Molecular Simulation, 2014
Vol. 40, Nos. 7 – 9, 516–536, http://dx.doi.org/10.1080/08927022.2013.832247
Molecular simulations in metal –organic frameworks for diverse potential applications
Jianwen Jiang*
Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore
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(Received 25 June 2013; final version received 28 July 2013)
As a new class of intriguing nanoporous materials, metal –organic frameworks (MOFs) have been considered for diverse
potential applications. The number of MOFs synthesised to date is extremely large; thus, experimental testing alone is
economically expensive and practically formidable. With rapidly growing computational resources, molecular simulation
has become an indispensable tool to characterise, screen and design MOFs. Our research group has conducted
comprehensive simulation studies in MOFs for carbon capture, hydrocarbon separation, alcohol adsorption and biofuel
purification, water treatment, bio- and chiral separation and drug loading; furthermore, mechanical moduli, structural
transition and thermal conductivity have also been examined. These systematic simulation studies are summarised in this
review to demonstrate that simulation at a molecular level can secure the quantitative interpretation of experimental
observation, provide the microscopic insight from bottom-up and facilitate the development of new MOFs.
Keywords: metal – organic frameworks; potential applications; molecular simulations
Jianwen Jiang’s research expertise is in computational materials modeling and statistical
thermodynamics. His current research activities are focused on porous and membrane materials for
energy, environmental, and pharmaceutical applications such as carbon capture, water treatment,
biofuel purification, and drug delivery. He has published over 140 technical manuscripts in peerreviewed journals and a number of invited reviews and book chapters. He is on the editorial boards of
Advances in Materials Research and ISRN Nanotechnology.
1. Introduction
In the last decade, metal–organic frameworks (MOFs) have
emerged as a new family of nanoporous materials.[1]
Assembled by direct bonding between metal clusters and
organic linkers, the structures of MOFs are largely
predictable. In contrast to conventional zeolitic materials
consisting of tetrahedral building blocks, MOFs can be
synthesised from various inorganic clusters (e.g. squareshaped, trigonal, tetrahedral and octahedral) and organic
linkers (e.g. carboxylates, imidazolates and tetrazolates).
Consequently, MOFs possess a wide range of surface area,
pore size and volume. With these salient features, MOFs
have been considered versatile materials for diverse potential
applications,[2–4] as illustrated in Figure 1, ranging from
gas storage, separation, water desalination, biofuel purification to catalysis, drug delivery, etc. Indeed, MOFs have
been identified as a topical area in materials science and
technology because of their foreseeable implications.[5]
Thousands of MOFs have been synthesised, and
several of them are commercially available under the trade
name BasoliteTM (e.g. Cu-BTC, Fe-BTC, MIL-53 and
*Email: [email protected]
q 2014 Taylor & Francis
ZIF-8). Enormous experimental studies have been
reported on the characterisation and applications of
various MOFs, primarily on H2 storage [6] and CO2
capture.[7] However, the number of MOF materials
synthesised is extremely large and in principle unlimited;
thus, experimental testing and screening of ideal MOFs
from infinite possible candidates are time-consuming and
practically infeasible.
With rapidly growing computational resources,
molecular simulation has become an indispensable tool
and plays an increasingly important role in materials
science and engineering. Sophisticated simulation at an
atomistic/molecular level provides microscopic insight
that is experimentally intractable, and elucidates underlying physics from bottom-up. In addition, simulation can
be used to secure the fundamental interpretation of
experimental observation and to establish the structure –
function relationship to guide the rational selection and
design of novel materials.[8]
To date, most simulation studies in MOFs have been
focused on gas storage and separation, particularly the
Molecular Simulation
CO2 Capture
Gas Storage
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Removal
of Toxics
Water
Desalination
Figure 1.
