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Porous MOFs as storage materials for methane and hydrogen
Structure Modelling [and GCMC Simulations]
Frank Hoffmann
Department Chemie
24./25.02.2009 Workshop SPP 1362 Dresden
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2
Part I
Basic Concepts – Force Fields – Modelling as a Tool in Crystallography
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3
Overview of methods used in computational chemistry
WF‐based e‐density‐based
semiempirical ab initio
EHTCNDOMNDO
HFMP‐nCI, CC
LDALSDAGGA
FF‐based
UFFCVFF, MMFF
MM2‐4
methodsclassical
mechanics quantum
mechanics
DFT
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4
Force Fields: Definition
mathematical expression describing the energy of a molecule as a
function of the coordinates of the nuclei
obtained empirically
applying the laws of classical mechanics to hard bodies (spheres),
which are connected by springs
force field
principle
stretch bend
non‐bond(electrostatics, vdW)
torsion
atom types
parameterization
kstr kb ktors
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5
Force Fields: Parameter Reduction and Transferability
…but a nitro group is a nitro group is a nitro group…
(hopefully)…
CH3
N+O O-
CH
N+O O-
CH3H3C
N+O O-
T ? T ?
a sp2‐hybridized carbon atom is not a sp3‐hybridized carbon atom…
H2C CH3 C_sp3
C_sp2
C_aryl_sp2
…if not, then the predicting power
of FF‐based calculation would be zero!
from experimental data or
high‐quality QM calculations
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6
Force Fields: Example and the Term Strain Energy
„strain
energy“
vdWCoulombcrossbendtorsbond EEEEEE totE
τ energy
dihedral angle τ
))cos(1( 0 nkE torstors
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7
Conceptual Background: PES
energy
reaction
coordinate
transition
state
(TS)
1
2
kinetics
thermo‐dynamics
energy
minima
1, 2 = equilibrium
structures
energy
maxima
= TS
stationary
points
0
xE
02
2
xE
02
2
xE
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8
UFF – a ‘generic’ force field
is a so‐called ‘all‐elements force field’, i.e.
comprises parameters for all
atom sorts of the PSE
uses a reduced parameter set and makes directed guesses for missing
interaction parameters
results in relatively good geometries, relatively bad relative energies, and
poor conformational energies for organic molecules
is (in my experience) quite well‐suited for structure simulations of MOFs
The Universal Force Field (UFF)
Rappé et al., J. Am. Chem. Soc., 114 (1992) 10024
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9
Modelling as an utility in crystallography
1
8
comparison, refinement…
calcexp
structural model
a sort of ‘Homology
Modelling’…
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10
Structure solution of Al-containing MOFs
Férey et al. , C.R. Chimie 8 (2005) 765
MIL‐69
Al(OH)(ndc)∙H2
O
M = 267.11 g mol–1
monoclinic
space group C2/c (no. 15),
a = 24.598 Å, b = 7.5305 Å, c = 6.5472 Å
b = 106.863°
V = 1160.6 Å3
Z = 4
‘opening angle’
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11
Experimental P-XRD pattern
MIL‐69 but DMF instead of water as solvent (and SDA)
TUD‐MIL‐69 (as)
intensity
2 theta
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12
Modelling protocol
Modelling
procedure
in principle
analogous
to Férey
et al.
MIL‐53‐as (CCDC 220475) Linker: 1,4‐benzene dicarboxylate
naked network of AlO
connectors
‐
elongation of the a‐axis to 24,6 Å‐
reduction of the symmetry to P1‐
insertion of the naphthalene cores in a regular way
TUD‐MIL‐69‐trial (P21)
‐
energy minimization, including optimization of the unit cell‐
UFF‐
finding symmetry
TUD‐MIL‐69‐sim (Pnna)
‐
removal of the benzene cores
Férey et al. , C.R. Chimie 8 (2005) 765
‐
generation of CIF‐
simulation of the P‐XRD
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13
Structural model of TUD-Al(OH)(ndc)
TUD‐Al(OH)(ndc)
primitive orthorhombic, , , = 90°, space group Pnna
(no. 52)
a = 19.1987 Å, b = 6.08336 Å, c = 16.3269 Å
80.51°
99.49°
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14
Comparison of the P-XRDs
TUD‐Al(OH)(ndc) (as)
TUD‐Al(OH)(ndc) (sim)
intensity
2 theta
TUD‐Al(OH)(ndc)
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15
Removing last doubts
TUD‐Al(OH)(ndc)
Whitfield et al. , Solid State Sci. 7 (2005) 1096
TUD‐Al(ndc)(dmf)or ?
