Vapor pressure measurements on linalool using a rapid and inexpensive method suitable for cannabis-associated terpenes

Abstract

Vapor pressure (p^sat) data are needed to assess the potential use of terpenes as breath markers of recent cannabis use. Herein, a recently introduced gas-saturation method for p^sat measurements, known as dynamic vapor microextraction (DVME), was used to measure p^sat for the terpene (±)-3,7-dimethylocta-1,6-dien-3-ol, commonly known as linalool. The DVME apparatus utilizes inexpensive and commercially available components, a low internal volume, and helium carrier gas to minimize nonideal mixture behavior. In the temperature range from 314 K to 354 K, DVME-based measurements of the p^sat of linalool ranged from 81 Pa to 1250 Pa. With a measurement period of 30 min, the combined standard uncertainty of these measurements ranged from 0.0358·p^sat to 0.0584·p^sat, depending on temperature. The DVME-based measurements agree with a Wagner correlation of available literature data. We demonstrate that DVME produces accurate results for values of p^sat that are 200 times higher than in the DVME validation study with n-eicosane (C₂₀H₄₂). The oxidative stability of linalool was improved by the addition of 0.2 mass % of the antioxidant tert-butylhydroquinone.

Graphical Abstract

1. Introduction

Dynamic vapor microextraction (DVME) was recently introduced¹ as a new type of gas-saturation method^2–10 for the measurement of saturated vapor pressure (p^sat) near 1 Pa. The DVME method was designed to (1) use only commercially available components, (2) minimize operating costs, and (3) achieve state-of-the-art measurement uncertainty by leveraging a careful assessment of the sources of uncertainty. DVME was validated previously with p^sat measurements on the linear alkane n-eicosane (C₂₀H₄₂) from 344 K to 374 K, where the p^sat ranged from 0.45 Pa to 5.8 Pa.¹ Eicosane is a useful vapor pressure standard because it is stable, non-hygroscopic, can be purchased in high purity, and reference correlations for the p^sat of n-eicosane exist in the literature.^{1, 11–13}

The goal of the current study was to use DVME to collect p^sat data for a cannabis-associated monoterpene. We believe that such p^sat data are a prerequisite for the potential use of cannabis-associated terpenes as breath markers of recent cannabis use. Currently, breathalyzer development strategies typically involve quantitative measurement of Δ⁹-tetrahydrocannbinol (THC), the main psychoactive cannabinoid in cannabis sativa. However, THC’s extremely low volatility² requires concentrating breath aerosols from multiple breaths into filter devices for offline analysis with specialized instrumentation such as liquid chromatography with tandem mass spectrometry.^14–19 While detecting THC in breath may provide insight into recent cannabis use, it is likely that the detection of multiple cannabis-associated compounds in breath would provide a more definitive identifier of impairment.

Many cannabis-associated terpenes do not have published p^sat data near body temperature because there are no commercial devices that measure p^sat in this pressure range. Terpenes are also less stable^{2, 4} than n-eicosane, which creates an additional barrier to good p^sat measurements. Difficulties notwithstanding, p^sat data for these compounds are useful because they define the upper limits of concentration in the vapor phase of breath. The compound chosen for this work, (±)-3,7-dimethylocta-1,6-dien-3-ol (racemic mixture), commonly known as linalool, is an unsaturated monoterpene alcohol that is present in cannabis sativa^{20, 21} and hemp²². Reliable p^sat data already exist for linalool,²³ which is an advantage in this study because DVME has not been proven reliable for substances more challenging than simple alkanes. Unlike n-eicosane, linalool is prone to oxidation²⁴ and is somewhat hygroscopic (see below).

In addition to cannabis breathalyzer development, p^sat measurements of linalool and other compounds in this p^sat range are of interest because indoor air exposure can be estimated from such data.^25–27 There is also a more general need for a robust technique to provide low-uncertainty p^sat data for compounds like terpenes^{24, 28} and cannabinoids^{2, 29}, which have oxidatively susceptible moieties such as hydroxyl groups and C=C double bonds.^{4, 30}

All gas-saturation methods employ an inert carrier gas that flows through a “saturator” where the carrier gas becomes saturated with analyte vapor before flowing through a “trap” where the analyte is condensed and removed from the carrier gas stream. Helium is the carrier gas used for DVME because it minimizes measurement uncertainty due to nonideal mixture behavior and because of its low solubility in the liquid phase.^{5, 11, 31} One of the unique features of DVME is that the total internal volume of the carrier gas flow path is only about 4 mL.¹ The small internal volume was achieved by making the saturator from a 2 mL gas chromatography (GC) autosampler vial filled with 1 mm glass beads coated in the analyte (with a second, empty GC vial to prevent upstream contamination by the analyte¹) and making the helium transfer lines and capillary vapor trap from fused silica capillary tubing with an inner diameter (ID) of 530 μm. A key advantage of the small internal volume of the DVME apparatus is that less total carrier gas flow is required to achieve a given relative uncertainty in the total flow; thus, short measurement periods can still provide low-uncertainty p^sat data.¹

2. Experimental Methods

2.1. Chemicals.

Table 1 shows purities of the HPLC grade acetone, tert-butylhydroquinone (TBHQ), research grade 6 helium, n-tetradecane (C14, olefin-free), analytical grade linalool (racemic mixture, lot BCCB5318, Millipore Sigma), purchased from commercial sources and used as received (except linalool).