517
Biofuel
Purification
Drug Delivery
Catalyts or
Supports
Synthetic
Channels
(Colour online) Diverse potential applications of MOFs.
storage of low-carbon footprint energy carriers (e.g. H2)
and the separation of CO2-containing gas mixtures for
carbon capture.[9 –14] In our research group, comprehensive simulation studies have been conducted in MOFs for a
wide range of diverse potential applications such as carbon
capture, hydrocarbon separation, alcohol adsorption and
biofuel purification, water treatment, bio- and chiral
separation, drug loading, as well as mechanical moduli,
structural transition and thermal conductivity. As invited
by the Editor, these systematic simulation studies are
summarised in this review.
2. Simulation methodology
The atomic coordinates of MOFs in simulation are usually
adopted from experimentally crystallographic data. It should
be noted that some crystallographic data contain the
coordinates of solvent or ligand molecules or diffraction
defects, and cannot be directly input into simulation. For this
case, the crystallographic data are required to be modified so
as to properly represent the crystalline structures. Unless an
interfacial region is examined, simulation box is mimicked
by periodic boundary conditions and surrounded by its
replicated images. Thus, simulation system can be
considered to be an infinitely large crystal.
In most simulation studies, the frameworks are
assumed being fixed. Such a treatment is acceptable for
relatively rigid MOFs, and indeed, it has two advantages:
first, there is no need to consider the intra-framework
interactions and second, the guest –framework interactions
can be pre-tabulated prior to simulation. Therefore, it is
crucial to accurately describe the guest – framework
interactions that exclusively determine the reliability of
simulation. The guest– framework interactions can be
represented by long-range electrostatic potential and shortrange van der Waals potential. For the electrostatic
potential, atomic charges in MOFs need to be evaluated,
and several methods have been proposed in the literature,
such as quantum mechanics (QM)-based electrostatic
potential method,[15,16] connectivity-based atom contribution method [17] and extended charge equilibration
method.[18] For the van der Waals potential, QM methods
can be used to derive the potential parameters in two steps.
Firstly, the interaction energies between guest and framework are calculated by QM at various representative
positions and orientations. Secondly, an analytic potential
function is adopted to fit the interaction energies.[19,20] To
accurately calculate the interaction energies, an appropriate level of QM method is needed. The most costeffective method is density functional theory (DFT).
However, DFT has deficiency in describing the non-local
dispersion forces induced by electron correlations. In
principle, wave function-based coupled-cluster and Møller –Plesset perturbation methods are more accurate, but
they are computationally very demanding particularly for
large systems. As an alternative, molecular mechanical
(MM) force fields can be used to describe the van der Waals
potential between guest and framework. For example,
universal force field (UFF) [21] and DREIDING [22] have
been widely used for MOFs. The potential parameters in
these force fields are usually derived from experimental
data over a limited range of conditions. Although useful
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518
J. Jiang
information can be obtained from them, the empirical
nature may lead to inaccurate or incorrect predictions.
Consequently, they should be used with caution.
A number of MOFs exhibit flexible/dynamic structures
upon stimuli (e.g. temperature, pressure, sorption and so
on). In contrast to rigid MOFs, the intra-framework
interactions should be incorporated to mimic framework
flexibility, including bond stretching, bending and
torsional potentials. These potentials can also be
determined from QM methods, but computationally
expensive; a more common way is to use MM force fields.
With a proper description of molecular interactions,
simulation can be performed using Monte Carlo (MC),
molecular dynamics (MD) or a hybrid MC and MD.
