Mitigating crystallization of saturated FAMEs (fatty acid methyl esters) in biodiesel: 2. The phase behavior of 2-stearoyl diolein–methyl stearate binary system

Energy 83 (2015) 647e657

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Mitigating crystallization of saturated FAMEs (fatty acid methyl esters) in biodiesel: 2. The phase behavior of 2-stearoyl dioleinemethyl stearate binary system Mark Baker, Laziz Bouzidi, Suresh S. Narine* Trent Centre for Biomaterials Research, Departments of Physics & Astronomy and Chemistry, Trent University, 1600 West Bank Drive, Peterborough, Ontario K9J 7B8, Canada

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 September 2014 Received in revised form 6 December 2014 Accepted 21 February 2015 Available online 18 March 2015

The phase behavior of a model binary system made of OSO (2-stearoyl diolein) and MeS (methyl stearate) was investigated with differential scanning calorimetry and X-ray diffraction. The study is part of a series of investigations of unconventional additives such as TAGs (triacylglycerols) and dimers of TAGs with a demonstrated potential to significantly alter the crystallization of biodiesel. The TAG (triacylglycerol) was found to be effective in depressing the crystallization onset of the FAME (fatty acid methyl ester) significantly even at low concentration. OSO was shown to affect the crystallization of the mixtures strongly, and to dramatically alter their polymorphism. The system's phase diagram involved marked transformation lines including eutectics and solidesolid transitions. The molecular interactions were evaluated using a simple thermodynamic model. A mechanism for disruption of crystallization was proposed to be dependent on the peculiar geometry of OSO: the “straight” stearic acid participates easily in the lamellar packing of the equally “straight” FAME, whilst its kinked oleic acids effectively halt additional saturated FAMEs from participating due to steric hindrances. The findings of the study indicate that judicious loadings of TAGs which would target biodiesel's saturated FAMEs will have a substantial beneficial effect on the low temperature performance of the fuel. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Biodiesel FAME (fatty acid methyl ester) TAG (triacylglycerol) Phase behavior Polymorphism Binary phase diagram

1. Introduction Biodiesel is a domestic and attractive renewable alternative which is increasingly replacing some of the conventional petroleum diesel fuels [1]. Its advantages and disadvantages are very well documented [2]. A critical inherent problem currently limiting the use of biodiesel in cold climates is its relatively poor lowtemperature flow properties, indicated by high CP (cloud points) and PP (pour points) [3e5]. The gelling of the fluid and subsequent operability problems, such as plugging of filters which occurs below the CP, is essentially dependent upon the amount and size of the crystals. The actual temperatures at which the operability of biodiesel is compromised are defined by standards (e.g., the CFPP (cold-filter plugging point); (ASTM D-6371, EN 116, IP-309)). A number of approaches have been investigated to mitigate the cold flow issues of biodiesel. The strategies employed are not only

* Corresponding author. Tel.: þ1 705 748 1011; fax: þ1 705 748 1652. E-mail address: [email protected] (S.S. Narine). http://dx.doi.org/10.1016/j.energy.2015.02.076 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

aimed at lowering the freezing point (CP and onset of crystallization) of biodiesel constituents but also at controlling the crystallizing solids (size and amount). They include winterization, dilution, additives and blending with petrodiesel and/or other fuels such as kerosene [5]. Alcohols other than methanol are used to make biodiesel with chemical compositions with inherent improved cold temperature performance and similar advantages to methyl ester fuel [2]. Nonetheless, these strategies are applied with varying degrees of success and come mostly at the detriment of other properties, or are not cost effective [2]. In fact, the behavior of biodiesel is dictated by its molecular composition, and its properties are largely linked especially to fatty acid structure [4]. Structural features such as chain length, degree of unsaturation, orientation of double bonds, symmetry, and type of ester head group strongly influence the MP (melting point) of individual chemical constituents of biodiesel. The wide diversity of biodiesel feedstock and the interdependencies of its properties make it very difficult to solve the problems simultaneously. However, the overall thermal behavior of the fuel is principally affected by the relative concentration of its saturated and unsaturated

648

M. Baker et al. / Energy 83 (2015) 647e657

Nomenclature CLM DCL DH DSC FAME MeS MSBO OSO PPP PPS PSP PSS SAXD

chain length mismatch double chain length enthalpy differential scanning calorimetry fatty acid methyl ester methyl stearate metathesized soybean oil 2-stearoyl diolein tripalmitin 1,2-Palmitoyl 3- Stearoyl sn-glycerol 1,3-Palmitoyl 2- Stearoyl sn-glycerol 1-Palmitoyl 2,3- Stearoyl sn-glycerol small angle X-Ray diffraction

FAMEs (fatty acid methyl esters) components. As thermodynamic simulation have indicated, low-temperature operability of a biodiesel fuel is mainly determined by the saturated FAMEs content or other higher melting minor components, regardless of the chemical nature of the unsaturated esters [6]. The highest melting components of biodiesel, such as MeS (methyl stearate) and MeP (methyl palmitate), disproportionately affect its cold flow properties even at low concentration [7]. The cold flow issue is primarily a multifaceted problem of crystallization (of saturated FAMEs) in solution (unsaturated FAMEs) which can be approached from several angles. Fundamentally, the objective, if not to prevent, would be to adequately disrupt the crystallization process at both the nucleation and growth stages in order to lower the onset temperature of crystallization and decrease the number and size of the crystals. This is not an easy task as the wide diversity of biodiesel systems involves complex molecular interactions, intersolubility issues, and promote special phase transformations. In this regard, a better understanding of the phase behavior of the biodiesel components and any potential additive that would serve as an “improver” of cold flow, or any other property for this matter, is of critical importance. The development of specific thermodynamic models for predicting crystallization/melting behavior of biodiesel and biodiesel/additive would be a valuable tool in the hands of the industry. Unfortunately, studies of the phase behavior of the individual FAMEs constituting the biodiesel and their mixtures as a means to better understand the thermodynamics and kinetics of phase change in biodiesel [4] are limited. Note that phase behavior and modelling of phase diagrams have been published for few binary FAME systems, providing valuable information that can be used to understand biodiesel performance [6,8,9]. The present work was triggered by promising cold flow results obtained with MSBO (metathesized soybean oil) additives to a commercial biodiesel [10]. The most effective fractions constituents of MSBO were determined in our laboratories [11]. Oligomers of TAGs (triacylglycerols) and TAGs with two unsaturated fatty acids in the cis-configuration and a fatty acid in the trans-configuration or a saturated fatty acid were found to be highly functional in depressing the onset of crystallization of biodiesel. The most effective stereospecificity is when the trans/saturated fatty acid is at the sn-2 position. This suggested that the particular molecular conformation of these TAGs has a profound effect on the cold flow properties of biodiesel. We have hypothesized that the peculiar geometry of the TAG (triacylglycerol) molecules which present two kinked and one “straight” fatty acid chains may disrupt the packing of the FAMEs at the nucleation stage and therefore delay crystallization significantly.

