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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

2

Part I

Basic Concepts – Force Fields – Modelling as a Tool in Crystallography

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

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

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

6

Force Fields: Example and the Term Strain Energy

„strain

energy“

vdWCoulombcrossbendtorsbond EEEEEE totE

τ energy

dihedral angle τ

))cos(1( 0 nkE torstors

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

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

9

Modelling as an utility in crystallography

1

8

comparison, refinement…

calcexp

structural model

a sort of ‘Homology

Modelling’…

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’

11

Experimental P-XRD pattern

MIL‐69 but DMF instead of water as solvent (and SDA)

TUD‐MIL‐69 (as)

intensity

2 theta

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

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°

14

Comparison of the P-XRDs

TUD‐Al(OH)(ndc) (as)

TUD‐Al(OH)(ndc) (sim)

intensity

2 theta

TUD‐Al(OH)(ndc)

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°

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

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°]

18

Structure solution of MIL-101_NDC

MIL‐53 MIL‐88B MIL‐101

MTN network

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

]

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)

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

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

23

Part II

GCMC simulations for evaluation of the adsorption properties of MOFs – Adaptation of van-der-Waals parameters

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

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

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

…

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

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

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)

30

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)

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)

32


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

33


ZIF‐1

exp. ‐

4.5 kJ/mol

sim. ‐

5.4 kJ/mol

isosteric


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.

34


exp. ‐

4.8 – 6.8 kJ/mol

sim. ‐

6.9 kJ/mol

isosteric


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

35


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

36


exp. ‐

10.1 kJ/mol

sim. ‐

5.4 kJ/mol (!)

isosteric


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

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

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

?

40


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

41


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

42


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 ()

43


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

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

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

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

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

48

The Monte Carlo Method

let‘s play some random(!) dart (‘hit & miss’) and evaluate thereby the value of π…

49


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

50


ntotal

= 126noutside

= 19ninside

= 107

π

= 3.3968

51


ntotal

= 987noutside

= 228ninside

= 759

π

= 3.07599

52


ntotal

= 7505noutside

= 1599ninside

= 5906

π

= 3.1478

53

microporous materials and H2 storage

a “tag cloud”

IRMOFsZIFs

MILs

COFsCNTs

PIMsMOPs

CAs

ZTCs

HPsCPLs

IRMOFsZIFs

MILs

COFsCNTs

PIMsMOPs

CAs

ZTCs

HPsCPLs

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

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

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

57


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

58

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

59

MOFs

Wong-Foy et al., JACS 128 (2006) 3494

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

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