Alkanes

We collected volatiles from the leaves of the two morphotypes under the same growth conditions and ambient temperature, in biological triplicates. Approximately 100 g of dry leaves from the two morphotypes, were extracted with 1000 mL of reverse osmosis water using a Clevenger apparatus⁸⁷ , following four hours of extraction by hydro-distillation. Samples of the essential oils extracted from the leaves were analyzed using gas chromatography with a flame ionization detector (GC-FID) (Shimadzu GC-2010 Plus) and gas chromatography coupled to mass spectrometry (GC–MS) (Shimadzu GCMS-QP2010 SE).
We conducted the analyses according to the following conditions: helium (He) as the carrier gas for both detectors, with the flow and linear speeds of 2.80 mL min⁻¹ and 50.8 cm s⁻¹ (GC-FID), and 1.98 mL min⁻¹ and 50.9 cm s⁻¹ (GC–MS), respectively; injection port temperature of 220 °C with a split ratio of 1:30; fused silica capillary column (30 m × 0.25 mm); stationary phase Rtx^®-5MS (0.25 μm film thickness); oven with an initial temperature of 40 °C, maintained for 3 min, then gradually increased by 3 °C min⁻¹ until 180 °C, where it remained for 10 min (total analysis time: 59.67 min); and FID and MS detector temperature of 240 °C and 200 °C, respectively^{49 (link)}. The used samples were taken from the vials in 1 μL of a solution containing 3% essential oil dissolved in hexane with 0.1 mol L⁻¹ dimethylacetamide (DMA; external standard for reproducibility control).
The GC–MS analyses were performed using electron impact equipment with an impact energy of 70 eV, scanning speed of 1000, scanning interval of 0.50 fragments s⁻¹, and fragments detected from 29 to 400 (m/z). The GC-FID analyses were carried out in a flame formed by H2 and atmospheric air at a temperature of 300 °C. Flow rates of 40 mL min⁻¹ and 400 mL min⁻¹ were used for H2 and air, respectively. Identification of the compounds in the essential oils was accomplished by comparing the obtained mass spectra with those available in the spectral library database (Wiley 7, NIST 05, and NIST 05 s) and retention indices (RI). To calculate the RIs, we used a mixture of saturated alkanes C7–C40 (Supelco-USA) and adjusted retention time of each compound, obtained by GC-FID. The values calculated for each compound were compared with those reported in literature^{88 –90} .
We calculated the relative percentage of each compound in the essential oil using the ratio between the integral area of the peaks and the total area of all sample constituents obtained via GC-FID analyses. The compounds with a relative area above 2% were identified and considered predominant if above 10%.

The chemical composition of the essential oils of catnip and oregano was determined using a Shimadzu 2010 Plus Gas Chromatograph equipped with a TQ8040 Mass Spectrometer (Shimadzu Scientific, Somerset, NJ). A Restek SH-Rxi-5Sil MS 30 m × 250 μm × 0.25 μm column was used for chromatographic separation. Helium was used as the carrier gas with a column flow rate of 1 mL/min. 1 μL of sample was injected with a split ratio of 25 and the injection temperature was set to 250°C. The column oven temperature was set to 35°C and held at 35°C for 4 min. The temperature was then raised to 250°C at a rate of 20°C/min and held at 250°C for 1.25 min. For the MS parameters, the ion source and interface temperatures were set at 200°C and 250°C respectively. The detector voltage was 0.04 kV and had a threshold of 1000. The solvent cut time was 3.5 min. The fragments were scanned within a range of 45 m/z to 500 m/z. For compound identification, the mass spectra of the compounds were compared to the mass spectra of compounds in the following mass spectral libraries: NIST05.LIB, NIST05s.LIB, W10N14.lib, and W10N14R.lib. To further confirm the identity of the compounds, the mass spectra was compared to Kovats indices generated from a series of n-alkanes (C8-C18) and literature (Adams, 2007 ). Representative chromatograms and mass spectra of the major compound of catnip and oregano are presented as supplementary material (Supplementary Figures S1, S2).

