Abstract
The correlations for vapor pressures of fatty acids, fatty acid methyl and ethyl esters, and simple triglycerides were given based on the available data in the literature. The developed equations enable easy estimation of the critical properties. The group contribution methods were used to develop the estimation method. The estimated properties of the most common lipids were tabulated and the differences between the estimation methods were critically discussed.
INTRODUCTION
Supercritical carbon dioxide extraction and fractionation of fatty acids, their esters and glycerides have received an ultimate attention over the recent decades. The design and development of these processes require physicochemical properties of these lipids as well as their transport properties. Vapor pressure is one of the important of these properties. Available vapor pressure data are mostly for saturated short-chain fatty acids and their esters Citation1-4 or for some simple triglycerides Citation[5]. Although the vapor pressure data of polyunsaturated fatty acid esters have been becoming available recently, their temperature ranges are limited Citation[6] or they are quite variable Citation[2]. Therefore, these available data have to be extrapolated to obtain vapor pressures at specific temperatures or to estimate boiling points.
Critical temperature, pressure, and volume play an important role when processing with supercritical fluids. These properties are needed for predicting solubilities Citation[7] or diffusion coefficients Citation8-9. The critical properties of lipids are not available and have to be estimated mostly using group contribution methods. The available methods Citation[10] require lengthy calculations based on the molecular structure of the lipid.
This study aims to estimate and use the vapor pressures, boiling points or critical properties of lipids. For this purpose, the available data and their correlations, developed equations that enable the easy estimation of the properties by the group contribution methods, tabulated results, and the critical discussion of the methods are presented.
CORRELATION DEVELOPMENT
Correlation of Vapor Pressure of Lipids
The simplest way to correlate vapor pressure data is to use the Clapeyron equation which is given as:
Estimation of Critical Properties of Lipids
The two common methods to estimate the critical properties are the Ambrose and Joback group contribution methods Citation[10]. They were reported to give comparable results. The Joback method, which is simpler, preferred over the other by the researchers most of the time.
The relations for calculating critical temperature, pressure and volume for the Joback method are given Citation[10] as:
The Joback group contributions specific to lipids were listed in Table . A systematic way was developed for calculating the number of each group in a lipid and the contribution of these groups to the critical property. Referring to Table , the corresponding relations for fatty acids and their esters were developed as:
| A | = |
1 + F |
| B | = |
CA − D + F (CE − 1)− 2 |
| D | = |
2 × (number of double bonds |
| E | = |
1 if the molecule is a fatty acid and, 0 if the molecule is a fatty acid ester |
| F | = |
1 if the molecule is a fatty acid ester, 0 if the molecule is a fatty acid |
| CA | = |
number of carbon atoms in the fatty acid |
| CE | = |
number of carbon atoms in the ester |
The relations developed for fatty acids and their esters were modified for simple glycerides (mono-, di- or tri-). Referring to Table ,
| A | = |
number of fatty acids attached to glycerol |
| B | = |
[A × (CE − DE − 2)]+ 2 |
| C | = |
1 |
| D | = |
A × DE |
| F | = |
number of ester bonds in the glyceride = A |
| G | = |
3 − A |
| CE | = |
number of carbon atoms in one ester (i.e. fatty acid attached to glycerol) |
| DE | = |
[2 × (number of double bonds)] in one fatty acid attached to glycerol |
Table 1. Joback and Fedors Group Contributions for Critical Properties and Normal Boiling Point of Lipids Citation[10]
The Joback method requires normal boiling point for estimation of critical temperature. When the normal boiling point is not known, the Fedors group contribution method is available Citation[10] for estimating critical temperature. The Fedors equation is given as,
The Ambrose group contribution estimates the critical properties through following equations Equation10 as,
| A | = |
(CA − 1)+ CE |
| C | = |
number of double bonds |
| D | = |
1 if the molecule is a fatty acid and, 0 if the molecule is a fatty acid ester |
| E | = |
1 if the molecule is a fatty acid ester, 0 if the molecule is a fatty acid |
| CA | = |
number of carbon atoms in the fatty acid |
| CE | = |
number of carbon atoms in the ester |
Table 2. Ambrose Group Contributions for Critical Properties of Lipids (10)
The relations developed for fatty acids and their esters were modified for simple triglycerides. Referring to Table ,
| A | = |
3(CA − 1)+ 3 |
| B | = |
1 |
| C | = |
3 × number of double bonds in one fatty acid attached to glycerol |
| E | = |
3 |
The contribution of ─OH group, for mono- or di-glycerides, was not in cluded in Table . The calculations of ∑ΔT c and ∑ΔP c for molecules containing ─OH groups can not be systematically formulated since they require additional corrections which are functions of the normal boiling point of the molecule. There are also exceptions for these corrections Citation[10] which should be followed individually.
