SolidâLiquid Equilibrium of Binary Systems Containing Fatty Acids

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

pubs.acs.org/jced

Solid−Liquid Equilibrium of Binary Systems Containing Fatty Acids and Fatty Alcohols Using Differential Scanning Calorimetry Filipe Hobi Bordoń Sosa,† Nataĺ ia Daniele Dorighello Carareto,‡ Guilherme Jose ́ Maximo,§ Antonio Jose ́ de Almeida Meirelles,§ and Mariana Conceiçaõ Costa*,†

Downloaded via BUFFALO STATE on July 23, 2019 at 10:08:17 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

Department of Process and Products Development, School of Chemical Engineering (FEQ), University of Campinas (UNICAMP), 13484-350 Campinas, São Paulo, Brazil ‡ Institute of Science and Technology Valenciennes, University of Valenciennes and Hainaut-Cambresis, Cambrai, France § EXTRAE, Department of Food Engineering (DEA), School of Food Engineering (FEA), University of Campinas (UNICAMP), 13083-862 Campinas, São Paulo, Brazil S Supporting Information *

ABSTRACT: Fatty alcohol and fatty acid compounds are responsible for some significant characteristics of pharmaceuticals, cosmetics, and food products, such as texture and stability. A knowledge of the solid−liquid equilibrium (SLE) behavior of such mixtures is necessary to enhance production processes as well as to upgrade their home and industrial usage. In this study, the SLE phase diagrams of five binary mixtures composed of fatty alcohol compounds and fatty acids, namely, 1-dodecanol, 1-tetradecanol, 1-hexadecanol, lauric acid, myristic acid, and palmitic acid, were determined using differential scanning calorimetry (DSC). A polarized light microscope was used to complement the characterization of phase diagrams, which have shown complex global behavior with eutectic and peritectic points as well as solid solution formation. The SLE data were fitted using the Margules 2-suffix and Margules 3-suffix and the UNIFAC and UNIFAC Dortmund models. The modeling approach using the Margules 3-suffix equation best represented the experimental data.

1. INTRODUCTION

purification, improving the production of these fatty compounds in the chemical industry. Furthermore, this study was designed to determine the SLE data of the following binary mixtures of fatty alcohols plus fatty acids: 1-dodecanol + lauric acid; 1-tetradecanol + myristic acid; 1-dodecanol + capric acid; 1-hexadecanol + stearic acid; 1-dodecanol + palmitic (C12H26O + C12H24O2, C14H30O + C14H28O2, C12H26O + C10H20O2, C16H34O + C18H36O2, and C12H26O + C16H32O2, respectively). Differential scanning calorimetry with linear heating rates6,7 and a temperaturecontrolled optical microscope were used to characterize the solid−liquid behavior of these binary mixtures.8 The SLE phase diagrams were obtained from the experimental data, and then the Margules 2-suffix and Margules 3-suffix and UNIFAC and UNIFAC Dortmund models were applied for the calculation of the activity coefficients of the compounds in the mixtures.

Fatty acids have been of interest to researchers since the early 19th century because they were the main constituents of fats and oils1 but also because they can be used in the manufacture of many products in the food, paint, plastics, fertilizer, agrochemical, pharmaceutical, and cosmetics industries.2 Additionally, fatty alcohol compounds, manufactured from fatty acids3 but naturally occurring in some specific vegetable and animal oils, are widely applied as structuring agents in chemical, pharmaceutical, and food ingredients. Fatty alcohol compounds as well as fatty acids have been responsible for some important characteristics in cosmetics, pharmaceuticals, and foods such as texture, stability, and spreadability, among others. Also, more recently, studies have shown that these fatty compounds are good materials for energy storage, being a more sustainable alternative for producing phase change materials.4,5 Therefore, because of increasing interest in these products in industry, a knowledge of the SLE behavior of mixtures formed by fatty acids and fatty alcohol compounds is of great value and can bring about innovations in many industrial segments. Moreover, phase equilibrium data is the most important tool for the development of new techniques of separation and © XXXX American Chemical Society

Special Issue: Latin America Received: October 31, 2018 Accepted: July 3, 2019

A

DOI: 10.1021/acs.jced.8b01006 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Fatty Compounds Used in This Work, CAS Number, Molar Mass, Supplier, and Purity component

name

CAS number

MM/g mol−1

supplier

puritya

C10H20O2 C12H24O2 C14H28O2 C16H32O2 C18H36O2 C12H26O C14H30O C16H34O

capric acid lauric acid myristic acid palmitic acid stearic acid 1-dodecanol 1-tetradecanol 1-hexadecanol

334-48-5 143-07-7 544-63-8 57-10-3 57-11-4 112-53-8 112-72-1 36653-82-4

172.26 200.32 228.37 256.42 284.48 186.34 214.38 242.45

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

>0.99 >0.99 >0.99 >0.99 >0.97 >0.99 >0.99 >0.99

a

According to the supplier.

2.3. Thermodynamic Modeling. The classical SLE equation10 (eq 1) was employed to model the experimental data. This equation is a simplified version and took into account that the difference between heat capacities of solid and liquid phases are very small and can be neglected if compared with the enthalpy term, and the solid phase is composed of independently crystallized crystals. In this equation, xi is the molar fraction of compound i in the liquid phase, γLi is the activity coefficient of compound i in the liquid phase, ΔfusH and Tm are the melting enthalpy and temperature of pure compound i, respectively, and T is the melting temperature of the mixture. In fact, the SLE of fatty acids plus the fatty alcohol compounds mixture evaluated here presents complex behavior that could not be fully characterized by applying eq 1 because it considers the solid phase to be an ideal one. This will be further discussed in the article. The activity coefficients in the solid−liquid equilibrium (γi) can be estimated with adjustable models such as the Margules equations or with predictive methods such as the UNIFAC group-contribution model, both based on the calculation of the excess Gibbs energy. For the calculation of γLi , the Margules 2-suffix and Margules 3-suffix equations and the group contribution methods, UNIFAC11 and UNIFAC Dortmund,12 were applied, and their accuracy in describing the phase behavior was evaluated.