Figure 4

(A) Examples of the isothermal nonlinearity parameter from the triple point to the normal melting point for saturated molecular liquids of different classes, where solid lines are point-wise thermodynamic values calculated explicitly with derivatives of the fundamental equations of state included in the NIST REFPROP^{30 (link)}, and the dashed lines are the average values defined as slopes of the linear fits of lines shown in (B). Liquids are marked by the same colours in both subpanels.

Figure 4A illustrates the comparison of the isothermal nonlinearity parameter $k^{\prime }$ for some examples of molecular liquids belonging to different chemical classes: n-alkanes, i.e. linear hydrocarbons with different chain lengths, a highly branched isomer (2,3-dimethylbutane), typical aromatic and polar compounds (toluene and ethanol, respectively). The reference for the majority of curves is taken from the triple point to the normal boiling point along the saturation curve (that is, in principle, does not differ from values determined to the ambient pressure condition for thermodynamic parameters of the bulk liquid) are calculated directly from the definition given by Eq. (20).
The only exception is 2,3-dimethylbutane, for which the lower temperature limit is chosen at $T=263.15\text{K}$ as was used for Table 1. This is connected with the properties of this branched compound, which exhibits a more complex behaviour in the region of low temperatures. The branched structure leads to specific oscillatory modes and this substance may exhibit metastability and glassy states after freezing^{53 (link)} that is also reflected in the properties of a cooled liquid. Thus, we are limited by the temperature range, which is closer to room temperatures when such anomalies are absent. Similar behaviour is noted for other branched hydrocarbons, e.g. for 3-methylpentane as additionally illustrated in Supplementary Material.
Another feature worth discussing is the isothermal nonlinearity coefficient for n-pentane, which is equal (in the rounded variant) to $k_r^{\prime }=9.5$ in Fig. 4A in contrast to $k_r^{\prime }=10$ in Table 1. For this lower value, ${\text{AAD}}_r=0.75\%$ , ${\max (\mathrm{RD}}_r)=1.12\%$ ( $T<T_b)$ and ${\text{AAD}}_r=0.43\%$ , ${\max (\mathrm{RD}}_r)=0.86\%$ ( $T>T_b)$ for Bridgman’s isotherms that is significantly better than results listed in Table 1 and confirms the statement formulated above that one needs to consider temperatures closer to the triple point for liquids with low melting/boiling temperatures to assure validity of the solid-like molecular oscillations properties required by the phonon theory.
The corresponding partial derivatives and density included in Eq. (20) for these substances are substituted as provided by the NIST REFPROP^{30 (link)} reference software from the fundamental equation of state. The values for the same source are also used to plot the dependencies (6) shown in Fig. 4B, which are sufficiently linear. The slopes of the linear fit lines of the latter are denoted in Fig. 4A as dashed straight lines and their roundings to either integer or half-integer values are dash-dotted straight lines. One can see that the latter are closer to the direct derivative-based curves, especially in the vicinity of the temperature range, for which the high-pressure density measurements are available. This supports the conclusion that such rounding having a physical background in the origin of Rao’s rule from the phonon theory of liquid thermodynamics in the quasi-harmonic approximation is plausible. In addition, such a check of linearity of the fit provides a criterion for the possibility to neglect by effects of anharmonicity and molecular diffusion, which may affect the isothermal nonlinearity parameter. Notably that the linearity in the double-logarithmic coordinates, i.e. the power-law dependence between the speed of sound and the density distinguishes liquids as more compressible substance from solids, for with such linearity fulfils between these quantities directly (Birch’s law).
It should be stressed also that the thermodynamic route of calculating $k^{\prime }$ from the fundamental equation of state itself has the uncertainty about 5–7 $\%$ taking into account the uncertainty of the derivative quantities (note that the same is true also for the thermodynamic route of estimating the adiabatic nonlinearity parameter, see, for example, the discussion in Ref.^{54 (link)}); thus, the difference between solid curved and straight dash-dotted lines bounded within this range in Fig. 4A does not principally affect this conclusion.