[23,24] In MC simulation, representative configurations
are randomly generated. Thus, MC simulation can be
performed with physically unnatural trial moves, e.g. a
jump from one position to the other or a random insertion/
deletion. MC simulation is well suited to investigate
adsorption in MOFs. Particularly, grand canonical MC
(GCMC) simulation is used very widely to simulate
adsorption isotherms and other thermodynamic properties
(e.g. Henry’s constant, isosteric heat and so on). Based on
the Newton’s second law of motion, MD simulation
mimics the natural pathway of molecular motion to sample
successive configurations. At each time during MD
simulation, the forces between molecules are calculated,
then the equations of motion are solved numerically and
finally, velocities and positions are updated. The time step
chosen should be sufficiently small; thus, the total energy
of system is conserved. In addition to thermodynamic
properties that can be simulated by MC method, transport
properties such as diffusivity and conductivity are usually
determined from MD method. For either method,
simulation is anticipated to run for a sufficient long time
to assure that equilibration or steady state is reached;
thereafter, ensemble averages can be estimated.
3.
Diverse potential applications
As listed in Table 1, our group has systematically
conducted a series of simulation studies in MOFs for
diverse potential applications including carbon capture (in
both MOF adsorbents and membranes), hydrocarbon
separation, alcohol adsorption and biofuel purification,
water treatment, bio- and chiral separation and drug
loading. Moreover, we have also developed force fields
incorporating framework flexibility to describe mechanical
moduli, structural transition and thermal conductivity.
3.1
Carbon capture
A vast amount of CO2 emissions have been produced by the
combustion of fossil fuels, as estimated to be 30 gigatons
per year worldwide.[63] Carbon capture and sequestration
(CCS) is critical for environmental protection and
sustainable development. As a key step in CCS, CO2 is
required to be captured in pre-combustion or postcombustion process. A handful of technologies have been
proposed for carbon capture such as cryogenic distillation,
amine scrubbing, membrane separation and sorbent
adsorption.[64] Due to the occurrence of phase transition,
cryogenic distillation is economically expensive. Although
amine scrubbing is commercially applied in industry,
regeneration step is energetically intensive. Comparatively, sorbents and membranes-based carbon capture are
more efficient with lower capital cost and larger separation
capability. The majority of experimental and simulation
studies in MOFs have been focused on carbon capture, as
summarised in several reviews.[12,65 – 67]
3.1.1
Adsorbents
Synthesised MOFs are crystallites and usually tested as
adsorbents for carbon capture. It is noteworthy that most of
experiments examine the adsorption of pure gases (e.g.
CO2, N2, CH4 and H2) due to the difficulty in measuring
mixture adsorption. On the contrary, simulation can be
readily used for mixtures. Therefore, quantitative understanding of mixture adsorption in MOFs has been largely
based on simulation.
Isoreticular MOFs. One of the earliest simulation studies
we carried out was carbon capture in IRMOF-1.[25] As a
prototype of MOF, IRMOF-1 consists of Zn4O as a metal
cluster and 1,4-benzenedicarboxylate (BDC) as an organic
linker.[68] The straight pore in IRMOF-1 possesses
˚ . Specifically, we
alternating diameters of 15 and 12 A
predicted the adsorption and separation of CO2 and CH4 in
IRMOF-1, silicalite and C168 schwarzite at 300 K.[25] The
separation of CO2/CH4 mixture is important in the
sweetening of nature gas. As illustrated in Figure 2, the
three materials have well-defined three-dimensional (3D)
structures, of which each represents a typical class of
nanoporous materials. The adsorption isotherms and
isosteric heats of pure gases from simulation agree well
with available experimental data. CO2 is preferentially
adsorbed over CH4 in all the three adsorbents, except C168
schwarzite at high pressures. All isotherms are of type I
(Langmuirian), which is the characteristic of microporous
adsorbents with a pore of molecular dimension (below
˚ ). The adsorption capacities of CH4 and CO2 in
20 A
IRMOF-1 are substantially larger than in silicalite and
C168 schwarzite. This implies that IRMOF-1 might be a
potential medium for gas storage. The predictions of
mixture adsorption from the ideal adsorbed solution theory
(IAST) [69] are in accord with simulation, particularly at
low pressures because the IAST becomes exact in Henry’s
Molecular Simulation
Table 1.
Summary of simulation studies in MOFs for diverse potential applications.
