Influence of Additives (Isoamyl Laurate or Isoamyl Nonanoate) in the

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Influence of Additives (Isoamyl Laurate or Isoamyl Nonanoate) in the Solid−Liquid Equilibrium of Fatty Acid Ethyl Esters Larissa Castello Branco Almeida Bessa,† Maria Dolores Robustillo,† Erica Corina da Silva,†,‡ Carmen Cecilia Tadini,†,‡ Antonio Jose ́ de Almeida Meirelles,§ and Pedro de Alcan̂ tara Pessôa Filho*,†,‡ †

Department of Chemical Engineering, Engineering School, University of São Paulo (USP), 05424-970 São Paulo, São Paulo, Brazil FoRC/NAPAN Food Research Center, University of São Paulo, 05508-080 São Paulo, São Paulo, Brazil § Department of Food Engineering (DEA), School of Food Engineering (FEA), University of Campinas (UNICAMP), 13083-862 Campinas, São Paulo, Brazil

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‡

S Supporting Information *

ABSTRACT: Solid−liquid equilibrium data of binary mixtures of fatty acid ethyl esters present in biodiesel, namely, ethyl laurate, ethyl palmitate, ethyl myristate, ethyl stearate, and ethyl oleate, and fatty esters of branched-chain alcohols used as additives (isoamyl laurate and isoamyl nonanoate) were obtained through differential scanning calorimetry. Most of these systems presented eutectic behavior, except for the system ethyl laurate + isoamyl laurate, which presented peritectic transition. Equilibrium data were thermodynamically modeled either using two different liquid-phase activity coefficient models or considering that the liquid phase is an ideal mixture. Best correlations were observed for the Flory− Huggins equation, but good agreement between calculated and experimental data was also obtained when using both the ideal and UNIFAC−Dortmund models.

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INTRODUCTION Biodiesel is a liquid mixture of fatty acid esters. It is a renewable fuel, with properties similar to those of conventional diesel, obtained from vegetable oils and animal fats. Biodiesel is nontoxic, biodegradable, and immiscible in water. In the form of fatty acid methyl or ethyl esters, it is produced through the catalytic transesterification of lipids with methanol or ethanol, respectively. The main biodiesel properties depend on the oils or fats used in its production. Its properties are similar to those of conventional diesel, and hence it may be used either as a neat fuel (100% biodiesel) or blended with petroleum diesel in compression−ignition engines.1 Compared to conventional diesel, biodiesel presents significant advantages: it is less toxic and more biodegradable, has a higher flash point, has lower (or insignificant) sulfur content, and results in lower emissions of regulated species.2 However, a major drawback of biodiesel is its comparatively poor cold-flow properties.1 Both the oil/fat and the alcohol employed in the transesterification reaction affect its cold-flow performance.3 A biodiesel rich in saturated fatty acid esters, for instance, despite being less vulnerable to oxidation and exhibiting better combustion properties, presents a poor performance at low temperatures due to its propensity to crystallize.4 Therefore, biodiesel performance must be supervised during cold seasons in regions of moderate temperature climates.1 Biodiesel performance at low temper© XXXX American Chemical Society

atures can be assessed through standard measurements, such as the cloud point and the pour point.3 The cloud point is the temperature of the onset of crystal formation, at which the liquid becomes cloudy.5,6 Decreasing the temperature, the material eventually reaches the pour point, below which it no longer flows.6 While the cloud point of diesel is around 257 K, the cloud point of biodiesel is close to 273 K, which restrains its use in lower temperatures.7 Cloud and pour points of biodiesel can be reduced by blending it with additives. Besides modifying cold-flow properties, additives used in biodiesel also affect other properties, including those relevant to transport, combustion, and emissions.8 There are essentially two categories of additives: those that lower the pour point and those that modify the structure of wax crystals.7 Additives used for conventional diesel are not effective for biodiesel, and additives specifically designed for biodiesel are still scarce.7 Fatty esters of branched-chain alcohols such as 3-methylbutyl dodecanoate (isoamyl laurate) or 3-methylbutyl nonanoate (isoamyl nonanoate) have provided satisfactory results as additives. Special Issue: Latin America Received: November 1, 2018 Accepted: March 19, 2019

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DOI: 10.1021/acs.jced.8b01019 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Suppliers and Mass Fraction Purity of Compounds Used in This Work component

CAS Registry No.

supplier

mass fraction puritya

molar fraction purityb

ethyl laurate ethyl palmitate ethyl myristate ethyl stearate ethyl oleate isoamyl nonanoate isoamyl laurate n-decane indium cyclohexane

106-33-2 628-97-7 124-06-1 111-61-5 111-62-6 7779-70-6 6309-51-9 124-18-5 7440-74-6 110-82-7

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich PerkinElmer Merck

>0.98 ≥0.99 0.99 ≥0.99 ≥0.98 ≥0.96 ≥0.97 ≥0.99 ≥0.9999 ≥0.99

0.994 0.981 0.993 0.978 0.991 0.973 0.974 0.997 1.0 0.999

a

As reported by the supplier. bObtained by the van’t Hoff plot method.

Lang et al.9 showed that the crystallization temperature of biodiesel can be lowered by 4 K by using a mixture of branched-chain fatty esters as additives. Nascimento et al.10 studied the effect of adding esters of carboxylic acids to lower the crystallization temperature of methyl palmitate, reaching a decrease of up to 10 K depending on the structure (either linear or branched alkyl chains), molar mass, and concentration of the ester. Finally, Soares et al.11 investigated the effect of several esters derived from branched chain in the crystallization behavior of methyl transesterified soybean oil. All compounds studied reduced the crystallization temperature of the biodiesel, and this reduction was a function of the concentration of the additive, even though the mechanism of action of these inhibitors in the solid-phase formation is not yet known. Ethyl esters have melting temperatures which are lower than those of the corresponding methyl esters, and this difference increases as the alkyl chain length decreases,12 which makes them interesting for low temperature applications. The solid− liquid equilibrium (SLE) data of binary mixtures containing fatty acid ethyl esters and additives were determined through differential scanning calorimetry and are analyzed in this work. The fatty acid ethyl esters studied are ethyl laurate, ethyl palmitate, ethyl myristate, ethyl stearate, and ethyl oleate; the additives are isoamyl nonanoate and isoamyl laurate. For the thermodynamic modeling, the liquid phase was described by three approaches: as an ideal mixture, by the Flory−Huggins equation,13 and by the UNIFAC−Dortmund (UNIFAC−Do) model.14