Table 1.

Grade and supplier-estimated purity for each chemical. The GC-FID purity for C14 and linalool was determined on each day of p^sat measurements, so the range of results is given (peak-area basis; assumed to correspond to mole % purity for p^sat calculations).

Chemical (CAS #)	Grade/Info	Supplier’s Purity	GC-FID Purity
Linalool (78-70-6)	Analytical Standard	99.6 %	99.6 – 99.7 %
Acetone (67-64-1)	HPLC grade	99 %	n/a
TBHQ (1948-33-0)	n/a	97 %	n/a
C14 (629-59-4)	Analytical Standard; Olefin-free	≥99.0 %	99.1 – 99.3 %
Helium (7440-59-7)	Grade 6	99.9999 %	n/a

Because GC-FID is insensitive to water, we also analyzed the linalool by coulometric Karl Fischer titration, which showed a water impurity of 4 mol % in the as-received material. This water impurity was removed from the linalool with a pretreatment step before p^sat measurements (see Section 2.4.).

2.2. DVME apparatus.

The DVME apparatus is shown in Figure 1. The carrier gas flows from a pressurized helium cylinder through the mass flow controller (MFC, used to set the flow rate), an adsorbent tube filled with the porous polymer poly-2,6-diphenyl-1,4-phenylene oxide, a transfer vial (to prevent upstream contamination), a transfer capillary, the saturator vial (where the carrier gas becomes saturated with linalool vapor), a capillary vapor trap (where the linalool vapor condenses), and finally through the mass flow meter (MFM, used to measure total flow). Saturators were made from 2 mL GC autosampler vials containing 1 mm borosilicate glass beads coated with linalool. The transfer capillary was cut from a spool of deactivated fused silica tubing (530 μm ID). Capillary vapor traps were cut from a spool of Al₂O₃-coated PLOT GC column (530 μm ID, film thickness 0.25 μm, 1.5 m in length). Most of the capillary trap was wound in a circle and secured on the thermoelectric cooling plate with aluminum tape and foam insulation. A repurposed GC oven controlled the saturator temperature and a 100 Ω platinum resistance thermometer (PRT) measured the saturator temperature. A barometer was used to determine the ambient pressure and the overpressure in the saturator vial.

Figure 1.

The DVME apparatus used to measure the vapor pressures of linalool.

2.3. Preparation and analysis of samples for gas chromatography with flame ionization detection (GC-FID).

Samples for GC-FID analysis were prepared by mass; volumes are given only for the reader’s convenience. The balance had a repeatability of 0.02 mg and an uncertainty of 0.1 mg. The GC-FID method for sample analysis employed a HP-5ms Ultra Inert GC column (17 m, 320 μm ID, film thickness 0.25 μm); an injection volume of 1 μL with a 20:1 split; an inlet temperature of 573 K at 34.5 kPa with a split flow of 28.0 mL/min; an initial oven temperature of 373 K with a ramp of 15 K/min to 463 K (total run time of 6 min); and FID settings of 523 K and 69 kPa.

2.4. Linalool saturator vial preparation.

A 1 mL ampule of linalool was opened, and 0.2 mass % of TBHQ was added to the full volume of linalool. The TBHQ was added as an antioxidant and is discussed further in Section 3.3.⁴ This mixture was stored in a −20 °C freezer in an amber GC vial and used within a week of preparation. The saturator was prepared by filling a 2 mL autosampler vial with 1.25 – 1.5 mL of glass beads (1 mm diameter) and then adding 0.10 g – 0.15 g of the linalool + TBHQ mixture with a glass pipette. The vial was capped, and the beads were shaken to ensure an even coating of linalool. The cap was then removed and replaced with a clean cap; this was done to prevent physical transfer of linalool from the septum cap to the capillary vapor trap.¹ A fresh linalool saturator was prepared for each day of measurements. To remove the water impurity in the linalool, the saturator was pretreated by flowing 700 scc of warm (354 K) helium through it at 10 sccm before making p^sat measurements (see Supporting Information, Section 1 and Figure S1).