Application
CO2 capture in adsorbents
Isoreticular MOFs
Catenated MOFs
Functionalised MOFs
Ionic MOFs
Moisture effects
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CO2 capture in membranes
MOF membranes
Polymer/MOF membranes
IL/MOF membranes
Hydrocarbon separation
Alkanes (C1 – C5)
Xylene isomers
Alcohol adsorption and biofuel purification
Alcohol adsorption (C1 – C4)
Biofuel purification
Dilute biofuel purification
Water treatment
Water desalination
Removal of toxic ions (Pd2þ)
Removal of organics (DMSO)
Bio- and chiral separation and drug loading
Bio-separation of amino acids
Chiral separation
Ibuprofen loading
Mechanical moduli, structural transition
and thermal conductivity
Mechanical moduli
Structural transition
Thermal conductivity
MOF examined
Reference
IRMOF-1, -13, -14
IRMOF-13, PCN-6
bio-MOF-11, ZTF, F-MOFs, MIL-101
soc-MOF, rho-ZMOF, rht-MOF, Li-MOF
soc-MOF, rho-ZMOF, rht-MOF, bio-MOF-11,
MIL-101, Zn(bdc)(ted)0.5
[25,26]
[26]
[27 – 32]
[33 – 37]
[27,33,35,38 –40]
IRMOF-1, ZIF-95, Zn(bdc)(ted)0.5
PBI/ZIF-7
[BMIM][X]/IRMOF-1 (X ¼ [Tf2N], [BF4],
SCN]), [BMIM][SCN]/ZIF-71, [BMIM][SCN]/
rho-ZMOF
[41 – 43]
[44]
[45 – 47]
IRMOFs, PCNs
MIL-101
[48,49]
[50]
Zn(bdc)(ted)0.5, rho-ZMOF, Zn4O(bdc)(bpz)2,
ZIF-71, ZIF-8
rho-ZMOF, Zn4O(bdc)(bpz)2
hydrophobic MOFs and ZIFs
[40,51– 53]
[52]
[54]
ZIF-8 membrane
rho-ZMOF
ZIF-71, Zn4O(bdc)(bpz)2, Zn(bdc)(ted)0.5
[55]
[56]
[57]
MIL-101
Zn2(bdc)(L-lac)(dmf)
MIL-101, UCMC-1
[50]
[58]
[59]
ZIF-8, ZIF-7, PBI/ZIF-7
ZIF-8
ZIF-8, MOF-5
law regime. At high pressures, however, the IAST either
underestimates or overestimates the simulated results. This
is attributed to the assumption used in the IAST, i.e. the
adsorbed phase of mixture is assumed to be ideally mixed.
Though IRMOF-1 has a significantly higher adsorption
capacity than silicalite and C168 schwarzite, CO2/CH4
selectivity is close in the three adsorbents.
Substituting the BDC linker in IRMOF-1 by a longer
linker namely pyrene dicarboxylate, IRMOF-14 can be
Figure 2.
519
[60,61]
[60,61]
[62]
˚ .[68]
generated with pore diameters of 20.1 and 14.7 A
From simulation, we observed that CO2/CH4 selectivity
in IRMOF-14 is lower than in IRMOF-1.[26] This is
because the larger pore in IRMOF-14 is less favourable
for separation. The presence of electrostatic interactions
between CO2 and framework was found to cause an
increase in CO2 adsorption and a decrease in CH4
adsorption; consequently, CO 2/CH 4 selectivity is
enhanced.
(Colour online) IRMOF-1, silicalite and C168 schwarzite.[25]
J. Jiang
Catenated MOFs. To improve carbon capture in MOFs,
several strategies have been proposed such as using
catenated, functionalised and ionic frameworks.[13] We
performed simulation to investigate the separation of CO2/
CH4 mixture in IRMOF-13 and IRMOF-14 at 300 K.[26]
Despite identical metal oxide and organic linker, IRMOF13 has a catenated framework and differs from noncatenated IRMOF-14. As a result, pore diameters in
˚ , smaller than in IRMOF-14.