2. MATERIALS AND METHODS 2.1. Materials. The fatty compounds used in this work (CAS (Chemical Abstracts Service) number, molar mass, supplier, and purity) are listed in Table 1. All compounds were used without further purification. Approximately one gram of the binary mixtures was prepared gravimetrically by varying the mass of each compound to have samples in all molar fraction ranges using an analytical scale (ADAM equipment, 1AAA250) with a precision of 2 × 10−4 g. To prevent the sample from changing during the course of the preparation, the substances were maintained inside an inert atmosphere of nitrogen during the melting, mixing, and crystallization processes and were stored in a refrigerated environment until their use. 2.2. Apparatus and Procedure. Samples of each mixture (2−5 mg) were weighed on an AD6 (PerkinElmer, Waltham) microanalytical scale with a precision of 2 × 10−6 g, put in sealed aluminum pans, and characterized by DSC at local ambient pressure p = 94.6 ± 0.3 kPa, using an MDSC 2920 calorimeter (TA Instruments). To avoid the effect of thermal memory on the systems and to control the effects of polymorphism, the samples were thermally treated in the DSC cell. Each sample was heated to 15 K above the melting point of the fatty compound with the highest melting point of the blend at a rate of 5 K min−1. The sample remained at this temperature for 20 min and was cooled at a rate of 1 K min −1 up to 25 K below the lower melting temperature of the mixture compounds. After 30 min at this temperature, the experimental run for data collection was started at a rate of 1 K min−1. The DSC was calibrated using indium (99.99% purity, CAS number 7440-74-6) certified by TA Instruments, naphthalene (≥0.99 molar fraction, CAS number 91-20-3), and cyclohexane (≥0.99 molar fraction, CAS number 110-82-7) from Merck at a heating rate of 1 K min−1. Some experimental runs were repeated for pure components and for some selected binary mixtures to calculate the experimental uncertainties as described previously by Maximo and co-workers.9 The mean standard deviations in temperature and enthalpy were not higher than 0.30 K and 1.80 kJ mol−1, respectively, and these values were taken as the temperature and enthalpy experimental uncertainty. The behavior of the solid−liquid transition of the 1-dodecanol + palmitic acid system was additionally analyzed using an optical microscope with a temperature controller (Leica DM2700M, Germany). The image (2048 pixels × 1536 pixels) were obtained by putting a sample on a coverslip on a hot stage (Linkam LTS420, United Kingdom) programmed to heat the sample at a rate of 0.01 K min−1 until the melting of the sample. The images were acquired at each 0.01 K with a magnification of 200×.

ln xiγi L =

ΔfusH ijj 1 1 yz − zzz jjj R k Tm T z{

(1)

3. RESULTS AND DISCUSSION The solid−liquid equilibrium of binary mixtures of fatty acids8,13 or mixtures of fatty alcohol compounds7,9 has been reported by our research group in the last few years. We observed that some of them are simple eutectic mixtures in which a minimum temperature value (the eutectic point) is observed, with a solid phase composed of two compounds, which crystallize independently. However, most of them presented very complex behavior, with several other thermal transitions such as peritectic, or metatectic reactions, including the formation of a solid solution in some cases. On the basis of this past experience and experimental results from DSC, some images captured using optical microscope summed to the evaluation of Tammann plots, and when applying the Gibbs phase rule, the SLE behavior of mixtures of fatty acids plus fatty alcohol compounds is described here. Before the analysis of the SLE of the mixtures, the experimental melting temperature and enthalpy of pure compounds were compared to values reported in the literature with the purpose of evaluating the coherence of the experimental data presented here. Values are presented in B



Article

Table 2. Thermal Properties of Pure Fatty Compoundsa Ttrans/K component

this work

b

literature

capric acid C10H20O2

304.54

291.46c

ΔfusH/kJ mol−1

Tm/K b

this work

13

literature 14

this workb

literature 27.38 28.617 27.218 28.213 38.58 40.316 38.47 34.68 35.518 34.720 36.321 45.88 45.725 47.69 49.524 43.98 48.413 45.221 43.427 53.425 58.424

305.28

305.3 304.915 304.616

28.0

296.55

296.407 296.958

297.58

297.87 297.96

40.2

lauric acid C12H24O2

317.65

317.5613 317.918

318.07

311.419 317.613 317.98

35.6

1-tetradecanol C14H30O

310.11

310.207 310.068 311.2022

311.29

312.023 312.26 312.224

47.6

myristic acid C14H28O2

328.23

328.1813 327.958

328.73

322.626 327.98 328.213

43.7

1-hexadecanol C16H34O

322.36

322.307 322.322

323.51

56.4

335.9513

336.47

343.3113

343.96

322.228 322.322 322.929 323.36 337.230 335.431 342.619 341.931

1-dodecanol C12H26O

palmitic acid C16H32O2 stearic acid C18H36O2

343.96

53.5

52.315

61.2

57.632

a Melting temperatures (Tm) and molar enthalpy of fusion (ΔfusH) at pressure p = 94.6 kPa. Standard uncertainties u are u(Tmelting) = 0.3 K, u(ΔfusH) = 1.80 kJ mol−1, and u(p) = 0.3 kPa. bStandard uncertainties u are u(Tmelting) = 0.3 K, u(ΔfusH) = 1.80 kJ mol−1, and u(p) = 0.3 kPa. c Comparative data was not found in the literature.