solid−liquid equilibrium of mixtures containing fatty esters.19,22−27 The temperature profile was specifically developed for the measurement of SLE data of fatty compounds, accounting for the uniformity of the crystalline structure. It comprises essentially a series of heating, cooling, and heating runs. Mixture samples were weighed and placed on hermetic aluminum pans. The temperature program consists of (i) a heating run at 5.0 K·min−1 to 15 K above the compounds’ highest melting point, followed by a 5 min isothermal period at this temperature, (ii) a cooling run at 1.0 K·min−1 to 25 K below the compounds’ lowest melting point, followed by a 5 min isothermal period at this temperature, and (iii) a heating run at 1.0 K·min−1 until the sample was completely melted.28−30 Nitrogen (99.99%) was fed at a rate of 50 mL· min−1 as purge gas. The equipment was previously calibrated using indium, cyclohexane, and n-decane. The uncertainties in the mole fractions and temperatures are estimated to be lower than 0.0002 and 0.3 K, respectively. Peak temperatures identify the corresponding transition temperatures.21,26,27,31−33 When peaks were partially superimposed, the temperature and enthalpy of each transition were obtained through the mathematical deconvolution of the thermograms. The software Origin 2018 was used to analyze peak temperatures and enthalpies of all transitions. The peaks of pure compounds’ thermograms are usually sharp, and the onset temperature is frequently taken as the melting point. This method was followed to calibrate the instrument with the standards. Nevertheless, for mixtures, polymorphic substances, and systems presenting transitions with overlapping peaks (among other circumstances), the corresponding peaks are not sharp and the determination of the onset temperature becomes imprecise and physically meaningless. The melting temperature is then defined by the peak temperature. Thermodynamic Modeling. Phase equilibrium calculations were performed considering only the occurrence of a eutectic reaction. Therefore, immiscibility in the solid phase was assumed. Solid−liquid equilibrium calculations were performed by solving eq 1 for each compound:

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EXPERIMENTAL METHODS Material. Table 1 presents suppliers and purities of the compounds used, including those used for calibration. Compounds were used as received without further purification. However, their purities were previously analyzed by the van’t Hoff plot method;15 corresponding calculations were carried out using the PerkinElmer analysis software. This method has been effectively used to analyze the purity of similar compounds.16−19 Experiments were conducted in a differential scanning calorimeter (model DSC 8500, PerkinElmer). Indium, cyclohexane, and n-decane were used as calibration standards. Sample masses were measured in a balance (Sartorius) with 220 g weighing capacity and 0.1 mg readability. Methods. Calorimetry is a well-established technique used to determine solid−liquid equilibrium data.20 The experimental procedure followed in this work was originally developed by Costa et al.21 and has been used previously for studying the

yz ΔfusHi ijj 1 jj − 1 zzz R jj T Tfusi zz k { ΔfusC p ij T fusi jij Tfusi zyzyzzz ij jj1 − − + ln jj zzzz R jk T k T {{

ln(aiL) = −

(1)

aLi

wherein is the activity of compound i in the liquid phase, ΔfusHi is the melting enthalpy of compound i, ΔfusCpi is heat capacity change upon fusion of compound i, R is the gas B



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constant, T is the absolute temperature, and Tfusi is the fusion temperature of pure compound i. The value of ΔfusCPi is considered to be temperature-independent in eq 1,3 and the term multiplying ΔfusCpi is often very small.34 This term was thus neglected in phase equilibrium calculations. Liquid-phase nonideality was evaluated using three approaches. The first one was the assumption of an ideal liquid phase. In the second one, the liquid-phase nonideality was calculated using the UNIFAC−Dortmund model, with parameters obtained from Gmehling et al.14 The third approach considers the Flory−Huggins equation13 to evaluate liquid-phase nonideality. The UNIFAC−Dortmund volume parameter was used as the molar volume of each compound, and the Flory−Huggins binary interaction parameter was fitted to the experimental data. Experimental melting temperature and total melting enthalpy of the stable polymorph of each compound were used in the calculations. The model performance was evaluated using the root meansquared deviation (RMSD) defined here as ij ∑N (T exp − T cal )2 yz fusi z j i = 1 fusi zz RMSD = jjj zz jj N z k {

Figure 1. Heating thermograms of ethyl palmitate for the different scan rates.

0.5

This result is fully in agreement with what has already been discussed in previous studies.23,24,26,27 Data with different heating rates suggest that kinetics does not change the occurrence of polymorphism at the investigated heating rates. Despite the kinetic limitation in the formation of the polymorphs at cooling, they are always observed. The melting temperature for the most stable polymorph of each compound are presented in Figure 2. Extrapolating the

(2)

wherein N is the number of experimental points and Texp fusi and cal Tfusi are the experimental and calculated melting temperatures, respectively.

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RESULTS AND DISCUSSION

Pure Components and Kinetic Effects. For the purposes of constructing an accurate phase diagram, with reliable values, the true melting temperatures must be clearly defined. Bhatnagar et al.,35 when studying a reliable determination of freeze-concentration using DSC, concluded that extrapolating the experimental temperatures obtained at different scan rates to a zero-scan rate leads to an estimated melting temperature closer to the values found in literature. Wang and Haymet36 determined the peak temperature at several heating rates for solutions of trehalose, sucrose, fructose, and glucose and analyzed the data in a similar way. Finally, Tan and Man37 extrapolated the offset temperature (i.e., the temperature that corresponds to the return to the baseline) to a zero-heating rate after the melting of vegetable oil products at numerous heating rates. These authors used this offset temperature to identify different products.37 In this work, prior to the phase diagram determination, the heating rate dependence of the thermal response during the experiments was studied to better understand the melting process. All pure compounds were chilled at a cooling rate of 1.0 K·min−1 to 25 K below the component’s melting point and heated at programmed rates (0.5−2.5 K·min−1). The temperatures owing to all heating rates were corrected by calibration at the heating rate 1.0 K·min−1. Figure 1 presents the heating thermograms of ethyl palmitate for the different scan rates. Each thermogram was shifted by 3 mW intervals from each other in order to assemble all the thermograms in a single figure. Two polymorphic transitions were observed: the first one, at a temperature around 295 K, is exothermic and corresponds to a metastable polymorph, and the second one, at a temperature close to 297.5 K, is related to the melting of the most stable polymorph.