IRMOF-13 are 12.4 and 8.7 A
CO2 adsorption at low pressures in IRMOF-13 is greater
than in IRMOF-14. The reason is that the formation of
constricted pores by catenation leads to a larger degree of
potential overlap and a stronger affinity for adsorbate. Due
to the smaller pore volume in catenated framework,
however, the opposite is true at high pressures. As shown
in Figure 3, IRMOF-13 has a higher selectivity than noncatenated counterpart for CO2/CH4 mixture. The effect of
electrostatic interaction on the selectivity is larger in
IRMOF-13 than in IRMOF-14.
PCN-60 and PCN-6 were also examined for the
separation of CO2/CH4 mixture.[26] Consisting of paddlewheel coppers linked with 4,40 ,400 -s-triazine-2,4,6-triyltribenzoate, PCN-60 is non-catenated and iso-structural to
Cu-BTC.[70] The square pore in PCN-60 possesses a large
˚ £ 21.44 A
˚ . In contrast, PCN-6 is catenated
size of 21.44 A
0
˚.
counterpart of PCN-6 with a triangular pore of 9.2 A
0
PCN-6 and PCN-6 exhibit adsorption behaviour similar to
IRMOF-14 and IRMOF-13, respectively. CO 2/CH4
selectivity in catenated PCN-6 is higher than in noncatenated PCN-60 .
Functionalised MOFs. Functionalisation is a commonly
used method to tailor material properties and has been
applied to tune MOFs. We simulated the separation of
7
2/CH4
IRMOF-13
5
SCO
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520
3
IRMOF-14
1
0
1000
2000
3000
4000
5000
P (kPa)
Figure 3. (Colour online) CO2/CH4 selectivity in IRMO-13 and
IRMOF-14.[26]
CO2/H2 and CO2/N2 mixtures in bio-MOF-11 with
adenine as a bio-linker.[27] The simulated and experimental adsorption isotherms of pure CO2, H2 and N2 are
in a perfect agreement. As attributed to the presence of
multiple Lewis basic sites (amino and pyrimidine groups)
and nano-sized channels, bio-MOF-11 has a larger
adsorption capacity and a higher selectivity than many
zeolites, activated carbons and MOFs. The study provides
microscopic insight into the adsorption mechanism in bioMOF-11 and suggests that bio-MOF-11 might be
interesting for pre- and post-combustion carbon capture.
By combining experiment and simulation, we
examined CO2 adsorption in amino-functionalised zeolitic
tetrazolate framework (ZTF).[28] The Zn · · · Zn distance
˚ , extended by replacing oxide ions with
in ZTF is 5.9 A
˚,
tetrazolate linkers. ZTF possesses a pore diameter of 4.5 A
with a diamond (dia) topology and extended 3D structure.
CO2 capacity was experimentally measured to be
5.6 mmol/g at 273 K, representing one of the highest
values. The high CO2 capacity was attributed to the narrow
pores, exposed ZNH2 functionality and free tetrazole
nitrogen. Good agreement was found between the
experimental isotherm and simulation. Furthermore, we
investigated CO2 adsorption in two iso-structuralinterpenetrated amino-functionalised Cd-ANIC-1 and
Co-ANIC-1 (ANIC: 2-amino-4-pyridine carboxylic
acid).[29] The two MOFs adopt dia topology with amino
groups lined along the pores. High CO2 uptake was
observed experimentally and validated by simulation, as
attributed to the presence of Lewis basic amino groups and
framework interpenetration.
