Supplementary Information

Isosteric heat of hydrogen adsorption on MOFs: Comparison between

adsorption calorimetry, isosteric method and analytical models

A. F. Kloutse,† R. Zacharia,†,* D. Cossement,† R. Chahine†, R. Balderas-Xicohténcatl‡, H. Oh‡, B.

Streppel‡, M. Schlichtenmayer‡, M. Hirscher‡

†Institut de recherche sur l'hydrogène, Université du Québec à Trois-Rivières, Trois-Rivières (QC), G9A

5H7, Canada

‡Max-Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany

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Figure S1. Schematic representation of the coupled volumetric-calorimetric setup. 1. sample cell,

2. calorimetric well, 3. heater, 4. thermopile, 5. sample, 6. reference cell, 7. Tian-Calvet

calorimeter, 8. needle valve, 9. pneumatically actuated ball valves.

Adsorption Calorimetry

Simultaneous calorimetric-manometric measurements were performed using an experimental

setup that couples a commercial Tian-Calvet type micro-calorimeter BT 2.15 (SETARAM) with

a home-built Sievert’s volumetric adsorption measurement system; a schematic of which is

shown in the Figure 2. The interior of the calorimeter consists of an insulated calorimetric block

with two identical calorimetric wells referred to as reference chamber and sample chamber. The

heat flux measurement zone of both calorimetric wells features a 3D Calvet heat fluxmeter

sensor which is essentially a thermopile consisting of an axial array of 9 cylindrically arranged

concentric rings containing a total of 684 thermocouples (sensitivity = 30 µV/mW, resolution =

0.10 µW). The measurement zone accommodates two high pressure stainless steel cells (rated

for 100 bar and 300 °C), one for samples and other used a reference. Cryogenic measurements

were carried out by coupling the calorimeter to liquid nitrogen cooling system (LNCS) while a

small flow of helium is maintained through the thermopiles which allows good thermal contact

between the sample cell, reference cell and thermopile. The simultaneous measurement of

adsorption and heats were achieved by attaching the sample cell and reference cells to the

Sievert’s volumetric measurement system by means of pneumatically actuated ball valves and a

needle valve. The volumetric measurement system consists of a gas dosing manifold which is

provided with a calibrated digital pressure transducer (Dresser DXD, Heise, range = 0–100 bar

accuracy = 0.02 % at full scale) and a type K thermocouple (Omega, accuracy = ± 0.5 °C) for

measuring pressure and temperature of the dosing and equilibrated gases. The temperature of

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manometric system installed within an isothermal box was controlled within ± 0.3 °C. The

control of valves and acquisition of pressure and temperature were carried out using National

Instruments FieldPoint controller and modules which is interfaced to a standard PC using NI

LabVIEW™ Professional Edition, while the acquisition of heat flow signals and the control of

liquid nitrogen flow into the calorimeter were made possible using the Calisto Software™

(SETARAM).

Calibration. (1) Calibration of calorimeter. Calorimeter was calibrated using both Joule-effect

method and reference material method. Joule-effect method is an absolute calibration which

makes use of high efficiency of Calvet calorimeter (up to 95 % of the heat produced is

transmitted to the sensor) and uses no metallic reference standard material. In the Joule-effect

method, the cells are heated by passing known dc currents (I) through a platinum resistance

electrical resistance (R) merged onto the thermopile of reference cell. The heat generated is

directly obtained from Joule’s first law, Q = I2R. In the second calibration method which uses a

reference material method, the temperature sensors and energy scale of the calorimeter were

calibrated in the standard differential scanning calorimetry mode using the extrapolated onset of

indium melting (429.75 K) and heat of fusion of indium (28.45 J K -1) performed at a heating rate

of 1 K min-1. Accuracy of calibrations was verified by comparing measured specific heat

capacities of pure synthetic sapphire (standard reference material 720, NIST) and copper from a

pristine high purity oxygen-free high conductivity copper gasket used for ultra-high vacuum

cryogenic applications with that of report data.34,35 Average relative deviation of our measured

heat capacities from the reported reference data is ~0.5% for sapphire and ~3% for copper. (2)

Calibration of reference, sample cell volume and cold volume of Sievert’s system. Calibration of

empty volumes of reference and sample cells were performed by expanding known helium gas

