An entropy-centric equilibrium cooperative theory for the melting behavior of nonideal triaclylglycerol mixtures

A new nonideal, equilibrium thermodynamics model was developed for the prediction of the solid fat content (SFC) of edible fats, which are mixtures of triaclylglycerols (TAGs). The SFC is the most dominant material structural parameter which influences macroscopic mechanical properties and functionality in foods, cosmetics and pharmaceutical incipients. By taking into consideration the entropy of mixing and the activity coefficient of a TAG in an effective solid medium, we calculate a freezing point depression. The new melting point is then nested into an equilibrium expression for the melting of that TAG in such effective solid medium. The model assumes that complex mixtures of TAGs consist of one solid phase in a specific polymorphic form and one liquid phase, obeying mass balances and the overall TAG composition determined experimentally. The SFC is then just the summation of the amount of solid TAG components in the mixture. Novel insights are gained from estimates of a cooperativity index for the melting of the different TAGs in the effective solid medium, while estimated solid-state activity coefficients speak to interactions of particular TAGs with the effective medium. The model was successfully fitted to eight different SFC-temperature profiles of complex fats and parameter estimates obtained and interpreted.     

Phase equilibria of mixtures containing CO2 and organic acids using the UMR-PRU model

The UMR-PRU model, which has been successfully tested in the past to the predictions of different type of phase equilibrium and thermodynamic properties in binary and multicomponent systems, is applied in this work to phase equilibria in mixtures containing CO₂ and organic acids. New interaction parameters are determined by fitting only binary vapor–liquid equilibrium data and then they are used to predict the vapor–liquid, solid–gas and solid–liquid–gas equilibria in CO₂/organic acid systems. Furthermore, the UMR-PRU model with the newly derived interaction parameters is applied to the prediction of the phase equilibrium in ternary mixtures consisting of CO₂, organic acids and water. Satisfactory results are obtained in all cases.     

HPLC‐APCI analysis of triacylglycerols in milk fat from different sources

Triacylglycerols (TAG) from milk‐fat from different sources (cow, goat and human milks) were characterised using non‐aqueous reversed phase high‐performance liquid chromatography–atmospheric‐pressure chemical ionisation, coupled to MS/MS (RP HPLC‐APCI MS/MS). The fatty‐acid content of all samples was also established by methyl transesterification and GC‐MS analysis. Optimisation of the HPLC gradient, combined with APCI tandem MS, enables TAGs complex mixtures to be analysed without prior separation. More than 160 different glycerides were identified; between 50 and 70 compounds were identified in the chromatograms of each sample. This method also enabled the principal TAG regioisomers to be recognized. The study focused on the investigation of the structure of TAGs containing very‐long‐chain PUFA, namely all cis‐ 4,7,10,13,16,19‐ DHA (DHA, C_{22:6, n‐3}) and all cis‐5,8,11,14,17‐eicosapentaenoic acid (EPA, C_{20:5, n‐3}), both in human and in n‐3‐enriched cow's milks. Ten TAGs containing DHA were identified in human milk and only one in milk from cows fed an n‐3 enriched diet.     

Quantifying the effect of polarity on the behavior of mixtures of n-alkanes with dipolar solvents using polar soft-statistical associating fluid theory (Polar soft-SAFT)

We present results concerning the phase equilibria and excess properties of binary mixtures of n-alkanes with a range of fluids from low to high dipolar strength, namely 1-hexene, chloroform, dichloromethane, tetrahydrofuran, acetone, dimethylformamide, and N-methyl pyrrolidone modeled by polar soft-statistical associating fluid theory. Polar interactions are considered through the theory of Gubbins and Twu, extended to chainlike fluids by Jog and Chapman, and a priori fixing the polar parameters of the pure fluids, instead of fitting to experimental data. The equation provides accurate predictions for low to moderate dipolar molecules with n-alkanes, while the induced dipoles created by very strong dipolar fluids (μ ≥ 3.5 D), is implicitly considered by the appropriate selection of pure component parameters and a binary parameter which can be transferred to predict other properties. The equation is used to systematically study the effect of asymmetrical energy scales between polar and nonpolar fluids on vapor–liquid equilibria and excess properties.     

