CHAPTER 2. LITERATURE REVIEW
2.4 Solid – Liquid Phase Behavior
2.4.3 Methyl Esters
Solid-liquid phase behavior of mixtures of fatty acid methyl esters is largely unexplored.
The desire to improve cold flow properties of biodiesel has brought the solid-liquid phase behavior of mixtures of fatty acid methyl esters to light.
Bailey et al. [73] examined the phase behavior of binary mixtures of methyl hetadecanoate, MeC17, with MeC12, MeC14, MeC18, methyl elaidate and methyl petroselaidate. Both stable and metastable polymorphic behavior was observed for these binary systems. The binary mixtures of saturated odd and even methyl esters are
influenced by the dimorphic characteristics of the even methyl ester. The mixtures of odd numbered methyl esters with the unsaturated methyl esters appear to have been stabilized by the unsaturated carbon chain. These phase diagrams were determined
through thermostatic sealed tube method, now through greater technical advances, the solid-liquid phase behavior can be determined more accurately.
Lockemann and Schlunder [37] investigated the solid-liquid phase equilibria of methyl myristate and methyl palmitate. This binary mixture is reported to have a eutectic type phase equilibria with partially miscible solid solutions. However, with more advance techniques, this phase diagram is inferior to a newer more complex phase diagram between methyl myristate and methyl palmitate that Costa et al. [74] established, though the liquidus lines are similar between the sources.
Costa et al. [74] established binary phase diagrams for methyl palmitate + methyl stearate, methyl myristate + methyl palmitate and methyl myristate + methyl stearate.
The systems that only differ by two carbon atoms; the phase behavior was complex with a eutectic, peritectic and metatectic reaction. The peritectic and metatectic reaction isotherms occur a few degrees above the eutectic isotherm, similar to fatty acid systems.
Also, there were two solid-solid polymorphic transitions, which is common for systems with long alkyl chains. These transitions can be confirmed with X-ray diffraction. Costa et al. mentions specifically for the MeC16 + MeC18 binary system, that the phase
diagram could easily be over simplified for a eutectic and peritectic behavior but with the use of polarized light optical microscope, the crystallization can be observed and note the presence of a metatectic reaction. The metatectic reaction, γ ↔ α + l, is an isothermal reversible reaction of a solid mixture (γ), which turns into a different solid phase (α) plus a liquid phase (l) during cooling of system [74]. The binary system with four carbon difference, methyl myristate and methyl stearate displayed a simple eutectic system based off of the thermograms and confirmed by the Tammann plot. The results of these three systems showed that the differences in alkyl chain size plays are more important role on mixtures of methyl esters than on fatty acids.
When analyzing thermograms for fatty acid methyl esters, the onset temperature can be very difficult to locate because of the presence of solid-solid transitions near the melting temperature. This solid-solid transition was noted in both by Costa et al. [74] and
Kouakou et al. [75]. This transition results in larger discrepancies between literature
values for the melting enthalpies. When the heating rate is very slow, the solid-solid transition is present; however, if the heating rate is faster, the solid-solid transition is completely merged with the melting temperature resulting in a larger melting enthalpy value.
Methyl ester mixtures can exhibit freezing point depression, when the freezing point of the solution is lower than the freezing point of the pure components. The freezing point and crystallization of mixtures of FAME follows patterns between two predicted theories, independent crystal freezing point depression theory and solid solution freezing point depression theory [41]. The melting curves are generally better behaved near the eutectic and may produce a sharp peak at the eutectic composition [39], [41], [42], [76].
2.4.3.1 Modeling Approach
As stated before, a model for predicting the onset crystallization temperature, also known as the cloud point, for mixtures of fatty acid methyl esters is important for the biodiesel industry. The freezing point depression theory which has often been used is only correct for modeling the crystallization process of organic liquids. However, in the case of FAME mixtures, they often follow independent crystallization of the solids described in Equation 2-2 [77].
1 1
ln( i i) fus P 1 ln
g f g f f
H C MP MP
x R T MP R T T
γ = −∆ − −∆ − +
( 2-2 )
Where γi and x are the activity and mole fraction of species “i” in the liquid phase, i Hfus
∆ enthalpy of fusion of the pure solute, R the universal gas constant, g T is the f crystallization onset temperature of the solute in solution, MP is the melting point of the solute in pure form, and ∆CP is the differential heat capacity of species “i” between the liquid and solid phase(CPL−CPS). The activity coefficient accounts for non-ideal behavior in the liquid phase. Imahara et al. [76] simplified this equation and assumed γi = and 1 neglected the ∆ for studying the cloud point of FAME mixtures. Dunn [39], [42], CP
investigated the model for cloud point behavior developed by Suppes et al. [77], shown in Equation 2-2. It was found for mixtures of unsaturated and saturated fatty acid methyl esters the ∆ can be neglected for calculatingCP T , and the accuracy of the calculated f T f is highly dependent on the accuracy of the ∆Hfusmeasurements. Also, there are some indications of non-ideal solution behavior in unsaturated and saturated FAME mixtures due to the calculated T values being consistently lower than the measures freezing f points.