Fe(bdc)(dmf)
54.4°
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16
Comparison of the P-XRDsrel. intensity
2 theta
TUD‐Al(OH)(ndc)
TUD‐Al(OH)(ndc) (as)
TUD‐Al(ndc)(dmf) (sim)
orthorhombic, , , = 90°, SG Pna21
(no. 33)
a = 22.2859 Å, b = 10.5211 Å, c = 6.6567 Å
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17
From Al(OH)(ndc) to Al(OH)(bpdc)
Al(OH)(bpdc)Al(OH)(ndc)
4,4’‐biphenyl dicarboxylate
94.7°
85.3°
TUD‐Al(OH)(bpdc) (as)
TUD‐Al(OH)(bpdc) (sim)
body‐centered orthorhombic
space group Imma
(no. 74)
a = 21.5798 Å, b = 6.11644 Å,
c = 20.1246 Å
intensity
2 theta
Senkovska et al., MMM (2009) accepted
[Al(OH)(ndc): 80.4°]
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18
Structure solution of MIL-101_NDC
MIL‐53 MIL‐88B MIL‐101
MTN network
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19
From MIL-101 to MIL-101_NDC
MIL‐101
Cr3
[µ3‐oxo(H2
O)3
(bdc)3
]
MIL‐101_NDC
Cr3
[µ3‐oxo(H2
O)3
(ndc)3
]
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20
Protocol and Comparison of the P-XRDs
P‐XRD
P‐XRD indexing
Fd‐3 (cubic, a
= 104.5435 Å)
‐
taking the fractional coordinates of MIL‐101 but
without the bdc
linkers‐
insertion of the naphthalene cores in a way that the
Fd‐3 symmetry is retained
MIL‐101_NDC trial
‐
energy minimization, including optimization of
the unit cell
‐
UFF
MIL‐101_NDC‐sim (a = 104.1264 Å)
‐
X‐Cell
‐
generation of CIF‐
simulation of the P‐XRD
Crystallographic/Modelling
procedure
Rietveld
refinement (a = 104.217 Å) space group validation
(F41
32 / Fd‐3)
Fd‐3
MIL‐101_NDC (exp)
MIL‐101_NDC(sim)
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21
Challenge: Symmetry reduction
Symmetry reduction
Fd‐3
a b
c
000
[110] diagonal plane
Fd‐3m
highest multiplicity (Wyckoff)
96(g)192(i)
Cr1 0.09473 -0.07201 0.51291…
(3rd viewing direction, cubic)
Cr1a 0.09473 -0.07201 0.51291Cr1b -0.07201 0.09473 0.51291….
atoms on general positions with a multiplicity
of 192 in Fd‐3m have to be split into two
positions with a multiplicity of 96
m
abc bac
b
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22
The Aufbau principle of MIL-101_NDC
Cr3
(µ3‐O)(H2
O)3
(ndc)3
Fd‐3
a = 104.1264 Å
V
= 1,124,000 Å3
SBET
= ~ 3,850 m2/g
Vp
= ~ 2.345 cm3/g
Sonnauer et al., Angew. Chem. Int. Ed. (2009), DOI: 10.1002/ange.200805980
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23
Part II
GCMC simulations for evaluation of the adsorption properties of MOFs – Adaptation of van-der-Waals parameters
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24
Different Ensembles and GCMC simulations
grand canonical ensemble
N, E, V
= const.
microcanonical
ensemble
isothermal‐isobaric ensemble
canonical ensemble
N, V,
T
= const.
N, T,
p
= const.µ, V, T,
p
= const.
for instance for the evaluation of
the number of particles, which a
porous material can adsorb!
each of the Monte Carlo moves
consist of one of the following
steps:
insertion (‘create’)
translation
rotation remove (‘destroy’)
µ, T
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25
GCMC simulations
each of the steps are connected to a certain probability of
acceptance or rejection, depending on a set of different
energy criteria and the Boltzmann distribution function at
the respective temperature (sampling)
with each Monte Carlo step different microstates, i.e.
configurations, are realized, which possess a certain
probability distribution
for each microstate, i.e.
