Hydrogen storage n nanoporous solid
Jan 16, 2016
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)