Article pubs.acs.org/jced
Thermal Diffusivity of Methanol to a Pressure of 5 GPa Evan H. Abramson* and J. Michael Brown† Department of Earth and Space Sciences, University of Washington, Seattle, Washington 98195-1310, United States ABSTRACT: Thermal diffusivities of methanol have been measured, using transient optical gratings, at 26 °C, up to a pressure of 5 GPa; together with previously reported measurements of thermal effusivities, they are used to estimate values of methanol’s specific heat and thermal conductivity to a pressure of 8 GPa. At lower pressures, the calculated quantities compare favorably with a published equation-of-state and a separate formulation for conductivity. Use of diffusivities in combination with effusivities is of particular interest, as both can be measured with optical techniques applicable to the high-pressure, diamond-anvil cell. Such experiments thus afford an experimental path to the determination of specific heats and thermal conductivities at the high compressions achievable with this experimental tool.
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include chemical diffusivities (to 0.38 and 0.5 GPa9), dielectric susceptibility (to 4.5 GPa),10 and viscosities (to 8.4 GPa11). The current study adds further information as to how the thermodynamic and transport properties of such a fluid are affected by density.
INTRODUCTION Little information exists concerning the thermal conductivities of methanol at elevated pressures. In 1923, Bridgman1 obtained data to a pressure of 1.2 GPa, but in the absence of subsequent experiments those results remained unconfirmed. Thus, a recent formulation2 is limited to 245 MPa and, moreover, beyond 60 MPa is based on a single study.3 Separately, but similarly, values of specific heats above 10 MPa are inferred,4 above 100 MPa primarily from speeds of sound (to 276 MPa) and one set of density measurements which extends to 800 MPa. Here we report thermal diffusivities, Dth, of methanol, measured in a diamond-anvil cell (DAC) to a pressure of 5 GPa. Diffusivities and conductivities, Kth, are related as Kth = DthCpρ (where Cp and ρ are, respectively, specific heat per mass and mass density). Recently,5 thermal effusivities, e = Cpρ sqrt(Dth), have also been reported, to 14 GPa. In combination, these two complementary data sets allow us to confirm the accuracy of Bridgman’s results, yield values of thermal conductivities and specific heats which may reasonably be extrapolated to 8 GPa, and, for lower pressures, offer a useful verification of standard formulations for conductivity2 and specific heat.4 Interpolation between quantities measured in the DAC and those taken at ambient (0.1 MPa) pressures is shown to be a reliable method of estimating data unavailable at intermediate pressures. In addition to being a common solvent, methanol is also extensively studied as a model of network-forming, hydrogenbonded liquids, yielding insights into, inter alia, the process of glassing. Happily, liquid methanol can be compressed far beyond its freezing point, the application of high pressures allowing us to follow changes in its properties over significant and continuous variations in density; for example, in a study6 up to 4.3 GPa the shortening of hydrogen bonds has been inferred from high-resolution NMR data, while speeds of sound have been measured to 30 GPa and a density of roughly twice the value under ambient conditions.7 Other properties of methanol which have been investigated at high pressures © XXXX American Chemical Society
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EXPERIMENTAL METHODS
Methanol (CAS 67-56-1) from a freshly opened bottle (Fisher Chemical, manufacturer’s stated purity >99.9%) was loaded directly into a DAC, with gaskets formed from either hardened Inconel 718 or rhenium. A small crystal of ruby within the load allowed pressure to be measured12 with a precision of 0.02 GPa; the accuracy of the ruby scale is believed to be 1%.13 The cell was held at ambient temperature, between 25 and 28 °C. Diffusivities were determined through use of transient optical gratings.14,15 Briefly, a 180 ps laser pulse of wavelength λ0 = 1.064 μm is beam-split and recombined in the sample at an angle 2θ. Absorption of a small fraction of the light produces a one-dimensional thermal grating of periodicity λth = λ0/(2 sin(θ)). After each excitation pulse a second laser pulse (of 2 ns duration and wavelength 0.532 μm) is introduced at the Bragg angle, and at successively longer delays. This second pulse diffracts off the thermal grating, and the diffracted light constitutes the signal. The amplitude of the thermal grating decays exponentially with time constant τ = λ2th/(4π2Dth) (the signal intensity, S, decays at twice this rate). In these experiments λth was held at 3.01 μm and τ ranged between 1 and 2.3 μs. Representative signals are plotted on a semilogarithmic scale in Figure 1 and are seen to be exponential over 2 orders of magnitude of intensity. Diffusivities measured at 0.1 MPa for methanol, and for water, scattered with a rms deviation of 2% about literature values.2,16,17 Received: February 26, 2017 Accepted: June 12, 2017
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DOI: 10.1021/acs.jced.7b00222 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Figure 2. Experimentally determined diffusivities (blue circles) are plotted against pressure; error bars represent 1σ uncertainties given solely by fits of the scattered intensities to exponential functions of time. The blue curve through the data is the result of fitting a straight line to the diffusivities as a function of density (see below). The short, black curve is calculated from the formulation2 of Sykioti et al. for a temperature of 26 °C, with a dashed continuation between the upper limit (245 MPa) of that formulation and the upper limit (0.8 GPa) of the associated EOS4 from which the necessary ρ and Cp were derived. Red squares indicate calculations from thermal conductivities reported by Bridgman,1 using for this purpose densities from ref 4 and a specific heat held constant at its 0.1 MPa value.
Figure 1. Intensities of light scattered from the transient thermal gratings, S, are plotted against time, t, at three different pressures (from top to bottom the pressures were 0.1 MPa, 0.88 GPa, and 5.3 GPa). Red, dashed lines are fits of the data to exponential functions.
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RESULTS AND DISCUSSION Measured diffusivities are given in Table 1 and plotted against pressure in Figure 2. Further analysis of the data requires Table 1. Measured Pressures (P), Temperatures (T), and Thermal Diffusivities (Dth) of Methanola P/GPa
T/°C
107·Dth/m2·s−1
0.00 0.37 0.40 0.86 0.88 1.29 1.29 1.75 2.43 3.10 3.12 4.22 5.00 5.30
26.0 27.0 26.7 27.8 26.0 27.9 27.9 27.6 26.0 26.0 26.0 25.0 26.6 24.8
0.97 (2) 1.35 (4) 1.32 (4) 1.57 (6) 1.59 (5) 1.70 (4) 1.66 (3) 1.80 (3) 1.86 (6) 1.92 (5) 1.99 (5) 2.17 (4) 2.37 (22) 2.19 (4)
Figure 3. Diffusivities plotted against density. A straight line, forced through the 0.1 MPa value,2 represents the current data within the limits of uncertainty. Symbols are the same as in Figure 2.
Dth /m 2·s−1 = b1(ρ /kg·m−3 − 800) + b2
a
Standard uncertainties are u(T) = 0.1 K, u(P) = 0.02 GPa. For the diffusivities, estimated 1σ uncertainties in the least significant figure are given parenthetically
−10
with b1 = 2.07 × 10 and b2 = 1.03 × 10 . Scatter about this line has a rms misfit of
