Relaxation calorimeter for hydrogen thermoporometryE. Van Cleve, M. A. Worsley, and S. O. Kucheyev Citation: Rev. Sci. Instrum. 84, 053901 (2013); doi: 10.1063/1.4803180 View online: http://dx.doi.org/10.1063/1.4803180 View Table of Contents: http://rsi.aip.org/resource/1/RSINAK/v84/i5 Published by the American Institute of Physics. Additional information on Rev. Sci. Instrum.Journal Homepage: http://rsi.aip.org Journal Information: http://rsi.aip.org/about/about_the_journal Top downloads: http://rsi.aip.org/features/most_downloaded Information for Authors: http://rsi.aip.org/authors

REVIEW OF SCIENTIFIC INSTRUMENTS 84, 053901 (2013)

Relaxation calorimeter for hydrogen thermoporometryE. Van Cleve, M. A. Worsley, and S. O. Kucheyeva)

Lawrence Livermore National Laboratory, Livermore, California 94550, USA

(Received 30 January 2013; accepted 15 April 2013; published online 3 May 2013)

A relaxation calorimeter for measuring the heat capacity of hydrogen isotopes in nanoporous solidsis described. Apparatus’ features include (i) cooling by a pulse tube refrigerator, (ii) a modu-lar 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 ca-pacity measurements of H2 in Vycor (silica) nanoporous glass, yielding a very detailed pore sizedistribution analysis with an effectively sub-Angstrom resolution. © 2013 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4803180]

I. INTRODUCTION

The phase diagram of condense matter is influenced bygeometric confinement.1 This is the basis of the thermo-porometry (TP),2 which is a relatively novel and still fastdeveloping technique for characterization of porous solids.3

According to the Gibbs-Thomson formalism applied to solidswith pores of simple geometries (such as cylinders, slits, andspheres), the suppression of the liquid-solid phase transitiontemperature scales inversely with the pore size.1, 3 Hence,the TP evaluates the pore size distribution (PSD) by measur-ing suppression of freezing (melting) temperature of a liquid(solid) confined in pores of an open-cell porous matrix.

The liquid-solid phase transition can be monitored byvarious methods, with calorimetry being one of the most com-monly used ones.3 Indeed, the measurement of the effectiveheat capacity of condensed matter as a function of tempera-ture reveals liquid-solid phase transitions due to the latent heatassociated with them. Most of previous calorimetric TP stud-ies have involved differential scanning calorimetry (DSC) andwater as the pore filling liquid,3 which has a large heat capac-ity and a convenient bulk freezing temperature close to roomtemperature.

However, although convenient, TP studies with DSC andwater have several limitations. These include (i) imperfectand material-dependent wetting of the pore walls by water;(ii) potential contributions from chemical interaction of watermolecules with pore surfaces; (iii) the effect of impurities dis-solved in water that could influence phase transition tempera-tures; (iv) a large liquid-vapor surface tension of water which,in limiting cases of fragile materials such as aerogels, couldresult in the structure collapse on wetting or drying; (v) possi-ble effects of stresses induced by water expansion on freezinginside the pores; (vi) undercooling affecting calorimetry scanson cooling; and (vii) the freezing-melting hysteresis1, 3 affect-ing DSC scans.

All of the above issues could be addressed by using hy-drogen as the pore filling liquid and relaxation calorimetry4

rather than DSC.5 Indeed, liquid hydrogen (i) appears to per-fectly wet all solids with a zero contact angle,6 (ii) is expectedto be chemically inert at temperatures of interest (<20 K),

a)Author to whom correspondence should be addressed. Electronic mail:kucheyev@llnl.gov.

(iii) is commercially available essentially free from chemicalimpurities (that are also relatively straightforward to controlsince they freeze out at much larger temperatures), and (iv)has a very low liquid-vapor surface tension of 3 mJ m−2 fornormal H2 at the triple point (compared to 72 mJ m−2 for wa-ter at 25 ◦C).6–11 Moreover, the undercooling commonly ob-served in the bulk liquid surrounding the filled nanoporousspecimen, which does affect the DSC and AC-calorimetrymethods,5 is not an issue for hydrogen relaxation calorime-try experiments. Indeed, as we show below, the latent heatreleased on solidification of undercooled bulk hydrogen (out-side the nanoporous matrix) rapidly brings the calorimetercell to the equilibrium freezing temperature during relaxationcalorimetry cooling scans.

