# Free Energy Contribution to Gas Chromatographic Separation of Petroselinate and Oleate Esters

Authors: Chanida Sansa-ard; Kornkanok Aryusuk; Supathra Lilitchan; Kanit Krisnangkura
Journal: Chromatography Research International
 (2011)

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## Abstract

The ease of separation by gas chromatography between petroselinic and oleic acids depends on the alcohol moieties of their esters. The esters of higher molecular weight alcohols tend to be better separated on a 90%-biscyanopropyl-10%-cyanopropylphenyl polysiloxane capillary column (30 m × 0.25 mm i.d.). By analysis of free energies contribution from different parts of the molecules, it is tentatively concluded that the interaction between the double bond and the column stationary phase is interfered by the bulky alkyl group, and it is the major driving force for the separation of the two fatty acids.


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## Body

## 1. Introduction

Petroselinic acid (18:1Δ6cis) is a major fatty acid in the seed oils of most of the members of the Apiaceae (Umbelliflerae), Araliaceae, Garryaceae species, Acer (Aceraceae), and Geraniaceae [1–4]. Petroselinic acid is an interesting oleochemical for food, cosmetics, and pharmaceutical industries [5]. Coriander seed oil, which contained about 70% petroselinic acid, showed a significant hypolipidomic effect on animals [6]. High petroselinic acid diets found to lower the n-6 long-chain fatty acids of the phospholipids [7]. Hence, petroselinic has become more and more important in industry and human health. In 1997, Santinelli and Damiani [8] pointed out that petroselinic acid was always accompanied by some oleic acid (18:1Δ9cis), and there was no single chromatographic technique suitable for their separation and quantitation. However, methods for its separation from oleic acid have gradually been improved. Lin et al. [9] and Liu and Hammon [10] reported the separation of these two positional isomers by reversed phase liquid chromatography. Kim et al. [11] were able to separate and quantitate petroselinic and oleic acids in coriander tissues as their methyl esters by gas chromatography (GC) on a 5%-phenyl-95%-methylpolysiloxane capillary column. In addition, Thies [12] reported the use of butyl esters for the separation of these two positional isomers at 220°C with a total run time of 13 min. Thies saw good resolution of the butyl esters under these conditions, but they were not baseline separated. On the other hand, with a highly polar column (100%-cyanopropyl polysiloxane) of 50 meters, the two isomers could almost be baseline separated as their isopropyl esters [13, 14]. These two isomers in coriander seed oil could also be separated and quantitated on a 30 m of 100%-cyanopropyl polysiloxane with two steps temperature program [15], but how well they were separated was not reported. Near-baseline separations of methyl petroselinate and oleate on 100%-cyanopropyl polysiloxane columns from two different manufacturers at 180°C were reported [16]. A recent report [17] showed that methyl petroselinate and oleate could be separated on ionic liquid stationary phase [1,9-di(3-vinyl-imidazolium) nonane bis-(trifluoromethyl) sulfonyl imidate] columns, with the lengths of 12 (the microbore capillary), 30, and 100 meters.A detailed study on the effects of alcohol chain lengths and branched chain on the separations of petroselinic and oleic acid esters was reported by Isbell [18]. Analyses were conducted on a 30 m of 100%-cyanopropyl polysiloxane column. The authors found that 2-ethyl-1-hexyl esters were promising derivatives for quantitative analysis of the oils containing the mixture of petroselinic and oleic acids. With the 2-ethyl-1-hexyl esters, the interaction of the polar carboxyl group with the stationary phase was sterically masked. Therefore, the main interaction would be that between the small polarity differences of the olefins and the polar stationary phase of the column, which caused the separation.However, methyl esters of these two acids could also be separated on a 100 m of 100%-cyanopropyl polysiloxane capillary column [19].In this study, oils containing petroselinic and oleic acids are transesterified with alcohols of different chain lengths. The gas chromatographic separations of these two positional isomers are discussed in term of their standard free energy of transfer from solution to gas (ΔslngGo). Thus, a general knowledge of GC related to ΔslngGo is briefly reviewed.In gas-liquid chromatography, the solute (at infinite dilution) partitioning between the stationary and the mobile phases is assumed to be at equilibrium or very close to equilibrium state. Thus, the change inΔslngGo directly relates to its equilibrium constant (K). The ΔslngGo, on the other hand, can be divided into ΔslngGf and δslngG [20] as described in the following:(1)Δsln⁡gGo=Δsln⁡gGf+zδsln⁡gG,
where z is the number of carbon atoms. If z=0, ΔslngGf = ΔslngGo, that is ΔslngGf is the free energy contributed from the hypothetical molecule of zero carbon atom or may be simply understood as the functional group. Differentiating (1) with respect to z, one obtains δslngG = δΔslngGo/δz. Thus, δslngG is the change in ΔslngGo per carbon atom. In addition, equation (1) can be expanded as described below [21].From basic thermodynamics,(2)ΔG0=ΔH0-TΔS0,ln⁡k=-ΔG0RT-ln⁡β,
where ΔH0 and ΔS0 are the changes in standard enthalpy and entropy, respectively. T is the absolute temperature, k is the retention factor, β is column phase ratio, and R is the universal gas constant. Equation (3) is obtained by substitution of (2) into (1),(3)ln⁡k=-Δsln⁡gHfRT+Δsln⁡gSfR-zδsln⁡gHRT+zδsln⁡gSR-ln⁡β
or (4)ln⁡tR-tMtM=a+bz+cT+zdT,
where
(5)a=-ln⁡β+Δsln⁡gSfR,b=δsln⁡gSR,c=-Δsln⁡gHfR,d=-δsln⁡gHR.ΔslngHf and ΔslngSf are the changes in standard enthalpy and entropy of transfer from solution to gas of an hypothetical molecule of z=0, respectively. δslngH and δslngS are the increments in standard enthalpy and entropy of transfer from solution to gas per carbon atom; tR and tM are retention times of the solute and unretained gas, respectivelyAt constantz, equation(4) is reduced to (6) or Vant’ Hoff’s equation. (6)ln⁡tR-tMtM=a′′+c′′T,
where(7)a′′=a+bz,c′′=c+dz.
It was reported that all the four numeric values of (4) (a, b, c, and d) remained unchanged when the column was broken or cut into different lengths [22]. They were still valid for predicting tR of fatty acid methyl esters (FAMEs) with good accuracy. On the other hand, for columns of the same stationary phase but differing in the inside diameters, only the numeric value of a was changed while the other three remained unchanged [23]. The β value is approximately equal to column inside diameter/(4 × film thickness), while the other coefficients are thermodynamic parameters and depend on type of solute and solvent (stationary phase) pair.For linear aliphatic solutes (RH and RX), having the same number of carbon atoms but differing in the X functional groups, the difference in the retention indices of RzX and  RzH is called homomorphic factor [24]. When the solutes are fatty acid alkyl esters (FAAEs) of different alcohols, the general structure would be  R1COORy, where  Rz =  R1COO- and X = Ry. In this study, the homomorphic factors of fatty esters of different alcohols are evaluated in term of thermodynamic parameters. Furthermore, the free energy of transfer from solution gas of the double bond (ΔslngGu) is postulated, and the relative change in ΔslngGu is responsible for the separations of 18:1∆6 and 18:1∆9 esters of different alcohols.


## 2. Experimental

### 2.1. Materials

Coriander seeds were obtained from a plant grower (Bangkok, Thailand). Olive oil was from local supermarket in Bangkok (Thailand). Fatty acid methyl esters (C16–C20) and oleic acid methyl ester were obtained from Sigma-Aldrich Chem. Co. (St. Loius, MO). C1–C3 alcohols and solvents were reagent grade obtained from Lab Scan Co. (Bangkok, Thailand). Higher alcohols (C4–C8) were from Sigma-Aldrich Chem. Co. (St. Loius, MO).


### 2.2. Extraction of Coriander Seed Oil

One gram of coriander seed kernel was ground in a mortar. The paste was transferred to a 4 mL vial, and 1 mL of toluene was added. The mixture was intermittently vortexed for 1 min. The toluene layer was decanted into a new vial and transesterified as described in the next section.