T TAG TCL WAXD X XRD

temperature triacylglycerol triple chain length wide angle X-ray diffraction molar fraction X-ray diffraction

Subscripts c crystallization p peak on onset off offset E1 eutectic-1 E2 eutectic-2

In order to shed light on the mechanisms at the origin of the crystallization delay observed in biodiesel induced by the addition of specifically structured TAGs, we have performed a series of binary phase behavior studies of the most prevalent saturated FAMEs contained in biodiesel and TAGs containing two cis-unsaturated fatty acids and one saturated fatty acid corresponding to the FAME. The present paper reports on the binary system made of MeS and OSO (2-stearoyl diolein). To our best knowledge, there is no other published work on FAME/TAG systems. 2. Experimental methods 2.1. Materials MeS (Methyl stearate) purchased from SigmaeAldrich (Oakville, Ontario) at a claimed purity of 96% was further purified in our laboratory to better than 99%. OSO was synthesized in our laboratory according to known procedures [12,13] with a purity exceeding 99%. The purity of MeS was determined by GC-FID. The sample was run as is in chloroform, using a Zebron Capillary GC (ZB-5HT Inferno) Column (Terrance, CA, USA). OSO purity was determined by a Waters Alliance (Milford, MA) e2695 HPLC system fitted with a Waters ELSD 2424 evaporative light scattering detector. The purified OSO and MeS were mixed in the desired molar fractions (OSO molar fraction being XOSO ¼ 0, 0.05, 0.25, 0.40, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.85, 0.95 and 1.00), then heated at 80  C and stirred for 5 min to ensure complete homogeneity. Special care was taken for the overall handling and storage (4  C) of the samples. 2.2. Thermal processing The samples were subjected to the same thermal protocol to allow for comparison between the different techniques used. The sample was first equilibrated at 80  C for 5 min, a temperature and a time over which crystal memory was erased, and then cooled at 5 K/min down to 40  C. For DSC measurements, the sample was subsequently held at 40  C for 5 min then reheated to 80  C at 2.0 K/min to obtain the melting profiles. All measurement temperatures are reported to a certainty of better than ±0.5  C. 2.3. Analytical methods 2.3.1. Xeray diffraction A Panalytical Empyrean X-ray diffractometer (PANalytical B.V., Lelyweg, The Netherlands) equipped with a filtered Cu-Ka radiation source (l ¼ 0.1542 nm) and a PIXcel3D detector was used in linescanning mode (255 lines over 3.347 wide detector). The XRD

M. Baker et al. / Energy 83 (2015) 647e657

patterns were recorded between 1.2 and 60 (2q) in 0.026 steps, at 45 kV and at 40 mA. The procedure was automated and controlled by PANalytical's Data Collector (V 3.0c) software. The samples were processed as described in Section 2.2 in the XRD chamber using a 700 Series Cryostream Plus cooling system (Oxford Cryosystems, Oxford, UK) fitted to the diffractometer. The temperature was controlled to better than ±0.5  C. The data were processed and analyzed using the Panalytical'sX’PertHighScoreV3.0 software. We refer to the range 2q ¼ [1.2e15] and [15e60] as the small- and wide-angle scattering regions (WAXD (wide-angle X-ray diffraction) and SAXD (small-angle X-ray diffraction)), respectively. 2.3.2. Differential scanning calorimetry The DSC measurements were carried out under a nitrogen flow of 50 mL/min on a Q200 model (TA Instruments, New Castle, DE). Samples of approximately 0.4e0.6 (±0.1) mg in a hermetically sealed aluminum DSC pan were processed as described in Section 2.2. The “TA Universal Analysis” software coupled with a method developed by our group [14] was used to analyze the data and extract the main characteristics of the peaks (peak temperature, Tp ; onset temperature, TOn ; offset temperature, TOff ; enthalpy, DH; and full width at half maximum, FWHM). The temperature window over which a thermal event occurs is defined as the absolute value of the difference between TOff and TOn of that event. Subscripts C and M are used for crystallization and melting, respectively. The positions of non-resolved thermal events were estimated using the first and second derivatives of the differential heat flow, and the other characteristics were simply estimated using the software elements. 2.4. Data analysis and modeling 2.4.1. X-ray data analysis and polymorphism The crystal structures are described by the layering type in the structure and the type of the subcell structure within the layers as usually done for TAGs. The main subcell hydrocarbon-chain packing modes are commonly denoted as the a, b0 and b polymorphs [15]. The chain packing of the a- polymorph is hexagonal with nonspecific chainechain interactions and is characterized by one strong wide-angle line in the XRD pattern at a lattice spacing of ~4.2 Å, originating from the (100)a basal plane reflection. The common subcell packing of the b0 -polymorph is orthorhombic, with the alternate acyl chains packing in planes perpendicular to each other (O⊥ ) and is characterized by two strong wideangle lines at lattice spacings of 4.2e4.3 Å originating from the (110)b0 reflection and 3.7e3.9 Å originating from the (200)b0 reflection. The hydrocarbon chains of theb-polymorph are commonly packed parallel to each other in a triclinic (or monoclinic, if the angles a and g are 90  C) parallel subcell (T== ). The b-form is characterized in the wide-angle region by a lattice spacing of ~4.6 Å originating from the (010)b reflection and a number of other strong lines around 3.6e3.9 Å. The b-polymorph is the most stable crystal form, with the highest melting temperature, and the a-polymorph is the least stable crystal form, with the lowest melting temperature [16]. The hydrocarbon chain layering is responsible for the characteristic small-angle (long-spacing) reflections. The d-value of the first order (001) reflection represents the thickness of the molecular layers. Higher order (00l)-reflections indicate regular, periodic structures and represent the periodical sequence of electronic density differences in multiple layers. In the case of hydrocarbons, such as alkanes, the series of (00l)-peaks originates from the region of lower scattering density in the gap between the layers [17,18]. The period of layers along the layer normally observed for TAG

649

structures is usually proportional to the acyl chain lengths by a factor of two or three, suggesting a DCL (double-chain length) or a TCL (triple-chain length) packing [19].

2.4.2. Thermodynamic analysis of the boundaries in the phase diagrams The liquidus line in the phase diagram was calculated using a thermodynamic model in which the contribution of pair interactions was added to a description of an ideal solution. The effort is based on the fact that physical properties of fatty mixture systems are primarily governed by the balance of the molecular interaction between the same molecules and the balance between different molecules [20,21]. The mathematical approach is based on the Hildebrand equation which describes so-called regular solutions in which chemical effects are considered not present, and in which the distribution and orientations are random [22,23]. In this model, only the enthalpy of the “solute” is taken into consideration as it is the crystallizing entity, and the solubility limit of the solute in the solvent is given by Ref. [23]:

ln xs ¼


 DHs 1 1  T Ts R

(1)

where xs is the solubility limit (in mole fraction units) at temperature T, DHs is the molar enthalpy of fusion of the solute, and Ts is the melting temperature of the pure solute. The phase line (liquidus line for instance) is therefore calculated simply with a knowledge of the melting point and heat of fusion of the solute. In a (A/B) binary mixture presenting a eutectic point, the solute may be A or B depending on whether the composition is smaller or larger than the eutectic composition (XE ). Both branches are described with Eq. (1) with s ¼ A or B, for the concentration region where A or B is the solute, i.e., the left- or right-hand side branch of the eutectic [24,25]. The non-ideality of mixing due to molecular interactions is introduced using the BraggeWilliams approximation framework [26]. This model attributes the origin of the non-ideality of mixing to the enthalpy term of the free energy of mixing and assumes the same entropy term as in the ideal mixing case [27]. In order to account for the free energy due to mixing the BraggeWilliams model introduces a non-ideality of mixing parameter (r (J/mol); Eq. (2)), which is the difference in interaction energy between pairs of unlike molecules and the interaction energy between pairs of like molecules.