2.5. Vapor pressure measurements.

The working equations for DVME are shown in eqs 1–4:^{1, 32}

$$p^{\text{sat}}=p_{\text{saturator}}\cdot y_2/x_2,$$ (eq 1)

$$p_{\text{saturator}}=p_{\text{ambient}}+p_{\text{overpressure}},$$ (eq 2)

$$y_2=\left(m_2/{\text{M}}_2\right)/\left(\left(m_1/{\text{M}}_1\right)+\left(m_2/{\text{M}}_2\right)\right),$$ (eq 3)

$$x_2=1-x_1-x_{\text{impurities}}.$$ (eq 4)

The p^sat of linalool was calculated from the pressure in the saturator vial (p_saturator), the mole fraction of linalool in the saturated vapor phase (y₂), and the mole fraction of linalool in the liquid phase in the saturator (x₂), (eq 1). The value of p_saturator was not determined directly but was instead calculated as the sum of the ambient pressure (p_ambient) and the overpressure (p_overpressure) (eq 2). The determination of is p_overpressure described in section 2.6. For the calculation of y₂ (eq 3), the molar masses of helium (M₁ = 4.002602 g/mol) and linalool (M₂ = 154.2493 g/mol) were taken from the NIST Chemistry WebBook.³³ The total mass of helium gas (m₁) for each experiment was determined from the MFM, where 1.0 standard cubic centimeter (scc) is the mass of 1.0 cm³ of helium at 298.15 K and 1.0 atm (i.e., 1.0 scc of helium is 0.16353 mg of helium³⁴). The mass of condensed linalool in the capillary vapor trap (m₂) was determined by GC-FID using an internal standard of n-tetradecane (C14).³⁵ For the calculation of the mole fraction purity of linalool, x₂ (eq 4), the helium solubility in linalool (x₁) was estimated to be 0.00017, which is actually the helium solubility in 1-decanol³¹ at 314.49 K and 1.0 atm (used instead due to the lack of helium solubility data in linalool). The value for 1-decanol was chosen because, like linalool, it is a ten-carbon alcohol. Excluding water and helium, the mole fraction of impurities in linalool, x_impurities, was estimated from the GC-FID purity analysis of linalool plus the 0.2 mass % of TBHQ (~0.002 mol fraction) added as an antioxidant⁴.

Each p^sat measurement began with a 10 min thermal equilibration period, during which the helium flow rate was 0.20 standard cubic centimeters per minute (sccm).¹ Then the flow rate was increased to 6.00 sccm for (20 ± 1) min, for a total helium flow of approximately 120 scc (i.e., ~20 mg of helium). Control experiments showed no influence of flow rate on the p^sat measurements between 2.00 sccm and 10.00 sccm. The temperature was recorded at the midpoint of the experiment (after 60 scc of total flow). At the end of the flow period, the helium flow was stopped, the total flow at the MFM was recorded, and the capillary vapor trap was immediately removed from the DVME apparatus.

The condensed linalool in the capillary vapor trap was eluted immediately after it was removed from the DVME. This was done by using helium pressure to force 1.3 mL of acetone through the trap and into a GC vial containing 0.2 mL of C14 internal standard solution. The internal standard solution was created by adding 30 μL of C14 to 3.5 mL of acetone (approximately 8,500 ppm by mass or 4.2×10⁻⁸ mol/kg). A second elution was done with 1.5 mL of acetone into an empty autosampler vial. Both eluent fractions were analyzed by GC-FID. The concentration of linalool in the second fraction never exceeded 0.1 % of the concentration in the first fraction, which demonstrates complete linalool recovery. The capillary vapor trap was rinsed with 1 mL of acetone and left to dry under flowing helium for at least 5 minutes before being used again. Two capillary vapor traps were made for each day of measurements. Each trap was used for two or three p^sat measurements and then discarded. The relative sensitivity of GC-FID to linalool and C14 (mass-to-area ratios) was used to determine the mass of linalool eluted from the capillary vapor trap. GC-FID showed a linear response across all sample concentrations³⁵ (see SI, Section 2, Figure S2, Table S1).

2.6. Determination of overpressure in the saturator vial.

A separate experiment was conducted to determine the overpressure (p_overpressure, i.e., pressure build-up) in the saturator vial due to viscous flow through the capillary vapor trap. We did not directly measure p_saturator during p^sat measurements for two reasons. First, such an arrangement creates an additional puncture in the septum of the saturator vial, which has the potential to leak. Second, and more important, is that the barometer capillary creates dead volume that is mostly at room temperature. Thus, the barometer capillary could act as a vapor trap during p_sat measurements. Therefore, we measured p_overpressure after p^sat measurements were completed for the day, and then calculated p_saturator for each p^sat measurement from eq. 2.

To measure p_overpressure the barometer inlet was fitted with a septum and connected to the saturator vial (with linalool present) with a fused silica capillary. Besides the connection between the saturator and the barometer, the DVME apparatus was configured in the same way as for a p^sat measurement, with the thermoelectric cooling plate at 263 K, a flow rate of 6.00 sccm, and one of the capillary vapor traps used for that day of p^sat measurements. No flow was lost to the barometer, as verified by the same flow rate on the MFC and the MFM.