Table 3. Experimental Solid−Liquid Equilibrium Data of 1-Dodecanol (1) + Lauric Acid (2) at p = 94.6 kPa.a Molar Fraction (x), Melting Temperature (Tm), Eutectic Temperature (Teut), Peritectic Temperature (Tper) Solid−Solid Transitions (Ttrans), and Pure Temperature Transitions (Ttrans,pure) x1‑dodecanol

Tm/K

0.0000 0.1019 0.2001 0.2946 0.4020 0.4994 0.6018 0.7009 0.7975 0.8979 1.0000

318.07 315.08 313.52 310.73 307.86 303.57 297.89 297.32 294.22 294.71 297.58

Teut/K

Tper/K

Ttrans1/K

296.40 297.07 297.24 297.52 297.86

292.12 292.47 292.55 291.89 293.08

Ttrans2/K

Ttrans3/K

Ttrans,pure1/K

Ttrans,pure2/K 317.65

294.71

293.01 292.62

289.84

296.82 295.45

293.56

290.48 291.46

296.55

a

Standard uncertainties u are u(x) = 0.0004, u(Tm) = 0.3 K, and u(p) = 0.3 kPa.

with the lower melting temperature of the mixture. Systems 1dodecanol + lauric acid and 1-tetradecanol + myristic acid present fatty acids and fatty alcohol compounds with the same number of carbons in the carbon chain. On the other hand, 1dodecanol + capric acid, 1-hexadecanol + stearic acid, and 1dodecanol + palmitic acid present differences of 2 and 4 carbon atoms between the fatty acid and fatty alcohol carbon chains, respectively.

Table 2. The relative deviation between experimental data and literature data was calculated, and the higher deviation value obtained was 1.2% for the melting temperature and 6.26% for the melting enthalpy, which indicate good coherence between the literature data and our experimental data. Therefore, Tables 3 to 7 show the melting temperatures and other transition temperatures obtained from the peak temperature of the DSC curves,9 for the five binary mixtures evaluated here. Concentrations are given as a molar fraction of the compound C



Article

Table 4. Experimental Solid−Liquid Equilibrium Data of 1-Tetradecanol (1) + Myristic Acid (2) at p = 94.6 kPa.a Molar Fraction (x), Melting Temperature (Tm), Eutectic Temperature (Teut), Peritectic Temperature (Tper) Solid−Solid Transitions (Ttrans), and Pure Temperature Transitions (Ttrans,pure) x1‑tetradecanol

Tm/K

0.0000 0.1037 0.2032 0.2973 0.3990 0.4962 0.5966 0.6972 0.7987 0.9040 1.0000

328.73 325.63 323.87 323.15 320.87 315.91 310.30 308.62 308.55 310.24 311.29

Teut/K

Tper/K

Ttrans1/K

Ttrans2/K

Ttrans,pure/K 328.23

308.95 309.14 309.47 309.87 311.52 310.30 305.34 304.98

307.33

301.93 310.11

a


Table 5. Experimental Solid−Liquid Equilibrium Data of 1-Dodecanol (1) + Capric acid (2) at p = 94.6 kPa.a Molar Fraction (x), Melting Temperature (Tm), Eutectic Temperature (Teut), Peritectic Temperature (Tper) Solid−Solid Transitions (Ttrans), and Pure Temperature Transitions (Ttrans,pure) x1‑dodecanol

Tm/K

0.0000 0.1032 0.2002 0.3008 0.3989 0.4955 0.5856 0.6929 0.7975 0.8966 1.0000

305.28 302.04 300.30 296.47 293.60 292.10 291.57 288.72 292.71 294.59 297.58

Teut1/K

Teut2/K

Ttrans1/K

Ttrans2/K

289.83 291.30 291.53 291.60

283.79 285.23 285.10

287.79 288.31 287.71

Ttrans,pure1/K

Ttrans,pure2/K

291.46

296.55

284.95 285.97 285.57 285.17

288.19 288.58 287.87

a


Table 6. Experimental Solid−Liquid Equilibrium Data of 1-Hexadecanol (1) + Stearic acid (2) p = 94.6 kPa.a Molar Fraction (x), Melting Temperature (Tm), Eutectic Temperature (Teut), Peritectic Temperature (Tper) Solid−Solid Transitions (Ttrans), and Pure Temperature Transitions (Ttrans,pure) x1‑hexadecanol

Tm/K

0.0000 0.1000 0.1979 0.4019 0.6029 0.7004 0.7997 0.9024 1.0000

343.96 341.08 339.09 334.75 329.72 325.11 319.97 321.29 323.51

Teut/K

Ttrans1/K

Ttrans2/K

Ttrans3/K

Ttrans,pure/K 343.44

317.79 318.74 318.52 319.48 319.12

298.81 291.28 291.24

308.66 309.01

303.67 322.36

a


Systems Presenting Equal Numbers of Carbon Atoms in the Carbon Chains. Figure 1 shows the solid−liquid phase diagram proposed for the 1-dodecanol + lauric acid system. The DSC curves are presented in the Supporting Information (Figure S1). For all samples, the DSC peak at higher temperature represents the melting of the sample, and the other peaks could be associated with other thermal transitions as discussed in our previous studies.6,7,9 From x1‑dodecanol ≈ 0.10 to 0.60, the thermal transitions immediately below the liquidus line (melting temperature of the system) could be associated with a peritectic reaction occurring at approximately 297 K.

(Peritectic and eutectic reactions are used according to IUPAC recommendations36 and do not indicate a chemical reaction.) The other peaks, at lower temperatures, could be related to thermal transitions in the solid phase, as explained in the following paragraphs. In fact, the shape of the liquidus line is similar to a system that presents a peritectic reaction.31 To verify these assumptions, a Tammann plot (Figure 2) was constructed and will be discussed later. At x1‑dodecanol ≈ 0.60, the melting peak overlaps the peritectic peak and the peak of the eutectic reaction starts to form at a temperature of ∼293 K. The peak attributed to the eutectic reaction became more D



Article

Table 7. Experimental Solid−Liquid Equilibrium Data of 1-Dodecanol (1) + Palmitic acid (2) p = 94.6 kPa.a Molar Fraction (x), Melting Temperature (Tm), Eutectic Temperature (Teut), Peritectic Temperature (Tper) Solid−Solid Transitions (Ttrans), and Pure Temperature Transitions (Ttrans,pure) x1‑dodecanol