u þ uBB r ¼ z uAB  AA 2

(2)

where z is the first coordination number, uAB , uAA and uBB the interaction energies for AB, AA and BB pairs, respectively. In this approximation, the phase line as described by the Hildebrand equation (Eq. (1)) is simply adjusted by introducing the extra energy term. According to this approximation, the solubility limit of the “solute” in the “solvent” is given by:

ln Xs þ


 rð1  Xs Þ2 DHs 1 1  ¼ T Ts RT R

(3)

Similarly to the Hildebrand model, the two branches of an equilibrium liquidus line of a system presenting a eutectic are described by Eq. (3) with s ¼ A or B, depending on whether the composition is smaller or larger than the eutectic composition [24,25]. The calculated boundary of Eq. (3), simplifies to a parameterized temperature versus molar composition curve, (Eq. (4))

650

M. Baker et al. / Energy 83 (2015) 647e657

"

rð1  xs Þ2 þ DHs Tðxs Þ ¼  RTs ln xs  DHs

# (4)

The pure component properties (temperature, Ts , and enthalpy of fusion, DHs ) were taken from the experimental data in this work. The fit of the experimental data (in our case Tp of the last endotherm of the experimental compositions) versus molar fraction (Ts ) to the parameterized equation was achieved by adjusting r in small steps to obtain a liquidus line which lies closest to the experimental boundaries, then refining to calculate the curve that has the least sum of squares of the difference between experimental and calculated temperatures. The method of least squares is a standard approach for curve fitting and is detailed in several books. See for example Press et al. [28] or Recktenwald [29]. The technique is relatively simple (in terms of required computing power) and is generally well understood. It minimizes the square of the error between the original data and the values predicted by the equation. The objective function was the RMSD (root mean square deviation, Eq. (5)) between the experimental temperature (Ts ) and the calculated one (Tcalc ) for the i ¼ 1  n experimental compositions.

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðTs  Tcalc Þi RMSD ¼ n

(5)

The BraggeWilliam model is a simple and powerful tool commonly used to simulate the phase boundaries in the phase diagram of binary lipid mixtures [25,30e36]. The method provides an interesting framework for the molecular interactions at play in these systems, and achieves a viable understanding particularly useful to practitioners in the field. The effort is sufficient to decipher the solubility behavior of these relatively complex systems and provides a reliable presentation of the real liquidesolid phase transformation through the parameter r. For ideal mixing, the intermolecular interaction of like-pairs is equal to that of mixed-pairs and consequently r ¼ 0, and the Hildebrand equation is obtained. An ideality parameter different from zero was explained by Knoester et al. [37] as being due to the formation of a solid solution between the high-melting and lowmelting components. A negative r is obtained when the formation of AB pairs is energetically more favorable than AA or BB pairs and reflects a tendency for order. A positive r is obtained when mixed-pair formation is energetically less favorable and reflects a tendency of like molecules to cluster, which beyond some critical value leads to phase separation [25,38]. 3. Results and discussion 3.1. Crystallization and polymorphism 3.1.1. Crystal structure of the OSO/MeS mixtures Selected XRD patterns of the different OSO/MeS mixtures obtained at 20  C are shown in Fig. 1(aec) for the wide-angle region and Fig. 1(d) for the small-angle region. Note that except for pure MeS, a liquid phase is still present at the measurement temperature in all the mixtures, as indicated by the wide background halo in the XRD patterns. The contribution of the liquid phase to the XRD signal was subtracted from the pattern before analysis of the crystal peaks. As can be seen, the polymorphism of the OSO/MeS binary system is complex. The characteristic lines of three different subcell structures (monoclinic, triclinic and orthorhombic) were unambiguously detected. Relevant peak positions and Miller indices are listed in Table 1. The XRD pattern of pure MeS was fully identified using the PDF (powder diffraction file) database of the ICDD and

found to be perfectly matching reference No 00-032-1764. MeS crystallized in the monoclinic form (labelled bM ) in the I2/a space group. The OSO- rich mixtures [0:65OSO to 1:0OSO ] crystallized mainly in the orthorhombic form as evidenced by the predominance of the characteristic reflections of the b0 - polymorph (3.7 Å and 4.13 Å originating from the (200) and (010) family of planes, respectively). The b0 - phase persisted in all the mixtures with OSO content higher than 25%. A third phase having the triclinic symmetry (bT - form) was detected in the 0:05OSO to 0:65OSO mixtures. The signature peak of the bM form, the ð1011Þ reflection at dspacing of 4.07 Å, is present with a quantifiable intensity in mixtures with up to the XOSO ¼ 0.65, and as a trace shoulder to the main peak of the b0 - polymorph (d010 ¼ 4.12 Å) for the mixtures with higher OSO content. The relative content of bM , as estimated from the relative intensity of the ð1011Þ reflection decreased exponentially with increasing OSO content up to 65% (Fig. 1b and c) after which it can no longer be considered. Both the ð100ÞT and ð010ÞT reflections of the triclinic form (lines at 3.65 Å and 4.50 Å, respectively) were first detected in the XRD pattern of the 0:05OSO mixture and disappeared after0:65OSO. Note that when OSO content was increased, and up to 0:50OSO , the relative intensity of ð010ÞT increased, whereas, that of ð100Þb decreased sharply (Fig. 1a). The intensity of both peaks remained constant afterwards; a very clear indication of the peculiarity of the 0:50OSO mixture. Note that a refined fit of the wide signal shouldering the line at d ¼ 4.07 Å in the XRD patterns of the 0:40OSO to 0:65OSO mixtures yielded two small peaks at d ¼ 4.12 and 4.18 Å suggesting that a b0 - phase may also be present in these mixtures. This would indicate that even at these relatively high MeS concentrations, a very small amount of OSO was crystallized in its orthorhombic form. However, this was not unambiguously established, due to the relatively large liquid phase in these samples. The XRD data collected in the wide e angle region highlights three groups of mixtures with fundamentally different polymorphism (Fig. 1e): (1) an exclusive b0 -phase in the OSO- rich [0:70OSO 1:0OSO ] mixtures range, (2) a dominating monoclinic phase in the MeS- rich [0:0OSO 0:25OSO ] mixtures range, and (3) a dominating b-phase in the triclinic form for the intermediary mixtures. The information provided by the SAXD data complemented that of the WAXD. As can be seen in Fig. 1d, several distinct peaks appeared in the SAXD patterns. The analysis of d-spacing ratios allowed a straight forward indexation of the planes (Table 2). The indexation was also confirmed by published data for MeS (PDF database) and OSO. The SAXD reflections have been grouped into three specific groups of (00l) families of planes that were directly related to the three groups of mixtures that were specified out of the WAXD data (Table 2). (1) The MeS- rich mixtures (XOSO < 0.40) as exemplified by the SAXD pattern of pure MeS presented two distinct series of 8 reflections each (l ¼ 1 to 8, Series 1 with d001 ¼ 47.64 Å and Series 2 d0001 ¼ 49.45 Å). The two series are characteristic of a parallel and perpendicular lamellar periodicity of the monoclinic crystal structure. These reflections match those of the reference pattern No 00-032-1764 of the PDF database and can therefore be undoubtedly assigned to the DCL packing of MeS. Note that the intensity of these reflections decreased as OSO content was increased, indicating that the MeS electronic environment that gave rise to the chain layering was increasingly altered. Note that there is no peak in this group that can be unambiguously attributed to an OSO crystal phase. (2) The SAXD data collected for the OSO- rich mixtures (XOSO > 0.65) also showed two series of three reflections each (l ¼ 1, 2 and 4, Series 1 with d001 ¼ 53.05 Å and Series 2 d0001 ¼ 55.99 Å). The intensity of the (001) and (002) reflections did not vary with concentration and there was no obvious feature that can be

