Vaporization enthalpies and vapor pressures of the major components of opopanax oil, α-santalene, cisα-bisabolene, cis α-bergamotene

The vapor pressures and vaporization enthalpies of the major components of opopanax oil, a medicinal that has been in use since biblical times, are evaluated by correlation gas chromatography. Two sets of hydrocarbon standards are used, n-alkanes and a mixture of cyclic and polycyclic hydrocarbons. Two of the oil’s sesquiterpene components, evaluated in a previous study, were used both as standards and also as targets. Their use as targets was in an effort to confirm both their identity in the oil and the reproducibility of their properties. All correlations produce reproducible vaporization enthalpies and vapor pressures at ambient temperatures. At elevated temperatures, the use of the two different sets of standards resulted in some divergence in vapor pressure. Experiments are described aimed at attenuating this divergence. The results are compared to existing data.


Introduction
Opopanax essential oil, also known as Sweet Myrrh, is steam distilled from the resin of trees of the same genus as Myrrh, and their odors both share some similarities. Opopanax has been used for the treatment of wounds as an antiseptic since biblical times. Other properties of the opopanax essential oil include use as an expectorant and as an antispasmodic. Much of its use is in the practice of traditional medicine [1]. An additional use of opopanax essential oil has been as a fixative in the perfume industry [2]. The chemical composition of the essential oil varies, depending on the species. The genus comprises of more than 200 species, all native to Africa, Arabia, Madagascar, and India [1]. The volatile oils in the two species used in this study, Commiphora guidotti and Commiphora glabrescenes, are rich in five sesquiterpenes, α-santalene, cis α-bisabolene, cis α-bergamotene, trans-α-bergamotene, and β-bisabolene [3,4]. The structures of all the sesquiterpenes and cyclic standards involved in this study are provided in Fig. 1.
α-Santalene (1), 1, 7-dimethyl-7-(4-methylpent-3enyl)tricyclo[2.2.1.0 2,6 ]heptane, is the most abundant sesquiterpene present in opopanax oil. It is found in all spice and used as a flavoring ingredient [5]. It is an important intermediate in the synthesis of (Z)-(+)-α-santalol, a major constituent responsible for the sweet-woody and balsamic aroma of sandalwood oil used in perfumes [6]. The recent availability of santalenes from biomass sugars has triggered additional interest in them, since they exhibit a greater energy density when compared to JP-5 and F76 fuels. As a renewable energy source, this has been suggested as a means of reducing the carbon footprint produced by the military [7].
This study reports the vaporization enthalpies and vapor pressures of the sesquiterpenes reported above. The properties of the two sesquiterpenes reported previously and also present in opopanax oil, trans-α-bergamotene (2) and β-bisabolene (5), were also included in correlations as both targets and as internal standards [10,11]. The main purpose for their inclusion as targets was as means of confirming their identity in the opopanax oil and for evaluating the reproducibility of previous work. Two sets of standards were used, a series of compounds that included in addition to the two mentioned above, 1,3-dimethyladamantane, 1,4-di-t-butylbenzene, β-elemene and diamantane, and the following series of n-alkanes: n-C 13 to n-C 16 . The former of these two sets of compounds are described in this article as oligocyclic compounds. trans-α-bergamotene (2) and β-bisabolene (5) are generally referenced separately, referred to as the sesquiterpenes. The Fig. 1 Structure of the targets and cyclic standards discussed in this article. From left to right: αsantalene (1), transα-bergamotene (2), cis α-bergamotene (3), cis α-bisabolene (4), β-bisabolene (5). Standards: β-elemene (6), 1,3-dimethyladamantane (7), diamantane (8), 1,4-di-tbutylbenzene (9). Structures of the n-alkanes used as standards are not shown vapor pressures of both of these sesquiterpenes were evaluated previously using similar oligocyclic standards. Their vapor pressures were also included in experiments with n-alkanes to determine the degree to which their vapor pressures correlated with those of the n-alkanes. This effort was directed toward identifying a protocol that could possibly attenuate some of the curvature observed with n-alkane standards in plots of ln(p/p o ) versus K/T and is discussed below.