We synergised ab initio calculation, molecular
simulation and breakthrough prediction to examine postcombustion carbon capture at 303 K in MIL-101
functionalised by a series of groups (X ¼ ZNH2, ZCH3,
ZCl, ZNO2 and ZCN).[32] MIL-101 is a chromium
terephthalate-based mesoscopic MOF and one of the most
porous materials reported to date.[71] It is stable in air and
boiling water, and its structure is not altered in organic
solvents or solvothermal conditions. In low-pressure
regime, CO2 uptake and isosteric heat increase in the
order of MIL-101 , MIL-101-CN , MIL-101-NO 2
, MIL-101-Cl , MIL-101-CH3 , MIL-101-NH2. Such
an order follows the strength of binding energies between
CO2 and functional groups calculated by ab initio method.
However, the effect of functional group is marginal for N2
adsorption. As shown in Figure 4, CO2/N2 selectivity is
enhanced by functionalisation, following MIL101 , MIL-101-CN , MIL-101-CH3 , MIL-101-NO2
, MIL-101-Cl , MIL-101-NH2. At infinite dilution, the
enhancement of selectivity is 2.5 times, from 16 in parent
MIL-101 to 40 in MIL-101-NH2. The predicted breakthrough time is extended by functionalisation, and the
longest breakthrough time in MIL-101-NH2 is 2 times that
in parent MIL-10. The multi-scale modelling study
Molecular Simulation
60
40
Mole fraction of outlet CO2
50
S(CO2/N2)
0.15
MIL-101-NH2
MIL-101-Cl
MIL-101-CH3
MIL-101-NO2
MIL-101-CN
MIL-101
30
20
0
20
40
60
80
MIL-101
MIL-101-NO2
MIL-101-CN
MIL-101-Cl
MIL-101-CH3
MIL-101-NH2
0.12
0.09
0.06
0.03
0.00
100
0
20
40
Ptotal (kPa)
60
80
100 120 140 160
Dimensionless time
Figure 4. (Colour online) (a) CO2/N2 selectivity in MIL-101-X and (b) mole fraction of outlet CO2 through a fixed bed packed with
MIL-101-X. The inlet gas mixture consists of 15 kPa CO2 and 85 kPa N2.[32]
suggests that the performance of carbon capture in MIL101 can be considerably improved by functionalisation.
eight-membered ring for the adsorption of CO2/CH4
mixture at a total pressure of 500 kPa. CO2 molecules are
observed to bind preferentially with Naþ ions, as also
demonstrated by the radial distribution functions in
Figure 5(b). The predicted CO2/CH4 selectivity is
significantly higher than in most MOFs. By artificially
switching off the charges in Na-rho-ZMOF, the selectivity
decreases substantially. This suggests that electrostatic
interaction is crucial for the high selectivity in Na-rhoZMOF.
We further investigated the separation of CO2/H2
mixture in three ionic MOFs (rho-ZMOF, soc-MOF and
rht-MOF).[33 –35] Similar to CO2/CH4 mixture in rhoZMOF, the predicted CO2/H2 selectivity in the three ionic
MOFs is much higher than in non-ionic MOFs. Particularly
noteworthy is that the selectivity behaves differently in the
three ionic MOFs with varying free volume and charge
Ionic MOFs. In a porous material, the presence of chargebalancing non-framework ions can enhance the interactions with guest molecules, which in turn increase
adsorption capacity and selectivity. We simulated the
separation of CO2/CH4, CO2/N2 and CO2/H2 mixtures in
Na-rho-ZMOF at 298 K.[34] The rho-ZMOF possesses a
widely open anionic framework and charge-balancing
doubly protonated 1,3,4,6,7,8-hexahydro-2H-pyrimido
[1,2-a]pyrimidine (HPP).[72] The HPP ions can be
exchanged with other cations, e.g. Naþ ions. The
simulation revealed that CO2 is predominantly adsorbed
over other small gases due to the strong electrostatic
interactions with Naþ ions and ionic framework. Figure 5
(a) demonstrates the typical locations of CO2 molecules in
(a)
(b)
1000
5
+
Na - CO2
g (r)
4
SCO2/CH4
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10
521
3
2
+
Na - CO4
1
100
0
2
4
6
8
10
r (Å)
10
0
500
1000
1500
2000
2500
3000
P (kPa)
Figure 5. (Colour online) Adsorption of equimolar CO2/CH4 mixture in Na-rho-ZMOF. (a) Locations of CO2 molecules in eightmembered ring. Naþ ions and CO2 molecules are represented by balls and sticks, respectively. (b) CO2/CH4 selectivity. The inset shows
the radial distribution functions.[34]
522
J. Jiang
decreases due to two factors. First, the adsorption sites are
heterogeneous and adsorbate molecules start to occupy less
favourable sites at high pressures. Second, H2 is smaller
than CO2 and can pack into the partially filled cages more
easily with increasing pressure.
