Skip to main content

Advertisement

SpringerLink
Log in

Recommended volumetric capacity definitions and protocols for accurate, standardized and unambiguous metrics for hydrogen storage materials

  • Invited Paper
  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

The ultimate goal of the hydrogen economy is the development of hydrogen storage systems that meet or exceed the US DOE’s goals for onboard storage in hydrogen-powered vehicles. In order to develop new materials to meet these goals, it is extremely critical to accurately, uniformly and precisely measure materials’ properties relevant to the specific goals. Without this assurance, such measurements are not reliable and, therefore, do not provide a benefit toward the work at hand. In particular, capacity measurements for hydrogen storage materials must be based on valid and accurate results to ensure proper identification of promising materials for further development. Volumetric capacity determinations are becoming increasingly important for identifying promising materials, yet there exists controversy on how such determinations are made and whether such determinations are valid due to differing methodologies to count the hydrogen content. These issues are discussed herein, and we show mathematically that capacity determinations can be made rigorously and unambiguously if the constituent volumes are well defined and measurable in practice. It is widely accepted that this occurs for excess capacity determinations and we show here that this can happen for the total capacity determination. Because the adsorption volume is undefined, the absolute capacity determination remains imprecise. Furthermore, we show that there is a direct relationship between determining the respective capacities and the calibration constants used for the manometric and gravimetric techniques. Several suggested volumetric capacity figure-of-merits are defined, discussed and reporting requirements recommended. Finally, an example is provided to illustrate these protocols and concepts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Abbreviations

BOS:

Balance of system

DOE:

US Department of Energy

EOS:

Equation of state

FOM:

Figure of merit

m ex :

Mass of excess adsorbed gas species on a sample

M g :

Molar mass of a gas species (g/mole)

\(m_{{i\,{\text{H}}_{2} }}\) :

Generic mass of H2 that can be included in the FOM with summation index i

m red :

Reduced mass signal output produced by a gravimetric instrument

m s :

Mass of sorbent sample

n :

Generic moles in gas EOS

n abs :

All the moles in the volume V ad, corresponding to ‘absolute’ capacity

n ads :

Moles sorbed in a single step of a manometric isotherm

N ads :

Cumulative moles sorbed in a manometric isotherm

n ex :

Number of excess moles in the volume V ad, corresponding to ‘excess’ capacity

n inst tot :

All the gas moles in a manometric instrument at any given moment

n net :

Number of net moles in the vessel volume corresponds to ‘net’ capacity

n net zero :

Effective null adsorption isotherm when determining ‘net’ capacity

n tot :

All the moles in the volume V gs tot, corresponding to ‘total’ capacity

n tot crys :

All the moles in the volume V crys, corresponding to ‘total crystalline’ capacity

P :

Generic gas pressure

P Ch :

‘Charging’ pressure for a two-state manometric instrument

P Cl :

‘Closed’ pressure for a two-state manometric instrument

P Eq :

‘Equilibrium’ pressure for a two-state manometric instrument

R :

Universal gas constant

T :

Generic temperature for gas, volume or system

V :

Generic volume in gas EOS

V abs cal :

Manometric headspace calibration volume for yielding absolute capacity

V ad :

Volume in an adsorbent that contains all the adsorbed gas species

V crys :

Idealized sorbent volume of a perfect single crystal of mass m s

V ΔT :

Volume of temperature-gradient region of non-isothermal manometric instrument

V ex cal :

Manometric headspace calibration volume that yields the excess capacity

V fgs :

Volume associated with sample that contains gas in the free state

V gs tot :

Volume of all gas associated with sample, free and adsorbed

V j :

Generic volume that can be included in the FOM with summation index j

V mt cal :

Manometric headspace calibration volume for an empty instrument

V mt S :

Headspace volume of isothermal sample region with no sample in non-isothermal instrument

V mt vessel :

Empty volume of sample vessel that could contain a sorbent

V pk :

Packing volume for a sorbent sample

V r :

Reference volume of a two-state manometric instrument

V S :

Headspace volume of isothermal sample region in non-isothermal manometric instrument

V sk :

Skeletal volume for a sorbent sample

V sys tot :

Total system volume can include vessel and BOS components

V t :

Headspace total volume of a two-state manometric instrument

V tot cal :

Manometric headspace calibration volume that yields the total capacity

z(P, T):

Compressibility factor for gases a function of P and T and unique to each gas

δn ex :

