Hydrogen storagein nanoporous solids

Porous solidsCatalysts/catalyst supportsAdsorbentsMembranesMaterials of constructionOil/gas containing rocksSoil…

What is a pore?(void, cavity, …)

In fact, not all pores are accessible to fluids from external surfaces …

Topology of Porous Solids

C - closed poresE - external surfaceB - blind poresT - transport or through poresO - open pores = B + T

C C

C

E

BB

Tsolid matrix

Porous systemspowdered, granular,

fibrous,monolithic

Matricesceramic, polymeric,

metallicflexible/rigidstrong/weaktough/brittlereactive/inert

accessiblesurfaces

Origins of Porosity

Natural during formation or processing of a material.

May arise or develop subsequently, deliberately or otherwise.

Importance of Porosity

Porosity influences

Transport of fluids to/from internal surfacesInternal surface area (and hence reactivity)Mechanical/electrical/thermal propertiesBulk density…

Key Pore Properties

Geometry (size, shape, orientation, …)LocationConnectivityTortuositySurface structureSurface chemistry

IUPAC classification of pore size

J. Rouquerol, et al. (1994).Pure. Appl. Chem., 66, 1739. mesopores

2 < w < 50 nmmacropores

width, w > 50 nmmicropores

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

Micropore interaction potentials

Nanopores

Familiar nanoporous materials

Mays, Stud. Surf. Sci. Catal.160 (2006) 57

Adsorption and absorption

0.0 0.5 1.0 1.5 2.0 2.5 3.00

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

31 kg m-3

70 kg m-3

76 kg m-3

to

tal m

ass

% u

ptak

e =

( 1

00 m

H /

mS )

specific accessible pore volume, Vp / cm3 g-1

88 kg m-3

densityof H

2 in pores

H2 storage in porous solids

solid

H2

Supercritical Adsorptives

Gas

Criticaltemperature

Adsorptive TC / K

He 5.26

H2 33.1

N2 126

O2 154

CH4 191

CO2 304

H2O 647

Supercritical Adsorptives

Gas

Criticaltemperature

Adsorptive TC / K

He 5.26

H2 33.1

N2 126

O2 154

CH4 191

CO2 304

H2O 647

z

adsorbate adsorptive

zA0

adsorbent

Babsoluteadsorption

Absolute Adsorption

absolute (or total) adsorption is the total amount of adsorbate within a defined boundary

control (or displacement)volume, VC = VS + VA

inhomogeneous adsorbate occupying volume VA = VP ( )

filling the open (accessible) pore volume VP

pure gas phase adsorptive at absolute pressure, P, absolute temperature, T, and uniform bulk density B ( P, T )

solid adsorbent occupyingvolume VS ( )(incl. closed or inaccessible pores)

Absolute Adsorption in a Porous System

z

adsorbate adsorptive

zA0

adsorbent

B

excess

bulk

absolute adsorption= excess + bulk

absolute (total) adsorption may be partitioned into excess (Gibbs or apparent) adsorption and “bulk” adsorption

Excess Adsorption

AA

AA

d VVnV

ABA

ABA

BE

d A

V

Vn

VnV

absolute (or total) adsorptioncannot be measured directly

… but… most theories/models/simulationsdeal with total adsorption

excess (or Gibbs) adsorptionmeasured directly

Analysis: Summary

term for account must otherwise

» only when

AB

BAAE

V

nn

gas) (ideal 0 as 1

adsorptive of state of equation from

P

PZ T

AABB AmaxAAAA

BAE

1 , V

RT

P

PZVnPnVn

t in poresbulk amounsnt in poretotal amouorptionexcess ads

nnn

TT

ideally ... law) s(Henry' 0 as

always ... n)(saturatio as 1

isotherm (relative) I type

H

A

PPTK

P

P T

Analysis: Further DetailsInspiration: Myers and Monson, Langmuir 18 (2002) 10261

Schematic Isotherms

Isotherm Classification

Donohoe and Aranovich, Fluid Phase Equilibria 158-160 (1999) 557

simpleexcess

Sing, et al., Pure Appl Chem 57 (1985) 603

m–LangmuirLangmuir, JACS 40 (1918) 1361

m

ii

i

im

ii an

Pb

Pban

1

maxA

1 A ,

1

Sips (or Langmuir–Freundlich)Sips, J Chem Phys 16 (1948) 490

maxAA

1 c

c

bP

bPnn

Type I Absolute Isotherms

TóthTóth, Acta Chim Acad Sci Hung 32 (1962) 39

—, — 69 (1971) 311

ccbP

bPnn

1

maxAA

1

UnilanHonig and Reyerson, J Phys Chem 56 (1952) 140

)cexp(bP

)cexp(bPln

cnn max

1

1

2

1AA

Jovanović–Freundlich Quiñones and Guiochon, JCIS 183 (1996) 57

1 AAcmax bPexpnn

Dubinin–AstakhovDubinin and Astakhov, Izv Akad Nauk SSSR,Ser Khim No.1 (1971) 5, 11; Russ Chem Bull 20 (1971) 3, 8

