Measurements of enthalpy of sublimation of Ne, N2, O2, Ar, CO2, Kr, Xe, and H2O using a double paddle oscillator

https://doi.org/10.1016/j.jct.2017.11.004Get rights and content

Highlights

Abstract

We report precise experimental values of the enthalpy of sublimation (ΔHs) of quenched condensed films of neon (Ne), nitrogen (N2), oxygen (O2), argon (Ar), carbon dioxide (CO2), krypton (Kr), xenon (Xe), and water (H2O) vapour using a single consistent measurement platform. The experiments are performed well below the triple point temperature of each gas and fall in the temperature range where existing experimental data is very limited. A 6 cm2 and 400 µm thick double paddle oscillator (DPO) with high quality factor (Q ≈ 4 × 105 at 298 K) and high frequency stability (33 parts per 10−9) is utilized for the measurements. The enthalpies of sublimation are derived by measuring the rate of mass loss during temperature programmed desorption. The mass change is detected due to change in the resonance frequency of the self-tracking oscillator. Our measurements typically remain within 10% of the available literature, theory, and National Institute of Standards and Technology (NIST) Web Thermo Tables (WTT) values, but are performed using an internally consistent method across different gases.

Introduction

The intermolecular interaction of the condensed solid phase is a critical thermodynamic property and measured as the enthalpy of sublimation (ΔHs). A variety of techniques has been developed experimentally to determine the sublimation energies. They are broadly categorized as either direct or indirect [4], [5], [6]. Direct techniques, utilizing appropriate calorimeters, involve the measurement of heat during the sublimation process [9], [10]. Indirect methods measure the vapour pressure at different temperatures and assume that the sublimation enthalpies remain constant in the experimental temperature range [8], [11], [12], [13]. The sublimation vapour pressure measurements are typically carried out by either using standard manometers or non-traditional resonant base micro-sensors. Resonant micro-sensors such as quartz crystal microbalances (QCMs) [15], [16], [17] and silicon micro-machined double paddle oscillators (DPOs) [7], [18], [19], [20] are two methods utilized to measure the sublimation vapour pressures and enthalpies of different atmospheric gases. The change in mass of the deposited solid film is measured as a change in the resonance frequency of the micro-sensor. Subsequently, the evaluation of sublimation enthalpy is carried out during a temperature programmed desorption (TPD) of the film. Compared to DPO measurements, QCM measurements have the advantage of being able to operate in air and liquid environments. However, DPOs can provide better mass sensitivity (≈0.027 ng/cm2) and frequency stability (33 parts per billion) [18], [22] under ultra-high vacuum and at cryogenic temperature conditions. QCMs have been able to measure vapour pressures between 10−1 Pa and 10−7 Pa for H2O, N2O and CO2 films [16] while DPOs have been able to reach vapour pressures down to 4.8 × 10−11 Pa for quenched condensed films of neon [20].

Despite a large number of experiments performed over the last century to experimentally evaluate enthalpies of sublimation of common atmospheric gases, we found limited experimental data for enthalpy values well below the triple point temperatures. For example, in the National Institute of Standards and Technology (NIST) Web Thermo Tables (WTT) [1], no data are included for sublimation experiments of neon below 10 K, nitrogen below 35 K, and oxygen below 36 K. Consequently, the sublimation energies reported on the WTT [1] at these temperatures for each film are extrapolated from their respective triple point values and therefore have both large absolute and relative uncertainties. According to the WTT [1], the enthalpy of sublimation of neon at 10 K is (2.16 ± 0.22) kJ·mol−1, nitrogen at 36 K is (6.9 ± 4.6) kJ·mol−1 and oxygen at 36 K is (8.7 ± 3.7) kJ·mol−1. Experiments have shown that nitrogen, CO2, and water films exist in different solid phases [8], [28] below their triple points and thus can have different activation energies. Therefore, a thorough experimental study is required to benchmark the enthalpies of different atmospheric gases well below their triple point temperatures.

To address this need, we employed a single 400 µm thick DPO (for all the experiments presented) which was excited in the 2nd anti-symmetric (AS2) torsional mode with a resonant frequency around 7.2 kHz. The AS2 mode of the DPO shows extremely high intrinsic quality factors both at room temperature (Q ≈ 4 × 105) and 5 K (Q ≈ 8 × 107). In general, the mass sensitivity of an oscillator is proportional to its mechanical quality factor. Therefore, a DPO excited in the AS2 mode provides an ideal measurement platform to study the evaporative mass loss during the sublimation process. In this study, we determined the enthalpy of sublimation for eight different atmospheric gases including Ne, N2, O2, Ar, CO2, Kr, Xe, and H2O with the 400 µm thick DPO. During the course of the current study, the same sensor was used for all measurements and was never removed from the chamber. The method presented here provides a single consistent measurement platform which reduces any systematic uncertainties that could be introduced during loading and unloading of the sensor. In the subsequent sections, we explain the theoretical background, apparatus, detailed example experiment using nitrogen, sources of uncertainties, and compile all results.