Tm/K

0.0000 0.1146 0.2174 0.3272 0.4340 0.5335 0.6270 0.7224 0.8172 0.9106 1.0000

336.47 333.18 331.38 329.15 326.84 323.14 320.12 315.19 310.36 299.89 297.58

Teut/K

295.67 296.73 295.21 295.33

Ttrans1/K

Ttrans2/K

Ttrans3/K

291.46 291.99 291.79 291.84

293.93 294.08 294.58 294.69 294.21 294.69 294.23 294.23

301.90 301.67 301.24 303.43 304.01 304.37 304.34

291.88 292.85

Ttrans,pure1/K

Ttrans,pure2/K

291.46

296.55

a


of the peak at x1‑dodecanol ≅ 0.8 and the occurrence of overlapped peaks at x1‑dodecanol ≅ 0.9, the eutectic point should be at a composition between these (as suggested by the line traced as guide to the eyes). Other thermal transitions in the solid phase were seen as shown in Figure 1 and was probably due to the common polymorphic behavior of fatty compounds. Figure 2 shows the Tammann plot of the invariant transitions observed in this system. In this chart, the transition enthalpies were plotted versus the molar fraction of the system. The enthalpy of the invariant transition (eutectic or peritectic) should increase linearly up to a maximum value (the eutectic or peritectic point), when it starts to decrease.33 For the assumed peritectic transition (at ∼297 K), the enthalpy increased up to x1‑dodecanol ≅ 0.50. The linear trend adjusted to this transition established that for x1‑dodecanol ≅ 0.05 the enthalpy of the transition is zero, x1‑dodecanol = 0.00, indicating the occurrence of a solid solution in this region. Despite the fact that the eutectic reaction seems to occur in the mixture composition (Figure 1 at approximately 292.5 K), the Tammann plot shows that such a transition does not have an increase in linear behavior (Figure 2), as expected for a eutectic reaction. As observed in Figure 2, the enthalpy value of these transitions observed at approximately 292.5 K presents a small and almost constant enthalpy value of up to x1‑dodecanol < 0.50, indicating that they cannot be attributed to a eutectic reaction at least for compositions smaller than x1‑dodecanol < 0.50 but to a solid−solid transition due to polymorphic effects. However, the linearly increase behavior is observed for 0.5 < x1‑dodecanol < 0.8 x1‑dodecanol ≈ 0.50 when it decreased up to pure 1-dodecanol. As mentioned before, the absence of experimental data at a composition of x1‑dodecanol ≅ 0.85 does not allow us to find the eutectic point composition even with the use of a Tammann plot. The experimental data, however, indicates 0.8 < x1‑dodecanol < 0.9. Additionally, the Tammann plot indicates that the eutectic reaction should start in an intermediate 1-dodecanol molar fraction of between 0.50 and 0.60 and also suggests the occurrence of a solid solution on the right side of the diagram. This behavior was previously reported by our research group for another fatty binary system.31,34 Applying the same principles, the SLE phase diagram for the system 1-tetradecanol + myristic acid was proposed and is presented in Figure 3. The DSC curves for this system are also presented in the SI (Figure S2). This phase diagram shows similar behavior. One invariant phase transition below the

Figure 1. Solid−liquid phase diagram with a guide for the eyes (solid and dashed lines) of system 1-dodecanol (1) + lauric acid (2): experimental melting temperatures (■);, eutectic transition (▲), peritectic transition (●), pure transitions (○), and other transitions (+, x).

Figure 2. Tammann diagram of the 1-dodecanol + lauric acid system: peritectic reaction (●), eutectic reaction (▲), and solid−solid transition (+).

intense, and at x1‑dodecanol ≅ 0.8, just one broad peak is observed in the DSC curve (Figure S1). With the 1-dodecanol composition increase to x1‑dodecanol ≅ 0.9, it is observed that three peaks are not very well defined. Because of the broadness E



Article

liquid phase diagram for the system 1-dodecanol + capric acid is presented in Figure 5. DSC differential thermal curves are

Figure 3. Solid−liquid phase diagram with a guide for the eyes (solid and dashed lines) for system 1-tetradecanol (1) + myristic acid (2): experimental melting temperatures (■);, eutectic transition (▲), peritectic transition (●), pure transitions (○), and solid−solid transitions (×).

Figure 5. Solid−liquid phase diagram with a guide for the eyes (solid and dashed lines) of the system 1-dodecanol (1) + capric acid (2): experimental melting temperatures (■), eutectic transition (▲,▼), pure transitions (○), and solid−solid transitions (×).

melting temperature occurring at approximately 310 K was noted up to x1‑dodecanol ≅ 0.6, which was attributed to a peritectic reaction, and overlaps at this composition (x1‑dodecanol ≅ 0.6) to the melting event. After this point and up to x1‑dodecanol ≅ 0.8, only one peak was observed (with the exception of a solid−solid transition in the solid phase). One might assume that the eutectic reaction peaks for x1‑dodecanol ≅ 0.7 and 0.8 were overlapped in this case with the melting temperature peak, appearing in DSC curves only for x1‑dodecanol ≅ 0.9 at approximately 306 K. In this case, it is possible to assume the occurrence of the eutectic point at x1‑dodecanol ≅ 0.75. Figure 4 presents the Tammann plot that was traced by