1e+5
Na
K
Rb
Cs
Mg
Ca
Al
SCO2/H2
1e+4
1e+3
1e+2
1
10
100
1000
Figure 6. CO2/H2 selectivity in Naþ, Kþ, Rbþ, Csþ, Mg2þ,
Ca2þ and Al3þ-exchanged rho-ZMOFs.[37]
density. The fractional free volume increases in the order of
rho-ZMOF , soc-MOF , rht-MOF, but the charge density increases in the opposite order. Consequently, rhoZMOF has the smallest porosity and the largest charge
density, and thus, exhibits the highest selectivity, followed
by soc-MOF and rht-MOF.
The Naþ ions in Na-rho-ZMOF can be exchanged
with other ions. To assess the effect of such exchange,
the separation of CO2/H2 mixture was simulated in
rho-ZMOFs exchanged with various cations including
Naþ, Kþ, Rbþ, Csþ, Mg2þ, Ca2þ and Al3þ.[37] Figure 6
shows CO2/H2 selectivities in the seven rho-ZMOFs versus
the total pressure. At a given pressure, the selectivity
increases as Csþ , Rbþ , K þ , Na þ , Ca 2þ
, Mg2þ < Al3þ. This is because the electric field of
cation increases with increasing charge-to-diameter ratio,
and hence, the interaction with CO2 is enhanced. With
increasing pressure, the selectivity in each rho-ZMOF
(a) 70
(b)
20
CO2 /H2 /CO/CH4 (15:75:5:5)
60
15
NO3–H2O
g(r)
SCO2/H2
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P (kPa)
Moisture effects. Moisture usually exists in gas mixtures
and can adversely affect separation performance. We have
systematically examined the moisture effects on the
adsorption and separation of CO2 in various MOFs, and
observed four intriguing effects depending on the nature of
framework. (1) In ionic rht-MOF, the presence of H2O
substantially reduces CO2/H2 selectivity as shown in
Figure 7(a).[35] The radial distribution functions in
Figure 7(b) reveal that H2O is much more strongly
adsorbed onto NO2
3 ions than CO2. Consequently, the
interaction between CO2 and NO2
3 ion is substantially
shielded by H2O, which in turn reduces CO2 adsorption and
CO2/H2 selectivity. A similar significant effect of H2O on
CO2/CH4 separation was also observed in rho-ZMOF.[38]
It is therefore important to remove H2O before carbon
capture in these ionic MOFs. (2) Though with ionic
framework, soc-MOF exhibits different behaviours from
rht-MOF and rho-ZMOF.[33] The non-framework NO2
3
ions in soc-MOF are located in carcerand-like capsules
connected via narrow windows with dimensions of
˚ £ 5.946 A
˚ . In the presence of a small amount
7.651 A
H2O, CO2/H2 selectivity in soc-MOF increases at low
pressures as a consequence of the promoted adsorption of
CO2 by H2O bound onto exposed indium atoms. This is
because H2O interacts preferentially with the readily
accessible indium atoms rather than NO2
3 ions in the
capsules, and thus, the bound H2O molecules act as
additional sites for CO2 adsorption. With increasing H2O at
50
CO2/H2 /CO/CH4/H2O (15:75:5:5:0.1)
40
10
5
NO3–CO2
NO3–H2
0
30
0
1000
2000
3000
P (kPa)
4000
5000
2
3
4
5
6
7
8
9
r (Å)
Figure 7. (Colour online) (a) CO2/H2 selectivity in CO2/H2/CO/CH4 mixture (15:75:5:5) and CO2/H2/CO/CH4/H2O mixture
(15:75:5:5:0.1). (b) Radial distribution functions between NO2
3 and adsorbates in CO2/H2/CO/CH4/H2O mixture (15:75:5:5:0.1).