configuration, all macroscopic
(thermodynamic) properties are calculated by means of the
respective equations from statistical mechanics
by taking the average of a huge number of all possible
(acceptable) configurations the desired macroscopic
observables can be obtained with high precision
insertion
translation
rotation remove
bad sampling
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26
GCMC simulations – equilibration and production
insertion
insertion
insertion
equilibration (C/D is high)
production (C/D ~ 1)
all accepted rejected
insertion insertion
accepted
translation
microstate 1 microstate 2 microstate 3 microstate n
…
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27
Hydrogen adsorption in MOFs – interactions
donor‐acceptor interactions
modelling
would require QM methods
for H2
weak interactions are expected
due to large HOMO‐LUMO gap
not
included
in force field
calculations
orbital interactions
electrostatic interactions
interactions between permanent charges
modelling: partial charges, Coulomb law
for H2
: no dipole moment, quadrupole
moment small
negligible
at first
approximation
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28
Hydrogen adsorption in MOFs – interactions (II)
interactions between fluctuating dipoles
QM treatment is complex
approximation: Lennard‐Jones potential
most important type of interactions
van der
Waals interactions
6min
12min
0 2)(r
rr
rDrEvdW
empirical parameters D0
and rmin
tabulated for distinct atom types (e.g.
UFF)
interactions between different atom types:
a) mixing of atomic parameters
b) explicit specification
D0
D0
= depth of potential curve (= Emin
)
rmin
= position of Emin
rmin
= 21/6
= vdW
diameter
rmin
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29
LJ parameter adoption for hydrogen adsorption in MOFs
reproduction of H2 adsorption properties of a broad range of
different MOFs
by means of GCMC simulations
objective
approach
modification of some LJ parameters of a well‐established force field
(UFF)
based on experimental data or theoretical results but not adsorption
data (no empirical a‐priori information)
using experimental adsorption data to validate the parameters
adaptations
H2
– H2
parameters
H2
– Caryl
parameters
Mn+
parameters
(excess correction and calculation of the pore volume)
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Hydrogen models in GCMC simulations
two‐point LJ fluid
H H
+ q + q- 2q
H H
realistic concerning the
quadrupole
moment
calc. of charges of the
framework necessary
energy evaluation time‐
consuming
not very realistic, no differentiation between
side‐on vs. end‐on orientation
but: rotational degrees of freedom of H2
molecule even at adsorption sites
calculations are much faster
new atom type H_2
adaption
of only one parameter
H2
two‐point LJ fluid, three‐point charge particle
one‐point LJ fluid (united‐atom model, UA)
(H2 )
d(H-H)
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31
Results and Discussion
Simulation of H2
@ MOFs
at T = 77 K and 0.05 bar ≤
P ≤
60 bar
Cu3
(btc)2
MOF‐505
PCN‐10
PCN‐11
IRMOF‐1
IRMOF‐20
MOF‐74
MOF‐177
ZIF‐8
Ni2
(dhtp)
Ni3
(btc)2
(pic)6
(pd)3
‘Mixed‐MOF’
13 different MOFs
in total
10 different framework geometries
4 different types of metal centers
Zn‐MOFs Cu‐MOFs Ni‐MOFs Mn‐MOFs
(Mn4
Cl)3
(btt)8
Zn3
(bdc)3
Cu(pyen)
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32
Results and Discussion
IRMOF‐1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 20 40 60 80 100p [kPa]
H2 u
ptak
e [w
t.-%
]
exp.sim.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 1000 2000 3000 4000 5000 6000p [kPa]
H2 u
ptak
e [w
t.-%
]exp.sim.
exp: ‐3.8 – 4.8 kJ/mol
sim: ‐3.8 kJ/mol
isosteric
enthalpy of adsorption:
Rowsell
et al., J. Am. Chem. Soc. 2004,
126, 5666 Kaye et al., J. Am. Chem. Soc. 2007,
129, 14176
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33
Results and Discussion
ZIF‐1
exp. ‐
4.5 kJ/mol
sim. ‐
5.4 kJ/mol
isosteric
enthalpy of adsorption:
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 1000 2000 3000 4000 5000 6000p [kPa]
H2 u
ptak
e [w
t.-%
]
exp.sim.
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34
Results and Discussion
exp. ‐
4.8 – 6.8 kJ/mol
sim. ‐
6.9 kJ/mol
isosteric
enthalpy of adsorption:
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 20 40 60 80 100p [kPa]
H2 u
ptak
e [w
t.-%
]
exp.sim.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 1000 2000 3000 4000 5000p [kPa]
H2 u
ptak
e [w
t.-%
]
exp.sim.