presented in Figure S3. In this system, the fatty alcohol chain has two extra carbon atoms than the fatty acid. The liquidus line of this system undoubtedly shows the existence of one inflection point at x1‑dodecanol ≈ 0.70 that can be attributed to the eutectic reaction and seems to have another inflection point at x1‑dodecanol ≈ 0.45 due to the shape of the liquidus line and also the presence of the transition observed at ∼292 K. The possible existence of this eutectic point (inflection point) at x1‑dodecanol ≈ 0.45 shows that the 1-dodecanol + capric acid system presents behavior very similar to that observed to the 1octanol + capric acid system shown by Carareto and coworkers.14 In such a system, in which the compounds also differ from two carbon atoms between its carbon chain, the authors suggested the formation of a congruent melting compound according to Nyvlt’s35 classification or a dystectic reaction according to IUPAC’s recommendation in 2008.36 Likewise, the formation of such a compound in the 1dodecanol + capric acid system here studied seems possible. The first indication of the congruent melting compound formation is the shape of the liquidus line of the phase diagram shown in Figure 5. This line seems to be a maximum value for the 1-dodecanol composition comprehended for 0.40 ≤ x1‑dodecanol ≤ 0.70. The second one represents the enthalpy values in the plot presented in Figure 6 that will be discussed later. Additionally, the occurrence of an exothermic peak at a composition of x1‑dodecanol ≈ 0.50 is clearly observed in the DSC curves of this system (Figure S3). The exothermic peak started at x1‑dodecanol ≈ 0.20, and its intensity increased with the increase in the molar fraction of 1-dodecanol in the mixture up to the composition of x1‑dodecanol ≈ 0.50, when it reached a maximum value. At x1‑dodecanol ≈ 0.60, the exothermic peak disappeared or its intensity was not energetic enough to be observed in the DSC curve. Exothermic peaks are commonly observed in triacylglycerol systems, and some authors attribute their occurrence to changes in the crystalline structure of the system.37 A Tammann diagram was plotted for both invariant transitions observed in the 1-dodecanol + capric acid system

Figure 4. Tammann diagram of the 1-tetradecanol + myristic acid system: peritectic reaction (●) and eutectic reaction (▲).

considering the peak overlaps. In other words, the enthalpy value used to plot the Tammann diagram was approximately half of the total enthalpy of compositions x1‑dodecanol ≅ 0.70 and 0.80. It is possible to observe that the behavior of both peritectic and eutectic reactions is exactly as expected for this kind of transition,15,21 and none of them go to zero and one, respectively, indicating the existence of a solid solution formation.31,34 Systems with Compounds Differing from Two or Four Carbon Atoms in the Carbon Chains. The solid− F



Article

295 K. In contrast, the Tammann plot shows us that the transition observed at 304 K does not behave as a peritectic reaction; that is, it does not present a linearly increasing enthalpy value and has a small value. From this perspective, this transition can be attributed to a polymorphic transition. For a more precise explanation of it, other analytical techniques should be used and are outside the objective of this study. Regarding the transitions observed at 295 K, it is possible to see in the Tammann plot that a change occurs in the energy behavior of this transition due to a break in the tendency increase, indicating that the eutectic reaction starts only at x1‑dodecanol ≅ 0.60. Optical microscope images were acquired for this system at a composition of x1‑dodecanol ≅ 0.40 in order to confirm the absence of a liquid phase at a temperature of around 295 K. As can be seen in Figure 8, at a temperature of 290 K, all sample is in a solid phase because of the irregular shape of the crystals. With the increase in temperature, no changes are observed in the images until a temperature of 305 K is achieved. This nonappearance of the liquid phase confirms the Tammann result and also the occurrence of a solid solution in a region rich in the acid compound. Another important fact noticed in the Tammann plot is the enthalpy value calculated for compositions smaller than x1‑dodecanol ≈ 0.70 at a temperature of 294 K. This transition consumes a significant amount of energy exhibiting the behavior of a strong transition33 as previously observed for binary systems formed by saturated fatty acids.13 All of the other observed transitions can be attributed to solid-phase rearrangement or polymorphic transitions. To summarize, the phase diagram of the 1-dodecanol + palmitic system presents only a eutectic reaction with the eutectic point located at x1‑dodecanol ≅ 0.95. The modeling approach using the Margules 3-suffix model was the one that best represented the experimental data, with a mean absolute deviation of 0.66 K, followed by the Margules 2suffix model, with a deviation of 0.78 K. The worst results were obtained using the group contribution methods, UNIFAC and UNIFAC-Dortmund, and the ideal approach with mean deviations of 1.24, 0.90, and 1.17 K, respectively. Considering the temperature uncertainty (T = 0.3 K), they are similar. In case of the UNIFAC and UNIFAC-Dortmund models, these

Figure 6. Tammann plot of the 1-dodecanol + capric acid system: eutectic reaction 1 (▲) and eutectic reaction 2 (▼).

(Figure 6). The first invariant transition observed for 0.10 ≤ x1‑dodecanol ≤ 0.50 at ∼292 K has an enthalpy increase with the increase in the 1-dodecanol molar fraction. The second one, observed for 0.60 ≤ x1‑dodecanol ≤ 1.00 at ∼288 K, has a maximum enthalpy value at x1‑dodecanol ≈ 0.70. We might assume that the first invariant transition is due to the first eutectic reaction, and another invariant transition, with a triangular shape, can be attributed to the second eutectic reaction. Both reactions would be related to a new compound formed as a result of the dystectic reaction. Although the shape of the phase diagram (liquidus line) and the Tammann plot support the hypothesis of the existence of a dystectic reaction, an affirmation of the existence of such a compound requires the use of other techniques as X-ray diffraction, and it will be the subject of future studies. The solid−liquid phase diagrams of the 1-dodecanol + palmitic acid system and its Tammann plot are shown in Figure 7A,B, and the DSC curves are shown in Figure S4. This system presents a difference of four carbon atoms between the carbon chains of the compounds. This system has some transitions under the liquidus line, and at first glance it can be assumed that they present both a peritectic reaction at approximately 304 K and a eutectic reaction at approximately

Figure 7. (A) Solid−liquid phase diagram with a guide for the eyes (solid and dashed lines). (B) Tamman diagram for the system 1-dodecanol (1) + palmitic acid (2): experimental melting temperatures (■), eutectic transition (▲), pure transitions (○), and other transitions (×). G



Article

Figure 8. Optical microscope images of the 1-dodecanol + palmitic acid system at a heating rate of 0.1 °C·min−1 and x1‑dodecanol ≅ 0.40.