Application of high-performance size-exclusion chromatography to study the autoxidation of unsaturated triacylglycerols

A combination of solid-phase extraction (SPE) and high-performance size-exclusion chromatography (HPSEC) was used to study the autoxidation of triacylglycerol (TAG) mixtures separated from low-erucic acid rapeseed oil and butter oil. The samples were autoxidized in the dark at 40°C for four weeks. The polar compounds of the autoxidated samples were separated by SPE (NH₂ stationary phase), and the polar fraction was further characterized by HPSEC with a series of three size-exclusion columns and an evaporative light-scattering detector. The polar fraction contained TAG polymers, polar TAG monomers (PTAG) and diacylglycerols. Peroxide values and anisidine values of the samples were also measured. By using three different types of TAG mixtures, it could be demonstrated that the PTAG content of the TAGs increases during autoxidation. A slight increase was also detected in polymer content. The correlation between PTAG content and the comparative measurements was considered significant. The results indicate that the measurement of PTAG and polymeric material content by HPSEC analysis can be used when studying the autoxidation level of edible oils and in characterizing the autoxidation products of different molecular sizes.     

High pressure measurements and molecular modeling of the water content of acid gas containing mixtures

Water content of three carbon dioxide containing natural gas mixtures in equilibrium with an aqueous phase was measured using a dynamic saturation method. Measurements were performed up to high temperatures (477.6 K = 400°F) and pressures (103.4 MPa = 15,000 psia). The perturbed chain form of the statistical associating fluid theory was applied to predict water content of pure carbon dioxide (CO₂), hydrogen sulfide (H₂S), nitrous oxide (N₂O), nitrogen (N₂), and argon (Ar) systems. The theory application was also extended to model water content of acid gas mixtures containing methane (CH₄). To model accurately the liquid‐liquid equilibrium at subcritical conditions, cross association between CO₂, H₂S, and water was included. The agreement between the model predictions and experimental data measured in this work was found to be good up to high temperatures and pressures. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3038–3052, 2015     

Permeation of mixtures of organic liquids through polymeric membranes: Role of liquid–liquid interactions

The permeation of pure organic liquids and mixtures of organic liquids through commercial butyl, neoprene, and nitrile membranes was studied using dynamic material deformation (swelling) and permeation techniques. The derived parameters, the breakthrough time (t_BT), steady‐state permeation rate (SSPR), and initial swelling rate (SR), show deviations from additivity for the mixtures, based on the parameters of the pure liquids on a mol fraction basis. In the majority of cases for the three membranes examined, the deviations are independent of the nature of the membranes, and the signs of the deviations for t_BT are opposite to those for SSPR or SR, provided that the membranes are not degraded by one of the solvents. An approach that considers only solvent–solvent interactions based on the enthalpy of mixing was used to predict deviations for mixtures. For mixtures where the enthalpy of mixing is large and exothermic, the permeation of the mixture is less than expected, while for systems where the enthalpy of mixing is large and endothermic, the permeation is larger than expected. A simple semiempirical model predicts the sign and magnitude of the permeation of 73% of the system–permeation property combinations investigated, which show significant deviations from ideality. It is interesting to note that the wrong predictions are for systems where the predictions are positive, that is, for SSPR and SR rates with endothermic systems and for t_BT with exothermic systems. The exceptions also seem to be for systems that correspond to materials having a high resistance to one of the solvents and a very low resistance to the other solvent. Examples of ternary–mixture permeation data are also given and show that, even if two of the pure components do not permeate through a membrane, the membrane will offer little protection if the third component shows a high affinity for the membrane and if the enthalpies of mixing of this component with the other liquids are endothermic. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 195–215, 2002     

Solubility of simple and mixed triacylglycerols in supercritical CO2

A simple mixture of triacylglycerols (TAGs) was synthesized enzymatically from palmitic acid and oleic acid. The mixture contained tripalmitoylglycerol (PPP), trioleoylglycerol (OOO), and various isomers of palmitoyl-dioleoylglycerol (POO) and oleoyl-dipalmitoylglycerol (PPO). The behavior of this TAG mixture in equilibrium with supercritical carbon dioxide (SF-CO₂) was studied at 40 and 60°C between 172 and 310 bar. Generally, the partition coefficients varied inversely with species molecular weight. The solubilities of PPP and OOO in SF-CO₂ were determined at the same conditions. PPP was markedly more soluble in SF-CO₂ when present in the TAG mixture than as a pure compound.     