Compounds: identity and purity controls
The origin of the standards and their mass fractions are reported in Table 1. The first portion of the table describes the properties of the standards available in relatively pure form.
trans-α-bergamotene was the major component in bergamotene oil studied previously; its mass fraction in the oil was 0.56 [10]. Its retention time was used to confirm the identity of same in the opopanax oil; similarly for βbisabolene. The composition of the major components in the two opopanax oils follows. The major components in the two different species were each identified by their composition as reported by their suppliers [3,4], and by their retention index. A comparison of the compositions of the two opopanax oils by gas chromatography to those reported by the suppliers is provided in the last column of Table 1. Retention index results used to confirm their identity are provided in Table S5 (Supporting information). Two different opopanax oils were examined since they differed regarding the presence of β-bisabolene as reported by their suppliers. The presence of β-bisabolene in both opopanax oils was identified and confirmed by co-injection with a sample from a different supplier  [11]; trans-α-bergamotene was identified similarly. Gas chromatograms of the two opopanax oils used in this study are provided as Figures S1 and S2 (Supplementary Information (SI)). As mentioned above, once trans-α-bergamotene and β-bisabolene were identified in the two oils, the two present naturally in the oil were used to confirm that their properties reproduced previous work [10,11] and to evaluate the effects of combining their vapor pressures with those of the n-alkanes generated from the simultaneous use of a mixture of both. The stereochemistry at the chiral carbon of β-bisabolene in opopanax oil in Fig. 1 is not shown. We were did not locate any literature information as to whether it has been assigned in opopanax oil; we presume the structure represents a single enantiomer.

Methods
The gas chromatographic experiments were conducted isothermally on an HP 5980 gas chromatograph using a 15 m SPB-5 capillary column with He as the carrier gas at a split ratio of approximately 80/1 and a head pressure of approximately 150 kPa. Duplicate experiments were performed under similar conditions of pressure and temperature. All retention times and correlations pertaining to vaporization enthalpies both with and without the use of trans-α-bergamotene and β-bisabolene as standards and details regarding their associated uncertainties are provided in the SI in Tables S1A-S4A, S1B-S4B, and S1C-S4C, respectively.

Vaporization enthalpy
A basic premise in correlation gas chromatography is that the amount of time a substance spends on the column, its residence time, t r , is related inversely to the substance's vapor pressure off the column. Residence time is evaluated by subtracting the retention time of a non-retained reference included in the chromatography from the retention time of each analyte. In these experiments, the non-retained reference, methylene chloride, was also the solvent. A plot of ln(t o /t r ) versus K/T over a 30 K temperature range at approximately 5 K intervals was linear, and the product of the absolute value of the slope of the line and the gas constant, R = 8.314 J·mol -1 · K −1 , provided the enthalpy of transfer of the analyte from the stationary phase of the column to the gas phase, Δ g trn H m T m ð Þ; t o refers to the reference time, 60 s. Thermodynamically, this enthalpy should be equal to the sum of two terms, the vaporization enthalpy and an enthalpy of interaction of the analyte with the column, Eq. 1 [12].

Vapor pressure
The same premise regarding the relationship between 1/t r and the vapor pressure of an analyte off the column suggests that 1/t r may also relate to p, the vapor pressure of the pure analyte, provided the standards and targets share a similar compositional and structural relationship. Indeed, a linear relationship has been observed between ln(p/p o ) and ln(t o /t r ), where p o and t o are a reference pressure and reference residence time. The linear relationship observed at T = 298.15 K has often been found to extend over a broad range of temperatures. In this work p o refers to 101,325 Pa. The retention times in the Supporting Information are reported as t/t o where t o = 60 s. Vapor pressures evaluated in this work as a function of temperature are reported either directly from the correlation at each temperature or are evaluated from fits of the correlated data to a second order polynomial, Eq. (2).
Uncertainties All uncertainties reported in this work refer to one standard deviation unless expressed otherwise [13]. Both linear and non-linear least squares were performed using Excel and Sigma Plot 14. All regression coefficients exceeded r 2 > 0.99. Uncertainties evaluated from logarithmic terms are reported as an average. Evaluation of uncertainties in boiling temperature at p o = 101,325 Pa is described below. Uncertainties evaluated from correlations, generally reflect how well the property of the standards correlate. Actual uncertainties in the target(s) may exceed the value(s) tabulated.

