Single-run determination of the saturation vapor pressure and enthalpy of vaporization/sublimation of a substance undergoing successive solid-solid and solid-liquid phase transitions: the case of $N$-methyl acetamide

We report on the dynamical measurement of the saturation vapor pressure of $N$-methyl acetamide in the temperature range $-30^\circ$C to $34^\circ$C. This is achieved by monitoring the pressure inside a vacuum chamber in which a precooled sample of the substance slowly thermalizes to the chamber temperature, undergoing first a phase transition between two crystalline structures around $1^\circ$C and then a solid-liquid phase transition around $30^\circ$C. Such a measurement provides in a single run accurate data for the saturation vapor pressure and the enthalpies of sublimation and vaporization of the different phases of the investigated substance.

💡 Research Summary

The authors present a novel dynamic method for measuring the absolute saturation vapor pressure (SVP) and the associated enthalpies of sublimation and vaporization of N‑methyl‑acetamide (NMA) over a broad temperature range (‑30 °C to 34 °C) in a single experimental run. The technique relies on a three‑chamber ultra‑high‑vacuum apparatus (load, transfer, and experimental chambers). A pre‑cooled sample is placed in the transfer chamber at about –30 °C, then introduced into the experimental chamber, which is held at a constant temperature above room temperature (either 20.5 °C or 36.4 °C in the two reported runs). As the sample slowly equilibrates with the chamber (thermalization time ≈ 3000 s), it evaporates and re‑condenses, and the chamber pressure is recorded continuously with a calibrated absolute pressure sensor (resolution 10⁻⁴ Pa).

Prior to measurement the sample undergoes repeated evacuation‑heating cycles to remove high‑volatility contaminants, chiefly water, which would otherwise cause an over‑estimation of the SVP. The authors demonstrate that sufficient purification yields reproducible pressure‑temperature curves, while insufficient purification produces spurious pressure spikes, especially at the solid‑solid transition near 1 °C.

The thermodynamic analysis combines the Clausius–Clapeyron relation with a temperature‑dependent enthalpy model that incorporates linear variations of the heat‑capacity difference (parameters β_u and α_u). These parameters are taken from literature heat‑capacity data for the gas, liquid, and crystalline phases; for the second crystalline polymorph (crII) the authors extrapolate from crI data. The measured chamber pressure p_V is related to the true SVP p_sat(T_S) through a statistical rate‑theory (SRT) model that accounts for the finite number of vibrational degrees of freedom of NMA. An effective degree of freedom D_e,u is derived from the gas heat capacity, allowing the authors to write an analytical expression (Eq. 8) that links p_V and p_sat via an exponential factor containing D_e,u and the temperature ratio T_V/T_S.

Fitting the experimental p_V‑T_S data in each temperature region (crI, crII, liquid) with Eq. 8 yields the reference saturation pressures p* sat and the reference enthalpies ΔH* for each phase. The results are summarized in Table 1. For the low‑temperature crystalline phase crI (‑20 °C → 0 °C) the authors find p* sat ≈ 0.38 Pa and ΔH* ≈ 65 kJ mol⁻¹. For the previously uncharacterized polymorph crII (‑30 °C → ‑1 °C) they obtain p* sat ≈ 0.38 Pa and ΔH* ≈ 66 kJ mol⁻¹, indicating a slightly lower sublimation enthalpy than the more disordered crI. In the liquid region (31 °C → 34.5 °C) the measured p* sat rises to ≈ 7.5 Pa with ΔH* ≈ 63 kJ mol⁻¹. The fitted curves reproduce the experimental data with residuals well within the measurement uncertainties, confirming the validity of the SRT‑based model.

Comparison with earlier literature (Gopal & Rizvi 1968; Kortüm & Biedersee 1970; Zaitsev et al. 2019; Štejfa et al. 2020) shows excellent agreement for the crI and liquid phases, typically within 5 % for both SVP and enthalpy values. The new crII data fill a gap in the thermodynamic database for NMA.

The authors conclude that their dynamical method enables accurate determination of SVP and phase‑specific enthalpies for low‑volatility, polymorphic substances in a single run, provided that careful sample purification and precise temperature/pressure control are maintained. The approach is limited by the time required for thorough outgassing and by the assumption of harmonic vibrational behavior; however, the introduction of an effective vibrational degree of freedom mitigates anharmonic effects. Future work will focus on automating the purification cycle and extending the technique to a broader class of organic, inorganic, and biomolecular systems, potentially offering a versatile tool for thermodynamic characterization in chemistry, materials science, and astrochemistry.