Figure 2. Heating rate dependency of the experimental melting temperature for the following: □, ethyl laurate; ●, ethyl palmitate; ○, ethyl myristate; ■, ethyl oleate; Δ, isoamyl laurate; ▲, isoamyl nonanoate.

melting temperatures to a zero-heating rate resulted in a value that does not differ significantly from the values obtained at higher rates. Results point out that there is no heating rate dependency in the investigated range: according to the Tukey test (95% confidence limit), only ethyl oleate at rates higher than 1.5 K·min−1 are significantly different. A heating rate of 1.0 K·min−1 is therefore sufficiently low to reduce kinetic effects to a minimum, guaranteeing equilibrium states. C



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Table 2. Transition Temperatures (Ttr) and Enthalpies (ΔtrH) Determined by DSC at Pressure p = 93.3 kPaa formula

type

Ttr/K

ΔtrH/(kJ·mol−1)d

ethyl laurate

C14H22O2

ethyl myristateb

C16H32O2

ethyl palmitateb

C18H36O2

ethyl stearateb

C20H40O2

ethyl oleateb

C20H38O2

isoamyl nonanoate

C14H28O2

isoamyl laurate

C17H34O2

metastable metastable stable metastable metastable stable metastable stable metastable metastable metastable stable metastable stable metastable metastable metastable stable stable

272.2 272.7 273.0 286.5 286.7 287.5 294.3c 297.7 302.7 303.5 304.9 307.4 252.0 254.0 213.3c 219.7 221.3c 233.2 258.0

23.73 10.54 4.00 15.71 10.65 18.79 −0.34 53.83 0.20 0.40 1.85 56.73 2.12 47.41 −1.95 0.84 −2.08 24.01 36.67

compound b

ΔtrH

−1 e,f total/(kJ·mol )

23.73 34.27 38.27 15.71 26.36 45.15 −0.34 53.49 0.20 0.60 2.45 59.18 2.12 49.53 - 0.95 −1.11 −3.19 20.82 36.67

Standard uncertainties u are u(T) ≈ 0.3 K and u(p) ≈ 0.7 kPa. bResults from Robustillo et al.26,27,32 cExothermic peak corresponding to a nonequilibrium transformation. dEnthalpy of the observed transition. eCumulative values, i.e., the summation of the enthalpy value of the corresponding polymorph transition and the enthalpy value of transitions at lower temperatures. fThe relative experimental uncertainty on melting enthalpy data is u(H)/H ≈ 0.03. a

Table 3. Experimental Solid + Liquid Equilibrium Data for the Systems Ethyl Laurate (1) + Isoamyl Nonanoate (6) and Ethyl Laurate (1) + Isoamyl Laurate (7) at Pressure p = 93.3 kPaa Ethyl Laurate (1) + Isoamyl Nonanoate (6) x1 0.00 0.06 0.11 0.20 0.30 0.40 0.50 0.60 0.69 0.80 0.90 1.00

Tt1b/K

Texo,1b/K

Tt2b/K

213.3 215.9 216.4 216.6 215.9 215.7 216.2 216.7

Tt3b/K

Tt4b/K

Teb/K

Tt5b/K

Tt6b/K

Tt7b/K

Tfusb/K 233.2

218.4

219.4 219.5 220.4

212.1

Texo,2b/K

220.3 220.1

221.9 221.4 222.3

232.3 232.6 232.4 232.5 232.4 232.4 232.4 232.2 231.9 233.0

242.9 249.2 253.3 256.9 261.4 264.3 266.1 268.8 272.8 273.0

236.1

240.3

255.6 254.4

Tt6b/K

Tt7b/K

Tt8b/K

Tfusb/K

c

c

c

258.0 256.2 254.6 253.3 252.1 254.5 255.8 259.2 266.2 269.0 273.0

Ethyl Laurate (1) + Isoamyl Laurate (7) x1 0.00 0.07 0.14 0.21 0.30 0.39 0.49 0.59 0.71 0.84 1.00

Tt1b/K

243.6 243.6 244.6 244.7

242.6

Tt2b/K

Tt3b/K

Teb/K

Tpb/K

Tt4b/K

Tt5b/K

252.7 252.5 252.3 252.1 252.4 251.9

247.9 247.5 248.4 247.9 247.4

250.9

247.0

250.9

256.9 256.6 256.3

259.2 258.2

262.0 266.2

Standard uncertainties u are u(T) ≈ 0.3 K, u(p) ≈ 0.7 kPa, and u(x) ≈ 0.0002. bSubscripts indicate the transitions related to the peaks in thermograms: Te = eutectic temperature; Tp = peritectic temperature; Tt = solid−solid or solid−liquid transition temperature; Texo = exothermic transition temperatures; Tfus = melting temperature. cNo temperature values determined for this transition.

a

The thermograms of ethyl esters showed the occurrence of solid−solid polymorphic transitions. These polymorphic

transitions have also been extensively discussed in previous works.23−27,32 For isoamyl nonanoate, four transitions were D