Several calorimetric studies of the liquid-solid phasetransition of H2 confined in nanoporous solids have previ-ously been reported.12–16 Interestingly, all of these previousstudies12–16 have been limited to hydrogen confined in Vycor(silica) nanoporous glass. These experiments12–16 have usedunique, custom built equipment that involved costly liquid Hecooling, heavily relied on glue and solder joints to assemblethe apparatus, and had a relatively gross temperature controlof �100 mK. Although these design and construction meth-ods are common in the low-temperature physics community17

and were appropriate for the purpose of those previous pi-oneering studies,12–16 they are prohibitively expensive andcumbersome for any routine hydrogen TP analysis. In thispaper, we describe a relatively rudimentary apparatus for aTP analysis of nanoporous solids by relaxation calorimetry attemperatures above ∼5 K, which overcomes the limitationsmentioned above.

II. DESIGN AND CONSTRUCTION

Before the presentation of the details of the design andconstruction of the calorimeter, it is instructive to describea typical relaxation calorimetry experiment. In relaxationcalorimetry,4, 5 the specimen is thermally well anchored toa specimen holder, which we will refer to as the calorime-ter cell (Fig. 1). The cell with the sample are weakly ther-mally connected to a heat sink held at a constant temperature,which we call the cell heat sink. The heat capacity can bemeasured during either cooling or warming of the sample. In

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053901-2 Van Cleve, Worsley, and Kucheyev Rev. Sci. Instrum. 84, 053901 (2013)

FIG. 1. Schematic of the calorimeter for hydrogen thermoporometry analy-sis of nanoporous materials. Heaters and thermometers are denoted with “H”and “T”, respectively.

the case of cooling, the cell with the sample are heated to atemperature above the temperature of the cell heat sink. Af-ter that, the cell heater is turned off, and the cell temperatureis recorded as a function of time as the cell cools down, ap-proaching the temperature of the cell heat sink, which is main-tained constant. In the case of warming, the temperature of thecell is first equilibrated with that of its heat sink. After that,a constant heating power is applied to the cell, and its tem-perature rise is recorded. The heat capacity is derived froma straightforward analysis of such temperature-time profiles,described in Sec. III.

For cryogenic TP measurements, we also need a meansto add (and subsequently remove) a cryogenic liquid to fillthe pores of the nanoporous solid under investigation. Thiscould be done with a capillary connecting the calorimeter cellwith a fluid reservoir at room temperature.12, 13, 15 Control ofthe thermal behavior of the capillary is important for TP mea-surements, and we discuss it below.

All the Cu components discussed below have been ma-chined from an OFHC-grade Cu (McMaster-Carr, copper al-loy 101, 99.99% purity) and have been gold plated to reducetheir emissivity and suppress the environmental corrosion ofthe Cu surface. The Cu was used as-received, without anyadditional thermal processing, and no measurements of theresidual resistivity ratio (RRR) of Cu were performed. A layerof thermal grease (Apiezon N) mixed with 340-mesh Cu pow-der has been placed between all the pressure joints to increasethe thermal conduction between components.

The calorimeter that we have built is schematically illus-trated in Fig. 1. Cooling is provided by a pulse tube refriger-ator, PTR (Cryomech, model PT410-RM with a remote mo-tor option). The cold working surface on which the calorime-ter components are assembled is provided by a Cu workingdisk (12.5 mm thick) that is separated from the 2nd stageof the PTR by a stainless steel (SS) disk with a thickness of12.5 mm. The diameters of both the SS and Cu working disks

are the same as the diameter of PTR’s 2nd stage (95 mm). InFig. 1, the SS disk is referred to as the “damper” since it isintroduced to damp thermal oscillations18 from ∼100 to 500mK on the 2nd stage of the PTR to �1 mK on the Cu work-ing disk. The Cu and SS disks are bolted to PTR’s 2nd stagewith SS bolts. Invar washers (3 mm thick) under the heads ofthe SS bolts are used to compensate for the difference in thethermal expansion coefficients of SS and Cu.