c

E

PPRTnn

* ln expmax

AA

Amankwah and Schwarz, Carbon 33 (1995) 1313

CC PTT*P

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)

normal hydrogen~25 % para-H2 for T ≥ ~300 K

~20 K ~80 K

Equilibrium Molecular Hydrogen

AABBAmaxAAAA

BAE

1 , V

RT

P

PZVnPnVn

nnn

TT

experimental data

estimate values of parameters in model for absolute adsorption

EOS foradsorptive

Application to Data

STATISTICAL ANALYSIS

Levenberg-Marquardt Non-linear Least SquaresLevenberg, Q Appl Math 2 (1944) 164; Marquardt, J Soc Ind Appl Math 11 (1963) 431

PC Windows SoftwareScientist 3.0 (Micromath); OriginPro 8.0 (OriginLab)

Goodness of Fit Measure statistic (corrected root mean square residual)

21

2

nm

rm

i

i

estimate volume of adsorption space

Gravimetric measurements

•Sample weighed as a function of P at constant T

•Hiden Intelligent gravimetric Analyser (IGA)

•w < ~5 g per sample•V < ~2 cm3 per sample•10-4 < P < 20 bar•77 < T < 800 K•Kinetic and equilibrium

physisorption isotherms•Mainly for testing in application

conditions

Schematic gravimetric adsorption data

Pressure

1200

1300

1400

1500

1600

1700

1800

1900

129 130 131 132 133 134 135 136 137 138

Time (mins)P

ress

ure

(m

bar

s)

Temperature

-195.5

-195.4

-195.3

-195.2

-195.1

-195

-194.9

130 131 132 133 134 135

Time (mins)

Sam

ple

Tem

per

atu

re

Weight % Uptake

3.053.1

3.153.2

3.253.3

3.353.4

128.5 130.5 132.5 134.5 136.5 138.5

Time (mins)

Wei

gh

t %

Kinetic gravimetric adsorption data

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

0

2

4

6

8

10

12

137 K

237 K

117 K

107 K97 K

exc

ess

am

ou

nt a

dso

rbe

d, n

E /

mo

l kg

-1

pressure, P / MPa

87 K2 wt% = 20 mg g-1

Hydrogen Adsorption on NaX Zeolite

10-3 10-2 10-1 100 101

0

2

4

6

8

10

12

137 K

237 K

117 K

107 K97 K

exc

ess

am

ou

nt a

dso

rbe

d, n

E /

mo

l kg

-1

pressure, P / MPa

87 K

Hydrogen Adsorption on NaX Zeolite

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

0

2

4

6

8

10

12

14

estimated absolute

am

ou

nt a

dso

rbe

d, n

/ m

ol k

g-1

pressure, P / MPa

estimated excess

87 K

V

bP

bPnn

cc

AB1

maxAE

1

Tóth analysis

10-3 10-2 10-1 100 101

0

2

4

6

8

10

12

14

estimated absolute

am

ou

nt a

dso

rbe

d, n

/ m

ol k

g-1

pressure, P / MPa

estimated excess

87 K

0 2 4 6 8 10

0

2

4

6

8

10

12

1487 K estimated absolute

am

ou

nt a

dso

rbe

d, n

/ m

ol k

g-1

pressure, P / MPa

estimated excessestimated pore volume,

VA = 0.35 cm3 g-1

simple Tóth fit

80 90 100 110 120 130 140 1500

50

100

150

nm

ax

A /

mo

l kg

-1

temperature, T / K

14.1

VA = 0.35 cm3 g-1

equivalent to maximum fluid densityin pores of 80 2 kg m-3

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

20.4 K

87 kg m-3 [Silvera, Rev Mod Phys 52 (1980) 393]