Estimations of vaporization enthalpy
A simple but usually reliable method of estimating vaporization enthalpies is provided by Eq. (3) [14]. Results are generally within 5%. For hydrocarbons, the equation is depended on two variables, the total number of carbon atoms, n C , and the number of quaternary sp 3 hybridized carbon atoms, n Q .
Vaporization enthalpies and vapor pressures of the standards The vaporization enthalpies and vapor pressure parameters of the standards used in this work are summarized in Table 2. Vaporization enthalpies of the n-alkanes and vapor pressures as a function of temperature used in this study are taken from the critically evaluated values reported by Ruzicka and Majer [15]. The vapor pressures reported by these workers are in the form of the Cox equation, Eq. (4). Constants for this equation are also included in Table 2 next to their corresponding vaporization enthalpies. The vaporization enthalpies for β-elemene, diamantane, trans-α-bergamotene, and β-bisabolene are from previous work from this laboratory [11,16]. The three sesquiterpenes were evaluated using oligocyclic compounds. Vapor pressures for both are reported in the form of Eq.
(2) also found next to their vaporization enthalpy. Finally, vaporization enthalpies and vapor pressure constants for 1,3-dimethyladamantane and 1,4-di-tbutylbenzene are from the work of Steele et al [17] and Chirico and Steel [18], respectively. Their properties are included at the bottom of the Wagner Eq.: where T r = T/T c

Vaporization enthalpies
Enthalpies of transfer, Δ g trn H m T m ð Þ; were evaluated from plots of ln(t o /t r ) verses K/T as described above. Vaporization enthalpies of the standards were then correlated against their enthalpies of transfer. Table 3 A and C summarize the results of one of two duplicate runs using both trans-α-bergamotene (2) and β-bisabolene (5) as standards. In Table 3A, the correlation involved the use of structurally similar standards; standards in Table 3C include use of the n-alkanes. In Tables 3 B and D, the two sesquiterpenes are used as targets. The correlation coefficients of Eqs. (6) through (9) describe the quality of the correlations. Results from these correlations and  (9) a All Uncertainties represent one standard deviation unless noted otherwise b Estimated combined expanded uncertainty (confidence level: 0.95) [17,18] c Uncertainty represents probable error [15] their duplicates along with the uncertainties associated with the slopes and intercepts of all runs are reported in the Supporting Information. Table 4 summarizes the vaporization enthalpies of all four runs using trans-αbergamotene and β-bisabolene both as standards and targets; results are also compared to estimated or literature values and are discussed below.

Vapor pressures: oligocyclic standards
Vapor pressures of the targets were evaluated from plots of ln(p/p o ) verses ln(t o /t r ) of the standards. Duplicate runs of each set of correlations were obtained under similar conditions of temperature and head pressure. Values of t o /t r evaluated from the slopes and intercepts of runs 1 and 2 at each temperature evaluated were averaged; similarly for runs 3 and 4. trans-α-Bergamotene (2) and β-bisabolene (5) were treated both as standards and as targets in separate sets of correlations. All correlations using the group of oligocyclic standards with or without the two sesquiterpenes as standards were conducted at T = (298.15, 310) and at 10 K intervals up to 450 K, Table 5 A and B. Equations (10) and (11)  Vapor Pressures: n-alkane standards Table 6 summarizes the results at T = 298.15 K of plots of ln(p/p o ) versus ln(t o /t r ) using n-alkanes as standards that included both trans-α-bergamotene (2) and cis α-bisabolene (5) as standards (Table 6A) and as targets (Table 6B). The vapor pressures used in correlations that included both of these sesquiterpenes as standards were those previously evaluated for the two sesquiterpenes using a series of oligocyclic compounds. Correlations were conducted at temperatures from T = (298.15, 310) and at 10 K intervals up to 410 K. Correlation coefficients (r 2 ) varied from 0.999 at T = 298.15 to 0.9931 at T = 410 K. Above 410 K, correlation coefficients rapidly dropped below r 2 = 0.99. As a result, these correlations were terminated at T = 410 K. Correlations using n-alkanes that included (2) and (5) as targets were extended to 450 K without any significant changes in the correlation coefficients; all r 2 values exceeded 0.999. Equations 12 and 13 in Table 6 describe the quality of the results at T = 298.15 K. Both sets of vapor pressures evaluated were fit independently to Eq. (2). Constants for Eq.
(2) generated using n-alkanes and the two sesquiterpenes as targets and as standards are reported in  Table 7 are reported as the difference in the two boiling temperatures evaluated. These uncertainties reflect the quality of the correlation; uncertainties in T B may be larger.