Error in excess capacity mole count due to error in V ex cal

δV ex cal :

Error in V ex cal

η ex :

Specific excess capacity for a material (moles/g)

Λ ec :

Volumetric capacity FOM based on excess capacity/crystal volume

Λ ep :

Volumetric capacity FOM based on excess capacity/packing volume

Λ nm :

Volumetric capacity FOM based on net capacity/empty vessel volume

Λ np :

Volumetric capacity FOM based on net capacity/packing volume

Λ tc :

Volumetric capacity FOM based on total crystalline capacity/crystal volume

Λ tp :

Volumetric capacity FOM based on total capacity/packing volume

Λ ts :

Volumetric capacity FOM based on total capacity/total system volume

Λ VC :

Generic volumetric capacity FOM

ρ crys :

Idealized sorbent mass density of a perfect single crystal (g/ml)

ρ ex :

Excess molar density defined by Eq. 25

ρ fg :

Molar density of a free gas, which is defined by the EOS (Eq. 6b)

ρ fg He :

Molar density of helium in the free-gas state (moles He/ml)

ρ g :

Actual gas molar density near the sample including adsorption density

ρ pk :

Packing mass density for a sorbent material (g/ml)

ρ sk :

Skeletal mass density for a sorbent material (g/ml)

ρ s,t :

Generic mass density (g/ml) corresponding to mass ‘s’ divided by volume ‘t’

References

  1. US Environmental Protection Agency, in Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990–2012 (2014). http://www.epa.gov/climatechange/emissions/usinventoryreport.html%3E

  2. US Department of Energy, National Hydrogen Energy Roadmap (2002). http://www.hydrogen.energy.gov/pdfs/national_h2_roadmap.pdf

  3. US Department of Energy, Office of Energy Efficiency and Renewable Energy and the Freedom CAR and Fuel Partnership, Technical System Targets: Onboard Hydrogen Storage for Light-Duty Fuel Cell Vehicles (2009). http://energy.gov/sites/prod/files/2015/01/f19/fcto_myrdd_table_onboard_h2_storage_systems_doe_targets_ldv.pdf

  4. US Department of Energy, in Office of Energy Efficiency and Renewable Energy and the Freedom CAR and Fuel Partnership, Targets for Onboard Hydrogen Storage Systems for Light-Duty Vehicles, US Department of Energy (2009). http://energy.gov/sites/prod/files/2014/03/f11/targets_onboard_hydro_storage_explanation.pdf

  5. US Department of Energy, Office of Energy Efficiency and Renewable Energy, National Hydrogen Storage Project. (2015). http://energy.gov/eere/fuelcells/national-hydrogen-storage-project

  6. G. Garberoglio, A.I. Skoulidas, J.K. Johnson, Adsorption of gases in metal organic materials: comparison of simulations and experiments. J. Phys. Chem. B 109, 13094–13103 (2005). doi:10.1021/jp050948l

    Article  Google Scholar 

  7. G. Sandrock, A panoramic overview of hydrogen storage alloys from a gas reaction point of view. J. Alloys Compd. 293–295, 877–888 (1999). doi:10.1016/S0925-8388(99)00384-9

    Article  Google Scholar 

  8. K.J. Gross, K.R. Carrington, S. Barcelo, A. Karkamkar, J. Purewal, S. Ma, H.-C. Zhou, P. Dantzer, K. Ott, T. Burrell, T. Semeslberger, Y. Pivak, B. Dam, D. Chandra, P. Parilla, in Recommended Best Practices for the Characterization of Storage Properties of Hydrogen Storage Materials, U.D.H. Program (2012). http://www1.eere.energy.gov/hydrogenandfuelcells/pdfs/best_practices_hydrogen_storage.pdf

  9. D.P. Broom, Hydrogen storage materials: the characterisation of their storage properties. Green energy and technology, vol. xii (Springer, London, New York, 2011), p. 258

    Book  Google Scholar 

  10. S. Sircar, Gibbsian surface excess for gas adsorption-revisited. Ind. Eng. Chem. Res. 38, 3670–3682 (1999)

    Article  Google Scholar 

  11. S. Sircar, Measurement of Gibbsian surface excess. AIChE J 47, 1169–1176 (2001)

    Article  Google Scholar 

  12. P.B.A.R. Chahine, Carbon nanostructures for hydrogen storage, in Solid-State Hydrogen Storage, ed. by G. Walker (Woodhead Publishing and Maney Publishing, Cambridge, 2008), p. 600