M. Baker et al. / Energy 83 (2015) 647e657

651

Fig. 1. XRD patterns of OSO/MeS mixtures measured at 40  C. Wide-angle XRD region of mixtures having an OSO concentration XOSO between (a) 0.0 and 0.50; (b) 0.50 and 0.65; and (c) 0.65 and 1.0; (d) small-angle XRD region; and (e) delimitation of the regions of concentration where different crystal phase coexist.

652

M. Baker et al. / Energy 83 (2015) 647e657

Table 1 Wide-angle X-ray diffraction (WAXD) data measured at 40  C of OSO/MeS mixtures. Miller indices of typical characteristic peaks of the b-forms (monoclinic and triclinic) and b0 -form (orthorhombic) are shown alongside their respective dspacing. Monoclinic (bM )

Orthorhombic (b0 )

Triclinic (bT )

dhkl (Å)

hkl

dhkl (Å)

4.45 4.32 4.08 3.07 2.44

ð011Þ ð611Þ ð1011Þ ð121Þ ð330Þ

4.51 4.12 3.65 e e

dhkl (Å) ð100Þ ð011Þ ð100Þ e e

4.20 3.70 e e e

ð110Þ ð200Þ e e e

Table 2 Small-angle X-ray diffraction (SAXD) data of OSO/MeS mixtures obtained at 40  C. Uncertainty attached to d00l is ~±0.15 Å. XOSO

d00l (Å)

0e0.25

47.79 49.47 44.74 53.05 56.00

l

0.40e0.65 0.70e1.0

¼

1

2

3

4

6

23.99 24.61 22.73 26.55 28.01

15.95 e 14.78 e e

12.00 12.35 e 13.37

8.00 8.23 e e e

unambiguously attributed to MeS. The crystal features of OSO seem to have overwhelmed those of MeS in this group of mixtures. These series are therefore assigned to the chain layering of OSO. Note that only the b0 - form has been detected in the 0:70OSO to 1:0OSO group of mixtures. Therefore, the two series are assigned to the parallel and perpendicular lamellar periodicity of the orthorhombic crystal structure. (3) The 0:40OSO to 0:65OSO mixtures presented only one series of reflections (l ¼ 1, 2, 3 and 4) with d001 ¼ 44.75 Å, outlining again the peculiarity of this range of mixtures. The (001) and (003) peaks of these mixtures were well resolved. They appeared in all the mixtures of the group at the same 2q positions and have the same intensity, indicating the same chain layering and length. Note that the ð003Þ reflection of this group was much stronger than its counterpart in the other groups, indicating a completely different electronic environment from MeS and OSO. This can be explained by a regular arrangement of OSO in a MeS matrix. The relatively large width of the 003 line suggests that the arrangement in the layer direction is probably very disordered. The XRD data, particularly the presence of singularities at the 0:50OSO mixture, support the presence of a 1:1 compound in the bT form in the mixtures having more than 25% and less than 70% of OSO. The compound coexisted with a monoclinic phase made of MeS in the MeS rich side (XOSO < 0.50) and with an orthorhombic (b0 )- phase made of OSO in the OSO rich side (XOSO > 0.50). The width of the peaks associated with the compound is relatively large indicating that its phase was not homogeneous and its structure not well ordered. This may be explained by loosely bound MeSeOSO pairs probably because the crystallization was not complete. The chain layering displayed by the 0:40OSO to 0:65OSO mixtures is also consistent with a disordered and inhomogeneous MeS/OSO compound. 3.1.2. Crystallization behaviour The DSC cooling thermograms of the OSO/MeS binary mixtures are displayed in Fig. 2a and the corresponding characteristic temperatures (Tp , TOn , and TOff ) in Fig. 2b. The corresponding characteristic thermal transition parameters are listed in Table 3. The cooling thermograms of Fig. 2a indicate that the overall

crystallization path of these mixtures is quite complex and depend strongly on concentration. The cooling thermogram of the0:50OSO mixture delineates two groups of mixtures with different features indicating qualitative differences in crystallization behavior. The variety of resolved intermediary exotherms showing in both groups (Fig. 2a), and the corresponding marked differences in crystallization values (Fig. 2b) point to a diversity of phases developing in this binary system. The cooling thermogram of pure MeS presented a unique sharp (FWHM ¼ 0.43 ± 0.03  C) and very intense exotherm (PMeS in Fig. 2a) centered at 33.27 ± 0.01  C; whereas, the thermogram of pure OSO displayed one strong relatively broad exotherm at ~ 10.41 ± 0.13  C (POSO in Fig. 2a, FWHM ¼ 2.37 ± 0.02  C) preceded by a small shouldering peak at 5.75 ± 0.88  C (S in Fig. 2a). This illustrates the qualitative difference in the ways the two molecules crystallize due their very different chemical and conformational structures. MeS, which is a linear chain, crystallized in its final and most stable crystal form (monoclinic) very rapidly, and as indicated by its small FWHM without any geometrical hindrance; whereas OSO with its two kinks at the sn-1 and sn-3 positions, achieved its final crystal structure (orthorhombic) starting first by a relatively slow and weak transformation as shown by the wide leading exothermic event of its DSC trace (S in Fig. 2a). As can be seen in Fig. 2a, the leading exotherm is prolonged and loses little of its height along the transformation path, indicating a process probably dominated by continuous nucleation rather than growth of pre-existing nuclei. The DSC thermogram of OSO suggests a crystallization process dominated by nucleation of starting lamellar structures or seeds and a very small growth rate followed by the rapid growth of the final phase (i.e., the phase associated with the main peak, POSO ). The plot of the characteristic crystallization temperatures versus OSO molar ratio (Fig. 2b) highlights two different crystallization behaviors delimited by the 0:40OSO mixture. Starling differences in span of crystallization, number of transitions and nature of phase development are manifest between the two concentration ranges. A dramatic point of change is observed at the 0:40OSO concentration in the offset (Toff in Fig. 2b) as well as enthalpy of crystallization (DHC in Fig. 2c) versus OSO content curves. DHC , which is almost constant (246 ± 16 J/g) for 0:0OSO to 0:40OSO mixtures, decreased exponentially plateauing at ~63 ± 16 J/g for the mixture with XOSO higher than 0.60. Although faint, a singularity is also noticeable at the 0:40OSO mixture in both the onset and Tp of crystallization versus XOSO curves. For convenience and clarity, the crystallization path of the OSO/ MeS binary mixtures are discussed in the following sections in terms of the effect of OSO on MeS and of MeS on OSO for the group of mixture with concentrations below and above 0:50OSO , respectively, acknowledging that the crystallization behavior of the system can be equally described and evaluated differently. As MeS content was increased from 0:55OSO to 1:0OSO the leading exotherm shifted to higher temperatures while extra resolved exotherms appeared in the thermograms. The development of such intermediary thermal events between the leading and final exotherm indicates a quantitative as well as qualitative change in the phase trajectories. This is attributable to a direct participation of the MeS molecules in the formation of the starting lamellar units which further transform and participate in the formation of the final phase composition. As MeS content was increased to 50%, the peak temperature of POSO remained almost constant, then widened dramatically and its height decreased almost linearly to completely disappear in the 0:50OSO mixture. This clearly indicates that the crystal phase with OSO characteristics remains predominant but gradually loses its homogeneity and disorganizes with the incorporation of more of the FAME. POSO can be safely assigned to a well-