Discussion
As noted in the introduction, two of the components in opopanax oil, trans-α-bergamotene and β-bisabolene, were studied previously. trans-α-Bergamotene was studied in a complex mixture; the mass fraction of β-bisabolene was 0.91. An objective of this work was to determine the reproducibility of the various physical properties evaluated for these two components identified in opopanax oil and also present in a complex mixture.

Vaporization enthalpies
As indicated in Table 4, the vaporization enthalpies at T = 2 9 8 . Consistent with previous results on other similar sesquiterpenes [11], α-santalene, a tricyclic sesquiterpene with two quaternary centers, has the smallest vaporization enthalpy followed by the two bicyclic α-bergamotenes with one quaternary center and then the two bisabolenes. Estimated values using Eq. (3) also reproduce the vaporization enthalpy values within the uncertainties cited for all compounds studied.

Vapor pressures
As has been observed previously, the use of either n-alkanes or oligocyclic hydrocarbons as standards in correlations of ln(p/p o ) versus ln(t o /t r ) produces similar vapor pressures for the targets at and near room temperature. All vapor pressures in Table 8 evaluated at T = 298.15 K, with and without the use of trans-α-bergamotene and β-bisabolene as standards, agree within their stated uncertainties. For the mixture containing nalkanes and both sesquiterpenes, as the temperature is raised, the vapor pressures evaluated for the two sesquiterpenes (derived from oligocyclic compound) begin to diverge from those of the n-alkane standards, resulting in a rapid decrease in the correlation coefficient. For this specific mixture of n-alkanes and sesquiterpenes, the decrease occurs above T = 410 K. This divergence results from the slightly greater curvature exhibited by the n-alkanes in plots of ln(p/p o ) versus K/T. Consequently, somewhat larger boiling temperatures are predicted at p o = 101,325 Pa when using n-alkanes as compared to using only oligocyclic compounds as standards. As indicated in the last column of Table 7 (B and C), roughly a 20 K difference is observed in boiling temperatures evaluated at p o = 101,325 Pa when vapor pressures are extrapolated over a temperature range of about 100 K using these two different sets of standards. The n-alkanes and oligocyclic compounds are each representative of a class of compounds that appear at opposite ends of the spectrum with regard to intramolecular flexibility. The n-alkanes have structures with the potential for great internal flexibility while the oligocyclic compounds are substances that are relatively rigid in comparison. The bergamotenes and bisabolenes are likely examples of substances with some intermediate degree of flexibility. As mentioned above, in an effort to better model somewhat more flexible sesquiterpene systems, vapor pressures derived from the set of constants of Eq. (2) for trans-α-bergamotene and β-bisabolene evaluated previously using oligocyclic standards were combined together with vapor pressures for the n-alkanes in correlations of ln(p/p o ) versus ln(t o /t r ) as a function of temperature. The experiments were designed to evaluate whether at the lower temperatures, where both sets of vapor pressures correlate reasonably well, inclusion of the two sesquiterpenes would result in a new set of hybrid constants for both that would cause some attenuation of the curvature observed with the nalkanes and simultaneously perhaps, somewhat enhance the curvature observed for the two sesquiterpenes. The last column of Table 7 lists the predicted boiling temperatures of each compound according to the standards used. A comparison of Table 7 C, which only used n-alkanes as standards, to D, which used a combination of standards, resulted in a decrease of roughly 10 K in the predicted boiling temperatures of the targets. This is about half the difference observed previously ( Table 7 B and C). A comparison of the boiling temperatures reported in Table 7 A and D, show roughly a similar increase in boiling temperature evaluated for the targets. Changes reported in Table 7D come at the expense of limiting the temperature range of the correlations, in this case from T = Table 6 Correlation of ln(p/p o ) versus ln(t o /t a ) avg at T = 298.15 K of all the major sesquiterpenes of opopanax oil for combined runs 3 and 4 using nalkanes with and without the use trans-α-bergamotene (2) and β-bisabolene (5) Tables (S6) and (S7) (Supporting Information) compare the vapor pressures evaluated in this work by correlation for the two bisabolenes and the two bergamotenes, respectively, using three different sets of standards, oligocyclics combined with the two sesquiterpenes, n-alkanes including the two sesquiterpenes and just n-alkanes. A fourth comparison, using only oligocyclic compounds resulted in virtually identical results to those including the two sesquiterpenes and are not tabulated. Vapor pressures rounded to two significant figures reported from T = 298.15 K to either T = (410 or 450) K were evaluated by correlation and those at higher temperatures are extrapolations of Eq. 2 evaluated by fitting each set of data evaluated from T = (298.15 to either (410 or 450)) K as described above. The vapor pressures of trans-α-bergamotene and β-bisabolene were both not used in correlations involving their own evaluation with either set of standards. A gradual decrease in the evaluated vapor pressures is generally observed in going from oligocyclic compounds (with or without the two sesquiterpenes) to a combination of n-alkanes and the two sesquiterpenes to the sole use of n-alkanes as standards. In the case of the bisabolenes (Table S6), the absolute average deviation between vapor pressures calculated using only oligocyclic standards (OC) and the mix of n-alkanes and the two sesquiterpenes as standards (A & αΒ) was approximately 13 %. This decreased to approximately 11% for the bergamotenes (Table S7), primarily due