### 2.3. Transesterification

Transesterification of FAMEs with other alcohols (C2–C8) was carried out via a microreactor as described by Kaewkool et al. [25]. A disposable syringe (3 mL) was plugged with a small piece of cotton wool. NaOH (0.5 g) was rapidly ground and packed into the disposable syringe.Five hundred microliters of a standard mixture of FAMEs (C16–C20) in toluene, about 2 mg/mL each, were mixed with 0.5 mL of the desired alcohol (C2–C8). Transesterification was started by passing the mixture through the microreactor gravitationally. Elution rate was controlled manually by the plunger, such that the mixture was eluted out in 30–45 s. Another 1 mL of the toluene-alcohol (1 : 1 v/v) mixture was added to wash the microreactor. The wash time was about 20 s. The combined eluent was acidified with 0.1 mL glacial acetic acid and washed with 1 mL of water. The organic layer was separated and dried over anhydrous Na2SO4. Transesterification and soap formation were checked by a liquid chromatography-based method according to Kittiratanapiboon and Krisnangkura [26].For coriander seed oil an equal amount of olive oil, was mixed in order to increase the oleate peak in the chromatogam. The oil was similarly transesterifed as described above. For secondary octanols, alkaline catalyst was not suitable due to its slow reaction rate and soap formation. Acid catalysis was performed according to Kalayasiri et al. [27].


### 2.4. Gas Chromatography (GC)

Gas chromatographic analysis was carried out on a Shimadzu gas chromatograph model 2010 (Shimadzu Inc., Tokyo, Japan) and equipped with an FID, a split-splitless injector, a data processor (CBM 102), and a 90%-biscyanopropyl-10%-cyanopropylphenyl polysiloxane (Rtx-2330) capillary column (30 m × 0.25 mm i.d., 0.25 μm film thickness; from Restek International, Bellefonte, PA). The chromatographic conditions were as follows: Nitrogen carrier gas flow, 1 mL/min; nitrogen makeup gas flow, 30 mL/min; detector/injector, 230°C; split ratio, about 50 : 1. Oven temperatures were set isothermally at 5°C intervals between 180°C and 200°C, for determination of the column coefficients (a, b, c, and d) and 180°C for the separation of petroselinic and oleic esters.


### 2.5. Determination of the Four Coefficients of (4) for Fatty Acid Butyl Esters (FABEs)

FABEs, which are approximately half way between methyl and octyl esters, were chosen as the references. The four numeric coefficients for FABEs were determined as described by Krisnangkura et al. [21].At constant absolute temperature (T), equation (4) is reduced to (8), the well-known Martin’s equation(8)ln⁡tR-tMtM=a′+b′z,
where(9)a′=a+cT,b′=b+dT
Thus, plotting a′ against 1/T would result in a straight line with a slope of c and an intercept of a.Plotting b′ against 1/T would also result in a straight line with a slope of d and an intercept of b.The mixture of FABEs (C16–C20) was chromatographed at 5°C intervals between 180°C and 200°C. The four column coefficients were solved by Microsoft Office Excel 2007.


### 2.6. Determination of the Four Coefficients of (4) for Fatty Acid Esters of Other Alcohols

The difference in retention indices of RX and RH (R = alkyl, X is functional group) is called homomorphic factor. According to (1), ΔslngGf is the free energy contributed from the characteristic functional group, X. zδslngG is the free energy contributed from the hydrocarbon chain of z carbon atoms. Thus, the difference in ΔslngGo between RX and RH would simply arise from the ΔslngGf of the two molecules, which have the same alkyl, R, group. Similarly, two fatty acid esters having the same z but differing in the alcohol moieties, the difference in ΔslngGo of the two fatty acid esters would be the difference in ΔslngGf. When (1) is expanded to (4), the numeric values of b and d would remain unchanged. Only the a and c, derived from ΔslngGf, are changed. Therefore, the numeric values b and d of FABEs are assigned for other fatty acid esters. The values of a and c were obtained by solving two simultaneous equations, at different temperatures. The numeric values of a and c for each fatty acid ester are averaged from 25 data (5 different temperature pairs and 5 fatty acids).


## 2.1. Materials

Coriander seeds were obtained from a plant grower (Bangkok, Thailand). Olive oil was from local supermarket in Bangkok (Thailand). Fatty acid methyl esters (C16–C20) and oleic acid methyl ester were obtained from Sigma-Aldrich Chem. Co. (St. Loius, MO). C1–C3 alcohols and solvents were reagent grade obtained from Lab Scan Co. (Bangkok, Thailand). Higher alcohols (C4–C8) were from Sigma-Aldrich Chem. Co. (St. Loius, MO).


## 2.2. Extraction of Coriander Seed Oil

One gram of coriander seed kernel was ground in a mortar. The paste was transferred to a 4 mL vial, and 1 mL of toluene was added. The mixture was intermittently vortexed for 1 min. The toluene layer was decanted into a new vial and transesterified as described in the next section.


## 2.3. Transesterification

Transesterification of FAMEs with other alcohols (C2–C8) was carried out via a microreactor as described by Kaewkool et al. [25]. A disposable syringe (3 mL) was plugged with a small piece of cotton wool. NaOH (0.5 g) was rapidly ground and packed into the disposable syringe.Five hundred microliters of a standard mixture of FAMEs (C16–C20) in toluene, about 2 mg/mL each, were mixed with 0.5 mL of the desired alcohol (C2–C8). Transesterification was started by passing the mixture through the microreactor gravitationally. Elution rate was controlled manually by the plunger, such that the mixture was eluted out in 30–45 s. Another 1 mL of the toluene-alcohol (1 : 1 v/v) mixture was added to wash the microreactor. The wash time was about 20 s. The combined eluent was acidified with 0.1 mL glacial acetic acid and washed with 1 mL of water. The organic layer was separated and dried over anhydrous Na2SO4. Transesterification and soap formation were checked by a liquid chromatography-based method according to Kittiratanapiboon and Krisnangkura [26].For coriander seed oil an equal amount of olive oil, was mixed in order to increase the oleate peak in the chromatogam. The oil was similarly transesterifed as described above. For secondary octanols, alkaline catalyst was not suitable due to its slow reaction rate and soap formation. Acid catalysis was performed according to Kalayasiri et al. [27].


## 2.4. Gas Chromatography (GC)

Gas chromatographic analysis was carried out on a Shimadzu gas chromatograph model 2010 (Shimadzu Inc., Tokyo, Japan) and equipped with an FID, a split-splitless injector, a data processor (CBM 102), and a 90%-biscyanopropyl-10%-cyanopropylphenyl polysiloxane (Rtx-2330) capillary column (30 m × 0.25 mm i.d., 0.25 μm film thickness; from Restek International, Bellefonte, PA). The chromatographic conditions were as follows: Nitrogen carrier gas flow, 1 mL/min; nitrogen makeup gas flow, 30 mL/min; detector/injector, 230°C; split ratio, about 50 : 1. Oven temperatures were set isothermally at 5°C intervals between 180°C and 200°C, for determination of the column coefficients (a, b, c, and d) and 180°C for the separation of petroselinic and oleic esters.


## 2.5. Determination of the Four Coefficients of (4) for Fatty Acid Butyl Esters (FABEs)

FABEs, which are approximately half way between methyl and octyl esters, were chosen as the references. The four numeric coefficients for FABEs were determined as described by Krisnangkura et al. [21].At constant absolute temperature (T), equation (4) is reduced to (8), the well-known Martin’s equation(8)ln⁡tR-tMtM=a′+b′z,
where(9)a′=a+cT,b′=b+dT
Thus, plotting a′ against 1/T would result in a straight line with a slope of c and an intercept of a.Plotting b′ against 1/T would also result in a straight line with a slope of d and an intercept of b.The mixture of FABEs (C16–C20) was chromatographed at 5°C intervals between 180°C and 200°C. The four column coefficients were solved by Microsoft Office Excel 2007.


## 2.6. Determination of the Four Coefficients of (4) for Fatty Acid Esters of Other Alcohols

The difference in retention indices of RX and RH (R = alkyl, X is functional group) is called homomorphic factor. According to (1), ΔslngGf is the free energy contributed from the characteristic functional group, X. zδslngG is the free energy contributed from the hydrocarbon chain of z carbon atoms. Thus, the difference in ΔslngGo between RX and RH would simply arise from the ΔslngGf of the two molecules, which have the same alkyl, R, group. Similarly, two fatty acid esters having the same z but differing in the alcohol moieties, the difference in ΔslngGo of the two fatty acid esters would be the difference in ΔslngGf. When (1) is expanded to (4), the numeric values of b and d would remain unchanged. Only the a and c, derived from ΔslngGf, are changed. Therefore, the numeric values b and d of FABEs are assigned for other fatty acid esters. The values of a and c were obtained by solving two simultaneous equations, at different temperatures. The numeric values of a and c for each fatty acid ester are averaged from 25 data (5 different temperature pairs and 5 fatty acids).


