.I. and Table S8.The linear regression coefficients indicated that the Murkerjee equation was a better representation for our system.

Solubility and extraction efficiency
One of the most important parameters to characterize the solvent power of a fluid is the parameter of solubility (d).It was defined by Hildebrand [70] as the root of the cohesive energy density (CED): where DE vap and V m are the enthalpy of vapourisation and the molar volume of the solvent, respectively.The d values could be obtained from experimental measures of DE vap , but sometimes it is not possible due to the thermal degradation of substances.Thus, other experimental properties related to the structuring of the liquid can be used, such as density and surface tension.If pqT data are available, as in this work, the CED can be approximated to the internal pressure.From c and q data under the same conditions, several equations have been proposed to obtain d.We have used that proposed by Pereira and Vebber [71] based on Stefan's rule.The equations are as follows: The units of c and V m are mNÁm -1 and cm 3 Ámol -1 , respectively.
Additionally, the PC-SAFT EoS predicted the Hildebrand parameter.Later, Hansen [72] separated the cohesive energy into three contributions due to the different attractive interactions: dispersive (d d ), polar (d p ), and hydrogen bonds (d H ). Thus, the total Hansen solubility parameter (HSP) denoted d T (¼ d) is calculated as: The dispersive interactions are proportional to the square of the polarizability (a) and cause very small fields that disperse the light through the materials.Then, d d is related to the refraction index [73].The polar contribution includes both the dipole-dipole attractions, proportional to the fourth power of the dipole moment (l), and the dipole-dipole induction, proportional to al 2 .Hansen and Beerbower [74] proposed a simplified equation to estimate d p .The last contribution is estimated from the energy of vapourisation of the OH À O hydrogen bond from infrared spectroscopy [75].The equations for the three contributions (MPa 1/2 ) are: where N is the number of hydroxyl groups in the solvent and the units of l and V m are D and cm 3 Ámol -1 .
Literature [76] reports HSP values of thymol and l-menthol estimated by group contribution methods.Then, we also calculated those for the mixtures as: where u i is the volume fraction of component i in the mixture and d HSP ð Þ i is each parameter.All of the calculated values are listed in Table 7.The similarity of the values obtained from different thermophysical properties indicates the goodness of the results.The highest average deviation, 10 %, was found to compare with d T estimated from the group contribution method.The Hildebrand parameter was slightly higher than the total HSP (Eq.( 12)), and the effect of the composition was only noticeable in the polar contribution.Next, the experimental results of the thermodynamic solubility (W i ¼ g i =g solvent ) of quercetin (Q ), nitrofurantoin (NF), and tetracycline (TC) in the characterized eutectic mixtures are presented.The first two APIs are insoluble in water, and the third is very slightly soluble (Table 8).In [TM]ESs, the solubility was increased in all cases, and it was especially pronounced for Q (Fig. 7a).Note that the trend of W Q with x Thy was opposite to those found for W NF and W TC .The studied drugs present different characteristics.From Table 1 and Fig. 1, it can be seen that Q has the smallest dipole moment of the three drugs but a high polarizability, and TC has the highest value of both properties.In relation to the formation of hydrogen bonds, Q and TC present a large number of donor and acceptor sites.On the other hand, NF exhibits the weakest interactions.The dissolution process can be summarized in three stages: relaxation of solute-solute and solvent-solvent interac-tions, relocation of the solvent around the solute, and establishment of new solute-solvent interactions.That is, thermodynamic solubility depends on entropic and enthalpic aspects.The former is related to the free volume of the solvent, which we calculated in the above section from the thermodynamic properties.The second is a consequence of the balance between cohesive and adhesive forces in the solute-solvent system.Fig. 8 illustrates both effects.Due to the number of hydroxyl groups and the flat structure, the Q solubility was favoured in the least compact solvent.On the other hand, the enthalpic factor prevailed for NF and TC.
The immiscibility of hydrophobic solvents in aqueous media allows their use in liquid-liquid extraction processes.Specifically, the mixtures studied here have shown efficiency in the removal of chlorophenols, drugs, organic acids and pesticides from polluted water [28,43,44,47,49,50].Next, we evaluated the extractions of Q , NF, and TC atT = 298.15from dilute aqueous mixtures with [TM] ESs and calculated the extraction efficiencies (EE) as described in Section 2.4.The partition coefficients (P ½TMESs=w ) are also obtained.The results are listed in Table S9 and displayed in Fig. 7b.For Q and NF, the efficiency was similar and ranged from 60 to 81 %.For TC, the EE was up to 46 %.For all drugs, it increased with increasing thymol composition.Solvent properties, such as the density, viscosity or polarity, influence this type of process.Fig. 9 shows that a high density and low viscosity and polarity increased the EE.The relative solubility had a lower effect.