to their lower boiling temperature. The major differences in vapor pressure between the uses of the different sets of constants of Eq. (2) occurred at elevated temperatures. Availability of some reliable The vapor pressures of the n-alkanes evaluated in these correlations were also affected by inclusion of the vapor pressures of the two sesquiterpenes as standards, but only minimally. Fitting the calculated vapor pressures of the n-alkanes that resulted from inclusion of the two sesquiterpenes as standards to Eq. 2 and extrapolating the resulting equations from T = 420 K to temperatures where ln(p/p o ) = 0 resulted in temperature decreases of ΔT = 5.8, 3.0, 4.5, and 6.4 K for ntridecane to n-hexadecane, respectively (all normal boiling temperatures > 500 K). The vaporization enthalpies at T = 298.15 K calculated using these hybrid alkane constants and the predicted boiling temperatures at p o =101,325 Pa are provided in Table S8. As indicated in the table, the vaporization enthalpies calculated at T = 298.15 K using Eq. (2) and the hybrid constants still remain within their original uncertainties. The vaporization enthalpies of two smaller nalkanes decreased in value while the two larger n-alkanes increased slightly.
As noted in the introduction, a goal of this work was to confirm reproducibility of properties evaluated previously. The vaporization enthalpies of trans-α-bergamotene and to a lesser extent β-bisabolene were both evaluated from complex mixtures, similarly in this study. While vaporization enthalpies are reproduced, it seem prudent to also examine the reproducibility of the vapor pressures evaluated. Table S9 compares the vapor pressures evaluated for βbisabolene and trans-α-bergamotene evaluated previously to results from this work using a similar set of oligocyclic compounds. For β-bisabolene and trans-α-bergamotene, average absolute fractional deviations of 0.026 and 0.024 were obtained prior to rounding the results to two significant figures, confirming that results obtained from complex mixtures, provided the compounds are properly identified and reasonably separated from other components, are reproducible.
Despite the availability of some experimental vapor pressure data for the compounds investigated, most data are in the region where vapor pressure differences between the predictions by the different standards studied are small and the scatter in the experimental data is sufficient to make unequivocal decisions difficult. Recommendations are based mainly on reproduction of the experimental boiling temperatures at various pressures; structure was also an important consideration, particularly with geometric isomers.
A limited amount of vapor pressure data from the literature was located for α-santalene. Results from this work and the data we have been successful in locating are summarized in Fig. 2. The line in Fig. 2 represents ln(p/p o ) data evaluated using oligocyclic standards when both trans-α-bergamotene and β-bisabolene are included as standards and the circles are results when the two sesquiterpenes were evaluated as targets. The solid squares represent literature values. The square at T =  Table S10. This table compares vapor pressures evaluated using standards, nalkanes, n-alkanes with both sesquiterpenes, and oligocyclic compounds without and with both sesquiterpenes; literature values are listed in the final column. As indicated in Table S10, vapor pressures evaluated by boiling temperatures at reduced pressures are generally fit by all sets of standards. The selection of the preferred standards for α-santalene is based on two criteria, a single vapor pressure, the experimental boiling temperature of 521.2 K at p o = 101,325 Pa (the other is an estimate), and the structural similarities of αsantalene to the oligocyclic standards. The following progression in estimated boiling temperatures is generally observed: n-alkanes > n-alkanes with both sesquiterpenes > oligocyclic compounds ≈ oligocyclic compounds with both sesquiterpenes. The constants of Eq. (2) generated using oligocyclic standards that include both sesquiterpenes have been selected as providing best vapor pressure model. The properties recommended for α-santalene are summarized in Table 9. Tables S11 compares the vapor pressures evaluated in this work to the limited data available for trans-α-and cis α-bergamotene. For both bergamotenes, the data evaluated using the combined mixture of n-alkanes and the two sesquiterpenes appear to provide the best overall agreement. The vapor pressure used to differentiate between the different sets of standards used is the boiling temperature at p o = 101,325 Pa. For trans-α-bergamotene, the boiling temperature of T B = 533.2 K appears to be experimental and compares to a calculated value of T B = (535.3±12.2) K. This recommendation for trans-α-bergamotene differs from the previous one which was based on the sole use of oligocyclic compounds [10]. Selection of constants for cis α-bergamotene is based on an estimated T B and the structural relationship to its trans-isomer. Properties selected for both bergamotenes are also summarized in Table 9.
For β-bisabolene (5) and similarly for cis α-bisabolene (4), assignment of which constants to recommend is more problematic. Previously, the constants derived using oligocyclic standards were selected for (5) based on an overall fit to literature data. In the present work, the combination of the nalkanes with the two sesquiterpenes reproduce boiling temperatures at reduced pressures nearly as well as the oligocyclic compounds and do slightly better at predicting the boiling temperature at p o = 101,325 Pa of β-bisabolene as indicated in Table S12. While there may be an inclination to recommend the same mixture of n-alkanes and sesquiterpenes for cis α-bisabolene (4) based on functional group similarities, in this case, the n-alkanes may provide slightly better overall predictions, admittedly, on the basis of very limited data (Table S12).