Two Cu thermal heat sinks (cell and capillary heat sinks)are attached to the Cu working disk with (vented) SS bolts,with 3-mm-thick invar washers under the bolt heads. Thecell heat sink is used to heat sink the wires attached to thecalorimeter cell. The capillary heat sink is designed to ther-molyze the SS hydrogen filling capillary described below.Both sinks are identical cylinders (40 mm in diameter and27 mm in height) with several holes to accept wire-heat-sinkbobbins, thermometers, heaters, and thermal link wires fromthe cell. Both heat sinks are thermally separated from theCu disk by 1-mm thick SS washers, with different areas tomatch the temperature range of interest without overloadingthe refrigerator with excess heat. For example, for the H2 mea-surements presented below, these washers have areas of 2.05and 0.16 cm2 for the calorimeter and capillary heat sinks, re-spectively. Each Cu thermal sink is equipped with a cartridgeheater (Lakeshore, model HTR-25) and a Ge resistance ther-mometer (Lakeshore, model GR-1400-CD). Additional Geresistance or Cernox thermometers (Lakeshore, models GR-1400-CD, CX-1070-CU, and CX-1080-CU) are positioned atthe Cu disk, the 2nd stage, and the 1st stage of the PTR. Thethermometers and heaters are monitored and controlled withtwo identical temperature controllers (Lakeshore, model 336).All the Ge resistance thermometers used were calibrated bythe manufacturer with a calibrated accuracy of ±4 mK.

The Cu heat sinks are positioned in the same radial po-sition on the Cu disk with 120◦ between the heat sinks. Thethird position (120◦ from both heat sinks) has been reservedfor a third thermal sink with a J-converter required for theortho-para conversion of hydrogen, which has not been im-plemented in this project.

The calorimeter cell is composed of two Cu pieces, thelid and the body, assembled together with twelve 2-56 brassbolts and sealed with an indium gasket. The capillary, ther-mometer, heater, and thermal link wires are attached to thecell lid, while the cell body has no components and can beused as a mold for casting aerogels or a container during sam-ple treatment. The cell body is 22 mm in diameter and 7.5mm tall with a circular hole, 20 mm in diameter and 6 mmdeep, machined out. Although the geometry of the cell bodycould be further optimized to minimize its heat capacity (i.e.,the addendum), it has been found to be sufficient for studyingnanoporous monoliths with volumes �0.1 cm−3 and porosi-ties �30%.

The cell lid is a disk, 30 mm in diameter and 3 mm inthickness. It has twelve through holes for 2-56 brass bolts anda 3.05-mm in diameter hole for a Ge resistance thermome-ter (Lakeshore, model GR-1400-AA). The thermometer leadwires are heat sunk on the lid with varnish (VGE-7031). Asingle hole, 1.59 mm in diameter, is in the middle of the lid,hosting the SS capillary brazed to the lid. The cell heater

053901-3 Van Cleve, Worsley, and Kucheyev Rev. Sci. Instrum. 84, 053901 (2013)

is wound in a groove made on the edge of the cell lid andthermally anchored with varnish (VGE-7031). The heater is anichrome wire, 0.202 mm in diameter and 500 mm in length,with a room temperature resistance of 48 Ohm.

The SS capillary (with inner and outer diameters of 0.254and 1.588 mm, respectively) that is used to load the calorime-ter cell with hydrogen is wrapped around and soft soldered toa Cu bobbin, which is attached to the capillary heat sink with abrass bolt (Fig. 1). Cajon (VCR) 1/8 in. connectors are used tojoin the capillary-bobbin and capillary-calorimeter-lid assem-blies to each other and to the rest of the capillary leading to theroom-temperature fluid reservoir. From the capillary heat sinkbobbin to the room-temperature feedthrough, the SS capillaryhas a nichrome heater wire wound around it and thermally an-chored with varnish (VGE-7031). This is done for situationswhen a rapid heating of the capillary is required to melt a plugwithin it.

The calorimeter cell is thermally connected to thecalorimeter sink via several Cu wires (0.127 mm in diam-eter and 76 mm long). The thermal link wires are soft sol-dered to brass washers and bolted onto the calorimeter lidand the calorimeter sink. These wires, along with the wiresof the heater and the thermometer on the cell lid provide theweak thermal link, while the heat flow through the SS capil-lary (∼100 mm long) connecting the cell with the capillaryheat sink is negligible. The number of Cu wires is selected tohave a characteristic relaxation time constant of ∼100 s fora “dry” cell (i.e., without hydrogen). For example, for the H2

experiments described in Secs. II and IV, 14 Cu wires wereused.

