1. Hydrogen storage in nanoporous solids

2. Porous solids Catalysts/catalyst supports Adsorbents Membranes Materials of construction Oil/gas containing rocks Soil …

3. What is a pore? (void, cavity, …) In fact, not all pores are accessible to fluids from external surfaces …

4. Topology of Porous Solids C - closed pores E - external surface B - blind pores T - transport or through pores O- open pores = B + T C C C E B B T solid matrix Porous systems powdered, granular, fibrous, monolithic Matrices ceramic, polymeric, metallic flexible/rigid strong/weak tough/brittle reactive/inert accessible surfaces

5. Origins of Porosity Natural during formation or processing of a material. May arise or develop subsequently, deliberately or otherwise.

6. Importance of Porosity Porosity influences Transport of fluids to/from internal surfaces Internal surface area (and hence reactivity) Mechanical/electrical/thermal properties Bulk density …

7. Key Pore Properties Geometry (size, shape, orientation, …) Location Connectivity Tortuosity Surface structure Surface chemistry

8. IUPAC classification of pore size J. Rouquerol, et al. (1994). Pure. Appl. Chem., 66, 1739. mesopores 2 < w < 50 nm macropores width, w > 50 nm micropores w < 2 nm mainly simple adsorbate- absorbent interactions on the surfaces of large pores and on external surfaces Langmuir and Brunauer- Emmett-Teller type models adsorbent-adsorbent interactions across medium sized pores (co- operative effects) leading to capillary condensation Kelvin equation overlap of adsorption forces from opposite walls in tiny pores micropore filling models (e.g., Dubinin) and molecular simulations

9. Micropore interaction potentials

10. Nanopores Familiar nanoporous materials Mays, Stud. Surf. Sci. Catal. 160 (2006) 57

11. Adsorption and absorption

12. H2 storage in porous solids solid H2H2

13. Supercritical Adsorptives Gas Critical temperature Adsorptive T C / K He5.26 H2H2 33.1 N2N2 126 O2O2 154 CH 4 191 CO 2 304 H2OH2O647

14. Supercritical Adsorptives Gas Critical temperature Adsorptive T C / K He5.26 H2H2 33.1 N2N2 126 O2O2 154 CH 4 191 CO 2 304 H2OH2O647

15.  z adsorbateadsorptive zAzA 0 adsorbent BB absolute adsorption Absolute Adsorption absolute (or total) adsorption is the total amount of adsorbate within a defined boundary

16. control (or displacement) volume, V C = V S + V A inhomogeneous adsorbate occupying volume V A = V P ( ) filling the open (accessible) pore volume V P pure gas phase adsorptive at absolute pressure, P, absolute temperature, T, and uniform bulk density  B ( P, T ) solid adsorbent occupying volume V S ( ) (incl. closed or inaccessible pores) Absolute Adsorption in a Porous System

17.  z adsorbateadsorptive zAzA 0 adsorbent BB excess bulk absolute adsorption = excess + bulk absolute (total) adsorption may be partitioned into excess (Gibbs or apparent) adsorption and “bulk” adsorption Excess Adsorption

18. absolute (or total) adsorption cannot be measured directly … but… most theories/models/simulations deal with total adsorption excess (or Gibbs) adsorption measured directly Analysis: Summary

19. Analysis: Further Details Inspiration: Myers and Monson, Langmuir 18 (2002) 10261

20. Schematic Isotherms

21. Isotherm Classification Donohoe and Aranovich, Fluid Phase Equilibria 158-160 (1999) 557 simple excess Sing, et al., Pure Appl Chem 57 (1985) 603

22. m–Langmuir Langmuir, JACS 40 (1918) 1361 Sips (or Langmuir–Freundlich) Sips, J Chem Phys 16 (1948) 490 Type I Absolute Isotherms Tóth Tóth, Acta Chim Acad Sci Hung 32 (1962) 39 —, — 69 (1971) 311 Unilan Honig and Reyerson, J Phys Chem 56 (1952) 140 Jovanović–Freundlich Quiñones and Guiochon, JCIS 183 (1996) 57 Dubinin–Astakhov Dubinin and Astakhov, Izv Akad Nauk SSSR, Ser Khim No.1 (1971) 5, 11; Russ Chem Bull 20 (1971) 3, 8 Amankwah and Schwarz, Carbon 33 (1995) 1313