Using Mettler Dropping Point Data from Dilute Soybean Oil-Triglyceride Mixtures to Estimate Thermodynamic Properties for Corresponding Pure Triglyceride

The enthalpy of fusion and melting temperature for ten symmetrical and seven asymmetrical triglycerides (TAGs) was estimated using mettler dropping points (MDP) of five concentrations of TAGs dissolved in a complex mixed solvent (soybean oil) and a modified Clapeyron equation, an approach we refer to as LIST estimation. The ten estimates generated using the LIST method were compared for accuracy to values measured using differential scanning calorimetry and MDP of pure TAG samples and to estimates calculated using effective carbon number and the Triglyceride Property Calculator. We find that LIST estimates for stearic acid and palmitic acid‐based monoacid and symmetrical TAGs agree well with measured and calculated values using alternative methods. Conversely, LIST estimates for stearic acid and palmitic acid based asymmetrical TAGs diverge substantially from alternative estimates, suggesting that the LIST approach is inadequate in describing asymmetric TAGs using the assessed concentrations of TAG in soybean oil. Elaidic acid containing TAGs behaved uniquely, with LIST estimates for trielaidin not agreeing with alternative estimates yet LIST estimates for distearic–monoelaidic in both symmetric and asymmetric configurations agreeing well with alternative estimates. We conclude that the LIST approach of using MDP of a high melting pure TAGs dissolved in soybean oil can be, at minimum, a viable approach in estimating melting behavior properties of symmetric stearic and palmitic acid containing TAGs. Further investigation for the behavior of asymmetric stearic and palmitic acid containing TAGs in soybean oil is required. As such, using known enthalpies of symmetric stearic and palmitic acid containing TAGs, we should be able to estimate the solubility of a high melting pure TAG in soybean oil using MDP and Clapeyron's equation.     

Enhanced Structuring of Fat with Reduced Saturates Using Mixed Molecular Compounds

Molecular compound formation between multicomponent triacylglyceride (TAG) mixtures was characterized using palm oil mid fraction enriched in sn‐1,3‐dipalmitoyl‐2‐oleoylglycerol (cPOP) and a commercial fraction enriched in sn‐1,3‐dioleyl‐2‐palmitoylglycerol containing a wide range of TAGs (cOPO). Compound formation occurred at a 1:1 (w/w) ratio of cPOP to cOPO corresponding to an equal parts ratio of two different families of TAGs. One family of TAGs consisted of a grouping of all TAGs composed of a saturated–oleic–saturated (StUSt) positioning of fatty acids. The second family consisted of a grouping of all TAGs composed of all oleic–saturated–oleic and saturated–saturated–oleic fatty acids (UStU, StStU). An increase in solid fat content, peak melting temperature, and crystalline domain size and a change in crystalline microstructure were observed at this ratio corresponding to an overall equality in the amount of cPOP to cOPO. This indicates that it is possible to achieve that same level of solid fat content and hardness as a mixture containing more saturates, simply by slightly decreasing the saturates and substituting an oleic monounsaturated fatty acid containing TAG mixture such that a molecular compound is formed. The increase in full‐width at half‐maximum indicated a decrease in crystalline order and/or decrease in crystal domain size. The characteristic spherulitic crystalline microstructure of OPO changed to small granular crystals upon addition of cPOP. This discovery may allow for the incorporation of a larger proportion of healthy monounsaturated fats into foods while decreasing the use of saturated and trans fats.     

Thermal antioxidative kinetics of sesamol in triacylglycerols and fatty acid methyl esters of sesame,olive, and canola oils

Oxidation kinetics of the triacylglycerols (TAGs) and fatty acid methyl esters (FAMEs) of sesame, olive, and canola oils were studied in the presence of the different concentrations of sesamol (0.1%–0.16%) at 60, 80, and 100°C. Sesamol increased the temperature coefficient, T_C, and Q₁₀ number of the TAGs more significantly compared to the FAMEs. All the sesamol-added TAG and FAME systems, respectively, of the olive, canola, and sesame oils, respectively, exerted increased values of the Arrhenius (activation energy, E_a, and frequency factor, A) and Eyring (enthalpy, ΔH⁺⁺, and entropy, ΔS⁺⁺) equation parameters. Sesamol improved the Gibbs free energy (ΔG⁺⁺) of the activated complex formation in the canola, sesame, and olive systems, respectively, and the effect was greater in the FAMEs.     