Conclusions
To achieve the first objective of this work, we studied the thermophysical behaviour of a hydrophobic eutectic system containing thymol and l-menthol ([TM]ESs).The diagram of the solid-liquid phase was measured and compared with the one calculated assuming ideal behaviour.The SLE was correlated with NRTL model and PC-SAFT EoS.For three mixtures of this system with molar ratios of (1:2), (1:1) and (2:1), several properties at 0.1 MPa and over a wide range of temperatures were determined: density, speed of sound, refraction index, isobaric heat capacity, static permittivity, surface tension and viscosity.Additionally, densities up to 65 MPa were measured.Correlations and calculations were performed on the experimental data.Therefore, the internal pressure, intermolecular free length, orientational dipolar parameter, enthalpy and entropy of the surface, critical temperature, and activation energy of the viscous fluid were obtained.
The second aim included an evaluation of the solubilities of the characterized mixtures.The Hildebrand and Hansen solubility parameters were estimated from the experimental above data.The thermodynamic solubilities of quercetin (Q ), nitrofurantoin (NF), and tetracycline (TC) in the [TM]ESs were measured and discussed.Finally, their extraction from the aqueous medium was carried out using the hydrophobic character of these liquids.
The SLE showed a strong interaction between both components that prevented the crystallization of the eutectic fraction and caused a negative deviation from the ideal behaviour.Then, the system thymol + menthol can be named a deep eutectic solvent.At any pressure and temperature within the range of this work, the densities were sufficiently lower than those of water to ensure a correct phase separation in liquid-liquid processes.Moreover, the most compact and structured mixture was that with the highest thymol ratio.Conversely, it was the least polar and viscous.Regarding the fluidity, a temperature higher than 288 K would assure an adequate functionality of these mixtures.No appreciable effect of the composition on the solubility parameters was observed.The solubility of Q in [TM]ESs was 10 4 -fold higher than that in water, being favoured in the least compact mixture.For NF and TC, the increase was lower, and the enthalpic effect was more significant.A high density and limited viscosity and polarity increased the extraction efficiencies of these compounds from contaminated water.For Q and NF, the eutectic system showed high efficiencies, up to 81 %, and a medium efficiency was achieved for TC, up to 46 %.

Fig. 1 .
Fig. 1.Structure of the compounds used in this study.

Table 2
Characteristics of the studied thymol + l-menthol eutectic solvents ([TM]ESs).a .Mw ¼ P i M w;i x i b This work; u Tm ð Þ¼ 0.5 K.

Table 3
Summary of the devices used in the thermophysical characterization.
a k = 2 (0.95 level of confidence).b MRDðYÞ ¼ 100 n P n i¼1 j Yi;lit ÀYi;exp Yi;exp j, F. Bergua, M. Castro, C. Lafuente et al.Journal of Molecular Liquids 368 (2022) 120789 Þ, and dynamic viscosity (g).They were determined at p ¼ 0.1 MPa and at temperatures ranging from 278.15 to 338.15 K.The experimental data at each temperature, composition and at 0.1 MPa are collected in TableS5.The density was also measured up to 65 MPa in the T range of 283.15-338.15K,and the pqT values are listed in TableS6.Moreover, the experimental and calculated values at 298.15 K for different properties are collected in Table ð

Table 4
Summary of the thermophysical properties at T ¼ 298.15K and p ¼ 0.1 MPa of the [TM]ESs.

Table 5
Fit parameters (AY ; BY ; CY ) and the regression coefficients, R 2 , for the thermophysical properties of the [TM]ESs.

Table 7
Solubility parameters of the [TM]ESs.