## 3. Results and Discussion

### 3.1. The Homomorphic Factor of Fatty Acid Esters

As pointed out in Section2.6, the homomorphic factor is the difference in retention indices of RX and RH. According to (1), two FAAEs (R1COORy) having the same R1but differing in the alcohol moieties (Ry), ΔslngGf would be characteristic of the homomorphic factor. In this section, attempts are made to prove that FAAEs of different alcohols would differ in ΔslngGf, while the δslngG values are unchanged.


#### 3.1.1. The Numeric Values for FAAEs

The four numeric coefficients for FAAEs were determined as described in Section2.6 and solved by Microsoft Office Excel 2007. The numeric values and the standard deviations (sd) of 95% confidence for a,b,c, and d are listed in Table 1. Although, only 4 significant numbers are shown in Table 1, it should be pointed out that the higher decimal number would give better agreement between the predicted and experimental values. Hence, unrounded values of the 4 coefficients were used in the calculations.Table 1
Numeric values of the coefficients of (4) for different alkyl esters. Numbers in the bracket are standard deviation.
FAAEabcdFAME−7.169 (0.154)−0.596 (0.003)1007 (80.43)401.3 (1.323)FAEE−7.459 (0.143)−0.596 (0.003)1175 (68.58)401.3 (1.323)FAPrE−7.978 (0.115)−0.596 (0.003)1523 (54.78)401.3 (1.323)FABE−8.392 (0.051)−0.596 (0.003)1825 (23.89)401.3 (1.323)FAPeE−8.398 (0.103)−0.596 (0.003)1936 (49.86)401.3 (1.323)FAHxE−10.02 (0.042)−0.596 (0.003)2837 (20.20)401.3 (1.323)FAHpE−10.55 (0.019)−0.596 (0.003)3198 (9.014)401.3 (1.323)FAOE−11.05 (0.052)−0.596 (0.003)3571 (24.69)401.3 (1.323)sd (intercept)0.298—157.7—sd (slope)0.059—31.22—The average values ofa and c for FAAEs and their sd are summarized in Table 1. The values of a are more negative as the carbon numbers of the alcohols are increased. The plot of a and carbon numbers of alcohols yield a straight line with the slope of −0.580 and intercept of −6.265. The r2, sd of intercept, and slope are 0.941, 0.298, and 0.059, respectively. On the other hand, the values of c increase positively as the carbon numbers of the alcohols are increased. The plot of c and carbon numbers of alcohols give a straight line with the slope and intercept, of 382.1 and 416.7, respectively. The r2, sd of intercept and slope are 0.961, 157.7, and 31.22, respectively.ΔslngGf is the difference between ΔslngHf and TΔslngSf. The values of ΔslngGf for each fatty acid ester at any temperature can be estimated from the coefficients a and c (in Table 1, with the nominal β value of 250). The value of ΔslngGf, for each fatty acid ester, at constant temperature, increases negatively as the carbon numbers of the alcohols are increased (Figure 1). However, the transformation of a solute in solution to gas involves two physical phenomena. The interaction between the solute and the column stationary phase is measured by free energy of solution, (ΔsGf), and the vaporization of the solute is measured by free energy of vaporization, ΔlgGo, [28, 29]. Therefore, the increment in ΔslngGf with Ry may involve ΔsGf or ΔlgGo or both of them, and the separation between 18:Δ6cis and 18:Δ9cis cannot be ascribed to ΔsGf at this moment.Figure 1
The change inΔslngGf with 1/T.


#### 3.1.2. Evaluation of Coefficients in (4)

The four numeric values (a,b,c, and d) for FAAEs of different alcohols are summarized in Table 1. The validations of these values were indirectly verified by comparing the calculated retention times (tR(cal)) with the experimental values (tR(exp)). Both tR(cal) and tR(exp) values are summarized in Table 2. All the tR(cal) are very close to the tR(exp) values. The greatest difference is 1.56% for methyl arachidate. There are only 3 tR(cal) values which differed greater than ±1.00% from the tR(exp) values. Forty one data points (21.0%) have the differences between 0.50 and 1.00. The rest (155 data points or 77.5%) have the differences less than 0.50%. The good agreement between the tR(cal) and tR(exp) values suggests that all the coefficients are valid for prediction retention times of FAAEs. The slopes, intercepts, r2 and standard deviations of the plots between tR(cal) and tR(exp) for each FAAE are summarized in Table 3. The r2, values of all the FAAE are greater than 0.997, and the slopes (the ratios of tR(cal)/tR(exp)) are very close to 1.00, except that of FAME. The anomaly of the C1 series was observed on other phenomenon, such as gas holdup time [30, 31]. Hence, they are additional information, which supports that all the column coefficients are valid for predicting the retention times of FAAEs. Therefore, it may conclude that when the alcohols are changed, the numeric values of δslngH of and δslngS remain unchanged, accordingly the δslngG value does not change. It would also imply that the interaction between the saturated hydrocarbon chain and the stationary phase is not affected by the alcohol moieties. Thus, the homomorphic factor is verified for fatty acid esters of different alcohols.Table 2
Comparison of thetR(cal) with the tR(exp) for fatty acids of different alkyl esters between temperatures 180 and 200°C, at 5°C interval.
180°C185°C190°C195°C200°CFAMEtR(cal)tR(exp)%ΔatR(cal)tR(exp)%ΔtR(cal)tR(exp)%ΔtR(cal)tR(exp)%ΔtR(cal)tR(exp)%Δ165.095.14−0.974.764.79-0.634.484.50−0.444.254.28−0.704.094.10−0.24175.815.85−0.685.345.36-0.374.954.96−0.204.634.66−0.644.404.41−0.23186.776.78−0.156.116.100.165.565.560.005.135.14−0.194.804.800.00198.068.010.627.137.070.856.376.350.315.785.760.355.325.310.19209.779.641.358.488.351.567.437.331.366.616.560.765.995.950.67FAEE165.185.21−0.584.804.84−0.834.504.51−0.224.274.28−0.234.064.07−0.25175.955.96−0.175.415.45−0.734.995.00−0.204.674.68−0.214.394.40−0.23186.976.970.006.236.25−0.325.645.640.005.195.190.004.814.810.00198.348.300.487.307.290.146.496.470.315.875.850.345.355.340.192010.1610.080.798.728.680.467.607.550.666.756.700.756.046.010.50FAPrE165.895.91−0.345.295.34−0.944.994.980.204.654.650.004.374.38−0.23176.896.90−0.146.076.12−0.825.625.610.185.165.150.194.784.79−0.21188.228.210.127.107.16−0.846.456.420.475.825.810.175.315.310.00199.999.970.208.468.52−0.707.547.490.676.686.650.455.995.980.172012.3712.300.5710.2610.33−0.688.978.890.907.797.740.656.866.840.29FABE166.826.84−0.296.176.150.335.615.590.365.145.140.004.774.770.00178.128.14−0.257.207.170.426.436.400.475.795.790.005.295.290.00189.869.88−0.208.578.530.477.507.460.546.636.620.155.955.96−0.171912.1712.21−0.3310.3710.310.588.908.850.567.727.710.136.816.810.002015.2715.32−0.3312.7612.680.6310.7410.680.569.149.120.227.917.92−0.13FAPeE168.118.17−0.737.137.16−0.426.376.38−0.165.805.780.355.265.28−0.38179.869.91−0.508.498.51−0.247.447.440.006.646.610.455.935.94−0.171812.2012.23−0.2510.2910.31−0.198.848.830.117.747.690.656.786.79−0.151915.3215.34−0.1312.6812.670.0810.6710.650.199.179.100.777.877.89−0.252019.4819.51−0.1515.8315.710.7613.0713.050.1511.0210.940.739.289.31−0.32FAHxE169.799.83−0.418.458.46−0.127.417.410.006.616.600.155.925.93−0.171712.1012.13−0.2510.2310.32−0.878.808.780.237.707.670.396.766.77−0.151815.1915.21−0.1312.6012.580.1610.6310.590.389.119.070.447.867.860.001919.3219.34−0.1015.7315.710.1313.0212.970.3910.9510.900.469.269.28−0.222024.8324.93−0.4019.8619.87−0.0516.1516.120.1913.3313.300.2311.0711.11−0.36FAHpE1611.9812.01−0.2510.1710.160.108.728.720.007.647.630.136.746.75−0.151715.0315.05−0.1312.5112.480.2410.5210.500.199.049.020.227.837.830.001819.1119.110.0015.6015.560.2612.8712.850.1610.8610.820.379.229.220.001924.5524.61−0.2419.6919.690.0015.9615.960.0013.2213.180.3011.0111.04−0.272031.8132.05−0.7525.1125.18−0.2820.0120.09−0.4016.2816.29−0.0613.3213.40−0.60FAOE1615.3015.270.2012.6312.67−0.3210.7110.680.289.149.15−0.117.987.980.001719.4619.380.4115.7715.79−0.1313.1313.070.4611.0010.990.099.429.400.211825.0324.920.4419.9319.95−0.1016.3016.210.5613.4013.380.1511.2711.240.271932.4632.430.0925.4325.54−0.4320.4520.390.2916.5216.53−0.0613.6513.630.152042.3842.60−0.5232.7133.03−0.9725.8925.94−0.1920.5820.69−0.5316.7216.75−0.18percenta different between tR(exp) and tR(cal).Table 3
Correlation oftR(cal) and tR(exp) of FAAEs. Numbers in parentheses are standard deviation.
FAAESlopeInterceptr2FAME0.970 (0.004)0.162 (0.021)0.997FAEE0.987 (0.002)0.086 (0.015)0.999FAPrE0.995 (0.002)0.034 (0.013)0.999FABE1.001 (0.003)0.025 (0.023)0.999FAPnE0.999 (0.002)0.004 (0.025)0.999FAHxE1.003 (0.002)−0.044 (0.021)0.999FAHpE1.008 (0.001)−0.112 (0.021)0.999FAOE1.007 (0.002)−0.121 (0.038)0.999