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(99.999%, Praxair Inc.) from the dosing volume to cells. This method based on the conservation

of mass involves two expansions: (1) expansion of helium at initial pressure and temperature in

the dosing manifold to an empty sample cell having final equilibrium pressure and temperature

and (2) expansion of helium from the dosing manifold to the sample cell containing a known

volume of non-adsorbing material, such as quartz or stainless steel beads. The volumes were

obtained by solving mass conservation equations where the real gas densities were determined

from the thermodynamic equation of state of real gases provided by NIST REFPROP Standard

Reference Database. The cold volume of the system was measured by immersing previously

expanded helium in the calorimetric cells into cryogenic tank at a pre-determined height. The

calculation of cold volume involves solving the mass balance for helium before and after

immersion. (3). Dead volume of MOFs. To measure the dead volume of MOFs samples,

accurately weighed samples (0.1 – 0.2 g) were loaded into the sample cell. The sample transfer

was done hermetically within an argon-filled glove box workstation to safeguard moisture and

air sensitive MOFs. Filled sample cell and the empty reference cell, latter required to stabilize

the heat flow signal are inserted into the calorimeter wells and argon gas is expelled. Prior to

measurements, the MOFs samples are outgassed by heating to 125 ºC and evacuating for 24

hours. The dead volume of the samples was measured by expanding helium from dosing volume

to the sample cell. For these measurements, the final temperature and pressure of helium gas

were respectively restricted to 298 K and less than 2 MPa so as to minimize any possible helium

adsorption by MOFs. Due to large volumes of system, we did not observe any influence of valve

volumes on the final equilibrium pressures.

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Figure S2. Spurious heat measured by dosing hydrogen into the blank calorimetric cells

maintained at 87, 97, 100, 113 and 117 K correlates linearly with incremental pressure. The

linear regression by fitting these data is used to calculate the spurious heat contributions during

adsorption tests.

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Figure S3. Representative excess adsorption of hydrogen on MOF-5, Cu-BTC, Fe-BTC, MOF-

177 and MIL53 measured at least two different temperatures using adsorption calorimetry. Also

shown are the excess adsorption isotherms of hydrogen on MOF-5 measured at 87 K36 and 100

K.14 The maximum uncertainty in our excess measurements is ± 3% of the reported excess.

HF=HF0+A ∙exp(−t−t0

τ ), [3]

where, HF0 is the baseline value of heat flow rate at equilibrium and τ is a characteristic time

constant. For Cu-BTC we obtained τMOF = 256.4 ± 2.2 s, τblank = 254.7 ± 2.6 s, where the standard

deviation is estimated for different incremental dosing at 77 K. This similar relaxation time scale

is rather expected because of thermal design aspect of calorimetric system with small sized

samples embedded inside a large heat conducting metal block.27

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Isosteric Method

Adsorption isotherms: An automated Sievert’s type apparatus (Setaram-HyEnergy PCTPro-

2000) was used with a so-called micro-doser (MD) from HyEnergy designed to measure the

storage properties accurately with only small amount of sample (~100 mg). The PCTPro-2000

with a micro-doser is capable of performing PCT measurements with the hydrogen gas at a

maximum pressure of 25 bar. A general illustration of this volumetric apparatus (PCTPro-2000)

with the main components is shown in Figure S4.

The original setup was coupled with an in-house made cooling-heating device regulated by a

temperature controller. This configuration allows us to perform hydrogen adsorption

measurements in a wide temperature range (77 K to 300 K). Figure S4a shows the schematic

illustration of PCTPro2000 setup. For isotherms at 77 K and 87 K, the sample holder is

submerged in liquid nitrogen or argon, respectively (Fig. S4a). For temperatures above 87 K, the

sample container is enclosed by a copper block (orange) with a cooling finger submerged in

liquid nitrogen (Fig. S4b). The liquid nitrogen level is controlled within 0.2 cm height by an

automatic liquid N2 refilling system. The copper block includes a K-type thermocouple and a

heater connected to a PID unit control. The experimental setup is capable to maintain a constant

temperature within ±1 K over the whole temperature range.