RESULTS AND DISCUSSION
The constants of the Clapeyron equation were determined using the available vapor pressure data for lipids. The results were tabulated in Tablea as well as the temperature and the pressure range that the correlations cover. The logarithm of the vapor pressure changed linearly with the inverse of temperature within these ranges, and the R 2 for the correlations changed between 0.9988 and 1.0.
Table 3. Constants of the Clapeyron Equation for Fatty Acids
Table 4. Constants of the Clapeyron Equation for Fatty Acid Methyl Esters
Table 5. Constants of the Clapeyron Equation for Fatty Acid Ethyl Esters
Table 6. Constants of the Clapeyron Equation for Simple Triglycerides Citation[5]
The normal boiling point of each lipid was estimated by extrapolating the data using the determined constants of the Clapeyron equation. These normal boiling points were also tabulated in Tables . As can be seen in Table , although the pressure range of the data for butyric acid is narrow, the estimated normal boiling point for butyric acid ethyl ester agreed with the reported one within 3% Citation[10].
The vapor pressures of fatty acids are available between 1 and 760 mmHg. Although there are several sources Citation[4], Citation[11] they are quite comparable with few exceptions. For these cases the data from both sources were utilised; omitting the one obviously deviating; to obtain the constants of the Clapeyron equation (Table ).
The vapor pressures of only short chain saturated fatty acid methyl esters are available within the same pressure range Citation[1]. The pressure range of the data for long chain saturated fatty acid methyl esters and especially for unsaturated fatty acid methyl esters are very narrow. Therefore, the data from couple of sources were combined, whenever possible (Table ). The combined data were quite in agreement with each other. However, there are inconsistencies between the data reported for oleic, linoleic and linolenic acid methyl esters Citation[2]. The measured diffusion coefficient of oleic acid methyl ester in supercritical carbon dioxide is higher than that of linolenic acid methyl ester at the same temperature and pressure Citation[12] indicating that oleic acid methyl ester have a higher vapor pressure compared to linoleic acid methyl ester. Therefore, the normal boiling point of oleic acid methyl ester is expected to be lower than the normal boiling point of linoleic acid methyl ester. Same trend is observed for eicosadienoic to eicosatetraenoic acid (C20:2, C20:3 and C20:4) methyl esters at 473.15 K Citation[6]. The data showing the opposite trend were excluded to determine the constants of the Clapeyron equation.
The vapor pressure data of fatty acid ethyl esters are quite limited. Generally, a fatty acid is expected to have higher normal boiling point than its esters, and ethyl ester of a fatty acid to have higher normal boiling point than its methyl ester. This trend was observed in the normal boiling points of fatty acids and their esters estimated by the Clapeyron equation except palmitic, stearic and docosohexanoic acid (DHA) ethyl esters (Table ). This was probably due to both the limited number and narrow range of the available data. The constants of the Clapeyron equation for simple triglycerides are already available in the literature Citation[5] and they were reported in Table , as well as the estimated normal boiling points.