    Google Scholar 

  13. S. Gumma, O. Talu, Gibbs dividing surface and helium adsorption. Adsorption 9, 17–28 (2003). doi:10.1023/A:1023859112985

    Article  Google Scholar 

  14. S. Gumma, O. Talu, Net adsorption: a thermodynamic framework for supercritical gas adsorption and storage in porous solids. Langmuir 26, 17013–17023 (2010). doi:10.1021/la102186q

    Article  Google Scholar 

  15. A.L. Myers, Thermodynamics of adsorption in porous materials. AIChE J 48, 145–160 (2002). doi:10.1002/aic.690480115

    Article  Google Scholar 

  16. A.L. Myers, P.A. Monson, Adsorption in porous materials at high pressure: theory and experiment. Langmuir 18, 10261–10273 (2002). doi:10.1021/la026399h

    Article  Google Scholar 

  17. A.V. Neimark, P.I. Ravikovitch, Calibration of pore volume in adsorption experiments and theoretical models. Langmuir 13, 5148–5160 (1997). doi:10.1021/la970266s

    Article  Google Scholar 

  18. O. Talu, A.L. Myers, Molecular simulation of adsorption: Gibbs dividing surface and comparison with experiment. AIChE J 47, 1160–1168 (2001). doi:10.1002/aic.690470521

    Article  Google Scholar 

  19. S.J. Gregg, K.S.W. Sing, Adsorption, surface area, and porosity, vol. xi, 2nd edn. (New York, Academic Press, London, 1982)

    Google Scholar 

  20. S. Lowell, S. Lowell, Characterization of porous solids and powders: surface area, pore size, and density, 4th edn. (Kluwer Academic Publishers, Boston, 2004)

    Book  Google Scholar 

  21. F. Rouquerol, J. Rouquerol, K.S.W. Sing, Adsorption by Powders and Porous Solids: Principles, Methodology, and Applications, vol. xvi (Academic Press, San Diego, 1999)

    Google Scholar 

  22. R.T. Yang, Adsorbents: Fundamentals and Applications, vol. xii (Wiley-Interscience, Hoboken, NJ, 2003)

    Book  Google Scholar 

  23. S. Lowell, J.E. Shields, M.A. Thomas, M. Thommes, in Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density. Particle Technology Series, ed. by B. Scarlett, (Kluwer Academic Publishers, Dordrecht Boston, 2004)

  24. D.P. Broom, The accuracy of hydrogen sorption measurements on potential storage materials. Int. J. Hydrogen Energy 32, 4871–4888 (2007). doi:10.1016/j.ijhydene.2007.07.056

    Article  Google Scholar 

  25. A. Myers, P. Monson, Physical adsorption of gases: the case for absolute adsorption as the basis for thermodynamic analysis. Adsorption 20, 591–622 (2014). doi:10.1007/s10450-014-9604-1

    Article  Google Scholar 

  26. O. Talu, Net adsorption of gas/vapor mixtures in microporous solids. J. Phys. Chem. C 117, 13059–13071 (2013). doi:10.1021/jp4021382

    Article  Google Scholar 

  27. P.A. Webb, Volume and density determinations for particle technologists (Micromeritics Instrument Corp., Norcross, GA, 2001), pp. 1–16

    Google Scholar 

  28. F.W. Giacobbe, A high-pressure volumetric gas adsorption system. Rev. Sci. Instrum. 62, 2186–2192 (1991)

    Article  ADS  Google Scholar 

  29. E. Poirier, R. Chahine, A. Tessier, T.K. Bose, Gravimetric and volumetric approaches adapted for hydrogen sorption measurements with in situ conditioning on small sorbent samples. Rev. Sci. Instru. 76, 055101/1–055101/6 (2005)

    Article  ADS  Google Scholar 

  30. T.P. Blach, E.M. Gray, Sieverts apparatus and methodology for accurate determination of hydrogen uptake by light-atom hosts. J. Alloys Compd. 446–447, 692–697 (2007). doi:10.1016/j.jallcom.2006.12.061

    Article  Google Scholar 

  31. E.M. Gray, Reliably measuring hydrogen uptake in storage materials, in Solid-State Hydrogen Storage, ed. by G. Walker (Woodhead Publishing and Maney Publishing, Cambridge, 2008), p. 600

    Google Scholar 

  32. J.A.J. Lachawiec, T.R. DiRaimondo, R.T. Yang, A robust volumetric apparatus and method for measuring high pressure hydrogen storage properties of nanostructured materials. Rev. Sci. Instrum. 79, 063906–063912 (2008)