### 3.2. GC Separation of Octadecenoic Acid Alkyl Esters of Different Alcohols and Free Energy Contribution from the Double Bond

Figure2 is the aligned chromatograms of FAAEs (with different alcohols) of a mixture of coriander seed and olive oils, separated on a 90%-biscyanopropyl-10%-cyanopropylphenyl polysiloxane (Rtx-2330) capillary column at 180°C. The methyl and ethyl esters of petroselinic and oleic are coeluted. Partial separations of these two acid esters are observed when the alkyl groups have 3–6 carbon atoms. FAAEs of higher alcohols (FAHpE, FAOE, and FAEHE) are baseline resolved. Results agree well with the report of Isbell et al. [18]. In Figure 2, the octyl esters show approximately the same resolution as those of the 2-ethyl-1-hexyl esters in separations of 18:1∆6 and 18:1∆9. However, the 2-ethyl-1-hexyl esters are eluted faster than the octyl esters. The retention times of the 2-ethyl-1-hexyl esters are comparable to those of the heptyl esters. The bulky 2-ethyl-1-hexyl group was ascribed for lowering the interaction between the polar carboxyl and the polar stationary phase. Therefore, the interaction between the small polarity differences of the olefin and the polar stationary phase became apparent and caused the separation [18]. Although the discussion of Isbell et al. [18] was theoretically sound, it lacked the supported evidence. On the contrary, results in Figure 1 show that ΔslngGf values increase as the alcohol groups are larger, which contradicted to the explanation of Isbell et al. [18]. Therefore, a new free energy term is proposed, and it is expected that it would be able to find the cause of the separation between petroselinic and oleic esters.Figure 2
2 Alignment of gas chromatograms of different alkyl esters of coriander seed oil + olive oil at 180°C. Peaks identification: 1, 18:1Δ6cis; 2, 18:1Δ9cis; 3, 18:1Δ11cis.Martin [20] were the first to divide a molecule into different parts, and a free energy term was assigned to each of them as shown in (1). Subsequently, different free energy terms were assigned to describe interactions between column stationary phase and different functional groups of the molecule [32, 33]. Hence, the free energy concept of Kollie and Poole [32] and Golovnya [33] was extended, in this work, to investigate the interaction between the double bond and the column stationary phase. The new free energy is called free energy of transfer from solution to gas of the double bond (ΔslngGu). Equation (10) is obtained by inserting the ΔslngGu into(1)(10)Δsln⁡gG2o=Δsln⁡gGf+zδsln⁡gG1o+Δsln⁡gGu,
where the subscripts 1 and 2 stand for saturated and unsaturated fatty acids, respectively.Equation (10) can also be derived as follows: (11)ΔslngG1o=-RTln⁡K1,ΔslngG2o=-RTln⁡K2.
Equation (12) is the difference between (11).(12)Δsln⁡gGu=Δsln⁡gG2o-Δsln⁡gG1o=-(RTln⁡K2-RTln⁡K1).
Equation (10) is obtained by substituting (1) into (12).ΔΔslngGu(Δ9-Δ6) is the difference between ΔslngG2(Δ9)o of 18:1Δ9 and ΔslngG2(Δ6)o of 18:1Δ6 as shown in .(13)Δsln⁡gG2(Δ9)o-Δsln⁡gG2(Δ6)o=Δsln⁡gGu(Δ9)-Δsln⁡gGu(Δ6)=ΔΔsln⁡gGu(Δ9-Δ6).
The ΔΔslngG2(Δ9-Δ6)o will be used as a tool to investigate the interaction of the double bond with the stationary phase of the column. The ΔslngG2o of petroselinic and oleic (and vaccenic 18:1Δ11cis) acid esters at 180°C are summarized in Table 4. The C1–C3 esters are not well separated from each other, and they are not listed in the table. The ΔslngGu values of these three esters at 180°C are approximately −151, −133, and 128 cal·mol−1, respectively. Partial separations are observed for FABEs. Separations of FAAE are gradually improved as the carbon numbers of the alcohols are increased.Table 4
TheΔslngGu(cal·mol−1) of esters of C18:1Δ6, C18:1Δ9, and C18:1Δ11.
ΔslngGu(cal·mol−1)Fatty acidsFABEFAPnEFAHxEFAHpEFAOEFAEHE18:00.00.00.00.00.00.018:1∆6−102.4−82.0−78.7−68.8−61.4−36.718:1∆9−120.1−103.8−102.2−92.1−85.9−61.418:1∆11−145.4−134.3−131.7−122.1−113.1−90.5ΔΔslngGu (cal·mol−1)(18:1Δ9) – (18:1Δ6)−17.7−21.8−23.5−23.3−24.5−24.7(18:1Δ11) – (18:1∆9)−25.3−30.5−29.5−30.0−27.2−29.1According to Isbell et al. [18], the bulky alkyl group interfered the interaction of the carboxyl group to the column stationary phase. The interference did not extend to the hydrocarbon chain. Hence, the relative changes in ΔslngGo should be the same for both saturated and unsaturated FAAEs. However, the ΔslngGu values of petroselinic, oleic, and vaccenic esters (Table 4) become less negative as the alkyl sizes are increased, suggesting that the alkyl groups interfere the interaction between the hydrocarbon chain and the stationary phase, and the degree of interferences increases as the carbon numbers of the alcohols are increased.TheΔslngGu values of the butyl esters of 18:1∆6, ∆9, and ∆11 are −102.4, −120.1, and −145.4 cal·mol−1, respectively. The values become less negative as the alkyl groups are larger. 2-Ethyl-1-hexyl esters have the lowest ΔslngGu compared with other alkyl esters. Their ΔslngGu values for 18:1Δ6,Δ9, and Δ11 are −36.7, −61.4, and −90.5 cal·mol−1, respectively. Therefore, the interaction of the double bond with the column stationary phase increases when the double bond is far away from the carboxyl group, that is, interference from the bulky alkyl group decreases along the distant.The difference inΔslngGu of 18:1Δ9 and 18:1Δ6 (ΔΔslngGu(Δ9-Δ6)) of butyl, pentyl, hexyl, heptyl, octyl and 2-ethylhexyl esters is −17.7, −21.8, −23.5, −23.3, −24.5, and −24.7 cal·mol−1, respectively. The increases in ΔΔslngGu(Δ9-Δ6) as the alkyl groups increased suggest that the relative interactions of the double bonds of the two acid esters with the stationary phase are increased. Thus, it may conclude that ΔΔslngGu(Δ9-Δ6) is the driving force for the separation of the two isomers. However, the ΔΔslngGu(Δ9-Δ6) values level after C6, implying that the resolution of these two positional isomers may not be further increased by simply increasing the size of the alcohol.TheΔΔslngGu(Δ9-Δ6) of 2-ethyl-1-hexyl esters is −24.7 cal·mol−1. It is estimated that a column of about 65,000 required plate numbers (Nreq) would be able to baseline separate the two positional isomers, while the butyl esters, whose ΔΔslngGu(Δ9-Δ6) is −17.7 cal·mol−1, would require up to 180,000 plate numbers. The ΔslngGu of 18:1∆9 and ∆11 have similar trend as the 18:1∆6 and 18:1∆9 pair, and discussion is not necessary.Petroselinic acid has a double bond closer to the carboxyl group than oleic acid. The interference from the bulky alkyl group should be stronger than that to the oleic acid. Similar observation was reported by Kuningas et al. [34] that the separation of geometric isomers (alkenes) depended on the differences in free energy.TheΔΔslngGu(Δ9-Δ6) the adjacent pairs of octadecenoic esters would reflect on the ease of separation for each pair. Results in Table 4 show that the separation of 18:1∆9 and 18:1∆11 is much simpler than the separation of 18:1∆6 and 18:1∆9.