M. Baker et al. / Energy 83 (2015) 647e657

653

Fig. 2. (a) DSC cooling (5.0 K/min) thermograms of OSO/MeS mixtures. OSO molar fraction (XOSO ) is reported on top of the right hand side of each curve. PMeS and POSO designate the crystallization peak associated to MeS phase and OSO phase, respectively, and S (shoulder) designate the leading crystallization peak; (b) characteristic temperatures obtained from the DSC cooling thermograms: onset temperature of crystallization (TOn ): down triangles; peak temperature of the leading peak: open circles; peak temperature of the last crystallization peak: stars; peak temperature of the intermediary transition peaks: filled circles; and offset temperature of crystallization (TOff ): squares; and (c) enthalpy of crystallization. Dashed lines in panel (c) serve as guides for the eye. They are fits of the data to straight line function for XOSO ¼ 0 to 0.4, and exponential decay function for XOSO ¼ 0.4 to 1.0.

Table 3 Characteristic thermal transition parameters of the OSO/MeS mixtures obtained from the DSC cooling thermograms. XOSO : OSO molar fraction; TOn ( C): onset temperature of crystallization; TOff ( C): offset temperature of crystallization; T14 ( C): peak temperature of the successive intermediary transition peaks; and DH(J/g): enthalpy of crystallization. XOSO

0

0.5

0.25

0.40

0.50

0.53

0.55

0.58

0.60

0.65

0.70

0.75

0.85

0.95

0.1

TOn TOff T1 T2 T3 T4 DH

33.3 31.4 33.1 e e e 245

31.4 9.0 30.9 9.0 e e 231

24.6 6.9 24.1 9.7 e e 215

20.3 4.9 19.7 17.3 12.9 8.7 234

16.8 8.5 16.4 10.7 5.6 1.4 132

16.7 11.3 16.3 10.9 5.6 2.9 89

16.2 11.8 15.8 10.8 5.8 4.0 67

15.4 13.4 15.0 10.5 3.7 6.3 118

14.8 13.9 14.4 10.4 6.6 e 75

13.8 14.5 13.4 9.8 5.9 10.8 63

12.8 14.6 12.3 9.1 5.2 10.7 61

11.5 14.7 11.0 8.2 4.0 10.5 83.4

9.9 13.6 9.4 6.0 1.1 10.1 41.9

7.6 13.1 7.1 e 9.2 10.1 57.0

6.8 12.2 5.7 e e e 63.1

defined polymorphic phase, the b0 - phase as is evidenced by XRD (see Section 3.1.1 above). The direct involvement of MeS in the early stages of OSO crystallization as a component of an OSOeMeS mixed phase is supported by the variation of the strength of leading exotherm (Fig. 2a), from a relatively weakly increasing shoulder in the mixture with XOSO  0.50, to a dominating peak for MeS-richer mixtures. On the MeS side of concentrations, the intensity of PMeS decreased dramatically as OSO content was increased and its peak shifted to lower temperatures, practically linearly up to 0:50OSO (Fig. 2b), after which it became confounded with the leading shoulder. One can safely assign PMeS to the crystallization of a phase made predominantly, if not exclusively, of MeS. Three other distinct exothermic events appeared as early as in the 0:05OSO mixture (arrows in Fig. 2a) indicating the growing effect of OSO on the

crystallization of the mixtures. Note that as OSO content was increased, the two exotherms following PMeS shifted to lower temperatures so far as to align with the second and third peaks of the prolonged leading event which appeared in the 0:55OSO to 1:0OSO mixtures, suggesting again the formation of a mixed MeSeOSO phase. While the intensity of the last exotherm of the 0:0OSO to 0:40OSO mixtures (peak at ~10  C in Fig. 2a) increased dramatically with increasing OSO content, its peak temperature remained almost the same (Fig. 2b), suggesting a phase in which OSO is the dominant contributor to crystallization. At the low temperature end of this last exotherm one can see a small shoulder which appears to be slowly increasing and shifting to low temperatures, then reaching the value recorded for POSO for the 0:60OSO mixture. This last exotherm is probably associated with a very inhomogeneous and disorganized small phase made exclusively of OSO.

654

M. Baker et al. / Energy 83 (2015) 647e657

3.2. Melting behavior and phase development The DSC heating thermograms of the OSO/MeS binary mixtures are displayed in Fig. 3a and the corresponding characteristic temperatures (Tp , TOn , and TOff ) in Fig. 3b. The corresponding characteristic thermal transition parameters are listed in Table 4. The pattern of thermal behavior during heating (2 K/min) of the OSO/ MeS binary system is relatively complex and depends strongly on OSO concentration (Fig. 3a). Pure MeS presented a unique and large endotherm characteristic of the melting of its monoclinic phase. Four extra resolved endotherms are observed for the 0:05OSO and 0:25OSO mixtures and only two endotherms for the 0.40 mixture. The 0:50OSO mixture presented one endotherm (20.75 ± 0.04  C). The heating thermograms of these mixtures did not display any exotherms suggesting the melting of different phases comprising both OSO and MeS. Note the increasing height of the extra endotherms showing the growing effect of OSO. All the mixtures with more than 50% OSO presented heating thermograms with common transformation features. The sequence of phase transitions recorded for these mixtures started with two relatively wide exotherms, albeit small in the case of the 0:55OSO and 0:60OSO , followed by two or three resolved endotherms (Fig. 3a), suggesting a complex polymorphism driven mainly and increasingly by OSO transformations. The onset and peak temperature of the first exotherm shifts linearly to lower temperature with increasing XOSO . However, the shift is relatively small (7.5