23. Adsorptive Equations of State Software (Pay) NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP): Version 8.0 Online (Free) http://webbook.nist.gov/chemistry/fluid/ [last accessed 14 September 2010] Hydrogen Fundamental Equations of State for Parahydrogen, Normal Hydrogen and Orthohydrogen (Leachman, MS thesis, University of Idaho, 2007)

24. normal hydrogen ~25 % para-H 2 for T ≥ ~300 K ~20 K ~80 K Equilibrium Molecular Hydrogen

25. experimental data estimate values of parameters in model for absolute adsorption EOS for adsorptive Application to Data STATISTICAL ANALYSIS Levenberg-Marquardt Non-linear Least Squares Levenberg, Q Appl Math 2 (1944) 164; Marquardt, J Soc Ind Appl Math 11 (1963) 431 PC Windows Software Scientist 3.0 (Micromath); OriginPro 8.0 (OriginLab) Goodness of Fit Measure  statistic (corrected root mean square residual) estimate volume of adsorption space

26. Gravimetric measurements Sample weighed as a function of P at constant T Hiden Intelligent gravimetric Analyser (IGA) w < ~5 g per sample V < ~2 cm 3 per sample 10 -4 < P < 20 bar 77 < T < 800 K Kinetic and equilibrium physisorption isotherms Mainly for testing in application conditions

27. Schematic gravimetric adsorption data

28. Kinetic gravimetric adsorption data

29. 2 wt% = 20 mg g -1 Hydrogen Adsorption on NaX Zeolite

31.   V bP nn c c    AB 1 max AE 1 Tóth analysis

34. V A = 0.35 cm 3 g -1 equivalent to maximum fluid density in pores of 80  2 kg m -3

35. Leachman’s EOS for Normal Hydrogen Leachman, et al. J Phys Chem Ref Data 38 (2009) 721

36. V A = 0.35 cm 3 g -1

38. 2009 Research Highlight Nature 462, 961

39. Hydrogen pore volumes NOTT-101: 0.91 cm 3 g -1 NOTT-102: 1.37 cm 3 g -1 NOTT-103: 0.97 cm 3 g -1

40. Data for UMCM-2 Sips model for absolute adsorption

41. control (or displacement) volume, V C = V S + V A inhomogeneous adsorbate occupying volume V A = V P ( ) filling the open (accessible) pore volume V P pure gas phase adsorptive at absolute pressure, P, absolute temperature, T, and uniform bulk density  B ( P, T ) solid adsorbent occupying volume V S ( ) (incl. closed or inaccessible pores)

42. hydrogen pore volume = 1.51 cm 3 g -1, limiting adsorbate density = 86 kg m -3

43. bptc = 3,3',5,5' biphenyl tetracarboxylate tptc = 3,3',5,5' terphenyl tetracarboxylate Poirier and Dailly, Energy Env Sci 2 (2009) 420

44. Lin, et al. (2006). Angew. Chem. 118, 7518

45. Sips Analysis for Cu 2 (tptc) equivalent to 77 kg m -3 maximum density in pores

46. Concluding Remarks  Excess model results in good fits to high-pressure H 2 adsorption data on a range of nanoporous materials  “Sensible” hydrogen pore volumes and (occasionally very high) limiting density of H 2 in pores may be estimated from adsorption data  Useful idea for determining conditions where adsorption storage is effective cf. compression  Statistical criteria used to select appropriate saturation isotherm  Thermodynamic analysis (e. g., enthalpies of adsorption) not straightforward

47. Clapeyron equation Note that:  For high P, bulk gas phase B is not ideal  For high P, is not small with respect to v B  Isostere,, must be with respect to constant n A not n E  Need to know (or assume) temperature dependence of all absolute isotherm parameters  At this stage only (reasonably) confident in  h AB in the limit of zero uptake Some Current Work Clapeyron, É Journal de l’ École Polytechnique 14 (1834) 153; Wisniak, Chem Educator 5 (2000) 83 differential molar isosteric enthalpy of adsorption Approximations leading to the Clausius- Clapeyron equation do not apply at high P

48. H 2 at 77 K in IRMOF-1 Experimental excess isotherm: Poirier and Dailly, J Phys Chem C 112 (2008) 13047 Simulated total adsorption: Courtesy of Fröba Group (Michael Fischer), Department of Chemistry, University of Hamburg, Germany Initial results from this work: Limiting in-pore density = 75.8 kg m -3 Pore volume = 1.84 cm 3 g -1 Zn 4 O units bridged by benzenedicarboxylate linkers

49. Increase in H 2 storage 300K