Fast chromatography of pulse triacylglycerols

A short 10-min ultra high performance liquid chromatography (UHPLC) method was used for separation and lipidomic analysis of triacylglycerols (TAGs) in 10 pulses: baby lima beans, black beans, black-eyed peas, butter beans, cranberry beans, garbanzo beans, green split peas, lentils, navy beans, and pinto beans. The lipids extracted using chloroform/methanol averaged 1.9–2.7% across all pulses except garbanzo beans, which gave 6.2% lipids. TAGs were analyzed using dual parallel mass spectrometry (LC1MS2), areas were integrated using LipidSearch 4.2 software, and percent relative TAG compositions were calculated. Fatty acid response factors were calculated by comparison to calibrated GC-FID, which were used to calculate response-factor adjusted TAG compositions. Principal component analysis revealed that the pulses separated into three clusters, which were further highlighted using hierarchical cluster analysis. A subset of TAGs was quantified using calibration curves made from alternating sets of regioisomers in the non-linear high concentration range (~2.5 nMol/ml to ~300 nMol/ml). A linear calibration curve for the sum of tocopherols detected by fluorescence was constructed with a coefficient of determination, r², >0.99 for low concentrations (0.50–50 μg/ml), but tocopherols in pulses appeared to be inefficiently extracted. TAG regioisomers were quantified based on a Critical Ratio (CR), [AA]⁺/[AB]⁺, interpolated between the CRs of two pure regioisomer standards taken from alternating calibration standards. TAG mole percent relative compositions are reported for the first time for most pulses and the compositions are given with more detail and specificity than previously reported.     

Separation of Triacylglycerols from Edible Oil Using a Liquid Chromatography–Mass Spectrometry System with a Porous Graphitic Carbon Column and a Toluene–Isopropanol Gradient Mobile Phase

This study presented a rapid and practical method of separating triacylglycerol (TAG) from edible oil using high‐performance liquid chromatography (LC) coupled with atmospheric‐pressure chemical ionization (APCI)/mass spectrometry (MS) system with a porous graphitic carbon column (150 mm × 2.1 mm, 5 μm) and a toluene–isopropanol–formic acid mobile phase. After investigating the experimental conditions, the gradient toluene–isopropanol mobile phase containing 0.1% formic acid was changed from 50:50 to 80:20 in 30 min; the column temperature was set to 35 °C, and APCI/MS was used in the positive‐ion acquisition mode. The TAG retention displayed a special order and was summarized to fit as follows: S‐ECN (special equivalent carbon number) = 2CN (carbon number) ? 3dB (double bond number) – 5uFA (unsaturated fatty‐acid number). Then, the LC–MS method was applied to separate TAG in 6 vegetable oils, resulting in the recognition of 27 TAG in corn oil, 21 TAGs in olive oil, 22 TAG in sunflower seed oil, 28 TAG in soybean oil, 25 TAG in sesame oil, and 31 TAG in peanut oil. The TAG separation through the LC–MS method was rapid, reproducible, and durable.     

Evaluation of the ratio of the evaporation energy to the activation energy for estimating the thermodiffusion coefficient

Thermodiffusion has an important role in displacements of hydrocarbon reservoir. The ratio of the evaporation energy to the activation energy of viscous flow in pure limits, τ_pure,k, is of a great importance in estimating the thermodiffusion coefficient for non‐associating fluid mixtures. Several methods may be used to estimate τ_pure,k which causes different values for thermodiffusion coefficients. A fixed value for τ_pure,k was considered to predict the thermodiffusion coefficient. In this paper, Abbasi et al.'s [J. Non‐Equilib. Thermodyn. 2010;35:1–14] model and Shukla and Firoozabadi's model have been applied to predict thermodiffusion coefficients for linear chain hydrocarbon binary mixtures. The results show a very good performance of the simple approach in respect to the previous models in estimating thermodiffusion coefficients. © 2011 Canadian Society for Chemical Engineering     

Effect of viscosity and volume on the specific conductivity of lithium salts in solvent mixtures

As part of a study on the optimization of the electrolyte for high energy lithium batteries, the conductivity, viscosity and density of LiAsF₆, LiBr, and LiClO₄ were measured in aprotic solvent mixtures. The conductivity of lithium bis(trifluoromethylsulfone)imide (LiTFSI) was also obtained in a large number of mixed aprotic solvents. The solvents were chosen to verify the effect of various parameters such as viscosity, permittivity, volume, acceptor number and donor number on the conductivity. These results were used to develop a simple model for excess conductivities based on the viscosity and volume of the pure solvents. Without adjustable parameters, this model predicts the correct sign of the excess conductivities in ≈90% of the cases and the magnitude of the conductivity of the ternary mixtures within an average of 15%. Deviations from the predictions are mostly observed with solvents of low permittivity and this supports the hypothesis that a different conduction mechanism is in operation at high concentration in these solvents, and the solvating power of these solvents plays an important role in this mechanism.     