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observed in the heating thermograms, and two of them are exothermic. To the best of our knowledge, no experimental datum for this compound has been reported in literature to compare with. The existence of these peaks can be explained by either the polymorphism of isoamyl nonanoate or by the structural relaxation during recrystallization and annealing of polycrystalline phase.38 Finally, thermograms of isoamyl laurate present one single transition, which means that no polymorphic transitions are presented. Melting properties of the pure compounds are shown in Table 2. The experimental uncertainty, estimated as not higher than 0.3 K, was calculated based on repeated runs with a heating rate of 1.0 K·min−1. The transition enthalpy of each polymorph in Table 2 is not related to the complete transition of a pure solid, but rather to the transition of a metastable solid incompletely formed in the cooling process. The total area of the peak (rightmost column) reflects the fusion enthalpy at atmospheric pressure of the most stable polymorph. Binary Mixtures. The thermograms of the second heating run of the mixtures herein studied are available in the Supporting Information. The convention adopted is that exothermic transitions are plotted up and endothermic ones are plotted down. The experimental data are summarized in Tables 3−7. In all tables and figures, xi is the mole fraction of compound “i”. The thermograms corresponding to the systems formed by ethyl laurate (1) + isoamyl nonanoate (6) and ethyl laurate (1) + isoamyl laurate (7) present many peaks. The peak at the highest temperature (which varies according to the composition) is the melting one. Table 3 shows the experimental data for these systems, and the proposed phase diagrams are presented in Figures 3 and 4, respectively. Thermograms for the system comprising ethyl laurate (1) and isoamyl nonanoate (6) show peaks at constant temperature close to 232.4 K. These peaks are related to the eutectic reaction. The eutectic point, in a solid−liquid phase diagram, corresponds to a specific liquid-phase composition, xeut, and temperature, Teut, wherein a liquid and two solid phases are in equilibrium.39 The eutectic temperature, Teut, corresponds to the lowest one at which a liquid phase exists. The eutectic reaction occurs at Teut, and the amount of liquid formed upon heating depends on the system composition: the closer to xeut, the higher the amount of liquid formed. The enthalpy associated with the eutectic reaction is hence proportional to the amount of liquid formed and depends on the system composition as well. The Tamman plot depicts the correlation between the system composition and the enthalpy associated with each thermal event.40 The enthalpy values of the eutectic transition increase linearly until the eutectic composition is reached, after which these enthalpy values decrease linearly. Figure 3b shows the Tamman plot for this system. As expected, the eutectic enthalpy presented linear behavior. The maximum eutectic enthalpy value is observed at x1 = 0.06; for x1 > 0.06 it starts to decrease. The thermogram at this composition has only one peak, which confirms that this is the eutectic point. Thermograms also presented an exothermic transition at around 216 K for compositions x1 ≤ 0.6. Since this transition occurs in a temperature close to the exothermic transition of pure isoamyl nonanoate, it probably reflects a transition associated with the pure component. Thermograms for the system containing ethyl laurate (1) and isoamyl laurate (7) show well-defined peaks close to 252.3 K for ethyl laurate compositions x1 ≤ 0.49. For ethyl laurate

Figure 3. (a) Proposed phase diagram and (b) Tamman plot for the binary system formed by ethyl laurate (1) + isoamyl nonanoate (6): ■, melting; □, eutectic isotherm; Δ, *, exothermic transitions; other symbols, other transitions; Sa = compound “a” solid; Sa,b = solid solution rich in “b”. Dashed lines are guides to the eyes.

mole fractions higher than 0.5, an invariant transition was observed at 256.6 K. The Tamman plot, Figure 4b, shows that the enthalpy of the first transition increases to a maximum value at an ethyl laurate mole fraction of x1 ≅ 0.25, after which the enthalpy value decreases linearly until x1 ≅ 0.57. This invariant transition refers to the eutectic reaction. The enthalpy values of the transition occurring for ethyl laurate mole fractions x1 ≥ 0.59 also present a linear trend, indicating that it is possibly associated with a peritectic reaction. A peritectic transition is described as a reversible and isothermal reaction between a solid and a liquid phase, producing another solid phase upon cooling.41 In the Tamman plot, the behavior of the enthalpy values related to a peritectic reaction is analogous to that of a eutectic one: these enthalpy values increase with the composition to a maximum. The composition wherein this maximum value occurs corresponds precisely to the peritectic composition. Regions of miscibility in solid phase can also be determined through the analysis of Tamman plots. If compounds are completely immiscible in solid phase, the enthalpy value of the eutectic transition tends to zero when the mole fraction of either compound tends to 1.0. The Tamman plot of these mixture shows that components are partially miscible in solid E



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experimental uncertainty of the melting temperature of the stable polymorph of isoamyl nonanoate (233.2 K). Thus, the eutectic composition cannot be precisely determined and is estimated to be around x2 = 0.0. The enthalpy of this transition decreases linearly, which is compatible with the behavior expected for a eutectic reaction. It is important to mention that, to not overload the work, Tamman diagrams of these systems and of those that will be discussed later are available in the Supporting Information. An exothermic transition at around 216.5 K was observed throughout the concentration range. Similarly to the system ethyl laurate (1) + isoamyl nonanoate (6), it probably reflects a non-equilibrium transformation, probably associated with a metastable molecular conformation of the additive. The maximum value of enthalpy associated with the eutectic reaction of the system ethyl myristate (2) + isoamyl laurate (7) is obtained at x2 = 0.10, which indicates that the eutectic composition was reached. For x2 > 0.10, the enthalpy of this transition decreases linearly. For both systems, the transition at the highest temperature, a function of the system composition, is simply the final of the melting process. According to the evaluation of the Tamman plot, these systems also presented partial miscibility at the right extreme of the diagram, since the straight line resulting from the fitting of the eutectic enthalpy values does not extend to zero for x2 = 1.0. The DSC thermograms for the mixture ethyl palmitate (3) + isoamyl nonanoate (6) present three clear thermal transitions throughout the concentration range. The transition at intermediate temperature, around 233 K, can be attributed to the eutectic reaction, and the composition-dependent transition at the highest temperature is the final of the melting process. The temperature of the eutectic reaction is within experimental uncertainty of the melting point of the stable polymorph of isoamyl nonanoate (233.2 K), and no thermogram with a single peak (which would indicate the eutectic composition) was obtained. Thus, the eutectic composition is close to x3 = 0.0. The transition at the lowest temperature is the exothermic transition associated with the pure isoamyl nonanoate. Besides these thermal events, other transitions were also observed; all of them with very low enthalpy values, though, and, therefore, associated with transitions in solid phase not possible to characterize by means of DSC solely. The proposed phase diagram for this system is presented in Figure 7. Two well-defined thermal transitions were observed in the thermograms for the system ethyl palmitate (3) + isoamyl laurate (7). The transition at the highest temperature determines the final of the melting process, corresponding to the liquidus line. The liquidus line is the locus of the boundary between the area of a single liquid phase and the areas where solid and liquid coexist.42 The other transition, which occurs at a lower and constant temperature of approximately 256.2 K, is related to the eutectic transition. The maximum value of eutectic reaction enthalpy occurs at a composition close to x3 = 0.024, after which it decreases (Tamman plot in the Supporting Information). The proposed phase diagram for this system is presented in Figure 8. Based on the DSC thermograms and on the Tamman plots (see the Supporting Information), these systems present a eutectic reaction with complete immiscibility in solid phase. The experimental data for these systems are presented in Table 5.

