Phase Equilibrium and Optimization Tools: Application for Enhanced Structured Lipids for Foods

Abstract

Solid–liquid phase equilibrium modeling of triacylglycerol mixtures is essential for lipids design. Considering the α polymorphism and liquid phase as ideal, the Margules 2-suffix excess Gibbs energy model with predictive binary parameter correlations describes the non ideal β and β′ solid polymorphs. Solving by direct optimization of the Gibbs free energy enables one to predict from a bulk mixture composition the phases composition at a given temperature and thus the SFC curve, the melting profile and the Differential Scanning Calorimetry (DSC) curve that are related to end-user lipid properties. Phase diagram, SFC and DSC curve experimental data are qualitatively and quantitatively well predicted for the binary mixture 1,3-dipalmitoyl-2-oleoyl-sn-glycerol (POP) and 1,2,3-tripalmitoyl-sn-glycerol (PPP), the ternary mixture 1,3-dimyristoyl-2-palmitoyl-sn-glycerol (MPM), 1,2-distearoyl-3-oleoyl-sn-glycerol (SSO) and 1,2,3-trioleoyl-sn-glycerol (OOO), for palm oil and cocoa butter. Then, addition to palm oil of Medium-Long-Medium type structured lipids is evaluated, using caprylic acid as medium chain and long chain fatty acids (EPA-eicosapentaenoic acid, DHA-docosahexaenoic acid, γ-linolenic-octadecatrienoic acid and AA-arachidonic acid), as sn-2 substitutes. EPA, DHA and AA increase the melting range on both the fusion and crystallization side. γ-linolenic shifts the melting range upwards. This predictive tool is useful for the pre-screening of lipids matching desired properties set a priori.

Appendix: Margules Model and Binary Interaction Parameter models

The definition of the activity coefficient is given by the following Eq. [27]:

$$ RT\ln \gamma_{i} (T,P,x) = \bar{g}_{i}^{E} = \left( {{\frac{{\partial ng^{E} }}{{\partial n_{i} }}}} \right)_{{T,P,n_{j \ne i} }} $$

(A1)

The two-suffix Margules model for multicomponent mixtures is given by:

$$ g^{E} = \sum\limits_{i = 1}^{nc} {\sum\limits_{j = i + 1}^{nc} {A_{ij} x_{i} x_{j} } } $$

(A2)

where

$$ A_{ij} = 2qa_{ij} $$

(A3)

The term q is a measure of the size of the molecules in the pair and $a_{ij}$are interaction parameters between molecules i and j. In the Margules equations is assumed that $q_{i} = q_{j} = q$ (molecules with similar size). However, it is used frequently for all sorts of mixtures, regardless of the relative sizes of the different molecules [27].

The work of Wesdorp [15] showed that there is a great correlation between the degree of isomorphism (coefficient of geometrical similarity) and the parameter $A_{ij}$. The degree of isomorphism between two TAG can be described by the following expression:

$$ \varepsilon = 1 - {\frac{{v_{\rm{non}} }}{{v_{o} }}} $$

(A4)

v_non is the sum of the absolute differences in carbon number of each of three chains and for v ₀ the sum of the carbon numbers of the smallest chain on each glycerol position. Linear regression of experimentally determined $A_{ij}$ parameters versus the calculated isomorphism as defined by Eq. A4 led to the following correlations [15]:

$$ \varepsilon > 0.93:\;{\frac{{A_{ij}^{\beta '} }}{RT}} = 0 \; \left( {{\text{highmolecular similarity}},{\text{ complete miscibility}}} \right) $$

(A5)

$$ \varepsilon \le 0.93:\;{\frac{{A_{ij}^{\beta '} }}{RT}} = - 19.5\varepsilon + 18.2 $$

(A6)

$$ \varepsilon > 0.98:\;{\frac{{A_{ij}^{\beta } }}{RT}} = 0\; \left( {{\text{highmolecular similarity}},{\text{ complete miscibility}}} \right) $$

(A7)

$$ \varepsilon \le 0.98:\;{\frac{{A_{ij}^{\beta } }}{RT}} = - 35.8\varepsilon + 35.9 $$

(A8)

The primary value of the Margules equations lies in their ability to serve as simple empirical equations for representing experimentally determined activity coefficients with only a few constants and when, as is often the case, experimental data are scattered and scarce, they serve as an efficient tool for interpolation and extrapolation with respect to composition [27].