    Article  ADS  Google Scholar 

  33. J.M. Blackman, J.W. Patrick, C.E. Snape, An accurate volumetric differential pressure method for the determination of hydrogen storage capacity at high pressures in carbon materials. Carbon 44, 918–927 (2006). doi:10.1016/j.carbon.2005.10.032

    Article  Google Scholar 

  34. A. Qajar, M. Peer, R. Rajagopalan, H.C. Foley, High pressure hydrogen adsorption apparatus: design and error analysis. Int. J. Hydrogen Energy 37, 9123–9136 (2012). doi:10.1016/j.ijhydene.2012.03.002

    Article  Google Scholar 

  35. I. Suzuki, K. Kakimato, S. Oki, Volumetric determination of adsorption of helium over some zeolites with a temperature compensated, differential tensimeter having symmetrical design. Rev. Sci. Instrum. 58, 1226 (1987)

    Article  ADS  Google Scholar 

  36. J. Zielinski, C. Coe, R. Nickel, A. Romeo, A. Cooper, G. Pez, High pressure sorption isotherms via differential pressure measurements. Adsorption 13, 1–7 (2007). doi:10.1007/s10450-007-9005-9

    Article  Google Scholar 

  37. P. Malbrunot, D. Vidal, J. Vermesse, R. Chahine, T.K. Bose, Adsorbent helium density measurement and its effect on adsorption isotherms at high pressure. Langmuir 13, 539–544 (1997)

    Article  Google Scholar 

  38. S. Sircar, Role of helium void measurement in estimation of Gibbsian surface excess (International Adsorption Society (IK international), Chiba, 2002)

    Google Scholar 

  39. J.U. Keller, R. Staudt, Gas adsorption equilibria: experimental methods and adsorptive isotherms, vol. xiv (Springer, New York, 2005)

    Google Scholar 

  40. C.J. Webb, E.M. Gray, The effect of inaccurate volume calibrations on hydrogen uptake measured by the Sieverts method. Int. J. Hydrogen Energy 39, 2168–2174 (2014). doi:10.1016/j.ijhydene.2013.11.121

    Article  Google Scholar 

  41. C. Zlotea, P. Moretto, T. Steriotis, A Round Robin characterisation of the hydrogen sorption properties of a carbon based material. Int. J. Hydrogen Energy 34, 3044–3057 (2009). doi:10.1016/j.ijhydene.2009.01.079

    Article  Google Scholar 

  42. C.J. Webb, E.M. Gray, Analysis of the uncertainties in gas uptake measurements using the Sieverts method. Int. J. Hydrogen Energy 39, 366–375 (2014). doi:10.1016/j.ijhydene.2013.09.155

    Article  Google Scholar 

  43. D.E. Demirocak, S.S. Srinivasan, M.K. Ram, D.Y. Goswami, E.K. Stefanakos, Volumetric hydrogen sorption measurements: uncertainty error analysis and the importance of thermal equilibration time. Int. J. Hydrogen Energy 38, 1469–1477 (2013). doi:10.1016/j.ijhydene.2012.11.013

    Article  Google Scholar 

Download references

Acknowledgments

We gratefully acknowledge support from the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office. We are also grateful for useful discussions with Channing Ahn, Richard Chahine, the Hydrogen Storage Tech Team (H2ST2) and participants of the IEA HIA Task 32. Work was performed under NREL prime contract number: DE-AC36-08GO28308. NREL is a national laboratory of the US Department of Energy Office of Energy Efficiency and Renewable Energy and Operated by the Alliance for Sustainable Energy, LLC.

Author information

Authors and Affiliations

  1. National Renewable Energy Laboratory, Golden, CO, 80401, USA

    Philip A. Parilla, Katherine Hurst & Thomas Gennett

  2. H2 Technology Consulting LLC, Alamo, CA, 94507, USA

    Karl Gross

Authors
  1. Philip A. Parilla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karl Gross
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Katherine Hurst
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas Gennett
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philip A. Parilla.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 1060 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Parilla, P.A., Gross, K., Hurst, K. et al. Recommended volumetric capacity definitions and protocols for accurate, standardized and unambiguous metrics for hydrogen storage materials. Appl. Phys. A 122, 201 (2016). https://doi.org/10.1007/s00339-016-9654-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-016-9654-1

Keywords

Search

Navigation