Figure 4. (a) Proposed phase diagram and (b) Tamman plot for the binary system formed by ethyl laurate (1) + isoamyl laurate (7): ■, melting; □, eutectic isotherm; ▲, peritectic isotherm; other symbols, other transitions; Sa = compound a solid; P = peritectic compound; Sa,b = solid solution rich in b. Dashed lines are guides to the eyes.

phase for mole fractions close to the pure ester, since eutectic enthalpy values tend to zero for x1 ≃ 0.9 in the system with isoamyl nonanoate and at x1 ≃ 0.88 in the system with isoamyl laurate. Other transitions were observed for both systems. These transitions occur in solid phase and have very low enthalpy. While they are likely to correspond to isomorphic transitions, they cannot be unequivocally characterized through differential scanning calorimetry. Thermograms for the mixtures formed by ethyl myristate (2) + isoamyl nonanoate (6) and ethyl myristate (2) + isoamyl laurate (7) also present a larger number of peaks. Table 4 shows the experimental data for these systems. Analogously to the systems with ethyl laurate, most of the thermal events observed probably correspond to another kind of transition in solid phase, since they are transitions of very low enthalpy. Sharp peaks around 232.6 and 255.3 K in the thermograms for the systems with isoamyl nonanoate and isoamyl laurate, respectively, are attributed to the eutectic reaction. The corresponding phase diagrams are depicted in Figure 5 (system ethyl myristate + isoamyl nonanoate) and Figure 6 (system ethyl myristate + isoamyl laurate). Regarding the system ethyl myristate (2) + isoamyl nonanoate (6), the eutectic temperature is almost within F



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Table 4. Experimental Solid + Liquid Equilibrium Data for the Systems Ethyl Myristate (2) + Isoamyl Nonanoate (6) and Ethyl Myristate (2) + Isoamyl Laurate (7) at Pressure p = 93.3 kPaa Ethyl Myristate (2) + Isoamyl Nonanoate (6) x2

Texo,1b/K

0.00 0.06 0.11 0.20 0.31 0.40 0.51 0.59 0.69 0.80 0.89 1.00

213.3 217.1 216.1 214.7 215.2 216.2 217.0 216.8 218.0 217.3 216.7

x2

Tt1b/K

0.00 0.10 0.19 0.27 0.36 0.47 0.55 0.66 0.75 0.88 1.00

c

Texo,2b/K

Tt1b/K

Tt2b/K

Teb/K

218.0 217.8 218.4 217.9 219.5 219.4 219.9 219.7

219.5 219.4 219.5

232.9 233.0 232.9 232.9 232.9 232.7 232.6 232.5 232.3 231.8

221.0 221.0 221.0 221.0 221.0 221.0 223.1

220.4

Tt3b/K

Tt4b/K

Tt5b/K

Tt6b/K

243.6 249.2 249.3

238.6 239.4

244.7 243.6

258.2 259.0

Tfusb/K 233.2 246.4 254.3 265.5 269.0 273.7 276.4 278.0 280.5 282.6 285.3 287.5

Ethyl Myrisitate (2) + Isoamyl Laurate (7) Tt1b/K

Tt2b/K

Teb/K

Tt3b/K

Tt4b/K

Tt5b/K

Tt6b/K

Tt7b/K

Tfusb/K 258.0

246.8 246.8 246.8

249.5

255.8 256.2 255.5 254.9 255.3 255.3 255.2 255.1 254.0

257.6 258.3 258.0 258.8 259.6

258.9

260.0 259.2 259.5 260.9 262.3 261.0

264.9 264.8

264.3 268.2 271.8 275.0 277.6 280.9 283.7 285.4 287.5

Standard uncertainties u are u(T) ≈ 0.3 K, u(p) ≈ 0.7 kPa and u(x) ≈ 0.0002. bSubscripts indicate transitions corresponding to the peaks in thermograms: Te = eutectic temperature; Tt = solid−solid or solid−liquid transition temperature; Texo = exothermic transition temperature; Tfus = melting temperature. cNo temperature values determined for this transition. a

Figure 5. Proposed phase diagram for the binary system formed by ethyl myristate (2) + isoamyl nonanoate (6): ■, melting; □, eutectic isotherm; Δ, exothermic transition; other symbols, other transitions; Sa = compound a solid; Sa,b = solid solution rich in b. Dashed lines are guides to the eyes.

Figure 6. Proposed phase diagram for the binary system formed by ethyl myristate (2) + isoamyl laurate (7): ■, melting; □, eutectic isotherm; other symbols, other transitions; Sa = compound a solid; Sa,b = solid solution rich in b. Dashed lines are guides to the eyes.

Figures 9 and 10 present the proposed phase diagram for the systems formed by ethyl stearate (4) + isoamyl nonanoate (6) and ethyl stearate (4) + isoamyl laurate (7), respectively. The experimental data for these systems are presented in Table 6. These systems presented eutectic transition temperature (233.1 and 257.4 K for the systems with isoamyl nonanoate and isoamyl laurate, respectively) very close to the melting

temperature of the pure additives (233.2 K for isoamyl nonanoate and 258 K for isoamyl laurate), and thus, no thermogram presenting a single peak was obtained. Analyzing the thermograms, the eutectic composition is close to x4 = 0.0 in both cases. Thermograms also presented a transition at higher temperatures, associated with the melting process. G



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Table 5. Experimental Solid + Liquid Equilibrium Data for the Systems Ethyl Palmitate (3) + Isoamyl Nonanoate (6) and Ethyl Palmitate (3) + Isoamyl Laurate (7) at Pressure p = 93.3 kPaa Ethyl Palmitate (3) + Isoamyl Nonanoate (6)

Figure 7. Proposed phase diagram for the binary system formed by ethyl palmitate (3) + isoamyl nonanoate (6): ■, melting; □, eutectic isotherm; Δ, exothermic transition; other symbols, other transitions; Sa = compound a solid. Dashed lines are guides to the eyes.