Figure 9. (A) Solid−liquid phase diagram with a guide to the eyes (solid lines). (B) Tammann diagram of the system 1-hexadecanol (1) + stearic acid (2): experimental melting temperatures (■), eutectic transition (▲), pure transitions (○), and solid−solid transitions (×).

results were expected because these models are not able to predict the melting profile of such systems. In fact, for more ideal systems, 1-dodecanol + palmitic acid and 1-hexadecanol + stearic acid, deviations were almost the same for all models considered, including the ideal assumption. In other words, all models are able to reasonably describe the melting temperature of fatty alcohol and fatty acid mixtures. When deviations were analyzed point by point through the concentration range, it was observed that the models did not provide a good description for 1-dodecanol + lauric acid and 1dodecanol + capric acid systems especially in the region of the peritectic and eutectic points. These results were expected because eq 1 neglects the formation of the compound and the occurrence of the solid solutio, resulting in large deviations close to these regions of the phase diagram. Figure S6 shows the experimental liquidus line of the systems, the ideal assumption, and the liquidus line adjusted by the Margules 3-suffix equation, which sketches the aforementioned analysis. On the other hand, systems presenting only eutectic events and excluding solid solution formation were well described even by the ideal approach.

The last system studied, 1-hexadecanol + stearic acid, has a difference of two carbon atoms between the compounds that form the mixture. It has a simpler phase diagram presenting only a eutectic transition at approximately 320 K (Figure 9A) with a eutectic point at x1‑hexadecanol ≅ 0.80. Some transitions were also observed in the solid phase and are attributed to rearrangements of the compounds or polymorphic transitions. The Tammann plot of this system (Figure 9B) show the increase of the enthalpy value until a composition of x1‑hexadecanol ≅ 0.70 and a value very similar to x1‑hexadecanol ≅ 0.80 are reached, indicating that the eutectic point is located at 0.70 < x1‑hexadecanol < 0.80. This behavior agrees with the Tammann plot proposal. Unfortunatelly, for x1‑hexadecanol ≅ 0.90 just one peak was observed in the DSC curve, again suggesting the overlapping of the eutectic event peak by the melting peak. Proceeding as in the case of the 1-tetradecanol + myristic acid system, the enthalpy value of such a peak was shared and used in the Tammann plot. The result obtained with this consideration agrees with the Tammann plot proposal and suggests the inexistence of a solid solution at the extremes of the phase diagram. H



Article

Table 8. Adjusted Parameters A and B for the Margules Equations and Mean Absolute Deviations σ between Predicted and Experimental Data for Some Activity Coefficient Models 2-suffix Margules system/model 1-dodecanol + lauric acid 1-tetradecanol + myristic acid 1-dodecanol + capric acid 1-hexadecanol + stearic acid 1-dodecanol + palmitic acid average

A/J mol

−1

1349.79 529.87 1900.25 −52.54 396.34

σ/K 0.74 0.72 1.38 0.81 0.24 0.78

3-suffix Margules −1

−1

A/J mol

B/J mol

1404.72 534.00 1810.43 −294.69 369.08

105.78 7.75 −118.37 −469.01 65.20

3.3. Thermodynamic Modeling of the SLE Data. Three of the systems evaluated here presented complex behavior with a peritectic event and the formation of a solid solution at the extremes of the phase diagram. This occurred for both systems with the same carbon atoms (1-dodecanol + lauric acid, 1tetradecanol + myristic acid) and for the system 1-dodecanol + capric acid. In fact, eq 1 was not designed for mixtures that present compound formation, such as what occurs when a peritectic compound is formed, and was not designed to predict the solid solution formation, which would require that ziγsi ≠ 1. Although eq 1 has not been designed for such complex systems, we decide to use it in order to evaluate its ability to predict the liquidus line. This could be quite useful because through the ideal assumption of the solid phase, the melting properties of the pure compounds are the only parameters required for the prediction of the melting temperature of the system. The last two systems present a simpler behavior in which eq 1 can be easily applied. Therefore, for all systems, Table 8 shows the adjusted binary parameters, and the deviations between experimental and calculated data by using the Margules 2-suffix and Margules 3-suffix models. Also, it shows the deviation between predicted data using group contribution method UNIFAC and UNIFAC-Dortmund models and experimental data. In an overall analysis, the liquidus line was well described by all models because the mean absolute deviations were less than 1.9 K for all of them. The modeling approach using the Margules 3-suffix model was the one that best represented the experimental data, with the mean absolute deviation of 0.66 K followed by the Margules 2-suffix model, with a deviation of 0.78 K. The worst results were obtained using the group contribution methods, UNIFAC and UNIFAC-Dortmund, and the ideal approach with mean deviations of 1.24, 0.90, and 1.17 K, respectively. Considering the temperature uncertainty (T = 0.3 K), they are similar. In the case of the UNIFAC and UNIFAC-Dortmund models, these results were expected because these models are not able to predict the melting profile of such systems. In fact, for more ideal systems, 1-dodecanol + palmitic acid and 1hexadecanol + stearic acid, deviations were almost the same for all models considered, including the ideal assumption. In other words, all models are able to reasonably describe the melting temperature of fatty alcohol and fatty acid mixtures. When deviations were analyzed point by point through the concentration range, it was observed that the models did not provide a good description for 1-dodecanol + lauric acid and 1dodecanol + capric acid systems especially in the region of the peritectic and eutectic points. These results were expected because eq 1 neglects the formation of the compound and the occurrence of the solid solution, resulting in large deviations close to these regions of the phase diagram. Figure S6 shows

ideal

UNIFAC

UNIFAC Dortmund

σ/K

σ/K

σ/K

σ/K

0.67 0.80 0.81 0.77 0.24 0.66

1.75 0.96 1.62 0.84 0.67 1.17

1.86 1.00 1.61 0.79 0.93 1.24

1.13 0.80 1.26 0.97 0.32 0.90

the experimental liquidus line of the systems, the ideal assumption, and the liquidus line adjusted by the Margules 3-suffix equation, which sketches the aforementioned analysis. On the other hand, systems presenting only eutectic events and without solid solution formation were well described even by the ideal approach.