Cu3
(btc)2
Chui et al., Science 1999, 283, 1148
Liu et al., J. Phys. Chem. C 2007,
111, 9305
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35
Results and Discussion
hot spots
Cu3
(btc)2
physisorption
occurs
mainly in smaller pores
very little adsorption near
metal sites
possible explanation for
underestimation of the
calculated loading
p = 0.5 bar
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36
Results and Discussion
exp. ‐
10.1 kJ/mol
sim. ‐
5.4 kJ/mol (!)
isosteric
enthalpy of adsorption:
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 1000 2000 3000 4000 5000 6000P [kPa]
H2-
Upt
ake
[wt-%
]
Experimental
Simulated0.0
0.5
1.0
1.5
2.0
2.5
0 20 40 60 80 100P [kPa]
H2-
Upt
ake
[wt-%
]
Experimental
Simulated
(Mn4
Cl)3
(btt)8
Dinca
et al., J. Am. Chem. Soc. 2006,
128, 16876
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37
Summary Part II
quantitative
agreement
for
MOFs
that
do
not
contain
open
metal
sites
for
quantities
that
depend
on
the
total
pore
volume
and
the
fluid‐fluid potential, i.e.
saturation uptake and saturation pressure
applicability for very different MOF systems
qualitative agreement of the curvature of the adsorption isotherms,
which depends on the pore geometry
discrepancies
of
the
calculated
loadings
arise
for
MOFs
with
open
metal
sites:
the
interaction
of
H2
with
these
sites,
which
is
not
a
normal vdW
interaction, cannot be modelled
by a simple LJ potential
evidence
for
a
Kubas‐type
interaction
between
hydrogen
and
open
metal sites
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38
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39
Hydrogen (and methane) adsorption in MOFs
Spencer et al., Chem. Commun. 2006, 278
H2
@ IRMOF‐1T = 5 K
neutron
diffraction
data
hydrogen
molecules
predominantly
at defined
positions
spatial
defined
interactions
which
interactions
do play
a role
?
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40
LJ parameter adoption for hydrogen adsorption in MOFs
H2
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
0.090
0 10 20 30 40 50 60p [MPa]
Den
sity
[g/c
m3 ]
exp.sim.
H2
Experimental data: NIST Chemistry WebBook, http://webbook.nist.gov/chemistry
H2
is represented as a single vdW
site
(UA model)
limiting case of large pores
necessity to reproduce the fluid –
fluid
interactions
fit of LJ parameters to the pressure –
density relationship at T = 77 K
intrinsic correction of quantum
effects
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41
LJ parameter adoption for hydrogen adsorption in MOFs
H2 Caryl
QM calculations (MP2): interactions
of H2
with benzene and other PAHs
fit of LJ parameters: reproduction of
these results in terms of
physisorption
energy
distance H2
–
ring
H2
@ coronene d (Å) E (kJ/mol)
MP2FF
3.083.09
5.15.0
Heine et al., Phys. Chem. Chem. Phys. 6 (2004) 980
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42
LJ parameter adoption for hydrogen adsorption in MOFs
H2 M2+
DFT calculations deliver electron density
distribution for free cations
(DMOL3)
(M2+) diameter at which the electron
density drops below a certain limit
choice of this limiting value: analogy with H2
molecule
Mn2+
= 3.04 ÅCo2+
= 2.68 ÅNi2+
= 3.00 Å
Cu2+
= 2.90 ÅZn2+
= 2.86 ÅH2
s
~ 2.92 Å
1. vdW
diameter ()
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43
LJ parameter adoption for hydrogen adsorption in MOFs
H2 M2+
attractive part of the LJ potential is linked to
the London approximation
rmin
is obtained from the calculated values of
Ionization energy I
is know from experiments
polarizability
: empirical values
2. potential depth (D0
)6
min
2
0 61
rID
rmin
(Å) D0
(kJ/mol)
3.42
3.00
3.38
3.25
3.22
Mn2+
Co2+
Ni2+
Cu2+
Zn2+
0.741
1.302
0.445
0.856
1.087scaling necessary to avoid
overestimation of H2
– metal
interaction
Shannon & Fischer, Phys. Rev. B 73 (2006) 235111
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44
LJ parameters and Mixing Rules
LJ parameters in publications
6min
12min
0 2)(r
rr
rDrEvdW
…means: how to treat heteroatomic
pairs?
most common: Lorentz‐Berthelot mixing, i.e.