At each temperature setpoint, the saturator pressure (p_saturator) and temperature were recorded after 6 min of thermal equilibration. The barometer was also used to measure ambient pressure (p_ambient) at the beginning and end of the temperature ramp. The average value of p_ambient was subtracted from the p_saturator to determine p_overpressure (eq 2). An exponential fit to a representative set of p_overpressure vs. temperature data (from 18 NOV 2021; see SI Section 3, Figure S3) for a 530 μm ID capillary vapor trap is given in eq 5,

$$p_{\text{overpressure}}\left(\text{kPa}\right)=6.104+\left(\left[4.89\times {10}^{-13}\right]\cdot \text{exp}\left[0.0749\times T\right]\right).$$ (eq 5)

Finally, as shown in eq 2, the value of p_saturator for each p^sat measurement was calculated from the average value of p_ambient (as measured with the barometer during the p^sat measurement) plus the value of p_overpressure from the curve fit of the p_overpressure vs. temperature data for that day.

2.7. Analysis of measurement uncertainties in the experimental variables.

A detailed analysis of uncertainties in temperature (u_T), mass of helium carrier gas (u_m1), mass of trapped linalool (u_m2), pressure in the saturator vial (u_psaturator), linalool purity (u_impurities), and helium solubility (u_x1) is available in our initial publication on DVME¹. Section 4 of the SI describes how the uncertainties for these variables, which are given in Tables 2 and 3, were derived from the specific parameters of the linalool p^sat measurements.

Table 2.

DVME-based vapor pressure (p^sat) measurements for linalool from 314 K – 354 K. The values of p^sat were calculated with eq 1–4 from the mass of helium carrier gas (m₁), the mass of trapped linalool vapor (m₂), and the pressure in the saturator vial (p_saturator). All measurements were made with a flow rate of 6.00 sccm and a thermal equilibration period of 10 min. Absolute standard (k=1) uncertainties are given for each experimental variable (see Section 2.7). The absolute combined standard uncertainty for p^sat (u_psat) was calculated as u_combined· p^sat from the relative combined standard uncertainties in Table 3. For ease of comparison, correlated vapor pressures from eq 6 (p_corr) are also given.

Date	T (K)	uT (K)	m1 (mg)	um1 (mg)	m2 (mg)	um2 (mg)	psaturator (kPa)	upsaturator (kPa)	psat (Pa)	upsat (Pa)	pcorr (Pa)	100*(psat−pcorr)/pcorr
21 SEP 2021	314.13	0.11	20.03	0.36	0.705	0.004	90.05	0.21	82.6	4.8	88.0	−6.15%
	324.08	0.12	20.31	0.37	1.502	0.013	90.06	0.21	173.4	7.0	183.6	−5.59%
	334.12	0.13	19.45	0.36	2.865	0.036	90.08	0.21	345	13	364	−5.21%
	344.03	0.15	19.36	0.36	5.280	0.039	90.11	0.21	637	23	679	−6.18%
	354.06	0.16	19.50	0.36	9.548	0.081	90.19	0.21	1138	42	1215	−6.40%
23 SEP 2021	314.13	0.11	19.92	0.36	0.752	0.006	89.11	0.21	87.7	5.1	88.0	−0.35%
	324.08	0.12	20.01	0.36	1.528	0.010	89.09	0.21	177.1	7.2	183.7	−3.58%
	334.09	0.13	20.01	0.36	3.018	0.021	89.07	0.21	349	13	363	−3.85%
	344.05	0.15	20.02	0.36	5.638	0.033	89.09	0.21	650	23	679	−4.38%
	354.06	0.16	20.00	0.36	10.178	0.065	89.20	0.21	1169	43	1215	−3.84%
10 NOV 2021	314.15	0.11	20.08	0.36	0.709	0.010	89.11	0.21	82.0	4.8	88.1	−6.94%
	324.13	0.12	21.54	0.37	1.671	0.024	89.11	0.21	180.1	7.3	184.2	−2.21%
	334.14	0.13	20.20	0.36	3.181	0.045	89.11	0.21	365	13	364	0.18%
	344.10	0.15	20.01	0.36	5.889	0.082	89.18	0.21	680	24	682	−0.24%
	354.11	0.16	20.01	0.36	10.709	0.173	89.30	0.21	1230	45	1219	0.95%
15 NOV 2021	314.18	0.11	21.19	0.37	0.759	0.013	89.14	0.21	83.3	4.9	88.4	−5.70%
	324.14	0.12	21.42	0.37	1.677	0.032	89.12	0.21	181.8	7.4	184.4	−1.41%
	334.17	0.13	20.40	0.37	3.136	0.044	89.15	0.21	356	13	365	−2.39%
	344.13	0.15	20.79	0.37	6.050	0.084	89.16	0.21	672	24	683	−1.52%
	354.14	0.16	21.03	0.37	10.936	0.158	89.26	0.21	1196	44	1221	−2.09%
17 NOV 2021	314.18	0.11	20.68	0.37	0.778	0.011	89.54	0.21	87.9	5.1	88.3	−0.52%
	324.13	0.12	20.51	0.37	1.621	0.023	89.44	0.21	184.2	7.5	184.3	−0.07%
	334.16	0.13	20.88	0.37	3.327	0.047	89.56	0.21	371	13	365	1.74%
	344.12	0.15	20.36	0.37	6.058	0.084	89.60	0.21	690	25	682	1.25%
	354.12	0.16	22.08	0.37	11.942	0.167	89.69	0.21	1249	46	1220	2.35%
	314.18	0.11	20.72	0.37	0.755	0.010	89.51	0.21	85.1	5.0	88.3	−3.68%
18 NOV 2021	314.17	0.11	20.64	0.37	0.736	0.011	89.40	0.21	83.2	4.9	88.3	−5.84%
	324.14	0.12	20.08	0.36	1.552	0.021	89.35	0.21	179.9	7.3	184.4	−2.42%
	334.15	0.13	20.66	0.37	3.221	0.044	89.33	0.21	362	13	365	−0.70%
	344.12	0.15	20.61	0.37	6.079	0.083	89.34	0.21	682	24	682	0.06%
	354.13	0.16	19.81	0.36	10.449	0.145	89.42	0.21	1215	45	1220	−0.43%
	314.18	0.11	20.80	0.37	0.729	0.010	89.27	0.21	81.6	4.8	88.4	−7.66%