x3

Texob/K

Teb/K

0.00 0.06 0.11 0.21 0.32 0.42 0.52 0.60 0.71 0.80 0.89 1.00

213.3 215.4 215.2 215.4 215.6 216.0 216.4 217.7 217.6 218.1 219.6

232.9 233.1 232.9 233.0 233.4 232.9 232.8 232.7 232.6 232.5

Tt1b/K

234.8 234.8 238.5 235.5 235.5 234.9

Tt2b/K

248.8 241.6 249.2

Tt3b/K

Tt4b/K

255.4 254.3 256.3

249.2 243.0 246.7 244.6

262.5 264.2 260.8

Tfusb/K 233.2 264.6 270.6 276.4 282.8 287.8 289.5 292.0 294.7 295.7 296.7 297.7

Ethyl Palmitate (3) + Isoamyl Laurate (7) b

x3

Texo /K

0.00 0.11 0.19 0.28 0.36 0.49 0.58 0.68 0.76 0.89 1.00

c

Teb/K 257.0 256.6 256.4 256.3 256.1 256.2 256.1 255.9 255.6

Tt1b/K

Tt2b/K

Tt3b/K

Tt4b/K

Tfusb/K

c

c

c

c

258.0 269.1 276.5 281.3 284.6 288.6 290.6 292.7 294.1 296.5 297.7

Standard uncertainties u are u(T) ≈ 0.3 K, u(p) ≈ 0.7 kPa, and u(x) ≈ 0.0002. bSubscripts indicate the transitions related to the peaks in thermograms: Te = eutectic temperature; Tt = solid−solid or solid− liquid transition temperature; Texo = exothermic transition temperature; Tfus = melting temperature. cNo temperature values determined for this transition. a

Figure 8. Proposed phase diagram for the binary system formed by ethyl palmitate (3) + isoamyl laurate (7): ■, melting; □, eutectic isotherm; Sa = compound a solid. Dashed lines are guides to the eyes.

Analogously to the other systems with isoamyl nonanoate, several other thermal events were observed in the thermograms for the system ethyl stearate (4) + isoamyl nonanoate (6), most of them with very low enthalpy value. Precise identification of these transitions demands additional analytical techniques, but this fact does not affect the liquidus line. The exothermic transition observed at around 216 K may correspond to a metastable molecular conformation of isoamyl nonanoate. In addition to the eutectic and melting transitions, thermograms for the system ethyl stearate (4) + isoamyl laurate (7) also presented other transitions above the eutectic temperature for ethyl stearate mole fractions x4 = 0.18 at 266.9 K, x4 = 0.26 at 277.6 K, and x4 = 0.35 at 263.2 K and at 268.1 K. However, they are transitions of very low energy, and no conclusive information about their nature can be obtained only through DSC. Finally, Tamman plots for both systems with ethyl stearate indicate that pure compounds crystallize independently over the entire concentration range.

Figure 9. Proposed phase diagram for the binary system formed by ethyl stearate (4) + isoamyl nonanoate (6): ■, melting; □, eutectic isotherm; Δ, exothermic transition; other symbols, other transitions; Sa = compound a solid. Dashed lines are guides to the eyes.

Figures 11 and 12 present the proposed phase diagrams for the systems formed by ethyl oleate (5) + isoamyl nonanoate H



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Figure 10. Proposed phase diagram for the binary system formed by ethyl stearate (4) + isoamyl laurate (7): ■, melting; □, eutectic isotherm; other symbols, other transitions; Sa = compound a solid. Dashed lines are guides to the eyes.

Figure 11. Proposed phase diagram for the binary system formed by ethyl oleate (5) + isoamyl nonanoate (6): ■, melting; □, eutectic isotherm; Δ, exothermic transition; other symbols, other transitions; Sa = compound a solid; Sa,b = solid solution rich in b. Dashed lines are guides to the eyes.

(6) and ethyl oleate (5) + isoamyl laurate (7), respectively. The experimental data for these systems are presented in Table 7. The thermograms of these systems show two clear peaks, both endothermic: the invariant transition at lower temperature, related to the eutectic reaction, and the compositiondependent transition, associated with the melting of the mixture.

Thermograms for the system ethyl oleate (5) + isoamyl nonanoate (6) indicate that the eutectic reaction occurs at around 230.8 K and the eutectic composition is x5 = 0.11. The enthalpy values decrease linearly for x5 ≥ 0.11, as shown in the Tamman diagram (see Supporting Information), which corresponds to the behavior of a eutectic reaction. Moreover,

Table 6. Experimental Solid + Liquid Equilibrium Data for the Systems Ethyl Stearate (4) + Isoamyl Nonanoate (6) and Ethyl Stearate (4) + Isoamyl Laurate (7) at Pressure p = 93.3 kPaa Ethyl Stearate (4) + Isoamyl Nonanoate (6) x4

Texob/K

Teb/K

0.00 0.11 0.19 0.29 0.37 0.48 0.58 0.66 0.76 0.89 1.00

213.3 216.9 215.0 215.5 214.9 216.2 215.9 215.7 216.6 217.5

233.3 233.3 233.2 233.2 233.1 233.0 232.9 232.9 232.8

x4

Texob/K

Teb/K

0.00 0.05 0.09 0.13 0.18 0.26 0.35 0.45 0.57 0.75 1.00

c

Tt1b/K

Tt2b/K

234.8 234.3 240.3 241.5 242.9 242.9

Tt3b/K

Tt4b/K

250.6 247.3 246.6 247.9 247.4 247.8

Tt5b/K

257.0 252.0

Tt6b/K

Tt7b/K

Tt8b/K

Tfusb/K 233.2 282.5 288.5 292.6 294.7 297.5 302.1 302.9 303.8 306.2 307.4

266.9 266.8 268.8 268.8 265.9 265.4

278.8 278.8 278.8

284.8 283.6

Tt5b/K

Tt6b/K

Tt7b/K

Tt8b/K

Tfusb/K

c

c

c

c

258.0 274.2 279.4 285.1 288.6 292.0 295.9 297.6 300.6 303.9 307.4

262.4 260.6 261.7 260.4

272.1

Ethyl Stearate (4) + Isoamyl Laurate (7)