critical point

solid

normal boiling point

real gasideal gas

real gas

de

nsity

/ kg

m-3

pressure / MPa

triple point

77 K

298 K

ideal gas

liqui

d de

nsiti

es

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

20.4 K

87 kg m-3 [Silvera, Rev Mod Phys 52 (1980) 393]

critical point

solid

normal boiling point

real gasideal gas

real gas

de

nsity

/ kg

m-3

pressure / MPa

triple point

77 K

298 K

ideal gas

liqui

d de

nsiti

es

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

20.4 K

87 kg m-3 [Silvera, Rev Mod Phys 52 (1980) 393]

critical point

solid

normal boiling point

real gasideal gas

real gas

de

nsity

/ kg

m-3

pressure / MPa

triple point

77 K

298 K

ideal gas

liqui

d de

nsiti

es

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

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.52.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

slope, E = 5.17 kJ mol-1

ln (

b /

MP

a-1)

(1000 / RT) / mol kJ-1

VA = 0.35 cm3 g-1

80 90 100 110 120 130 140 1500.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

c / -

temperature, T / K

VA = 0.35 cm3 g-1

2009 Research HighlightNature 462, 961

Hydrogen pore volumesNOTT-101: 0.91 cm3 g-1

NOTT-102: 1.37 cm3 g-1

NOTT-103: 0.97 cm3 g-1

Data forUMCM-2

0 20 40 60 80 100-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

resi

dual

/ m

g g-1

pressure / bar

Sips model forabsolute adsorption

SBE

SBABABE

SABCBA

Vn

VVVn

VVVn

control (or displacement)volume, VC = VS + VA

inhomogeneous adsorbate occupying volume VA = VP ( )

filling the open (accessible) pore volume VP

pure gas phase adsorptive at absolute pressure, P, absolute temperature, T, and uniform bulk density B ( P, T )

solid adsorbent occupyingvolume VS ( )(incl. closed or inaccessible pores)

hydrogen pore volume = 1.51 cm3 g-1, limiting adsorbate density = 86 kg m-3

bptc = 3,3',5,5' biphenyl tetracarboxylate tptc = 3,3',5,5' terphenyl tetracarboxylate

CC

max

*

* ln exp

PTTP

E

PPRTnn

m

AA

Poirier and Dailly, Energy Env Sci2 (2009) 420

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

45 50 55 60 65 70 75 80 85 90 95 10070

75

80

85

90

95

100

105

nma

x

A /

mg

g-1

temperature/ K

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5-1

0

1

2

3

4

5

E = 4.28 kJ mol-1

ln (

b / b

ar-1)

(1000/RT) / mol kJ-1

45 50 55 60 65 70 75 80 85 90 95 1000.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.58

0.60

c / -

temperature / K

45 50 55 60 65 70 75 80 85 90 95 1000.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

V /

cm3 g

-1

temperature / K

Sips Analysis for Cu2 (tptc)

equivalent to77 kg m-3 maximumdensity in pores

maxAA

1 c

c

bP

bPnn

Concluding Remarks

Excess model results in good fits to high-pressure H2 adsorption data on a range of nanoporous materials

“Sensible” hydrogen pore volumes and (occasionally very high) limiting density of H2 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

BAAB

AB

AB

A

vvv

vT

h

T

P

n

Clapeyron equation

Note that: For high P, bulk gas phase B is not ideal For high P, is not small with respect to vB

Isostere, , must be with respect to constant nA not nE

Need to know (or assume) temperature dependence of all absolute isotherm parameters

At this stage only (reasonably) confident in hAB in the limit of zero uptake

Some Current Work

Clapeyron, É Journal de l’ École Polytechnique14 (1834) 153; Wisniak, Chem Educator 5 (2000) 83

differential molar isosteric enthalpy of adsorption

Av

AnTfP

Approximations leading to the Clausius-Clapeyron equation do not apply at high P

H2 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 cm3 g-1

Zn4O units bridged bybenzenedicarboxylate linkers

0.1 1 10 1000

20

40

60

80

100

am

ou

nt a

dso

rbe

d /

mg

g-1

pressure / bar

0 10 20 30 40 50 60 700

20

40

60

80

100

am

ou

nt a

dso

rbe

d /

mg

g-1

pressure / bar

Increase in H2 storage300K

0 10 20 30 40

0

5

10

15

20

25

30g(

H2)

L-1

Absolute Pressure / MPa

Quantity empty container (EOS) 100g MOF 200g MOF 300g MOF 400g MOF 500g MOF 504g MOF (full of adsorbent)