### 3.3. Separation of Octadecenoic Acid Octyl Esters

As discussed in Section3.2, the lowering in ΔslngGu was ascribed to the reduction in the interaction between the double bond in the FAAEs and the column stationary phase. 1-Octyl and 2-ethy-1-hexyl esters are two of the best derivatives for separation of petroselinic and oleic acids. However, esters of secondary octyl alcohols have not been reported (to our knowledge). Thus, they were investigated for their interferences to the interaction of the double bond with the stationary phase. The retention times, retention factors, ΔΔslngGu(Δ9-Δ6), and resolution (Rs) between secondary octyl petroselinate and oleate are summarized in Table 5. The ΔΔslngGu(Δ9-Δ6) values of secondary octyl esters of petroselinate and oleate range from −24.5 to −25.8 cal·mol−1. The resolutions of these two acid secondary octyl esters (1.15-1.26) are close to that of the 1-octyl ester (1.26). However, more symmetric or compact alcohol had the shorter retention time. The order of elution for the esters is 4-octyl, 3-octyl, 2-octyl, and 1-octyl, respectively.Table 5
Separations of petroselinic and oleic octyl esters on Rtx 2330 at 190°C.
ΔΔslngGu(Δ9-Δ6)OctanoltR1(min)atR2 (min)k1k2(cal·mol−1)Rs1-octanol17.2717.716.196.35−24.51.262-octanol12.6712.974.514.64−25.81.153-octanol12.0012.294.004.12−25.11.174-octanol11.4111.693.743.84−25.11.20thesubscriptsa; 1 and 2 represent petroselinate and oleate, respectively.


## 3.1. The Homomorphic Factor of Fatty Acid Esters

As pointed out in Section2.6, the homomorphic factor is the difference in retention indices of RX and RH. According to (1), two FAAEs (R1COORy) having the same R1but differing in the alcohol moieties (Ry), ΔslngGf would be characteristic of the homomorphic factor. In this section, attempts are made to prove that FAAEs of different alcohols would differ in ΔslngGf, while the δslngG values are unchanged.


### 3.1.1. The Numeric Values for FAAEs

The four numeric coefficients for FAAEs were determined as described in Section2.6 and solved by Microsoft Office Excel 2007. The numeric values and the standard deviations (sd) of 95% confidence for a,b,c, and d are listed in Table 1. Although, only 4 significant numbers are shown in Table 1, it should be pointed out that the higher decimal number would give better agreement between the predicted and experimental values. Hence, unrounded values of the 4 coefficients were used in the calculations.Table 1
Numeric values of the coefficients of (4) for different alkyl esters. Numbers in the bracket are standard deviation.
FAAEabcdFAME−7.169 (0.154)−0.596 (0.003)1007 (80.43)401.3 (1.323)FAEE−7.459 (0.143)−0.596 (0.003)1175 (68.58)401.3 (1.323)FAPrE−7.978 (0.115)−0.596 (0.003)1523 (54.78)401.3 (1.323)FABE−8.392 (0.051)−0.596 (0.003)1825 (23.89)401.3 (1.323)FAPeE−8.398 (0.103)−0.596 (0.003)1936 (49.86)401.3 (1.323)FAHxE−10.02 (0.042)−0.596 (0.003)2837 (20.20)401.3 (1.323)FAHpE−10.55 (0.019)−0.596 (0.003)3198 (9.014)401.3 (1.323)FAOE−11.05 (0.052)−0.596 (0.003)3571 (24.69)401.3 (1.323)sd (intercept)0.298—157.7—sd (slope)0.059—31.22—The average values ofa and c for FAAEs and their sd are summarized in Table 1. The values of a are more negative as the carbon numbers of the alcohols are increased. The plot of a and carbon numbers of alcohols yield a straight line with the slope of −0.580 and intercept of −6.265. The r2, sd of intercept, and slope are 0.941, 0.298, and 0.059, respectively. On the other hand, the values of c increase positively as the carbon numbers of the alcohols are increased. The plot of c and carbon numbers of alcohols give a straight line with the slope and intercept, of 382.1 and 416.7, respectively. The r2, sd of intercept and slope are 0.961, 157.7, and 31.22, respectively.ΔslngGf is the difference between ΔslngHf and TΔslngSf. The values of ΔslngGf for each fatty acid ester at any temperature can be estimated from the coefficients a and c (in Table 1, with the nominal β value of 250). The value of ΔslngGf, for each fatty acid ester, at constant temperature, increases negatively as the carbon numbers of the alcohols are increased (Figure 1). However, the transformation of a solute in solution to gas involves two physical phenomena. The interaction between the solute and the column stationary phase is measured by free energy of solution, (ΔsGf), and the vaporization of the solute is measured by free energy of vaporization, ΔlgGo, [28, 29]. Therefore, the increment in ΔslngGf with Ry may involve ΔsGf or ΔlgGo or both of them, and the separation between 18:Δ6cis and 18:Δ9cis cannot be ascribed to ΔsGf at this moment.Figure 1
The change inΔslngGf with 1/T.