Molecular geometry effects and the Gibbs–Helmholtz Constrained equation of state

Differences in molecular size and shape have long been known to cause difficulties the modeling and simulation of fluid mixture behavior and generally manifest themselves as poor predictions of densities and phase equilibrium, often resulting in the need to regress model parameters to experimental data. A predictive approach to molecular geometry within the Gibbs–Helmholtz Constrained (GHC) framework is proposed. The novel aspects of this work include (1) the use of NTP Monte Carlo simulations coupled with center of mass concepts to determine effective molecular diameters for non-spherical molecules, and (2) the use of effective molecular diameters in the GHC equation to predict phase behavior of mixtures with components that have distinct differences in molecular size and shape. Numerical results for a CO₂–alkane, alkane–water and CO₂–alkane–water mixtures show that the proposed approach of combining molecular geometry with the GHC equation provides accurate predictions of liquid densities and two- and three-phase equilibrium.     

Free volume model and diffusion of organic solvents in natural rubber

The concentration dependence of the diffusion coefficients and the equilibrium isotherms of benzene, o-xylene, ethylbenzene, and chloroform in natural rubber membranes at 303 K were experimentally determined. The data were used to critically test the predictive capability of the Vrentas–Duda free volume model. It was found that although the model works well for some polymer–solvent systems such as toluene-polystyrene, the use of some of the parameters from pure component properties yields unacceptably low diffusion rates for the rubber–solvent systems studied. The parameters D_o1 and ξ obtained from experimental zero-concentration diffusivity data, and parameter V?₁^* calculated from the solvent molecular geometries are needed to achieve good predictions. The diffusion coefficients described by the revised model can be used to predict quite well the breakthrough times of the rubber–solvent systems that were also experimentally measured by a permeation method. © 1995 John Wiley & Sons, Inc.     

Measurement and prediction of phase diagrams of the enantiomeric 3-chloromandelic acid system

The identification of racemic species of enantiomeric 3-chloromandelic acid (3-ClMA) as well as ternary solubility measurement in a mixture of water and isopropanol (IPA) was studied in this paper. Thermal analyses were carried out for mixtures of the two enantiomers with different compositions. The binary fusion diagram suggested the presence of a racemic compound for racemate 3-ClMA. It was verified with the ternary solubility phase diagram by dissolving various mixtures into the H₂O/IPA solution. Ternary phase diagram revealed a strong temperature dependency of solubility for the 3-ClMA system. In order to shorten the experimental time in the solubility measurement, a semi-empirical thermodynamic model (UNIQUAC) was used to predict the solubility of various compositions of enantiomers at different temperatures. Results indicate that UNIQUAC model can provide good predictions in the solubility of racemate, eutectic and (R)-3-ClMA in both pure water and H₂O/IPA (9/1 weight ratio) system. In addition, structures of racemate and pure (R)-3-ClMA were also studied using a powder X-ray diffractometer. Thermodynamic prediction, thermal analysis, and structural study are in excellent agreement for identifying the enantiomeric 3-ClMA system as a racemic compound forming system.     

非电解质液体混合物表面张力的统计热力学模型

运用Davis模型导出一个统计热力学的表面张力模型．对22个双组分体系的表面张力作了推算和关联,总平均相对偏差分别为5.45％和1.95％.并利用关联双组分体系得到的参数值,直接推测了三组分体系的表面张力,平均相对偏差为2.21％.结果令人满意.表明该方法简单、精确,便于工程应用．     

Description of the thermodynamic properties and fluid-phase behavior of aqueous solutions of linear,branched, and cyclic amines

The SAFT-γ Mie group-contribution equation of state is used to represent the fluid-phase behavior of aqueous solutions of a variety of linear, branched, and cyclic amines. New group interactions are developed in order to model the mixtures of interest, including the like and unlike interactions between alkyl primary, secondary, and tertiary amine groups (NH₂, NH, N), cyclic secondary and tertiary amine groups (cNH, cN), and cyclic methine-amine groups (cCHNH, cCHN) with water (H₂O). The group-interaction parameters are estimated from appropriate experimental thermodynamic data for pure amines and selected mixtures. By taking advantage of the group-contribution nature of the method, one can describe the fluid-phase behavior of mixtures of molecules comprising those groups over broad ranges of temperature, pressure, and composition. A number of aqueous solutions of amines are studied including linear, branched aliphatic, and cyclic amines. Liquid–liquid equilibria (LLE) bounded by lower critical solution temperatures (LCSTs) have been reported experimentally and are reproduced here with the SAFT-γ Mie approach. The main feature of the approach is the ability not only to represent accurately the experimental data employed in the parameter estimation, but also to predict the vapor–liquid, liquid–liquid, and vapor–liquid–liquid equilibria, and LCSTs with the same set of parameters. Pure compound and binary phase diagrams of diverse types of amines and their aqueous solutions are assessed in order to demonstrate the main features of the thermodynamic and fluid-phase behavior.