All heater wires (Cu) are heat sunk19 at the 1st and2nd stages of the PTR, while thermometer wires (phosphorbronze) are heat sunk at the Cu working disk only. The lowesttemperature part of the apparatus illustrated in Fig. 1 is en-closed in a cylindrical Cu shield bolted to the first stage of therefrigerator. The shield has 4 windows made of Schott KG-1 heat absorbing glass (purchased from Edmund Optics) foroptical access when necessary. The entire cryogenic assemblyis hosted in a 6-way-cross chamber (MDC Vacuum ProductsCorp.) evacuated with a turbomolecular pump.

A specific amount of gas is transferred to the cell from aroom-temperature reservoir with standard gas-handling tech-niques. Pressure is measured at room temperature with capac-itance diaphragm sensors (MKS, Baratron 690A).

Figure 2 shows a temporal evolution of temperatures ofthe 2nd stage, the cell heat sink, and the calorimeter cell for acase when the cell and the cell heat sink are kept at 15 and 5.5K, respectively. It demonstrates damping of thermal oscilla-tions present on the 2nd stage of the PTR (with an amplitudeof ∼200 mK for the heat load conditions of Fig. 2). The tem-perature resolution for both the calorimeter cell and its sink is�1 mK.

III. RELAXATION CALORIMETRY

The heat capacity of the cell thermally linked to a heatsink held at temperature Tsink is given by

C = dq

dT=

dq

dt

dTdt

= q

T= P − keff (T − Tsink)

T, (1)

FIG. 2. Temporal evolution of temperatures of (a) the 2nd stage, (b) the cellheat sink, and (c) the calorimeter cell for the case when the cell and the cellheat sink are kept at 15 and 5.5 K, respectively.

where q is the power leaving or entering the cell, resultingin a change of its temperature T over time t; P is the powerof the cell heater; and keff is the effective (integrated) thermalconductance between the cell at T and the cell heat sink atTsink. Equation (1) assumes one-dimensional heat flow, spa-tially uniform cell temperature, and a negligible heat capacityof the thermal link, which are common assumptions of thethermal relaxation calorimetry method.4 Units of C, q, T, andkeff are J/K, J, K, and W/K, respectively. In a special case whenC, keff, and P are constants, Eq. (1) can be analytically inte-grated, yielding an exponential decay or growth with a timeconstant τ = C/keff for cases of zero and non-zero constantheating power P, respectively. In this special case, for cooling(P = 0),

T (t) = Tsink + [T (0) − Tsink] exp

(− t

τ

), (2)

and, for warming (P > 0),

T (t) = Tmax − [Tmax − T (0)] exp

(− t

τ

), (3)

where Tmax = P/keff + Tsink is the maximum temperature thatthe cell can reach with a constant cell heater power P.

For either cooling or warming, before measuring the C(T)dependence, both the cell and capillary heat sinks are set atthe same temperature Tsink, which is in the range of ∼5−18K, determined by the temperature interval of interest and thedesired rate of cooling. For cooling scans, the calorimeter cellis set at a temperature above that of the heat sink Tsink. Af-ter that, the cell heater is turned off, and the cell temperatureis recorded as a function of time with a data acquisition rateof ∼2 Hz. In the case of the measurement of C(T) on warm-ing, the cell temperature is first equilibrated with that of itssink. After that, a constant heating power is applied to the cellheater, and the cell temperature rise is recorded as a functionof time.