### 3.1.2. Evaluation of Coefficients in (4)

The four numeric values (a,b,c, and d) for FAAEs of different alcohols are summarized in Table 1. The validations of these values were indirectly verified by comparing the calculated retention times (tR(cal)) with the experimental values (tR(exp)). Both tR(cal) and tR(exp) values are summarized in Table 2. All the tR(cal) are very close to the tR(exp) values. The greatest difference is 1.56% for methyl arachidate. There are only 3 tR(cal) values which differed greater than ±1.00% from the tR(exp) values. Forty one data points (21.0%) have the differences between 0.50 and 1.00. The rest (155 data points or 77.5%) have the differences less than 0.50%. The good agreement between the tR(cal) and tR(exp) values suggests that all the coefficients are valid for prediction retention times of FAAEs. The slopes, intercepts, r2 and standard deviations of the plots between tR(cal) and tR(exp) for each FAAE are summarized in Table 3. The r2, values of all the FAAE are greater than 0.997, and the slopes (the ratios of tR(cal)/tR(exp)) are very close to 1.00, except that of FAME. The anomaly of the C1 series was observed on other phenomenon, such as gas holdup time [30, 31]. Hence, they are additional information, which supports that all the column coefficients are valid for predicting the retention times of FAAEs. Therefore, it may conclude that when the alcohols are changed, the numeric values of δslngH of and δslngS remain unchanged, accordingly the δslngG value does not change. It would also imply that the interaction between the saturated hydrocarbon chain and the stationary phase is not affected by the alcohol moieties. Thus, the homomorphic factor is verified for fatty acid esters of different alcohols.Table 2
Comparison of thetR(cal) with the tR(exp) for fatty acids of different alkyl esters between temperatures 180 and 200°C, at 5°C interval.
180°C185°C190°C195°C200°CFAMEtR(cal)tR(exp)%ΔatR(cal)tR(exp)%ΔtR(cal)tR(exp)%ΔtR(cal)tR(exp)%ΔtR(cal)tR(exp)%Δ165.095.14−0.974.764.79-0.634.484.50−0.444.254.28−0.704.094.10−0.24175.815.85−0.685.345.36-0.374.954.96−0.204.634.66−0.644.404.41−0.23186.776.78−0.156.116.100.165.565.560.005.135.14−0.194.804.800.00198.068.010.627.137.070.856.376.350.315.785.760.355.325.310.19209.779.641.358.488.351.567.437.331.366.616.560.765.995.950.67FAEE165.185.21−0.584.804.84−0.834.504.51−0.224.274.28−0.234.064.07−0.25175.955.96−0.175.415.45−0.734.995.00−0.204.674.68−0.214.394.40−0.23186.976.970.006.236.25−0.325.645.640.005.195.190.004.814.810.00198.348.300.487.307.290.146.496.470.315.875.850.345.355.340.192010.1610.080.798.728.680.467.607.550.666.756.700.756.046.010.50FAPrE165.895.91−0.345.295.34−0.944.994.980.204.654.650.004.374.38−0.23176.896.90−0.146.076.12−0.825.625.610.185.165.150.194.784.79−0.21188.228.210.127.107.16−0.846.456.420.475.825.810.175.315.310.00199.999.970.208.468.52−0.707.547.490.676.686.650.455.995.980.172012.3712.300.5710.2610.33−0.688.978.890.907.797.740.656.866.840.29FABE166.826.84−0.296.176.150.335.615.590.365.145.140.004.774.770.00178.128.14−0.257.207.170.426.436.400.475.795.790.005.295.290.00189.869.88−0.208.578.530.477.507.460.546.636.620.155.955.96−0.171912.1712.21−0.3310.3710.310.588.908.850.567.727.710.136.816.810.002015.2715.32−0.3312.7612.680.6310.7410.680.569.149.120.227.917.92−0.13FAPeE168.118.17−0.737.137.16−0.426.376.38−0.165.805.780.355.265.28−0.38179.869.91−0.508.498.51−0.247.447.440.006.646.610.455.935.94−0.171812.2012.23−0.2510.2910.31−0.198.848.830.117.747.690.656.786.79−0.151915.3215.34−0.1312.6812.670.0810.6710.650.199.179.100.777.877.89−0.252019.4819.51−0.1515.8315.710.7613.0713.050.1511.0210.940.739.289.31−0.32FAHxE169.799.83−0.418.458.46−0.127.417.410.006.616.600.155.925.93−0.171712.1012.13−0.2510.2310.32−0.878.808.780.237.707.670.396.766.77−0.151815.1915.21−0.1312.6012.580.1610.6310.590.389.119.070.447.867.860.001919.3219.34−0.1015.7315.710.1313.0212.970.3910.9510.900.469.269.28−0.222024.8324.93−0.4019.8619.87−0.0516.1516.120.1913.3313.300.2311.0711.11−0.36FAHpE1611.9812.01−0.2510.1710.160.108.728.720.007.647.630.136.746.75−0.151715.0315.05−0.1312.5112.480.2410.5210.500.199.049.020.227.837.830.001819.1119.110.0015.6015.560.2612.8712.850.1610.8610.820.379.229.220.001924.5524.61−0.2419.6919.690.0015.9615.960.0013.2213.180.3011.0111.04−0.272031.8132.05−0.7525.1125.18−0.2820.0120.09−0.4016.2816.29−0.0613.3213.40−0.60FAOE1615.3015.270.2012.6312.67−0.3210.7110.680.289.149.15−0.117.987.980.001719.4619.380.4115.7715.79−0.1313.1313.070.4611.0010.990.099.429.400.211825.0324.920.4419.9319.95−0.1016.3016.210.5613.4013.380.1511.2711.240.271932.4632.430.0925.4325.54−0.4320.4520.390.2916.5216.53−0.0613.6513.630.152042.3842.60−0.5232.7133.03−0.9725.8925.94−0.1920.5820.69−0.5316.7216.75−0.18percenta different between tR(exp) and tR(cal).Table 3
Correlation oftR(cal) and tR(exp) of FAAEs. Numbers in parentheses are standard deviation.
FAAESlopeInterceptr2FAME0.970 (0.004)0.162 (0.021)0.997FAEE0.987 (0.002)0.086 (0.015)0.999FAPrE0.995 (0.002)0.034 (0.013)0.999FABE1.001 (0.003)0.025 (0.023)0.999FAPnE0.999 (0.002)0.004 (0.025)0.999FAHxE1.003 (0.002)−0.044 (0.021)0.999FAHpE1.008 (0.001)−0.112 (0.021)0.999FAOE1.007 (0.002)−0.121 (0.038)0.999


## 3.1.1. The Numeric Values for FAAEs

The four numeric coefficients for FAAEs were determined as described in Section2.6 and solved by Microsoft Office Excel 2007. The numeric values and the standard deviations (sd) of 95% confidence for a,b,c, and d are listed in Table 1. Although, only 4 significant numbers are shown in Table 1, it should be pointed out that the higher decimal number would give better agreement between the predicted and experimental values. Hence, unrounded values of the 4 coefficients were used in the calculations.Table 1
Numeric values of the coefficients of (4) for different alkyl esters. Numbers in the bracket are standard deviation.
FAAEabcdFAME−7.169 (0.154)−0.596 (0.003)1007 (80.43)401.3 (1.323)FAEE−7.459 (0.143)−0.596 (0.003)1175 (68.58)401.3 (1.323)FAPrE−7.978 (0.115)−0.596 (0.003)1523 (54.78)401.3 (1.323)FABE−8.392 (0.051)−0.596 (0.003)1825 (23.89)401.3 (1.323)FAPeE−8.398 (0.103)−0.596 (0.003)1936 (49.86)401.3 (1.323)FAHxE−10.02 (0.042)−0.596 (0.003)2837 (20.20)401.3 (1.323)FAHpE−10.55 (0.019)−0.596 (0.003)3198 (9.014)401.3 (1.323)FAOE−11.05 (0.052)−0.596 (0.003)3571 (24.69)401.3 (1.323)sd (intercept)0.298—157.7—sd (slope)0.059—31.22—The average values ofa and c for FAAEs and their sd are summarized in Table 1. The values of a are more negative as the carbon numbers of the alcohols are increased. The plot of a and carbon numbers of alcohols yield a straight line with the slope of −0.580 and intercept of −6.265. The r2, sd of intercept, and slope are 0.941, 0.298, and 0.059, respectively. On the other hand, the values of c increase positively as the carbon numbers of the alcohols are increased. The plot of c and carbon numbers of alcohols give a straight line with the slope and intercept, of 382.1 and 416.7, respectively. The r2, sd of intercept and slope are 0.961, 157.7, and 31.22, respectively.ΔslngGf is the difference between ΔslngHf and TΔslngSf. The values of ΔslngGf for each fatty acid ester at any temperature can be estimated from the coefficients a and c (in Table 1, with the nominal β value of 250). The value of ΔslngGf, for each fatty acid ester, at constant temperature, increases negatively as the carbon numbers of the alcohols are increased (Figure 1). However, the transformation of a solute in solution to gas involves two physical phenomena. The interaction between the solute and the column stationary phase is measured by free energy of solution, (ΔsGf), and the vaporization of the solute is measured by free energy of vaporization, ΔlgGo, [28, 29]. Therefore, the increment in ΔslngGf with Ry may involve ΔsGf or ΔlgGo or both of them, and the separation between 18:Δ6cis and 18:Δ9cis cannot be ascribed to ΔsGf at this moment.Figure 1
The change inΔslngGf with 1/T.