Section snippets

DPO mechanics

The basic equation for the resonance frequency of the DPO in the torsional mode is given byf=12πkI

where k is the torsional spring (elastic) constant and I is the moment of inertia of the paddle. Mass loading on the surface of the DPO will change both the elastic constant and the moment of inertia in Eq. (1). The resulting change in the resonance frequency upon mass loading is the primary mechanism used to quantitatively derive different properties (thickness, elastic modulus, porosity, internal

Materials

The 400 µm thick DPO was fabricated from a 100-mm-wide, double side polished, un-doped, float zone and a (1 0 0) oriented single crystal silicon wafer with a high resistivity at room temperature (>10 k ohm-cm). All the gases (Table 1), except for neon, used in the experiments were of research grade purity (99.9999%). Neon was purchased as an ultra-high purity grade (99.999%) gas. Water was degasified using a freeze-vacuum-thaw method [3] for at least three cycles.

Apparatus

Because the apparatus utilized

Results and discussion

The apparent sublimation vapour pressures of all the target gases, after accounting for different sources of uncertainty listed in Table 2, are plotted in Fig. 7. The error bars in the figure are smaller than the symbols. The enthalpies of sublimation for each gas are determined by averaging the fitted values from the individual experimental runs. The various uncertainties from each run are then added in quadrature along with the standard deviation of variations between each experimental run.

Conclusions

According to the NIST thermodynamic reference data, the sublimation enthalpies of Ne, Ar, N2, O2, Kr, Xe, CO2, and H2O below their triple point temperatures are unavailable, limited or imprecise. We utilized a single 400 µm thick DPO, providing extremely high quality factors and mass sensitivity, for the precise determination of the sublimation enthalpies of target atmospheric gases. The use of a single DPO across all experiments provides an internal consistency among the measurements carried

Acknowledgements

We would like to especially thank Dr Tom Metcalf at Naval Research Laboratory, Dr Peihao Huang, Dr Corey Stambaugh, and Dr James A. Fedchak at National Institute of Standard and Technology (NIST) for their valuable feedback during the course of this study. The fabrication of double paddle oscillator was carried out at the Center for Nanoscale Science and Technology (CNST) nanofab facility at NIST.

References (45)

  • M.A.R. Da Silva et al.

    Thermochim. Acta

    (1990)
  • N. Fray et al.

    Planet Space Sci.

    (2009)
  • L.M. Santos et al.

    Thermochim. Acta

    (2004)
  • E.R. Grilly

    Cryogenics

    (1962)
  • T.A. Scott

    Phys. Rep. (Sect. C Phys. Lett.)

    (1976)
  • C. Boiziau et al.

    Surf. Sci.

    (1973)
  • Y.A. Freiman et al.

    Phys. Rep.

    (2004)
  • P. Korpiun et al.

    J. Phys. Chem. Solids

    (1972)
  • J. Hessinger et al.

    J. Non-Cryst. Solids

    (1996)
  • T.H. Metcalf

    Mater. Sci. Eng., A

    (2004)
  • J. Hessinger et al.

    Planet Space Sci.

    (1996)
  • http://wtt-pro.nist.gov/wtt-pro/,...
  • R. Balzer et al.

    Phys. Rev. B

    (1971)
  • D. Brown et al.

    J. Phys. Chem.

    (1996)
  • S. Dushman et al.

    Am. J. Phys.

    (1962)
  • C. Kittel et al.

    Thermal Physics

    (1980)
  • B. White et al.

    J Low Temp Phys.

    (1998)
  • R. Beaumont et al.

    Proc. Phys. Soc.

    (1961)
  • C.W. Leming et al.

    Phys. Rev. B

    (1970)
  • W.F. Huebner et al.

    Heat and Gas Diffusion in Comet Nuclei

    (2006)
  • C.E. Bryson et al.

    J. Chem. Eng. Data

    (1974)
  • R. Perry, G. Meadows, L. Mosier, M. Woronowicz, Measurement of cryogenic ice sublimation using quartz crystal...
  • Cited by (24)

    View all citing articles on Scopus
    View full text