an
arithmetic average is used for the collision
diameter, while a geometric average is used for
the potential depth
])(2)[(])()[(4 612612Rr
Rr
RRmmE
Frost, Düren, Snurr, J. Phys. Chem. B 110 (2006) 9565
X H2‐X
[Å] H2‐X
/ kB
[K]
H2
C
H
O
Zn
2.958
3.216
2.902
2.996
3.501
36.7
41.924
16.761
42.056
31.882 1000/)/(]/[0 RkmolkcalD B
Mixing schemes
2
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45
Absolute vs. excess adsorption
GCMC simulations deliver the total
amount of molecules per unit cell;
absolute adsorption
experimental accessible is only the so‐
called Gibbs’
excess adsorption
this is: the absolute amount minus the
number of molecules that would
occupy the free pore volume if the
interaction energy would be zero
excess correction
Kaye et al., J. Am. Chem. Soc. 129 (2007) 14176
excN
poreV
absN
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0 2000 4000 6000 8000P [kPa]
H2-
Upt
ake
[wt-%
]
Excess-Adsorption
Absolute Adsorption
H2
@ IRMOF‐1
2Hporeexcabs VNN
2Hporeabsexc VNN
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46
Calculation of the pore volume
GCMC simulation of He ‘physisorption’
at T = 298 K and low pressures
adaptation of LJ parameters that determine the He –
solid interaction
good agreement with experimental values from N2
physisorption
determination of Vpore
0.00.20.40.60.81.01.21.41.61.82.0
V (c
m^3
/g)
V_pore (Exp)
V_pore (Sim)
MOF‐74Cu3(btc)2
IRMOF‐1 MOF‐177
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47
From Numbers to Volumetric or Gravimetric units
Nabs
/per UC [g/cm‐3] or [g/g] or wt.‐%
Nabs Nabs
/Å Nabs
/cm‐3
1024
nabs
/cm‐3
NA‐1
VUC‐1
g/cm‐3
MAdsorptive
[g/mol]
Nabs
/UC
MAdsorptive
/ MUCg/g
100 / (1+ mAdsorptive
)
wt.‐%
volumetric
gravimetric
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48
The Monte Carlo Method
let‘s play some random(!) dart (‘hit & miss’) and evaluate thereby the value of π…
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49
The Monte Carlo Method
let‘s take the first quadrant of a unit circle…
the graph can be expressed as:
a random number generator creates x,y
values [0;1]
these coordinates are points,
which can lie inside … … or outside of the circle:
the relative frequency is a value:
…that matches the
value of the respective area:
x
y
r2
= x2
+ y2
=1
x2
+ y2
≤
1 x2
+ y2
> 1
fr
= ninside
/ ntotal
A = π/4 = ninside
/ ntotal
π
= 4
ninside
/ ntotal
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50
The Monte Carlo Method
ntotal
= 126noutside
= 19ninside
= 107
π
= 3.3968
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51
The Monte Carlo Method
ntotal
= 987noutside
= 228ninside
= 759
π
= 3.07599
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52
The Monte Carlo Method
ntotal
= 7505noutside
= 1599ninside
= 5906
π
= 3.1478
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53
microporous materials and H2 storage
a “tag cloud”
IRMOFsZIFs
MILs
COFsCNTs
PIMsMOPs
CAs
ZTCs
HPsCPLs
IRMOFsZIFs
MILs
COFsCNTs
PIMsMOPs
CAs
ZTCs
HPsCPLs
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54
design guidelines
a multidimensional optimization problem
high free volumelong linkers
no interactionwith pore wall
interpenetrationis an issue
low frameworkdensity
stability athigh pressures
guidance valueDHads ~ 15 – 20 kJ/mol
relatively strong inter-action w. framework
fueling with and providingof H2 have to be fast
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55
IRMOFs
protoype
MOF‐5 IRMOF‐1
Zn4
O cluster linked by chelating carboxylate
ligands
Eddaoudi et al., Science 295 (2002) 469
1 6 8
10 14 18
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56
IRMOFs – Interpenetration / Catenation
in terms of gaining absolute pore volume interpenetration is not
desirable
but catenation
can enhance
uptake at low pressure (< 1 bar) up to 40 % rel. to non‐
catenated
species
Rowsell, Yaghi , MMM 73 (2004) 3 – 14
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57
Results and Discussion
hot spots
physisorption
occurs
mainly in cage‐like pores
very little adsorption near
metal sites
possible explanation for
underestimation of the
calculated loading
p = 1.0 bar(Mn4
Cl)3
(btt)8
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MOF-177 – world record holder
Chae et al. , Nature 427 (2004) 523
1,3,5‐benzenetribenzoate (BTB)
SBET
~ 4500 m2
g‐1
SLangmuir
~ 5800 m2
g‐1
Vpore
~ 1.59 cm3
g‐1
COOH
COOHHOOC
7.5 wt. % H2
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MOFs
Wong-Foy et al., JACS 128 (2006) 3494
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60
NANOSORB
funded by the BMBF
target: developing a real storage system for hydrogen/methane based on microporous materials
Prof. Fröba Prof. Kaskel
screening of known materials
designing new materials in- silico
developing and synthesis of new materials
investigation of the sorption properties
feasability studies
technical upscaling
construction of the tank
heat management