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Relaxation calorimeter for hydrogen thermoporometry
2.Thermoporometry is also sometimes referred to as cryoporometry, thermoporosimetry, and phase transition porosimetry. The terminology of choice is often related to the experimental approach used to monitor the phase transition.
6. P. C. Souers, Hydrogen Properties for Fusion Energy (University of California Press, Berkley, 1986).
7. CRC Handbook of Chemistry and Physics, 84th ed., edited by D. R. Lide (CRC Press, New York, 2003).
8. R. J. Corruccini, National Bureau of Standards Technical Note TN-322 (1965).
9. V. N. Grigorev and N. S. Rudenko, Sov. Phys. JETP 20, 63 (1965).
10. Y. P. Blagoi and V. V. Pashkov, Sov. Phys. JETP 22, 999 (1966).
11. V. G. Baidakov, K. V. Khvostov, and V. P. Skripov, Sov. J. Low Temp. Phys. 7, 463 (1981).
17. J. W. Ekin, Experimental Techniques for Low-Temperature Measurements (Oxford University Press, Oxford, 2006).
18. K. Allweins, L. M. Qiu, and G. Thummes, Adv. Cryog. Eng. 53, 109 (2008).
20.The Vycor glass monolith studied here was obtained from Advanced Glass & Ceramics. Before loading into the cell, the monolith was dehydrated by annealing it at 150 °C for ∼24 h. The monolith was also kept under vacuum (at ∼10−7 Torr) for ∼48 h at room temperature before beginning the cool down.
21.The ortho-para composition has been estimated based on the measurement of the bulk freezing temperature (). The value has been found to obey the following dependence obtained by a solution of a differential equation with assumptions of the second order self-conversion22,23 and the first order catalyst-assisted conversion24 processes and negligible rates of back-conversion to the J = 1 state: , where T0 is the bulk freezing temperature of (J = 0) para-hydrogen, k2 = 0.0153 h−1 is the rate of self-conversion of H2, ΔTJ = 0.203 K is the freezing temperature difference between ortho- and para-H2, C0 = 0.75 is the initial fraction of ortho-H2 (equilibrium at room temperature),6 and k1 is the rate of catalytically-assisted conversion of H2 molecules due to their interaction with Cu cell and SS capillary walls.
22. E. Cremer and M. Polanyi, Z. Phys. Chem. Abt. B 21, 459 (1933).
25.In addition, it is commonly assumed that all the parameters in Eq. (4) (σsl, ρl, and ΔH) are independent of temperature, which is a limitation of the TP analysis.
27.Pore volume and size analysis was performed by the BJH method with an ASAP 2000 Surface Area Analyzer (Micromeritics Instrument Corporation). Nitrogen was used as the adsorbate at 77 K. Prior to cooling down the sample, it was heated to 150 °C under vacuum (∼10 Torr) for ∼24 h to remove adsorbed species.
28.Figure 4 reveals that the C(T) dependence of normal H2 in Vycor does not follow the expected C ∝ T3 dependence of the Debye model, which is consistent with previous observations.6,13
29.Moreover, PSD plots derived from C(T) curves of Fig. 4 span a large range of pore radii of ∼10−3000 Å (for clarity, not shown in Fig. 5).
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A relaxation calorimeter for measuring the heat capacity of hydrogen isotopes in nanoporous solids is described. Apparatus’ features include (i) cooling by a pulse tube refrigerator, (ii) a modular design, allowing for rapid reconfiguration and sample turn around, (iii) a thermal stability of ≲1 mK, and (iv) a bottom temperature of ∼5 K. The calorimeter is tested on effective heat capacity measurements of H2 in Vycor (silica) nanoporous glass, yielding a very detailed pore size distribution analysis with an effectively sub-Angstrom resolution.
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