■

CONCLUSIONS The SLE phase diagram of five binary mixtures (1-dodecanol + lauric acid, 1-tetradecanol + myristic acid, 1-dodecanol + capric acid, 1-hexadecanol + stearic acid, and 1-dodecanol + palmitic acid) was determined by differential scanning calorimetry. This study demonstrated that three of the phase diagrams for 1-dodecanol + lauric acid and 1-tetradecanol + myristic acid exhibited a peritectic and eutectic points and also small regions of solid solution formation. Moreover, the 1dodecanol + capric acid system seems to present a dystectic reaction. The existence of the peritectic point can be related, in this set of systems, to compounds with a small number of carbon atoms in the carbon chain. In summary, when the number of carbon atoms of each mixture compound increases, the system behavior seems to become simpler, that is, the case of 1-hexadecanol + stearic acid acid. The best representation of the experimental data was obtained by employing the 3-suffix Margules model, and the ideal assumption can be applied with a small deviation for simple euteutic systems such as 1dodecanol + palmitic acid and 1-hexadecanol + stearic acid.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b01006.

■

DSC curves and figures with the thermodynamic model results and experimental points (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel: +55 19-3521-3962. E-mail: mcosta@feq unicamp.br. ORCID

Mariana Conceiçaõ Costa: 0000-0003-1710-7202 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are grateful to FAPESP (2014/21252-0 and 2016/08566-1); CNPq (310272/2017-3, 305870/2014-9, and 169459/2017-9), Coordenação de Aperfeiçoamento de ́ Superior, Brasil (CAPES), Finance Code Pessoal de Nivel I



Article

001; and FAEPEX/UNICAMP for financial support and to CEPAGRI/UNICAMP for making the pressure data available.

Caprylic Acid (Octanoic Acid). Chem. Phys. Lipids 2004, 132, 225− 234. (16) Schaake, R. C. F.; van Miltenburg, J. C.; de Kruif, C. G. Thermodynamic Properties of the Normal Alkanoic Acids II. Molar Heat Capacities of Seven Even-Numbered Normal Alkanoic Acids. J. Chem. Thermodyn. 1982, 14, 771−778. (17) Song, S.; Dong, L.; Chen, S.; Xie, H.; Xiong, C. Stearic-Capric Acid Eutectic/Activated-Attapulgiate Composite as Form-Stable Phase Change Material for Thermal Energy Storage. Energy Convers. Manage. 2014, 81, 306−311. (18) Wei, D.; Han, S.; Wang, B. Solid-Liquid Phase Equilibrium Study of Binary Mixtures of n-Octadecane with Capric, and Lauric Acid as Phase Change Materials (PCMs). Fluid Phase Equilib. 2014, 373, 84−88. (19) Sharma, A.; Tyagi, V. V.; Chen, C. R.; Buddhi, D. Review on Thermal Energy Storage with Phase Change Materials and Applications. Renewable Sustainable Energy Rev. 2009, 13, 318−345. (20) Misra, a. K.; Misra, M.; Panpalia, G. M.; Dorle, a. K. Thermoanalytical and Microscopic Investigation of Interaction between Paracetamol and Fatty Acid Crystals. J. Macromol. Sci., Part A: Pure Appl.Chem. 2007, 44, 685−690. (21) Inoue, T.; Hisatsugu, Y.; Ishikawa, R.; Suzuki, M. Solid-Liquid Phase Behavior of Binary Fatty Acid Mixtures: 2. Mixtures of Oleic Acid with Lauric Acid, Myristic Acid, and Palmitic Acid. Chem. Phys. Lipids 2004, 127, 161−173. (22) Domalski, E. S.; Hearing, E. D. Heat Capacities and Entropies of Organic Compounds in the Condensed Phase, Vol 3. J. Phys. Chem. Ref. Data 1996, 25, 1−525. (23) Zeng, J. L.; Cao, Z.; Yang, D. W.; Xu, F.; Sun, L. X.; Zhang, L.; Zhang, X. F. Phase Diagram of Palmitic Acid-Tetradecanol Mixtures Obtained by DSC Experiments. J. Therm. Anal. Calorim. 2009, 95, 501−505. (24) Mosselman, C.; Mourik, J.; Dekker, H. Enthalpies of Phase Change and Heat Capacities of Some Long-Chain Alcohols. Adiabatic Semi-Microcalorimeter for Studies of Polymorphism. J. Chem. Thermodyn. 1974, 6, 477−487. (25) Eckert, T.; Müller, J. Zur Schmelzenthalpie Und Schmelzentropie von Fettalkoholen. Arch. Pharm. (Weinheim, Ger.) 1978, 311 (1), 31−34. (26) Zalba, B.; Marín, J. M.; Cabeza, L. F.; Mehling, H. Review on Thermal Energy Storage with Phase Change: Materials, Heat Transfer Analysis and Applications. Appl. Thermal Eng. 2003, 23, 251−283. (27) Karaipekli, A.; Sari, A.; Kaygusuz, K. Thermal Properties and Long-Term Reliability of Capric Acid/Lauric Acid and Capric Acid/ Myristic Acid Mixtures for Thermal Energy Storage. Energy Sources, Part A 2008, 30, 1248−1258. (28) Xing, J.; Tan, Z. C.; Shi, Q.; Tong, B.; Wang, S. X.; Li, Y. S. Heat Capacity and Thermodynamic Properties of 1-Hexadecanol. J. Therm. Anal. Calorim. 2008, 92 (2), 375−380. (29) Kolp, D. G.; Lutton, E. S. The Polymorphism of NHexadecanol and n-Octadecanol. J. Am. Chem. Soc. 1951, 73, 5593−5595. (30) Lane, D. G. A. Low Temperature Heat Storage with Phase Change Materials. Int. J. Ambient Energy 1980, 1, 155−168. (31) Costa, M. C.; Rolemberg, M. P.; Boros, L. A. D.; Kra, M. A.; Oliveira, M. G. de; Meirelles, A. J. de A. Solid - Liquid Equilibrium of Binary Fatty Acid Mixtures. J. Chem. Eng. Data 2007, 52, 30−36. (32) Farid, M. M.; Khudhair, A. M.; Razack, S. A. K.; Al-Hallaj, S. A Review on Phase Change Energy Storage: Materials and Applications. Energy Convers. Manage. 2004, 45, 1597−1615. (33) Chernik, G. G. Phase Equilibria in Phospholipid-Water Systems. Adv. Colloid Interface Sci. 1995, 61, 65−129. (34) de Matos, F. C.; da Costa, M. C.; Meirelles, A. J. de A.; Batista, E. A. C. Binary Solid-Liquid Equilibrium Systems Containing Fatty Acids, Fatty Alcohols and Trilaurin by Differential Scanning Calorimetry. Fluid Phase Equilib. 2016, 423, 74−83. (35) Nyvlt, J. Solid-Liquid Phase Equilibria; Elsevier/North Holland: Amsterdam, 1977.