The C(T) dependence is then evaluated based on Eq. (1)from measured T(t) curves and an additional measurementof the keff(T) dependence. The thermal conductance [keff(T)= P/(T − Tsink)] is measured by adding a known amount of

053901-4 Van Cleve, Worsley, and Kucheyev Rev. Sci. Instrum. 84, 053901 (2013)

FIG. 3. Temporal evolution of the temperature of the calorimeter cell witha Vycor nanoporous glass specimen (a) on cooling when the cell heater isturned off (at 0 s) and (b) on warming when the cell heater is turned on (at 0s) with a constant power. Shown are curves for both a “dry” cell (i.e., the cellwith a Vycor specimen inside) and the cell with the Vycor specimen (witha volume of 0.62 cm3 and a density of 1.47 g cm−3) filled with 3.3 × 10−2

mol of H2 with an ortho-fraction of 0.47. The bulk melting temperature of H2is shown by a horizontal dash line. For clarity, only every 20th experimentalpoint is displayed. The inset in (b) shows details of the cooling curve from(a) for crystallization of H2 outside the Vycor monolith, revealing an under-cooling of ∼40 mK followed by a plateau corresponding to crystallization ata constant temperature.

heat P to the cell heater and recording the cell temperature atequilibrium. The sink temperature Tsink is again kept constantduring such measurements. The contribution of hydrogen tothe total heat capacity of the cell is obtained by subtraction ofthe so called addendum, which is the heat capacity of the celland a “dry” (i.e., without hydrogen) nanoporous solid withinit.

Due to a weak thermal link between the cell heat sinkand the cell itself, a parasitic thermal radiation and ortho-paraconversion loads on the cell, the accuracy of thermometry,and the limited experimental time allocated for every coolingcurve, the temperature of the cell at the end of the coolingcurve is not necessarily equal to Tsink. The final temperatureof the cell could, however, be determined by fitting the end ofthe cooling curve T(t) with Eq. (2) since both keff and C areessentially constant in the narrow temperature interval (�0.2K in our experiments) of cooling curve tails.

Figure 3 shows the temporal evolution of the tempera-ture of the calorimeter cell with a Vycor nanoporous glassspecimen20 for both cooling and warming scans for both casesof a “dry” cell (i.e., the cell with a Vycor specimen inside)and the cell (with Vycor) filled with H2 (obtained from Math-eson Tri-Gas) with a purity of �99.999% and natural iso-topic content with a J = 1 species (i.e., ortho-hydrogen) frac-tion of 0.47.21–24 Figure 4 shows C(T) dependences evaluatedbased on the analysis of the cooling and warming curves fromFig. 3 with Eq. (1) without any data filtering during themeasurement or any post-measurement processing (such assmoothing) of the temperature-time dependences measured.Crystallization of bulk hydrogen located outside the Vycormonolith manifests as a plateau in the cooling and warmingcurves in Fig. 3 and as a large peak in the heat capacity inFig. 4 at ∼14 K. An undercooling effect is better illustrated bythe inset in Fig. 3(b), which also demonstrates a temperature

FIG. 4. The heat capacity of 3.3 × 10−2 moles of H2 with an ortho-fractionof 0.47 in a calorimeter cell containing a Vycor nanoporous glass specimen(with a volume of 0.62 cm3 and a density of 1.47 g cm−3) measured duringcooling and warming. The sharp peak at ∼14 K (marked by a vertical dashline) is caused by crystallization of hydrogen outside the Vycor monolith,while broader peaks at lower temperatures are due to hydrogen crystallizationinside Vycor.

stability and resolution of �1 mK. The undercooling does notaffect the cooling scans since, after the initial crystallizationevent, the cell temperature is rapidly brought to the equilib-rium freezing temperature [evident as a plateau following theundercooling peak in the inset of Fig. 3(b)] due to the releasedlatent heat of crystallization of bulk hydrogen.

IV. THERMOPOROMETRY

Temperature dependences of the heat capacity C(T) ofhydrogen confined inside nanoporous solids, such as shownin Fig. 4, can be converted to PSDs, dV

dr(r), where V and r

are the pore volume and radius, respectively.3 For this, the Tscale is converted to the r scale, while C could be correlatedwith dV

dr. The retardation of the crystallization temperature of

a liquid inside a nanoporous scaffold can be expressed as

�T = T mbulk − T = βT m

bulkσsl

ρl�H (r − δ)= α

r, (4)

where T mbulk is the solid-liquid phase transition temperature

of the unconstrained material [corresponding to the crystal-lization plateau in T(t) curves as illustrated in the inset ofFig. 3(b)], ρ l is the density of the liquid, σ sl is the solid-liquidsurface energy, �H is the latent heat of crystallization, β is aconstant that depends on the pore geometry and on whetherfreezing or melting is considered,3 δ is the thickness of thepre-molten liquid layer on the pore walls, and α is a constantcombining all of the material dependent parameters with anassumption of r � δ.