## 3.1.2. Evaluation of Coefficients in (4)

The four numeric values (a,b,c, and d) for FAAEs of different alcohols are summarized in Table 1. The validations of these values were indirectly verified by comparing the calculated retention times (tR(cal)) with the experimental values (tR(exp)). Both tR(cal) and tR(exp) values are summarized in Table 2. All the tR(cal) are very close to the tR(exp) values. The greatest difference is 1.56% for methyl arachidate. There are only 3 tR(cal) values which differed greater than ±1.00% from the tR(exp) values. Forty one data points (21.0%) have the differences between 0.50 and 1.00. The rest (155 data points or 77.5%) have the differences less than 0.50%. The good agreement between the tR(cal) and tR(exp) values suggests that all the coefficients are valid for prediction retention times of FAAEs. The slopes, intercepts, r2 and standard deviations of the plots between tR(cal) and tR(exp) for each FAAE are summarized in Table 3. The r2, values of all the FAAE are greater than 0.997, and the slopes (the ratios of tR(cal)/tR(exp)) are very close to 1.00, except that of FAME. The anomaly of the C1 series was observed on other phenomenon, such as gas holdup time [30, 31]. Hence, they are additional information, which supports that all the column coefficients are valid for predicting the retention times of FAAEs. Therefore, it may conclude that when the alcohols are changed, the numeric values of δslngH of and δslngS remain unchanged, accordingly the δslngG value does not change. It would also imply that the interaction between the saturated hydrocarbon chain and the stationary phase is not affected by the alcohol moieties. Thus, the homomorphic factor is verified for fatty acid esters of different alcohols.Table 2
Comparison of thetR(cal) with the tR(exp) for fatty acids of different alkyl esters between temperatures 180 and 200°C, at 5°C interval.
180°C185°C190°C195°C200°CFAMEtR(cal)tR(exp)%ΔatR(cal)tR(exp)%ΔtR(cal)tR(exp)%ΔtR(cal)tR(exp)%ΔtR(cal)tR(exp)%Δ165.095.14−0.974.764.79-0.634.484.50−0.444.254.28−0.704.094.10−0.24175.815.85−0.685.345.36-0.374.954.96−0.204.634.66−0.644.404.41−0.23186.776.78−0.156.116.100.165.565.560.005.135.14−0.194.804.800.00198.068.010.627.137.070.856.376.350.315.785.760.355.325.310.19209.779.641.358.488.351.567.437.331.366.616.560.765.995.950.67FAEE165.185.21−0.584.804.84−0.834.504.51−0.224.274.28−0.234.064.07−0.25175.955.96−0.175.415.45−0.734.995.00−0.204.674.68−0.214.394.40−0.23186.976.970.006.236.25−0.325.645.640.005.195.190.004.814.810.00198.348.300.487.307.290.146.496.470.315.875.850.345.355.340.192010.1610.080.798.728.680.467.607.550.666.756.700.756.046.010.50FAPrE165.895.91−0.345.295.34−0.944.994.980.204.654.650.004.374.38−0.23176.896.90−0.146.076.12−0.825.625.610.185.165.150.194.784.79−0.21188.228.210.127.107.16−0.846.456.420.475.825.810.175.315.310.00199.999.970.208.468.52−0.707.547.490.676.686.650.455.995.980.172012.3712.300.5710.2610.33−0.688.978.890.907.797.740.656.866.840.29FABE166.826.84−0.296.176.150.335.615.590.365.145.140.004.774.770.00178.128.14−0.257.207.170.426.436.400.475.795.790.005.295.290.00189.869.88−0.208.578.530.477.507.460.546.636.620.155.955.96−0.171912.1712.21−0.3310.3710.310.588.908.850.567.727.710.136.816.810.002015.2715.32−0.3312.7612.680.6310.7410.680.569.149.120.227.917.92−0.13FAPeE168.118.17−0.737.137.16−0.426.376.38−0.165.805.780.355.265.28−0.38179.869.91−0.508.498.51−0.247.447.440.006.646.610.455.935.94−0.171812.2012.23−0.2510.2910.31−0.198.848.830.117.747.690.656.786.79−0.151915.3215.34−0.1312.6812.670.0810.6710.650.199.179.100.777.877.89−0.252019.4819.51−0.1515.8315.710.7613.0713.050.1511.0210.940.739.289.31−0.32FAHxE169.799.83−0.418.458.46−0.127.417.410.006.616.600.155.925.93−0.171712.1012.13−0.2510.2310.32−0.878.808.780.237.707.670.396.766.77−0.151815.1915.21−0.1312.6012.580.1610.6310.590.389.119.070.447.867.860.001919.3219.34−0.1015.7315.710.1313.0212.970.3910.9510.900.469.269.28−0.222024.8324.93−0.4019.8619.87−0.0516.1516.120.1913.3313.300.2311.0711.11−0.36FAHpE1611.9812.01−0.2510.1710.160.108.728.720.007.647.630.136.746.75−0.151715.0315.05−0.1312.5112.480.2410.5210.500.199.049.020.227.837.830.001819.1119.110.0015.6015.560.2612.8712.850.1610.8610.820.379.229.220.001924.5524.61−0.2419.6919.690.0015.9615.960.0013.2213.180.3011.0111.04−0.272031.8132.05−0.7525.1125.18−0.2820.0120.09−0.4016.2816.29−0.0613.3213.40−0.60FAOE1615.3015.270.2012.6312.67−0.3210.7110.680.289.149.15−0.117.987.980.001719.4619.380.4115.7715.79−0.1313.1313.070.4611.0010.990.099.429.400.211825.0324.920.4419.9319.95−0.1016.3016.210.5613.4013.380.1511.2711.240.271932.4632.430.0925.4325.54−0.4320.4520.390.2916.5216.53−0.0613.6513.630.152042.3842.60−0.5232.7133.03−0.9725.8925.94−0.1920.5820.69−0.5316.7216.75−0.18percenta different between tR(exp) and tR(cal).Table 3
Correlation oftR(cal) and tR(exp) of FAAEs. Numbers in parentheses are standard deviation.
FAAESlopeInterceptr2FAME0.970 (0.004)0.162 (0.021)0.997FAEE0.987 (0.002)0.086 (0.015)0.999FAPrE0.995 (0.002)0.034 (0.013)0.999FABE1.001 (0.003)0.025 (0.023)0.999FAPnE0.999 (0.002)0.004 (0.025)0.999FAHxE1.003 (0.002)−0.044 (0.021)0.999FAHpE1.008 (0.001)−0.112 (0.021)0.999FAOE1.007 (0.002)−0.121 (0.038)0.999


## 3.2. GC Separation of Octadecenoic Acid Alkyl Esters of Different Alcohols and Free Energy Contribution from the Double Bond