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Figure S4. Schematic diagram of the Sieverts´ apparatus coupled with a cooling system (77 K-

300 K) a) Dipping method with dewar cryostat for cooling at liquid nitrogen (77K) and liquid

argon (87 K) temperature. b) Cooling system for temperatures above 87 K where the sample

container is enclosed by a copper block (orange) and partially sank in the liquid nitrogen. The

liquid nitrogen level is constantly controlled by automatic liquid N2 refilling system.

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Volume calibration: The sample container volume (Vcon) is defined as volume of the empty

sample holder minus the skeletal volume of the sample (Vske) and can be directly measured by a

helium expansion test at room temperature. The helium expansion test consists in the measure of

the pressure change when we let expand a known volume of helium given by reservoir volume

(Vres) into the sample container. However, the helium expansion test at low temperatures results

in an inaccurate value of Vcon for microporous materials due to a significant helium adsorption.

In order to subtract the contribution of the non-adsorbed hydrogen in the sample container

volume (Vcon), we measure the hydrogen uptake for a non-adsorbing reference material (sea

sand) for different Vske and temperatures. Using the reference material uptake we can calculate

the so-called ‘excess amount of hydrogen’, nexcess(p,T), which is given by

nexcess(p,T) = nexperiment(p,T) –nsea sand (p,T)

where nexperiment(p,T) is the raw data of hydrogen uptake measurement for the porous sample (total

amount of hydrogen present in the sample container) and nsea sand (p,T) is the sea sand calibration

for a given temperature and Vske. The Figure S5 shows an example of the application of volume

calibration corrections to hydrogen adsorption data (in wt% uptake) for the material MIL-53 at

77 K. It shows that the calibration corrections at low temperatures can be significant even at

pressures below 20 bar.

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Figure S5 Hydrogen adsorption by MIL-53 at 77 K exhibiting the raw data (nexperiment(p,T))

without cold volume correction (Red) and excess hydrogen uptake (nexcess(p,T)) corrected for cold

volume (Blue).

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Calculation of absolute adsorption: The absolute adsorption is calculated from the excess

adsorption with approximated excess volume of the adsorbed layer and adsorbed gas density. We

assume that the adsorbed layer density is equal to the hydrogen liquid density (ρl = 0.07 g ml-1),

and then the excess volume, Vexcess, of the adsorbed layer can be approximated as

V excess=nexcess · M H2

ρl

In addition, we should also consider the amount of gas that would be present in the pores due to

the external pressure in the absence of adsorbent-adsorbate interaction. This can be calculated

from the corrected ideal gas equation

ngas=P ∙V excess

Z · R ∙T

with the correction (compression) factor37 for non-ideal gas Z given by

Z = (1.000547- (6.07•10-7)T+(0.000912-(1.0653•10-6)T)•P+((7.373407-0.0901T)•10-7)•P2)

where pressure, P, is given in atm, T is temperature and R is a gas constant.

The absolute adsorbed amount, nabsolute, is therefore:

nabsolute=ngas+nexcess=nex cess ·(1+P · M H 2

Z · ρlq · R ∙T)

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MOF Adsorption Isotherms: Data obtained for Cu-BTC, MOF-5, MOF-177, MIL-53 and Fe-

BTC-Xerogel adsorption isotherms. The MIL-53 heat of adsorption was calculated based on the

isotherm experiments for the temperatures 77 K and 87 K.

Figure S6: Excess hydrogen adsorption (full symbols) and desorption (open symbols) isotherms of Cu-

BTC ( 77 K, 87 K, 93 K, 128 K, 158 K, 218 K, 296 K)

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Figure S7: Excess hydrogen adsorption (full symbols) and desorption (open symbols) isotherms of MOF-

5 ( 77 K, 87 K, 97 K, 107 K, 117 K, 296 K)

Figure S8: Excess hydrogen adsorption (full symbols) and desorption (open symbols) isotherms of MOF-

177 ( 77 K, 87 K, 97 K, 107 K, 117 K, 296 K)

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Figure S9: Excess hydrogen adsorption (full symbols) and desorption (open symbols) isotherms of MIL-

53 ( 77 K, 87 K, 296 K)

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Figure S10: Excess hydrogen adsorption (full symbols) and desorption (open symbols) isotherms of Fe-

BTC-Xerogel ( 77 K, 83 K 87 K, 91 K, 100 K, 110 K, 125 K)

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