The value of α in Eq. (4) is not known a priori largely be-cause σ sl is not known for H2.25 However, the value of α couldbe estimated empirically by comparing PSDs measured by TPand by better established gas sorption or mercury porosime-try methods. Figure 5 shows the PSD of the Vycor specimenstudied in this work derived from adsorption and desorption

053901-5 Van Cleve, Worsley, and Kucheyev Rev. Sci. Instrum. 84, 053901 (2013)

FIG. 5. Pore size distributions of Vycor nanoporous glass derived from aBJH analysis of gas sorption isotherms (on adsorption and desorption) andfrom thermoporometry (on freezing and melting). For clarity, only every 10thexperimental point is displayed in thermoporometry-derived curves.

branches of the nitrogen sorption isotherm according to theBarrett-Joyner-Halenda (BJH) theory.26, 27 As discussed in de-tail previously,3 melting (warming) TP curves are comparedwith adsorption, while freezing (cooling) TP curves are simi-lar to desorption branches of isotherms. A comparison of BJHand TP curves gives α values of ∼115 and 60 K Å, for casesof freezing and melting, respectively. A factor of two differ-ence between α values for melting and freezing suggests thepredominantly cylindrical shape of pores in Vycor, consistentwith previous reports.3

The heat capacity could be related to the pore volume asfollows:

dV

dr= Clatent�T 2

�Hα= Clatentα

�Hr2, (5)

where Clatent is the contribution of latent heat of crystalliza-tion to the total heat capacity measured, which is calculatedby subtracting a smoothly varying background from the C(T)curve.28 Figure 5 shows PSDs calculated by converting C(T)data from Fig. 4 with Eqs. (4) and (5) with constant valuesof �H = 117 J/mol (Ref. 6) and α given above. Qualita-tive agreement between the general shapes of PSDs measuredwith TP and BJH methods is revealed by Fig. 5.

However, it is clearly seen from Fig. 5 that the hydro-gen TP curves are much more detailed, providing an effec-tively sub-Angstrom resolution in the pore size scale. Indeed,Fig. 5 reveals that PSDs of Vycor measured by the gas sorp-tion technique are characterized by a single peak centered on∼31 and ∼45 Å for desorption- and adsorption-derived PSDs,respectively. In contrast, TP-derived PSDs contain more in-formation and have more complex shapes than those mea-sured by BJH. In particular, the broad peak seen in the BJH-desorption-derived PSD corresponds to two peaks centered on∼26 and 33 Å clearly resolved in the PSD derived from a TP-cooling scan. This is directly related to the excellent thermalstability and resolution of the calorimeter described here.29

The total pore volume measured by the TP is, however, lowerthan that measured by gas sorption in both cases of Fig. 5.The reason for this is not clear. It could be related to expected

temperature dependences of �H, σ sl, and ρ l and to limita-tions of the BJH analysis. More work is currently needed tounderstand these effects.

V. CONCLUSION

An apparatus for measurements of the heat capacity ofhydrogens by relaxation calorimetry has been designed andbuilt. The calorimeter has been tested on effective heat ca-pacity measurements of H2 in Vycor nanoporous glass. Poresize distributions of Vycor measured by hydrogen thermo-porometry and a conventional gas sorption technique are inqualitative agreement, but with the hydrogen thermoporome-try analysis yielding an effectively sub-Angstrom resolution,revealing additional features of the pore size distribution notresolved by a conventional gas sorption analysis.

ACKNOWLEDGMENTS

We are grateful to R. R. Miles, B. J. Kozioziemski, J. B.Lugten, and E. R. Mapoles for valuable discussions and toBill Benett and Noel Peterson for technical assistance. Thiswork was performed under the auspices of the U.S. DOE byLLNL under Contract DE-AC52-07NA27344.

1See, for example, a review by H. K. Christenson, J. Phys.: Condens. Matter13, R95 (2001).

2Thermoporometry is also sometimes referred to as cryoporometry, thermo-porosimetry, and phase transition porosimetry. The terminology of choiceis often related to the experimental approach used to monitor the phasetransition.

3See, for example, reviews by O. V. Petrov and I. Furo, Prog. Nucl. Magn.Reson. Spectrosc. 54, 97 (2009); M. R. Landry, Thermochim. Acta 433, 27(2005).