to 5.2  C) suggesting the occurrence in these mixtures of a direct recrystallization (solid-soli transformation) from the same preexisting b0 -phase (see Section 3.1.2). The last endotherm appearing for these mixtures can be safely related to the melting of an OSO rich b- phase recrystallized from the melt. The plot of the characteristic melting temperatures versus OSO molar ratio (Fig. 3b) highlights also the peculiarity of 0:40OSO mixture. Differences in span of melt, number of transitions and nature of phase development are also evident between the two concentration ranges. A dramatic point of change at the 0:40OSO concentration is observed in the enthalpy of melting versus OSO content curves (DHM , Fig. 3c). DHM which was almost constant (220 ± 8 J/g) for 0:0OSO to 0:40OSO mixtures, decreased exponentially to level at ~45 ± 11 J/g for the mixtures with XOSO higher than 0.60. Furthermore, two very distinguishable eutectics separated by a singularity are observed in the liquidus line just above the 0:40OSO concentration. The first eutectic is located at XE1 ¼ 0:50OSO (Arrow E1 in Fig. 3b) and the second at XE2 ¼ 0:80OSO (Arrow E2 in Fig. 3b), and the singularity at ~0:55OSO (Arrow S in Fig. 4). This type of phase boundary is indicative of the formation of a 1:1 (mol:mol) compound which forms a eutectic with both pure components [39]. Similar types of phase boundaries with a 1:1 molecular compound which forms two eutectics with both molecules in each side of the concentration range are commonly observed in binary systems of lipids, such as PSP/PPS [32,40], SPS/PSS and PPP/PPS [37]. As will be explained in the next section, the formation of such a compound is

Fig. 3. (a) DSC heating thermograms of OSO/MeS mixtures; (b) characteristic temperatures obtained from the DSC heating thermograms: offset temperature of melting (TOff ): down triangles; peak temperature of the leading peak: filled circles; peak temperature of the intermediary transition peaks: open circles; and onset temperature of melting (TOn ): squares; S: singularity at the 1:1 molecular compound, E1, E2: Eutectic 1 and 2, respectively, and (c) enthalpy of melting. Dashed line in panel (c) serve as guides for the eye. They are fits of the data to straight line function for XOSO ¼ 0 to 0.4, and exponential decay function for XOSO ¼ 0.4 to 1.0.

M. Baker et al. / Energy 83 (2015) 647e657

655

Table 4 Characteristic temperatures of the OSO/MeS mixtures obtained from the DSC heating thermograms. XOSO : OSO molar fraction; TOn ( C): onset temperature of melting; TOff ( C): offset temperature of melting; T15 ( C): peak temperature of the successive intermediary transition peaks; and DH(J/g): enthalpy of melting. XOSO TOn TOff T1 T2 T3 T4 T5 DH

0 36.2 38.3 37.2

238

0.5

0.25

17.7 36.8 36.0 28.4 25.1 21.8 19.7 216

18.3 31.1 30.2 29.0 25.4 22.0 19.7 201

0.40 18.6 25.8 25.0 20.3

226

0.50 14.6 21.5 20.7

120

0.53

0.55

10.4 21.8 20.6 17.5 15.3 12.6

10.2 23.2 21.6 20.4 17.2 14.9 12.7 66

84

the result of synergies between OSO and MeS, due to their particular structural configurations. The presence of the compound justifies the two eutectics and explains the solubility behavior of the OSO/MeS binary mixtures as well as the nucleation and growth stages of their crystallization process. A series of transformation lines are also drawn from the melting temperatures of the different endotherm displayed by the mixtures upon heating. Of particular interest, two eutectic lines associated with E1 and E2 (dashed lines in Fig. 3b) were determined. Note that the reported position of the eutectic point as well as of the transformation lines depends on the thermal procedure used to identify the phase development. The heating at constant rates is a thermal protocols used produce thermogram that are used to construct socalled kinetic phase diagrams in which the liquidus line that is constructed using the most stable crystal. Such phase diagrams allow the study of solubility and can be extrapolated to describe equilibrium states. 3.3. Thermodynamic analysis of the boundaries in the phase diagram The liquidus line of the binary system was simulated using the thermodynamic model described in Section 2.4.2. The experimental and calculated liquidus lines are shown in Fig. 4. Tp of the last endotherm (open squares in Fig. 4) was used to construct the experimental liquidus line, as typically done in the study of binary lipid mixtures [30e36]. This point is much more suitable for studying equilibrium properties because it is determined by the most stable crystal.

Fig. 4. Liquidus line in the phase diagram of the OSO/MeS binary system. Solid lines are fits to the BraggeWilliam approximation, Equation (5).

0.58 10.1 22.5 21.8 20.8 19.2 16.6 120

0.60

0.65

0.70

0.75

0.85

0.95

0.1

9.6 22.6 21.8 20.3 17.7 16.0

9.1 22.2 21.2 20.0 16.6

9.6 22.1 20.6 17.7 16.8 12.8

9.9 20.6 19.5 17.2 13.3

11.4 18.5 16.9 13.2

13.4 22.1 20.2 16.9

13.7 21.5 21.1 15.9

80

64

59

82

35

56

47

As can be seen in Fig. 4, the compound (composition, XC , molar heat of fusion, DHC , and melting point, TC ) form a eutectic with OSO (eutectic composition XE1 ) and a eutectic with MeS (eutectic composition XE2 ). The values of (DHA , TA ), (DHB , TB ) and (DHC , TC ) obtained from the DSC heating curves of the purified OSO (A),MeS (B) and compound (C), respectively, used to model the liquidus line in the phase diagram are listed in Table 4. The calculation of the liquidus line in the OSO/MeS binary phase diagram was performed considering its singular points. One can notice two distinct eutectic regions separated by a singularity at the 0:59OSO mixture. The singularity in such a kinetic phase diagram is indicative of a 1:1 molecular compound similar to other lipid systems of TAGs which contain an unsaturated fatty acid [39,41e45]. As is generally accepted, the formation of molecular compounds in such systems is justified by conformational considerations and explained by specific molecular interactions (molecular interactions of acyl chain packing, glycerol conformation, and methyl end stacking) [42,44,46]. The modeling could not be performed without taking into consideration the particularities of the liquidus line. It was therefore performed considering the both eutectics and considering the melting point and heat of fusion of the appropriate solute for each eutectic branch. The left (right)-hand curve of the first (second) eutectic corresponds to a phase composed of the crystallizing pure OSO (MeS) component and the right (left)-hand curve to a phase of the pure 1:1 component, and the predicted eutectic mixture occurs at their intersection. The calculations did not reproduce the experimental liquidus line of the binary system when assuming an ideal fluid phase (Hildebrand model, Eq. (1), not shown). It was reproduced very well with the introduction of a non-ideality of mixing parameter r (Bragg-William model, Eq. (4)) to the two sides of each eutectic. Moreover, the singularity has been successfully confirmed at 0:59OSO . The simulated four segments of the liquidus line (labeled I to IV) are represented by solid lines in Fig. 4. The simulation yielded negative values of r for all segments. The singularity has been confirmed at 0:59OSO and the eutectic points obtained by the intersection of the two segments were confirmed at 0:52OSO and0:85OSO . The calculated values of r, XE and TE are listed in Table 5. The experimental kinetic phase diagram of the OSO/MeS binary system was well described by the introduction of negative values of r for all the segments considered (Table 5). The uncertainty attached to the calculated r-value is less than 2.5 kJ/mol. Recall that the BraggeWilliams approximation attributes the origin of the non-ideality of mixing to the enthalpy term of the free energy of mixing and assumes the same entropy term as in the ideal mixing case [27]. The molecular interactions, as depicted by the negative r-values, are strong and tend to favor the formation of unlike pairs in the liquid state. These values are comparable to published values for binary lipid systems such as binary mixtures of diacylphosphatidyl - ethanolamines [47], fatty acids [34], propanediol diacetates [30] and TAGs [31,32,36].