257.7 257.6 257.8 257.7 257.7 257.6 257.2 256.8 256.6

Tt1b/K

Tt2b/K

Tt3b/K

Tt4b/K

266.9 277.6 263.2

268.1

Standard uncertainties u are u(T) ≈ 0.3 K, u(p) ≈ 0.7 kPa, and u(x) ≈ 0.0002. bSubscripts indicate the transitions related to the peaks in thermograms: Te = eutectic temperature; Tt = solid−solid or solid−liquid transition temperature; Texo = exothermic transition temperature; Tfus = melting temperature. cNo temperature values determined for this transition. a

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The other two are endothermic transitions and occur at around 217.9 K for ethyl oleate mole fractions x5 ≥ 0.50 and close to 220.6 K for ethyl oleate mole fractions x5 = 0.70 and x5 = 0.79. Both transitions are associated with a solid−solid transition. Other transitions of low enthalpies, whose nature is not identifiable only by means of DSC, were observed above the eutectic temperature. The thermograms for the system ethyl oleate (5) + isoamyl laurate (7) present an invariant transition (corresponding to the eutectic transition) close to 246.4 K. The well-defined inflection in the liquidus line, shown in Figure 12, suggests that the eutectic point for this binary is close to x5 ≃ 0.52, which can also be confirmed by the Tamman diagram (see the Supporting Information). The analysis of the Tamman plot shows that this mixture also presents partial solid-phase miscibility at both extremes of the phase diagram, for ethyl oleate mole fractions x5 ≤ 0.06 and x5 ≥ 0.95, since straight lines fitted to the enthalpy points do not extend to the pure compounds. Besides the endothermic transitions below eutectic temperatures, which correspond to solid−solid transitions, other welldefined endothermic peaks are observed for ethyl oleate mole fractions x5 = 0.41, 0.69, 0.79, and 0.87. These transitions occur at temperatures slightly lower than the melting points of the mixtures in the respective compositions. By analyzing the Tamman plot (see the Supporting Information), if each transition is considered separately (melting transition and the transition at the lower temperature), the melting enthalpy values do not present the expected linear behavior, especially at

Figure 12. Proposed phase diagram for the binary system formed by ethyl oleate (5) + isoamyl laurate (7): ■, melting; □, eutectic isotherm; other symbols, other transitions; Sa = compound a solid; Sa,b = solid solution rich in b. Dashed lines are guides to the eyes.

the Tamman plot of this mixture indicates a region of partial miscibility, since enthalpy values tend to zero at x5 ≃ 0.9. Thermograms of this mixture also presented additional invariant transitions below the eutectic temperatures; the first one, at around 216 K, corresponds to the exothermic nonequilibrium transformation, probably associated with a metastable molecular conformation of isoamyl nonanoate.

Table 7. Experimental Solid + Liquid Equilibrium Data for the Systems Ethyl Oleate (5) + Isoamyl Nonanoate (6) and Ethyl Oleate (5) + Isoamyl Laurate (7) at Pressure p = 93.3 kPaa Ethyl Oleate (5) + Isoamyl Nonanoate (6) x5

Texob/K

0.00 0.11 0.20 0.31 0.40 0.50 0.58 0.70 0.79 0.89 1.00

213.3 216.3 214.6 214.7 215.4 218.7 218.4

x5

Texob/K

0.00 0.11 0.21 0.30 0.41 0.52 0.62 0.69 0.79 0.87 1.00

c

Tt1b/K

Tt2b/K

Teb/K

Tt3b/K

Tt4b/K

Tt5b/K

Tfusb/K 233.2

217.4 216.4 219.1 218.5 218.1

220.4 220.8

231.7 231.4 230.6 230.5 230.6 230.4 230.7 230.5 230.5

236.9 235.5 234.8 231.2 232.8 230.9

240.9 239.6 234.9

236.3 242.2 243.0 245.9 247.4 249.8 251.2 252.8 254.0

Ethyl Oleate (5) + Isoamyl Nonanoate (6) Tt1b/K

Tt2b/K

242.6 243.3

Tt3b/K 245.4

244.3 244.6 244.8 244.8

Teb/K 246.1 246.1 246.3 246.6 246.8 246.7 246.5 246.2 245.9

Tt4b/K

248.8

248.6 250.2 251.4

Tt5b/K

.

c

258.0 255.4 253.7 251.9 250.8 248.4 249.7 251.2 252.5 254.0

Standard uncertainties u are u(T) ≈ 0.3 K, u(p) ≈ 0.7 kPa, and u(x) ≈ 0.0002. bSubscripts indicate the transitions related to the peaks in thermograms: Te = eutectic temperature; Tt = solid−solid or solid−liquid transition temperature; Texo = exothermic transition temperature; Tfus = melting temperature. cNo temperature values determined for this transition. a

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Table 8. Melting Temperatures Reduction (K) as a Function of Additive Concentration melting temperature reduction (K) for given additive concentration additive isoamyl nonanoate

isoamyl laurate

ester ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl

laurate myristate palmitate stearate oleate laurate myristate palmitate stearate oleate

0.1 wt %

0.5 wt %

1.0 wt %

2.0 wt %

5.0 wt %

10.0 wt %

0.65 0.25 0.02 0.17 0.14 0.18 0.41 0.02 0.02 0.21

0.66 0.32 0.09 0.22 0.18 0.22 0.45 0.08 0.08 0.26

0.67 0.40 0.18 0.27 0.22 0.27 0.49 0.15 0.16 0.32

0.71 0.56 0.35 0.40 0.33 0.37 0.58 0.30 0.31 0.45

0.92 1.06 0.88 0.84 0.68 0.73 0.91 0.74 0.78 0.86

1.56 1.93 1.79 1.76 1.42 1.49 1.58 1.53 1.59 1.58

Table 9. Thermodynamic Modeling: Deviations between Experimental and Calculated Values (K) system compound i ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl

laurate myristate palmitate stearate oleate laurate myristate palmitate stearate oleate

root mean-squared deviation, eq 2 compound j

ideal

Flory−Huggins

UNIFAC−Do

χi,ja

isoamyl nonanoate

1.13 1.75 1.01 1.01 1.02 2.93 0.72 0.33 1.44 0.63

1.13 1.71 1.00 0.64 0.86 2.88 0.72 0.33 0.49 1.36

1.30 1.85 1.08 0.99 1.13 3.06 0.97 0.25 1.50 0.61

0.000 0.000 0.006 0.023 0.000 0.000 0.000 0.000 0.020 0.000

isoamyl laurate

a

Fitted binary parameters of Flory−Huggins model.