Figure2 is the aligned chromatograms of FAAEs (with different alcohols) of a mixture of coriander seed and olive oils, separated on a 90%-biscyanopropyl-10%-cyanopropylphenyl polysiloxane (Rtx-2330) capillary column at 180°C. The methyl and ethyl esters of petroselinic and oleic are coeluted. Partial separations of these two acid esters are observed when the alkyl groups have 3–6 carbon atoms. FAAEs of higher alcohols (FAHpE, FAOE, and FAEHE) are baseline resolved. Results agree well with the report of Isbell et al. [18]. In Figure 2, the octyl esters show approximately the same resolution as those of the 2-ethyl-1-hexyl esters in separations of 18:1∆6 and 18:1∆9. However, the 2-ethyl-1-hexyl esters are eluted faster than the octyl esters. The retention times of the 2-ethyl-1-hexyl esters are comparable to those of the heptyl esters. The bulky 2-ethyl-1-hexyl group was ascribed for lowering the interaction between the polar carboxyl and the polar stationary phase. Therefore, the interaction between the small polarity differences of the olefin and the polar stationary phase became apparent and caused the separation [18]. Although the discussion of Isbell et al. [18] was theoretically sound, it lacked the supported evidence. On the contrary, results in Figure 1 show that ΔslngGf values increase as the alcohol groups are larger, which contradicted to the explanation of Isbell et al. [18]. Therefore, a new free energy term is proposed, and it is expected that it would be able to find the cause of the separation between petroselinic and oleic esters.Figure 2
2 Alignment of gas chromatograms of different alkyl esters of coriander seed oil + olive oil at 180°C. Peaks identification: 1, 18:1Δ6cis; 2, 18:1Δ9cis; 3, 18:1Δ11cis.Martin [20] were the first to divide a molecule into different parts, and a free energy term was assigned to each of them as shown in (1). Subsequently, different free energy terms were assigned to describe interactions between column stationary phase and different functional groups of the molecule [32, 33]. Hence, the free energy concept of Kollie and Poole [32] and Golovnya [33] was extended, in this work, to investigate the interaction between the double bond and the column stationary phase. The new free energy is called free energy of transfer from solution to gas of the double bond (ΔslngGu). Equation (10) is obtained by inserting the ΔslngGu into(1)(10)Δsln⁡gG2o=Δsln⁡gGf+zδsln⁡gG1o+Δsln⁡gGu,
where the subscripts 1 and 2 stand for saturated and unsaturated fatty acids, respectively.Equation (10) can also be derived as follows: (11)ΔslngG1o=-RTln⁡K1,ΔslngG2o=-RTln⁡K2.
Equation (12) is the difference between (11).(12)Δsln⁡gGu=Δsln⁡gG2o-Δsln⁡gG1o=-(RTln⁡K2-RTln⁡K1).
Equation (10) is obtained by substituting (1) into (12).ΔΔslngGu(Δ9-Δ6) is the difference between ΔslngG2(Δ9)o of 18:1Δ9 and ΔslngG2(Δ6)o of 18:1Δ6 as shown in .(13)Δsln⁡gG2(Δ9)o-Δsln⁡gG2(Δ6)o=Δsln⁡gGu(Δ9)-Δsln⁡gGu(Δ6)=ΔΔsln⁡gGu(Δ9-Δ6).
The ΔΔslngG2(Δ9-Δ6)o will be used as a tool to investigate the interaction of the double bond with the stationary phase of the column. The ΔslngG2o of petroselinic and oleic (and vaccenic 18:1Δ11cis) acid esters at 180°C are summarized in Table 4. The C1–C3 esters are not well separated from each other, and they are not listed in the table. The ΔslngGu values of these three esters at 180°C are approximately −151, −133, and 128 cal·mol−1, respectively. Partial separations are observed for FABEs. Separations of FAAE are gradually improved as the carbon numbers of the alcohols are increased.Table 4
TheΔslngGu(cal·mol−1) of esters of C18:1Δ6, C18:1Δ9, and C18:1Δ11.
ΔslngGu(cal·mol−1)Fatty acidsFABEFAPnEFAHxEFAHpEFAOEFAEHE18:00.00.00.00.00.00.018:1∆6−102.4−82.0−78.7−68.8−61.4−36.718:1∆9−120.1−103.8−102.2−92.1−85.9−61.418:1∆11−145.4−134.3−131.7−122.1−113.1−90.5ΔΔslngGu (cal·mol−1)(18:1Δ9) – (18:1Δ6)−17.7−21.8−23.5−23.3−24.5−24.7(18:1Δ11) – (18:1∆9)−25.3−30.5−29.5−30.0−27.2−29.1According to Isbell et al. [18], the bulky alkyl group interfered the interaction of the carboxyl group to the column stationary phase. The interference did not extend to the hydrocarbon chain. Hence, the relative changes in ΔslngGo should be the same for both saturated and unsaturated FAAEs. However, the ΔslngGu values of petroselinic, oleic, and vaccenic esters (Table 4) become less negative as the alkyl sizes are increased, suggesting that the alkyl groups interfere the interaction between the hydrocarbon chain and the stationary phase, and the degree of interferences increases as the carbon numbers of the alcohols are increased.TheΔslngGu values of the butyl esters of 18:1∆6, ∆9, and ∆11 are −102.4, −120.1, and −145.4 cal·mol−1, respectively. The values become less negative as the alkyl groups are larger. 2-Ethyl-1-hexyl esters have the lowest ΔslngGu compared with other alkyl esters. Their ΔslngGu values for 18:1Δ6,Δ9, and Δ11 are −36.7, −61.4, and −90.5 cal·mol−1, respectively. Therefore, the interaction of the double bond with the column stationary phase increases when the double bond is far away from the carboxyl group, that is, interference from the bulky alkyl group decreases along the distant.The difference inΔslngGu of 18:1Δ9 and 18:1Δ6 (ΔΔslngGu(Δ9-Δ6)) of butyl, pentyl, hexyl, heptyl, octyl and 2-ethylhexyl esters is −17.7, −21.8, −23.5, −23.3, −24.5, and −24.7 cal·mol−1, respectively. The increases in ΔΔslngGu(Δ9-Δ6) as the alkyl groups increased suggest that the relative interactions of the double bonds of the two acid esters with the stationary phase are increased. Thus, it may conclude that ΔΔslngGu(Δ9-Δ6) is the driving force for the separation of the two isomers. However, the ΔΔslngGu(Δ9-Δ6) values level after C6, implying that the resolution of these two positional isomers may not be further increased by simply increasing the size of the alcohol.TheΔΔslngGu(Δ9-Δ6) of 2-ethyl-1-hexyl esters is −24.7 cal·mol−1. It is estimated that a column of about 65,000 required plate numbers (Nreq) would be able to baseline separate the two positional isomers, while the butyl esters, whose ΔΔslngGu(Δ9-Δ6) is −17.7 cal·mol−1, would require up to 180,000 plate numbers. The ΔslngGu of 18:1∆9 and ∆11 have similar trend as the 18:1∆6 and 18:1∆9 pair, and discussion is not necessary.Petroselinic acid has a double bond closer to the carboxyl group than oleic acid. The interference from the bulky alkyl group should be stronger than that to the oleic acid. Similar observation was reported by Kuningas et al. [34] that the separation of geometric isomers (alkenes) depended on the differences in free energy.TheΔΔslngGu(Δ9-Δ6) the adjacent pairs of octadecenoic esters would reflect on the ease of separation for each pair. Results in Table 4 show that the separation of 18:1∆9 and 18:1∆11 is much simpler than the separation of 18:1∆6 and 18:1∆9.


## 3.3. Separation of Octadecenoic Acid Octyl Esters

As discussed in Section3.2, the lowering in ΔslngGu was ascribed to the reduction in the interaction between the double bond in the FAAEs and the column stationary phase. 1-Octyl and 2-ethy-1-hexyl esters are two of the best derivatives for separation of petroselinic and oleic acids. However, esters of secondary octyl alcohols have not been reported (to our knowledge). Thus, they were investigated for their interferences to the interaction of the double bond with the stationary phase. The retention times, retention factors, ΔΔslngGu(Δ9-Δ6), and resolution (Rs) between secondary octyl petroselinate and oleate are summarized in Table 5. The ΔΔslngGu(Δ9-Δ6) values of secondary octyl esters of petroselinate and oleate range from −24.5 to −25.8 cal·mol−1. The resolutions of these two acid secondary octyl esters (1.15-1.26) are close to that of the 1-octyl ester (1.26). However, more symmetric or compact alcohol had the shorter retention time. The order of elution for the esters is 4-octyl, 3-octyl, 2-octyl, and 1-octyl, respectively.Table 5
Separations of petroselinic and oleic octyl esters on Rtx 2330 at 190°C.
ΔΔslngGu(Δ9-Δ6)OctanoltR1(min)atR2 (min)k1k2(cal·mol−1)Rs1-octanol17.2717.716.196.35−24.51.262-octanol12.6712.974.514.64−25.81.153-octanol12.0012.294.004.12−25.11.174-octanol11.4111.693.743.84−25.11.20thesubscriptsa; 1 and 2 represent petroselinate and oleate, respectively.


## 4. Conclusion

When the alcohol moieties of FAAE are changed, theδslngG does not change. It implies that the interaction between the saturated hydrocarbon chain and the stationary phase is not affected by the alcohol moieties. On the other hand, petroselinic and oleic have one cis-double bond in the hydrocarbon chain; its interaction with the column stationary phase would differ from that of the saturated hydrocarbon. Therefore, ΔslngGu is introduced and it would provide an insight into the interaction of the double with the column stationary phase. The bulky alkyl group attached to the carboxyl group affects the interaction between the double bond and the stationary phase. The steric effect decreases along the distance. In addition, for FAAEs having the same carbon numbers, the more compact is alcohol moiety, the shorter is the retention time, while the resolutions of the adjacent positional isomers are approximately the same. For petroselinic and oleic acids, the driving force for their separation is the difference in ΔslngGu of the two geometrical isomers.


## 5. Symbols and Abbreviation


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*Source: 252543-2010-12-12.xml*