656

M. Baker et al. / Energy 83 (2015) 647e657

Table 5 (a) Parameters used in the BraggeWilliam approximation for the different segments of the liquidus line and values of the non-ideality of mixing parameter obtained. (Enthalpy of melting, DHA and melting temperature, TA ), and (b) Concentration of OSO in eutectic mixtures, compound and corresponding melting temperatures. a) Segment

TA (K)

DHA (kJ/mol)

r (kJ/mol)

I (0.0 OSO to XE1) II (XE1 to Compound) III (Compound to XE2) IV (XE2 to 100% OSO)

310.2 295.0 295.0 294.1

64.00 76.14 76.14 53.22

7.0 49.5 7.5 15.0

b)

XE1 XE2 Compound

XE

TE ( C)

50.8 84.9 58.5

20.0 17.1 21.9

Little work has been reported on the molecular structures and kinetic properties of systems which form molecular compounds. The formation of a 1:1 molecular compound is also observed in systems of two TAGs which both contain an unsaturated fatty acid such as POP/OPO [41], SOS/OSO [42], POP/PPO and POP/OPO [39,43], and SOS/SSO [44,45] and justified by conformational considerations. It is suggested that the shape of the molecules is such that a very dense packing becomes possible with equal amounts of both molecules, though the crystals of each of the pure components can accommodate only a small amount of the other component. The formation of such a compound in OSO/MeS can be explained by specific molecular interactions through the acyl chain moieties similarly to what has been suggested in the case of SOS/ SSO [44] and SOS/OSO [42]. The FAME and the symmetrical saturated/biunsaturated TAG form a molecular compound because of specific interactions (molecular interactions of acyl chain packing, head groups conformation, and methyl end stacking) that confer to the pair high synergistic compatibility. It is hypothesized that a chair or fork configuration of OSO would have a negligible steric hindrance effect for the stearic acid to arrange and pack closely with the equally linear MeS. The DSC data are consistent with the crystal structures and layering arrangements evidenced by XRD. For instance, the three groups of mixtures with fundamentally different polymorphism (Fig. 1e) are also those delimited by the two eutectics. The formation of a loosely bound 1:1 compound in the bT -form was probably initiated in the liquid phase where the mobility of MeS was still not obstructed. The XRD data revealed that the addition of OSO to MeS results in the formation of disordered and inhomogeneous phases; evidenced notably in the packing arrangements along the layer direction. Furthermore, it revealed that the electronic environment of MeS was profoundly altered in the presence of OSO. The disruptive effect of OSO on the packing of MeS was effective at both the nucleation and growth stages of the crystallization process. OSO was shown to be a very effective crystallization depressant which significantly delays nucleation and alters the growth of MeS. The effect was so strong that it lowered the melting point of MeS by ~17  C in the first eutectic concentration. The presence of eutectic reactions taking place in relatively large concentration ranges of the phase diagram indicates that the addition of OSO also reduces crystal size. This effect will be further investigated in a separate study. 4. Conclusions The study of the OSO/MeS binary system by DSC and XRD revealed a complex phase behavior in which OSO plays a central role. The kinetic phase diagram of the OSO/MeS binary system

involved marked transitions including solidesolid transformation. OSO was shown to strongly affect the phase trajectories of MeS and to dramatically alter its polymorphism starting at low concentration. The liquidus line in the phase diagram demonstrated two eutectics, separated by a 1:1 (mol:mol) compound. The polymorphism uncovered by XRD revealed the coexistence of monoclinic, triclinic and orthorhombic subcell structure in concentration regions delimited by the two eutectics. The 50% concentration was confirmed as a loosely bound compound in the triclinic symmetry. A mechanism for disruption of crystallization was proposed to be dependent on the peculiar geometry of OSO: the “straight” stearic acid chain participates easily in the lamellar packing of the equally “straight” FAME, whilst its two kinked unsaturated oleic acids effectively halt additional saturated FAMES from participating in the packing due to steric hindrances. The disruptive effect of the TAG on the packing of the saturated FAME was shown to effectively begin at low concentration and to result in significant suppression of FAME crystallization. The rate at which melting point decreased from MeS to the eutectic was estimated at approximately 0.33 K/%OSO. This relatively steep drop implies that judicious loadings of OSO which would target the saturated FAMEs of biodiesel will have the same large beneficial effects on the low temperature performance of the fuel. Certainly, much smaller concentrations than the eutectic of the OSO/MeS binary system will depress similarly the crystallization temperature of an actual biodiesel. Acknowledgments We would like to thank the Grain Farmers of Ontario, Elevance Renewable Sciences, Trent University, the GPA-EDC, Ontario Ministry of Agriculture, Food and Rural Affairs, Industry Canada and NSERC for financial support. References [1] Moser BR. Biodiesel production, properties, and feedstocks. In: Tomes D, Lakshmanan P, Songstad D, editors. Biofuels. New York: Springer; 2011. p. 285e347. [2] Dunn RO. Effects of minor constituents on cold flow properties and performance of biodiesel. Prog Energy Combust 2009;35(6):481e9. [3] Dunn RO. Cold-flow properties of soybean oil fatty acid monoalkyl ester admixtures. Energy Fuel 2009;23(8):4082e91. [4] Knothe G. Dependence of biodiesel fuel properties on the structure of fatty acid alkyl esters. Fuel Process Technol 2005;86(10):1059e70. [5] Misra RD, Murthy MS. Blending of additives with biodiesels to improve the cold flow properties, combustion and emission performance in a compression ignition enginedA review. Renew Sust Energy Rev 2011;15(5):2413e22. [6] Imahara H, Minami E, Saka S. Thermodynamic study on cloud point of biodiesel with its fatty acid composition. Fuel 2006;85(12e13):1666e70. [7] Chastek TQ. Improving cold flow properties of canola-based biodiesel. Biomass Bioenerg 2011;35(1):600e7. [8] Rocha SA, Guirardello R. An approach to calculate solid-liquid phase equilibrium for binary mixtures. Fluid Phase Equilib 2009;281(1):12e21. €henbühl MA, Meirelles AJA. Low[9] Costa MC, Boros LAD, Coutinho JoAP, Kra temperature behavior of biodiesel: solideliquid phase diagrams of binary mixtures composed of fatty acid methyl esters. Energy Fuels 2011;25(7): 3244e50. [10] Christensen SA, DiBiase SA, Rizvi SQA. Cold flow additives. Patent number: WO2012138513 A1 2012. [11] Mohanan A, Bouzidi L, Li S, Narine SS. Mitigating crystallization of saturated FAMES in biodiesel: 1. Lowering the crystallization temperature via addition of metathesized soybean oil. Not published. [12] Bentley PH, McCrae W. Efficient synthesis of symmetrical 1,3-diglycerides. J Org Chem 1970;35(6). 2082-3. [13] Chandran DV, Bhatnagar RK. A method for synthesis of a-monoricinolein. J Am Oil Chem Soc 1968;45(8):581e2. [14] Bouzidi L, Boodhoo M, Humphrey KL, Narine SS. Use of first and second derivatives to accurately determine key parameters of DSC thermographs in lipid crystallization studies. Thermochim Acta 2005;439(1e2):94e102. [15] Larsson K. Physical properties e structural and physical characteristics. In: Gunstone FD, Harwood JL, Padley FB, editors. The lipid handbook. London: Chapman and Hall; 1986. p. 335e77.