The normal boiling points and critical properties of the common lipids were systematically calculated and reported in Tables . The estimation of critical temperatures needs the knowledge of normal boiling points. The critical temperatures of lipids were estimated by the Joback method using both the known (reported or estimated by using the Clapeyron equation constants) and estimated normal boiling points by the same method. The critical temperatures, which were estimated by using the estimated normal boiling points, deviated from the ones that were calculated by the known normal boiling points, as the chain length and degree of unsaturation of the lipids increased. This deviation was higher for triglycerides being more than 100% for the triglyceride of stearic acid. The critical temperatures estimated by the Joback and Ambrose methods by using the known boiling points were comparable except that for triglycerides. The critical temperatures estimated for triglycerides by the Ambrose method were lower but more reasonable than the ones estimated by the Joback method. The critical temperatures estimated by the Fedors method were within 1 to 7% range of the ones estimated by the two contribution methods with the known normal boiling points for fatty acids and their esters, especially better for long chain and polyunsaturated lipids. The critical temperatures estimated for triglycerides by the Fedors method were more comparable with the ones estimated by the Ambrose method (Table ). The critical temperatures of butyric acid, its methyl and ethyl esters are reported Citation[10] as 628, 554.4 and 569 K, respectively. The critical temperatures estimated by the two methods for these lipids were within ± 0.6%.
Table 7. Estimated Critical Properties for Fatty Acids
Table 8. Estimated Critical Properties for Fatty Acid Methyl Esters
Table 9. Estimated Critical Properties for Fatty Acid Ethyl Esters
Table 10. Estimated Critical Properties for Simple Triglycerides
Although the Joback and Ambrose methods yielded similar critical pressures for short chain lipids, the Joback method yielded lower critical pressures as the chain length and unsaturation increased. This difference between the critical pressures estimated by the two methods was almost doubled as the lipid molecule got bigger. This might be due to the difference between the two estimation methods, the Joback method using the number of atoms in the molecule (Eq. Equation3) and the Ambrose method using the molecular weight (Eq. Equation16). The Ambrose method which is reported to yield smaller errors Citation[10] than the Joback method should be considered for predicting critical pressures. The critical pressures of butyric acid, its methyl and ethyl esters are reported Citation[10] as 52.7, 34.8 and 29.6 bar, respectively. The Joback and Ambrose methods understimated the critical pressure of butyric acid by 17 and 22%, respectively. The errors in estimating the critical pressure of butyric acid methyl ester was 0.3% and of butyric acid ethyl ester was 5%, maximum.
The both contribution methods however, yielded comparable critical volumes for the lipids even for simple triglycerides. The critical volumes of butyric acid, its methyl and ethyl esters are reported Citation[10] as 290, 340 and 421 cm3/mole, respectively. The both methods estimated the critical volume of butyric acid within 2% and the esters within 1%.
CONCLUSIONS
The vapor pressure data of lipids are essential for both designing separation processes and predicting their transport properties. Since the data are limited for mostly short-chain saturated fatty acids, the data bank for unsaturated fatty acids and their esters, and mono- and diglycerides need to be built up. The data for structural isomers are of special importance since the available group contribution methods can not account for these structural differences, as in oleic (cis-C18:1) and elaidic (trans-C18:1) acids, and linolenic (C18:3 ω-3) and γ-linolenic (C18:3 ω-6) acids. The critical temperatures of fatty acids and their esters can be estimated either by the Joback or the Ambrose group contribution methods with known boiling points. However, the Ambrose method should be preferred for triglycerides. If the normal boiling points are not known, Fedors method is recommendable rather than estimating the both by the Joback group contribution method. Although the Joback and the Ambrose methods give comparable critical pressures for short chain lipids, the Ambrose method might be preferred for long chain lipids especially for triglycerides. Either of the methods could be used for predicting critical volumes.
Acknowledgments
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