Table 3.

Uncertainty budget for DVME-based vapor pressure (p^sat) measurements for linalool. Seven sources of uncertainty in the p^sat measurement are considered (see Sections 2.7 and 2.8). The relative combined standard (k=1) uncertainty (u_combined) in p^sat is the quadrature sum of all these sources of uncertainty.

Source of Uncertainty	314 K	324 K	334 K	344 K	354 K
m 1	0.0178·psat	0.0177·psat	0.0179·psat	0.0179·psat	0.0177·psat
m 2	0.0124·psat	0.0126·psat	0.0124·psat	0.0112·psat	0.0119·psat
T	0.0539·psat	0.0337·psat	0.0284·psat	0.0282·psat	0.0295·psat
eq 1 simplifications	0.005·psat	0.005·psat	0.005·psat	0.005·psat	0.005·psat
p saturator	0.0023·psat	0.0023·psat	0.0023·psat	0.0023·psat	0.0023·psat
x impurities	0.0029·psat	0.0029·psat	0.0029·psat	0.0029·psat	0.0029·psat
x 1	0.00017·psat	0.00017·psat	0.00017·psat	0.00017·psat	0.00017·psat
u combined	0.0584·psat	0.0406·psat	0.0364·psat	0.0358·psat	0.0369·psat

2.8. Uncertainty budget for p^sat.

The uncertainty budget given in Table 3 shows the uncertainty in the p^sat measurement that results from uncertainty in each experimental variable. The effects of u_T, u_m1, u_m2, u_psaturator, u_impurities, and u_x1 on the value of p^sat were determined from a sensitivity analysis. For example, the Wagner correlation (see Table 4 and eq 6) was used to determine the vapor pressure at p_corr(T) and p_corr(T+u_T). The fractional difference between the two values, calculated as |(1-(p_corr(T)/p_corr(T+u_T))|, is reported in Table 3 as the uncertainty in the p^sat measurement that results from uncertainty in the experimental temperature. For the other experimental variables, the sensitivity analysis was performed with eqs 1–4. The low solubility of helium³¹ means that u_x1 is an insignificant source of uncertainty in the p^sat measurement, but we report it for completeness. In Table 3, the entry called “eq 1 simplifications” refers to the absence of the Poynting correction or the effect of the vapor-phase fugacity coefficient. For helium, these are expected roughly cancel each other³² but a systematic error of about 0.005·p^sat is introduced by ignoring them.

Table 4.

Coefficients for Wagner correlations of linalool vapor pressure (p_corr) where T_c = 668 K, p_c = 2907 kPa, τ = 1 – T/T_c, and p₀ = 1 kPa. Eq 6 is a Wagner correlation of all literature data from 270 K to 425 K (excluding the present work), eq 7 is a Wagner correlation of the same literature data plus the DVME data, and eq 8 is a Wagner correlation of the DVME data alone.

pcorr = p0 · exp((Tc/T)·(Aτ+Bτ1.5+Cτ2.5+Dτ5)+ln(pc/p0))
Coefficient	Eq 6	Eq 7	Eq 8
A	−14.882	−14.395	−14.617
B	18.521	17.472	15.039
C	−20.822	−20.137	−12.121
D	2.4678	2.5165	−11.851