4R. Bachmann et al., Rev. Sci. Instrum. 43, 205 (1972).5See, for example, a review by G. R. Stewart, Rev. Sci. Instrum. 54, 1 (1983).6P. C. Souers, Hydrogen Properties for Fusion Energy (University ofCalifornia Press, Berkley, 1986).

7CRC Handbook of Chemistry and Physics, 84th ed., edited by D. R. Lide(CRC Press, New York, 2003).

8R. J. Corruccini, National Bureau of Standards Technical Note TN-322(1965).

9V. N. Grigorev and N. S. Rudenko, Sov. Phys. JETP 20, 63 (1965).10Y. P. Blagoi and V. V. Pashkov, Sov. Phys. JETP 22, 999 (1966).11V. G. Baidakov, K. V. Khvostov, and V. P. Skripov, Sov. J. Low Temp.

Phys. 7, 463 (1981).12J. L. Tell and H. J. Maris, Phys. Rev. B 28, 5122 (1983).13R. H. Torii, H. J. Maris, and G. M. Seidel, Phys. Rev. B 41, 7167 (1990).14D. F. Brewer, J. Rajendra, N. Sharma, and A. L. Thomson, Physica B 165–

166, 569 (1990).15E. Molz, A. P. Y. Wong, M. H. W. Chan, and J. R. Beamish, Phys. Rev. B

48, 5741 (1993).16D. F. Brewer, J. C. N. Rajendra, and A. L. Thomson, Physica B 194–196,

687 (1994).17J. W. Ekin, Experimental Techniques for Low-Temperature Measurements

(Oxford University Press, Oxford, 2006).18K. Allweins, L. M. Qiu, and G. Thummes, Adv. Cryog. Eng. 53, 109

(2008).19J. G. Hust, Rev. Sci. Instrum. 41, 622 (1970).20The Vycor glass monolith studied here was obtained from Advanced Glass

& Ceramics. Before loading into the cell, the monolith was dehydrated byannealing 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 cooldown.

21The ortho-para composition has been estimated based on the measurementof the bulk freezing temperature (T m

bulk). The T mbulk value has been found

to obey the following dependence obtained by a solution of a differential

053901-6 Van Cleve, Worsley, and Kucheyev Rev. Sci. Instrum. 84, 053901 (2013)

equation with assumptions of the second order self-conversion22, 23 and thefirst order catalyst-assisted conversion24 processes and negligible rates ofback-conversion to the J = 1 state: T m

bulk = T0 + �TJk1

k1+k2C0C0

exp(k1 t)−k2,

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, �TJ = 0.203 K is thefreezing temperature difference between ortho- and para-H2, C0 = 0.75 isthe initial fraction of ortho-H2 (equilibrium at room temperature),6 and k1is the rate of catalytically-assisted conversion of H2 molecules due to theirinteraction with Cu cell and SS capillary walls.

22E. Cremer and M. Polanyi, Z. Phys. Chem. Abt. B 21, 459 (1933).23A. H. Larsen, F. E. Simon, and C. A. Swenson, Rev. Sci. Instrum. 19, 266

(1948).24C. M. Cunningham and H. L. Johnston, J. Am. Chem. Soc. 80, 2377

(1958).

25In addition, it is commonly assumed that all the parameters in Eq. (4) (σ sl,ρl, and �H) are independent of temperature, which is a limitation of theTP analysis.

26E. P. Barrett, L. G. Joyner, and P. P. Halenda, J. Am. Chem. Soc. 73, 373(1951).

27Pore volume and size analysis was performed by the BJH method with anASAP 2000 Surface Area Analyzer (Micromeritics Instrument Corpora-tion). Nitrogen was used as the adsorbate at 77 K. Prior to cooling downthe sample, it was heated to 150 ◦C under vacuum (∼10 Torr) for ∼24 h toremove adsorbed species.

28Figure 4 reveals that the C(T) dependence of normal H2 in Vycor doesnot follow the expected C ∝ T3 dependence of the Debye model, which isconsistent with previous observations.6, 13

29Moreover, PSD plots derived from C(T) curves of Fig. 4 span a large rangeof pore radii of ∼10−3000 Å (for clarity, not shown in Fig. 5).