M. Baker et al. / Energy 83 (2015) 647e657 [16] Ghotra BS, Dyal SD, Narine SS. Lipid shortenings: a review. Food Res Inter 2002;35(10):1015e48. [17] Dorset D. The crystal structure of waxes. Acta Crystallogr Sect B: Struct Sci 1995;51(6):1021e8. [18] Dorset DL. From waxes to polymers e crystallography of polydisperse chain assemblies. Struct Chem 2002;13(3):329e37. [19] Mykhaylyk OO, Smith KW, Martin CM, Ryan AJ. Structural models of metastable phases occurring during the crystallization process of saturated/unsaturated triacylglycerols. J Appl Crystallogr 2007;40(s1):s297e302. [20] Ohta N, Hatta I. Interaction among molecules in mixtures of ceramide/stearic acid, ceramide/cholesterol and ceramide/stearic acid/cholesterol. Chem Phys Lipids 2002;115(1e2):93e105. € ter E. Phase diagram of mixtures of stearic acid and [21] Gandolfo FG, Bot A, Flo stearyl alcohol. Thermochim Acta 2003;404(1e2):9e17. [22] Hildebrand JH. Solubility XII. Regular solutions. J Am Chem Soc 1929;51(1): 66e80. [23] Hildebrand JR, Prausnitz RL, Scott RL. Regular and related solutions: the solubility of gases, liquids, and solids. New York, NY: Van Nostrand Reinhold Co.; 1970. [24] Tenchov BG. Non-uniform lipid distribution in membranes. Prog Surf Sci 1985;20(4):273e340. [25] Lee AG. Lipid phase-transitions and phase-diagrams .2. Mixtures involving lipids. Biochim Biophys Acta 1977;472(3e4):285e344. [26] Bragg WL, Williams EJ. The effect of thermal agitation on atomic arrangement in alloys. Proc R Soc A 1934;145(855):699e730. [27] Moore WJ. Physical chemistry. 4th ed. Englewood Cliffs, New Jersey: PrenticeHall; 1972. [28] Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes: the art of scientific computing. 3rd ed. New York, NY: Cambridge University Press; 2007. [29] Recktenwald GW. Numerical methods with MATLAB: implementations and applications. Prentice Hall; 2000. [30] Abes M, Bouzidi L, Narine SS. Crystallization and phase behavior of fatty acid esters of 1,3 propanediol III: 1,3 propanediol dicaprylate/1,3 propanediol distearate (CC/SS) and 1,3 propanediol dicaprylate/1,3 propanediol dipalmitate (CC/PP) binary systems. Chem Phys Lipids 2008;151(2):110e24. [31] Boodhoo MV, Bouzidi L, Narine SS. The binary phase behavior of 1,3dicaproyl-2-stearoyl-sn-glycerol and 1,2-dicaproyl-3-stearoyl-sn-glycerol. Chem Phys Lipids 2009;157(1):21e39. [32] Boodhoo MV, Bouzidi L, Narine SS. The binary phase behavior of 1, 3dipalmitoyl-2-stearoyl-sn-glycerol and 1, 2-dipalmitoyl-3-stearoyl-sn-glycerol. Chem Phys Lipids 2009;160(1):11e32.

657

[33] Costa MC, Rolemberg MP, Boros LAD, Krahenbuhl MA, de Oliveira MG, Meirelles AJA. Solid-liquid equilibrium of binary fatty acid mixtures. J Chem Eng Data 2007;52(1):30e6. [34] Inoue T, Hisatsugu Y, Yamamoto R, Suzuki M. Solid-liquid phase behavior of binary fatty acid mixtures 1. Oleic acid/stearic acid and oleic acid/behenic acid mixtures. Chem Phys Lipids 2004;127(2):143e52. [35] MacNaughtan W, Farhat IA, Himawan C, Starov VM, Stapley AGF. A differential scanning calorimetry study of the crystallization kinetics of tristearintripalmitin mixtures. J Am Oil Chem Soc 2006;83(1):1e9. [36] Bouzidi L, Boodhoo MV, Kutek T, Filip V, Narine SS. The binary phase behavior of 1,3-dilauroyl-2-stearoyl-sn-glycerol and 1,2-dilauroyl-3-stearoyl-sn-glycerol. Chem Phys Lipids 2010;163(6):607e29. [37] Knoester M, Vandente M, Debruijn P. Solid-liquid equilibrium of binarymixtures of triglycerides with palmitic and stearic chains. Chem Phys Lipids 1972;9(4):309e19. [38] Lee AG. Lipid phase-transitions and phase-diagrams .1. Lipid phase-transitions. Biochim Biophys Acta Mol Cell Res 1977;472(2):237e81. [39] Minato A, Ueno S, Yano J, Smith K, Seto H, Amemiya Y, et al. Thermal and structural properties of sn-1,3-dipalmitoyl-2-oleoylglycerol and sn-1,3dioleoyl-2-palmitoylglycerol binary mixtures examined with synchrotron radiation x-ray diffraction. J Am Oil Chem Soc 1997;74(10):1213e20. [40] Ollivon M, Perron R. Study of binary mixtures of triglycerides derived from palmitic and stearic acids. Chem Phys Lipids 1979;25(4):395e414. [41] Rossell JB. Phase diagrams of triglyceride systems. Adv Lipid Res 1967;5(4): 353e408. [42] Koyano T, Hachiya I, Sato K. Phase behavior of mixed systems of SOS and OSO. J Phys Chem 1992;96(25):10514e20. [43] Minato A, Ueno S, Smith K, Amemiya Y, Sato K. Thermodynamic and kinetic study on phase behavior of binary mixtures of POP and PPO forming molecular compound systems. J Phys Chem B 1997;101(18):3498e505. [44] Engstrom L. Triglyceride systems forming molecular compounds. Fett Wiss Technol-Fat Sci Technol 1992;94(5):173e81. [45] Takeuchi M, Ueno S, Sato K. Crystallization kinetics of polymorphic forms of a molecular compound constructed by SOS (1,3-distearoyl-2-oleoyl-sn-glycerol) and SSO (1,2-distearoyl-3-oleoyl-rac-glycerol). Food Res Int 2002;35(10):919e26. [46] Timms RE. Phase-behavior of fats and their mixtures. Prog Lipid Res 1984;23(1):1e38. [47] Nibu Y, Inoue T. Miscibility of binary phospholipid mixtures under hydrated and non-hydrated conditions .2. Phosphatidylethanolamines with different acyl-chain lengths. Chem Phys Lipids 1995;76(2):159e69.