3. Results and Discussion

One of the primary goals of this work was to establish that DVME can provide low-uncertainty measurements at higher values of p^sat than the maximum of ~6 Pa reported in our previous work with n-eicosane.¹ For gas-saturation methods, nonideal mixture behavior limits p^sat measurements to ≤7000 Pa.⁸ Measurements near this high-pressure limit generate relatively large quantities of analyte vapor, which is a consideration for instrument design and operational parameters. This is especially important given that DVME uses much smaller capillary vapor traps and saturators than conventional designs. The present work demonstrates p^sat measurements up to about 1250 Pa with linalool. Note that the use of DVME at lower pressures does not require the same kind of demonstration because the ability to measure lower values of p^sat is mainly a function of the total carrier gas flow and the sensitivity of the analytical method used to determine the recovered mass of analyte (e.g., GC-FID, GC-MS, etc.).

3.1. Plugging, breakthrough, and overpressure.

One challenge with using DVME to measure higher p^sat values is that the capillary vapor trap can become plugged with condensate. Even a thin coating of condensate on the inner wall of the capillary is visible to the eye—it appears as a section of darkened capillary (compared to the lighter, tan color of clean capillary). During p^sat measurements, a stationary band of darkened capillary is typically observed just outside the oven where the capillary temperature drops to ambient. However, during the initial linalool experiments with a 320 μm ID capillary vapor trap (as used for the n-eicosane study¹), we visually observed multiple darker bands moving along the capillary in the direction of gas flow. This suggests that liquid condensate had entirely filled sections of the capillary trap and that slugs of liquid linalool were being pushed along by the carrier gas. This is undesirable because it creates a significant flow restriction that is not accounted for in the p_saturator determination. Increasing the capillary vapor trap ID from 320 μm to 530 μm eliminated the formation of liquid slugs.

The relatively high p^sat of linalool raised concerns about vapor trapping efficiency. Consequently, we increased the capillary length to 1.5 m (from 1.0 m used in the n-eicosane study¹), and a thermoelectric cooling plate was installed to cool the capillary vapor trap to 263 K (Figure 1). Sufficient trapping efficiency was verified in triplicate at 354 K with a total flow of 240 scc and a flow rate of 10 sccm—more demanding conditions than any of the p^sat measurements. During helium flow, the outlet of the capillary vapor trap was immersed in a “breakthrough vial” containing 1 mL of acetone (instead of being inserted into the MFM) to collect any linalool that was not trapped. Afterward, the acetone in the breakthrough vial was analyzed by GC-FID (Figure 2). No linalool was detected in the breakthrough vial for any of the three replicates, demonstrating the chilled stationary phase in the capillary vapor trap operated at 100% efficiency under conditions that were more extreme than the actual p^sat measurements.

Figure 2.

GC-FID chromatograms demonstrating the absence of linalool degradation and the trapping efficacy of the capillary vapor trap when cooled to 263 K. Chromatograms are shown for the following samples: (1) neat acetone solvent; (2) the eluent of a capillary vapor trap after a typical p^sat measurement at 334 K with a flow rate of 6.00 sccm and a total flow of 120 scc; (3) a breakthrough experiment performed at 354 K with a flow rate of 10.00 sccm and a total flow of 240 scc; (4) a purity check of linalool from the saturator vial after a series of p^sat measurements over the entire temperature range.

The increase in capillary vapor trap ID had a secondary benefit: p_overpressure, (eq 2), was reduced by a factor of three. Given that p_overpressure is caused by viscous flow through the capillary vapor trap, it varies with flow rate, temperature, and capillary ID and length. Figure 3 shows p_overpressure curves from 304 K to 364 K with a 320 μm or a 530 μm ID capillary at a helium flow rate of 6.00 sccm. Smaller p_overpressure values were observed with the 530 μm ID capillary, which makes helium leaks less likely, makes the overpressure correction smaller, and potentially allows for significantly higher flow rates than were used herein.

Figure 3.

The overpressure (p_overpressure) in the saturator vial versus oven temperature for capillary vapor traps with an ID of 320 μm (triangles) or 530 μm (circles). See Figure S4 of the SI for a plot of the overpressure data for the capillary vapor trap with 530 μm ID with an expanded y-axis.

3.2. Sample Purity.

Sample purity is important for obtaining high-quality p^sat measurements. The presence of a volatile impurity in linalool was initially inferred from the observation that the first p^sat measurement with a new saturator vial always yielded an anomalously low value. The identity of the impurity, which did not appear in the GC-FID chromatogram, was verified as water by coulometric Karl Fisher titration. The initial water content in a freshly opened ampule of linalool was approximately 4 mol %, which depresses the measured p^sat by about 4 %. Fortunately, the relatively high p^sat of water allowed it to be removed by pretreatment with a flow of warm helium. The required quantity and temperature of helium for the drying procedure was informed with a simple numerical model of the drying process (see SI, section 1). The effectiveness of the drying procedure was then confirmed with replicate measurements of p^sat, which showed that, after the drying procedure, the initial p^sat measurement with a new saturator vial was not significantly lower than later replicates (e.g., see the 314 K replicates on 18 NOV 2021 and 17 NOV 2021 in Table 2).