Summary
The vapor pressures and vaporization enthalpies of three of the major sesquiterpenes present in opopanax oil were evaluated by correlation gas chromatography using several different sets of standards. Both vaporization enthalpy and vapor pressures result at T = 298.15 K obtained for trans-α-bergamotene and β-bisabolene are consistent with their assignment in opopanax oil and with previous work [10,11]. Vaporization enthalpies at T = 298.15 K evaluated for the target substances using the different sets of standards are all well within their stated uncertainties. Values from this and previous studies are provided in Table 9. The vaporization enthalpies for cis α-bergamotene, α-santalene, and cis α-bisabolene are an average of all eight entries from Table 4. The vaporization enthalpies reported for both trans-α-bergamotene and β-bisabolene are an average of the four entries from this work where they were used as targets and the four entries reported in references [10,11], respectively.
The oligocyclic standards appear to provide the best agreement with available literature vapor pressures for α-santalene. Comparisons are provided in Table S10 and summarized in Table 9. For the two bergamotene isomers, the combination of n-alkanes and the two sesquiterpenes as standards seem to provide the best fit as summarized in Table S11, albeit on very limited data. As noted above, assignment of which constants to recommend for β-bisabolene (5) and cis α-bisabolene (4) is more problematic. Constants generated using n-alkanes are recommended for cis α-bisabolene and the the n-alkanes combined with the two sesquiterpenes are recommended for βbisabolene.
The set of hybrid constants for the n-alkanes generated in this study may also prove useful for evaluating vapor pressures of other sesquiterpenes whose curvature in plots of ln(p/ p o ) versus ln(t o /t r ) at elevated temperatures is less than that of the n-alkanes, but more than the oligocyclic standards currently used. These hybrid constants are provided in the Supporting Information, Table S8. Finally, as noted previously, the availability of a reliable experimental vapor pressure at elevated temperatures would be extremely useful for fine-tuning the results obtained by correlation at elevated temperatures when appropriate standards are not available. Funding This research was funded by the principal author's consulting fees.
Availability of data and material Supporting information on-line.
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