■

ABBREVIATIONS activity coefficient of component i in the liquid phase ΔfusH, molar enthalpy of fusion MM, molar mass R, gas constant T, temperature Teut, eutectic temperature Tm, melting temperature Tper, peritectic temperature Ttrans, solid−solid transition temperature Ttrans,pure, pure component transition temperature u, uncertainty xi, liquid-phase molar fraction of a component i zi, solid-phase molar fraction of a component i γLi ,

■

REFERENCES

(1) Hill, K.; Hirsinger, F.; Kgaa, H. Oils and Fats Manual: A Comprehensive Treatise: Properties, Production, Application; Wolff, J.-P., Eds.; 1997, Vol. 99, pp 229−229. (2) Johnson, R. W.; Fritz, E. Fatty Acids in Industry: Processes, Properties, Derivatives, Applications; M. Dekker, 1989. (3) Kreutzer, U. R. Manufacture of Fatty Alcohols Based on Natural Fats and Oils. J. Am. Oil Chem. Soc. 1984, 61, 343−348. (4) Hasan, A.; Sayigh, A. A. Some Fatty Acids as PCM Energy Storage Materials. Renewable Energy 1994, 4, 69−76. (5) Gandolfo, F. G.; Bot, A.; Flöter, E. Phase Diagram of Mixtures of Stearic Acid and Stearyl Alcohol. Thermochim. Acta 2003, 404, 9−17. (6) Carareto, N. D. D.; Costa, M. C.; Rolemberg, M. P.; Krähenbühl, M. A.; Meirelles, A. J. A. The Solid−liquid Phase Diagrams of Binary Mixtures of Even Saturated Fatty Alcohols. Fluid Phase Equilib. 2011, 303, 191.e1−191.e8. (7) Carareto, N. D. D.; Dos Santos, A. O.; Rolemberg, M. P.; Cardoso, L. P.; Costa, M. C.; Meirelles, A. J. A. On the Solid-Liquid Phase Diagrams of Binary Mixtures of Even Saturated Fatty Alcohols: Systems Exhibiting Peritectic Reaction. Thermochim. Acta 2014, 589, 137−147. (8) de Matos, F. C.; da Costa, M. C.; Meirelles, A. J. de A.; Batista, E. A. C. Binary Solid-Liquid Equilibrium Systems Containing Fatty Acids, Fatty Alcohols and Trilaurin by Differential Scanning Calorimetry. Fluid Phase Equilib. 2016, 423, 74−83. (9) Maximo, G. J.; Carareto, N. D. D.; Costa, M. C.; dos Santos, A. O.; Cardoso, L. P.; Krähenbühl, M. A.; Meirelles, A. J. A. On the Solid-Liquid Equilibrium of Binary Mixtures of Fatty Alcohols and Fatty Acids. Fluid Phase Equilib. 2014, 366, 88−98. (10) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (11) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Groupcontribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21, 1086−1099. (12) 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, 178−193. (13) Costa, M. C.; Rolemberg, M. P.; Meirelles, A. J. A.; Coutinho, J. A. P.; Krähenbühl, M. A. The Solid-Liquid Phase Diagrams of Binary Mixtures of Even Saturated Fatty Acids Differing by Six Carbon Atoms. Thermochim. Acta 2009, 496, 30−37. (14) Carareto, N. D. D.; Castagnaro, T.; Costa, M. C.; Meirelles, A. J. A. The Binary (Solid + Liquid) Phase Diagrams of (Caprylic or Capric Acid) + (1-Octanol or 1-Decanol). J. Chem. Thermodyn. 2014, 78, 99−108. (15) Inoue, T.; Hisatsugu, Y.; Suzuki, M.; Wang, Z. N.; Zheng, L. Q. Solid-Liquid Phase Behavior of Binary Fatty Acid Mixtures: 3. Mixtures of Oleic Acid with Capric Acid (Decanoic Acid) and J



Article

(36) Gamsjäger, H.; Lorimer, J. W.; Scharlin, P.; Shaw, D. G. Glossary of Terms Related to Solubility (IUPAC Recommendations 2008). Pure Appl. Chem. 2008, 80, 233−276. (37) Singh, S. K.; Jalali, A. F.; Alden, M. Modulated Temperature Differential Scanning Calorimetry for Examination of Tristearin Polymorphism: 2. Isothermal Crystallization of Metastable Forms. J. Am. Oil Chem. Soc. 1999, 76, 507−510.

K


SolidâLiquid Equilibrium of Binary Systems Containing Fatty Acids

Recommend Documents

SolidâLiquid Equilibrium of Binary Systems Containing Fatty Acids