3.3. Sample stability.

DVME allows for relatively short measurement periods (30 min for the measurements reported herein), which is advantageous for p^sat measurements with compounds such as linalool, which are less stable than alkanes.^{2, 4} However, instability is difficult to predict and it is convenient to make multiple measurements on the same sample material. Therefore, three precautions against sample decomposition were taken for the measurements on the linalool. First, to minimize the potential for oxidative decomposition, 0.2 mass % of the antioxidant TBHQ was added to the linalool before the p^sat measurements. The specific decomposition pathway of concern was the autoxidation of the C=C double bonds.^{4, 30} The small decrease in measured p^sat caused by the addition of TBHQ was corrected via the x_impurities term (eq 4). The addition of an antioxidant has been used successfully in the past for p^sat measurements of unsaturated molecules.⁴ The second precaution was to measure from the lowest to the highest temperature, then repeat the initial 314 K (lowest) data point at the end of the measurement series.^{4, 36, 37} These replicate data points, shown in Table 2, were within 3.2 % of the initial values, which is less than the combined standard uncertainty (see Section 3.4) of the p^sat measurement. Third, a given saturator was used for only a single day (5 or 6 measurements). With these precautions in place, no evidence of linalool decomposition was observed, even in the linalool remaining in the saturator vial after a complete series of p^sat measurements (Figure 2, panel 4).

3.4. Linalool p^sat measurements, uncertainty budget, correlations, and enthalpy of vaporization.

The p^sat of linalool was measured by the DVME method over two months, Table 2. The absolute uncertainties in each variable are given in Table 2 (see Section 2.7 for more details about how these were derived). A full uncertainty budget for the p^sat measurements is given in Table 3, as described in Section 2.8.

The p^sat measurements were repeatable over daily, weekly, and monthly timeframes. Such repeatability is a key indicator of quality for less stable compounds.⁴ To facilitate comparisons of our measurements with existing data, all published p^sat data for linalool between 270 K and 425 K^{23, 38–42} were taken from the NIST Thermodata Engine (TDE)³⁴ and fit to the Wagner equation⁴³ with equal weighting of all experimental data points. This Wagner correlation (eq 6 from Table 4) used a critical temperature of T_c = 668 K and a critical pressure of p_c = 2907 kPa (where τ = 1 – T/T_c, and p₀ = 1 kPa), both taken from the NIST TDE.³⁴ Figure 4 is a deviation plot of experimental linalool p^sat data (multiple colored data points) from this Wagner correlation (black line). In Table 2, values of vapor pressure from the correlation (p_corr) are given at each measurement temperature.

Figure 4.

The percent deviation plot for experimental linalool p^sat values from literature (varied colors and shapes) and the current measurements (pink stars). The black zero line represents the Wagner correlation of all published p^sat data for linalool between 270 K to 425 K (excluding the present work, Table 4 eq 6). Panel A is the full range, and panel B is a zoom in to ±10 %.

In Figure 4, our measurements of linalool p^sat with DVME are the pink stars. The Wagner correlation, represented by the black zero line in Figure 4, is heavily influenced by the two data sets from Zaitsau et al. (gold triangles and teal triangles)²³ because of its numerous data points. The data from Zaitsau et al. appear to be of exceptionally high quality, as indicated by the relatively small scatter and the good agreement obtained with two different measurement methods: a gas saturation method (called “transpiration” by Zaitsau et al.) and a static method.²³ The transpiration data from Zaitsau et al. are, on average, a little higher and a little more scattered than their static data, but it is not clear which data set is more accurate. In any case, the DVME-based measurements have a similar level of scatter as the transpiration data from Zaitsau et al., Figure 4. Notably, 22 of 32 data points in the DVME data set (Table 2) deviate from the Wagner correlation by less than the u_combined of the DVME-based measurements. Such agreement is evidence that the uncertainty estimates for the DVME method are reasonable. The large deviations and scatter for the other published data sets in Figure 4 are typical of p^sat measurements in this temperature and pressure range.

Of course, the literature data and, therefore, the Wagner correlation have uncertainty as well. See the SI, Section 5 for more details about the Wagner correlation, including Tables S4 (literature data) and S5 (correlated values). In addition to the Wagner correlation of the literature data alone (eq 6), we created a Wagner correlation of the literature data plus the DVME data (Table 4, eq 7). Finally, we created a Wagner correlation of the DVME data alone (Table 4, eq 8). These are provided to facilitate comparisons with any future measurements.