by ethyl oleate, for which isoamyl laurate was a little more effective. According to Chiu et al.,43 most additives induce transformations in the crystalline structure, changing the shape and diminishing the size of the crystals without affecting the temperature of the onset of crystal formation. They offer a barrier to crystal agglomeration, therefore hindering the growth of crystals to a size sufficiently large to plug filters. This mechanism can be related to the performance of the additives herein studied: small concentrations of additives do not result in significant reductions in melting temperature but may influence crystal morphology. Thermodynamic Modeling. Three approaches were used to describe the liquid phase: ideal model, Flory−Huggins equation,13 and UNIFAC−Dortmund14 model. The Flory− Huggins interaction parameter was obtained by adjusting the model to the experimental equilibrium data. A pure solid phase was assumed in all cases, and the partial miscibility observed for most of the systems was not considered, as the composition ranges wherein it occurs are small and their precise boundaries are not sharp. Thus, miscibility in solid phase was disregarded, emphasizing a good description of the liquidus line. Values of eq 2 for all approaches are presented in Table 9. In general, all approaches for calculating the solid−liquid equilibrium resulted in accurate description of those binary systems, except for the system ethyl laurate (1) + isoamyl laurate (7). These higher values of root-mean-squared deviations are imputable to the presence of a peritectic compound, which was not taken into account. The calculated liquidus line for this binary is shown in Figure 13. The description resulting from the use of Flory−Huggins equation was slightly better than the description resulting from

ethyl oleate mole fractions higher than the eutectic composition. On the other hand, if the enthalpy values of all transitions associated with the melting are summed up, the expected linear trend is recovered. This discontinuity can be associated with a combination of metastable transitions before the total melting of the mixture. The studied mixtures present phase diagrams very much alike. The liquidus lines of the phase diagrams present a single inflection point, characterizing the eutectic point. Three principal phase diagrams were identified: (i) simple-eutectic mixtures, when compounds crystallize independently during the cooling process (systems with ethyl palmitate or ethyl stearate with both additives); (ii) mixtures presenting partial solid-phase miscibility close to pure compounds (systems with ethyl oleate or ethyl myristate with both additives and the mixture ethyl laurate + isoamyl nonanoate); and (iii) diagram with a peritectic reaction, for the system ethyl laurate + isoamyl laurate (in this case, the phase diagram comprises eight different regions; three of them are solid−liquid regions, involving the equilibrium of a liquid phase and either one of the pure compounds in solid form or a new compound (peritectic)). The peritectic compound exists only in solid phase: as the system melts, it disappears. The impacts of both additives on the melting temperatures of ethyl esters are summarized in Table 8. One can see that additives had little effect on reducing melting points of the studied esters: for example, the melting temperature of ethyl myristate can only be reduced by almost 2 K, depending on the additive concentration. When additives are compared with each other at a given concentration, it was observed that isoamyl nonanoate decreased the melting temperature of ethyl esters to a slightly higher extent than isoamyl laurate, excepted K



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points of the studied esters, and the best result is a melting temperature decrease of almost 2 K for ethyl myristate. In general, isoamyl nonanoate decreased the melting temperature of ethyl esters to a slightly higher extent than isoamyl laurate. Additional analytical techniques, e.g., optical microscopy and X-ray diffraction, should be considered for future studies to confirm whether, despite not being able to significantly decrease the melting points, the presence of these additives, even in small amounts, influences the crystal morphology of ethyl esters.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b01019.

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Figure 13. Modeling for binary system ethyl laurate (1) + isoamyl laurate (7): ■, experimental melting; □, experimental eutectic isotherm; ▲, experimental peritectic isotherm; other symbols, other experimental transitions; ···, predicted liquidus line considering ideal liquid phase; ---, predicted liquidus line using Flory−Huggins; −, predicted liquidus line using UNIFAC−Do.

Thermograms and Tamman plot for the binary systems studied (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Pedro de Alcântara Pessôa Filho: 0000-0003-4315-7238 the other approaches, due to fact that its parameters were fitted to the experimental data. On the other hand, deviations resulting from the use of UNIFAC−Dortmund model were slightly larger than those obtained using the Flory−Huggins equation. This can be ascribed to its predictive nature, as no additional parameter fitting was done to improve its performance, even though the UNIFAC−Dortmund model presented good results, confirming that these systems are simple-eutectic ones (excepted for the system ethyl laurate (1) + isoamyl laurate (7)), regardless of the presence of small regions of solid solutions. Finally, the fact that assuming an ideal liquid phase resulted in an overall good description demonstrates that liquid-phase nonideality is barely significant for these systems. These results suggest that, in spite of the high number of transitions present, simple approaches are sufficient to describe the general behavior of the solid−liquid equilibrium of these systems.

Funding

We gratefully acknowledge FAPESP (Grant Nos. 2018/069562, 2016/08566-1, 2015/17946-0, 2013/07914-8, 2014/212520, and 2010/18355-1), CAPES (Finance Code 01), and CNPq (Grant Nos. 306440/2013-0, 304906/2014-0, and 150950/ 2014-4) for financial support. Notes

The authors declare no competing financial interest.

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CONCLUSIONS Solid−liquid phase diagrams of five ethyl esters and two additives were determined by the DSC technique. Regions of partial miscibility were observed close to the pure compounds, except for systems formed by either ethyl palmitate or ethyl stearate, for which no partial miscibility was observed in any composition. The system composed by ethyl laurate + isoamyl laurate presented a peritectic reaction, besides the eutectic and melting transitions. All other systems seem to be simpleeutectic ones. Results show that the DSC method is satisfactory for the measurement of SLE, but complementary analyzes may be necessary to interpret conclusively some observed transitions. UNIFAC−Dortmund, Flory−Huggins, and ideal models were successfully used, resulting in an adequate description of the liquidus line of these binary systems. Results also point out that there is no heating rate dependency of DSC thermal responses and that a heating rate of 1 K·min−1 is sufficiently low to reduce kinetic effects to a minimum. Additives had little effect on reducing melting L



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