As shown in Table 3, the DVME-based p^sat measurements had the three dominant sources of uncertainty: the temperature of the saturator (T, as measured by the PRT), the mass of helium carrier gas (m₁, as measured by the MFM), and the mass of linalool (m₂, as measured by GC-FID).¹ Because of the drying procedure, water contamination was assumed to not contribute to the uncertainty in linalool purity. Even though the solubility of helium in linalool was estimated from helium solubility in 1-decanol,³¹ this does not introduce significant measurement uncertainty because helium’s solubility is low compared to the concentration of other impurities. The relative combined standard uncertainty (u_combined) at 314 K is estimated at 0.0584·p^sat and ranged from 0.0358·p^sat to 0.0406·p^sat at the other temperatures, Table 3.

The measurement uncertainties for linalool p^sat are higher than our previous measurements for n-eicosane, which ranged from 0.0203·p^sat to 0.0282·p^sat at temperatures from 344 K to 374 K.¹ One reason for the difference is that, with n-eicosane, more carrier gas flow (240 scc to 800 scc) was needed to obtain optimal quantities of condensed analyte in the capillary vapor trap to analyze by GC-FID, which lengthened the measurement period but minimized the uncertainty in the mass of helium, m₁. Also, for the GC oven used, the temperature setpoint had relatively high uncertainty near ambient temperature; for this reason, measurements below 314 K were not made. This limitation could presumably be overcome with different hardware (such as adding a chiller to balance the heater in the oven).

The enthalpy of vaporization (ΔH_vap) was determined from a Clausius-Clapeyron plot of the DVME data, ΔH_vap(T range 314 K – 354 K) = 61.8 ± 0.4 kJ/mol (see Figure S5). This value agrees with (but slightly outside the standard uncertainty intervals for) the value determined from the Wagner correlation (Table 4 eq 6) for the same temperature range, ΔH_vap(corr) = 60.8 ± 0.4 kJ/mol (see Figure S4). At the median experimental temperature of 334 K, NIST TDE web application predicts a ΔH_vap(334 K) = 59.3 ± 2.2 kJ/mol (https://wtt-pro.nist.gov; subscription to TDE required). The experimentally determined ΔH_vap value is within the uncertainty of the predicted value.

3.5. Implications for cannabis breathalyzer development.

It is instructive to compare the p^sat curve for linalool to the p^sat curves for ethanol and THC (Figure 5). Breathalyzer tests for ethanol intoxication are relatively easy because of ethanol’s high p^sat at body temperature. Cannabis breathalyzer development that is based (solely) on the detection of THC is much more challenging, in large part because the p^sat of THC is about one millionth that of ethanol.² Monoterpenes like linalool have p^sat curves closer to ethanol than to THC (the p^sat of linalool is about one hundredth that of ethanol). We propose that this fundamental behavior makes cannabis-associated terpenes potentially valuable as additional breath markers of recent cannabis use. Breath studies for terpenes are lacking, but it is noteworthy that linalool has been detected in the vapor phase above human whole blood following dermal exposure.⁴⁴ A better understanding of terpene metabolism is also needed. However, for linalool, gastric exposure in rats⁴⁵ or dermal exposure in humans⁴⁴ resulted in peak blood concentrations of linalool after 15−40 minutes. Therefore, we believe that further research into the concentration of linalool in both breath and blood after recent cannabis use may be useful in the development or validation of meaningful breath-based measurements for law enforcement.

Figure 5.

Vapor pressure (p^sat) data for ethanol³⁴, linalool (current work), and THC² over a similar temperature range.

4. Conclusions

The DVME method was optimized to measure the p^sat of linalool up to 1250 Pa, which is about 200 times higher p^sat than previous measurements with DVME on n-eicosane. This greatly extends the utility of the method for measuring a variety of compounds important to criminal justice and public health. Two key changes were made to the apparatus to allow this increase in measurement range: the capillary vapor trap had a larger inner diameter and was cooled to 263 K with a thermoelectric cooling plate to increase trapping efficiency. Measurements at even higher p^sat are presumably possible; the suggested strategy would be to use lower flow rates and less total helium, although this would increase the uncertainty of the mass of helium carrier gas. Additionally, multiple precautions were taken to ensure that linalool purity did not affect the measurement results: a fresh saturator was made daily, a drying step was included, and TBHQ was added as an antioxidant. With these precautions, there was no evidence that impurities or sample decomposition significantly influenced the p^sat measurements.

Abbreviations

DVME

dynamic vapor microextraction

GC-FID

gas chromatography with flame ionization detection

ID/OD

inner and outer diameter

MFC

mass flow controller

MFM

mass flow meter

PRT

platinum resistance thermometer

scc(m)

standard cubic centimeters (per minute)

C14

tetradecane

TBHQ

tert-butylhydroquinone

THC

Δ⁹-tetrahydrocannbinol