The inset illustrates a simulation snapshot.[35]
high pressures, however, H2O competitively replaces CO2
and the selectivity decreases. (3) In non-ionic MIL-101,
terminal H2O molecules enhance the adsorption of CO2
and CH4 at low pressures particularly for CO2.[39] The
reason is that the terminal H2O molecules act as additional
adsorption sites and CO2 interacts more strongly with them
than CH4. At high pressures, however, the terminal H2O
molecules reduce the free volume of MIL-101 and lead to a
smaller adsorption capacity compared with dehydrated
MIL-101. CO2/CH4 selectivity is slightly higher in
hydrated MIL-101.(4) In a hydrophobic MOF namely Zn
(bdc)(ted)0.5 (bdc ¼ benzenedicarboxylate and ted ¼
triethylenediamine), H2O adsorption is vanishingly small
as verified by both experiment and simulation, attributed to
the highly hydrophobic nature of Zn(bdc)(ted)0.5.[40] The
bdc and ted linkers surround metal oxides; thus, Zn(bdc)
(ted)0.5 interacts with H2O very weakly. Consequently, the
adsorption and selectivity of CO2/CH4 mixture remain
nearly identical in the absence or presence of H2O.
3.1.2
Membranes
The above-discussed simulation studies for carbon capture
are based on MOF adsorbents. There is an increasing
interest in the application of MOF membranes for gas
separation, though it is not in a mature stage.[73] We have
also investigated MOF membranes and composite
membranes for carbon capture. To calculate permeation
in a membrane, both equilibrium and dynamic properties
are required; thus, it is more challenging and timeconsuming to simulate.
MOF membranes. The diffusion and separation of CO2
and CH4 in IRMOF-1, silicalite and C168 schwarzite at
300 K were compared by simulation.[41] As loading
increases, the self-diffusivities in the three structures
decrease due to steric hindrance; the corrected diffusivities
remain nearly constant or decrease approximately in a
linear manner depending on the type of adsorbate and
structure; the transport diffusivities generally increase
except for CO2 in IRMOF-1. The correlation effects
reduce in the order of silicalite . C168 . IRMOF-1,
opposite to the increasing hierarchy of porosity
(silicalite , C168 , IRMOF-1) in the three structures.
The predicted self-, corrected and transport diffusivities of
CO2 and CH4 from the Maxwell –Stefan formulation are
consistent with simulation results. The permselectivity is
marginal in IRMOF-1, slightly enhanced in silicalite and
C168 schwarzite. Overall, the three structures are not
suitable for CO2/CH4 separation.
By combining experiment and simulation, we
examined H2/CO2 separation in a highly permeable and
selective ZIF-95 membrane.[42] In the synthesised ZIF-95
membrane, single gas permeances follow the order of H2
523
. N2 . CH4 . CO2 . C3H8, which mainly corresponds
to their kinetic diameters with the exception of CO2. The
reason is that CO2 has a strong quadrupolar interaction
with nitrogen atoms present in the linkers of ZIF-95,
leading to a high adsorption capacity but lowering
diffusional mobility, which results in a lower CO2
permeance than other small gas molecules (e.g. N2 and
CH4). The molecular sieve performance of ZIF-95
membrane was confirmed by the separation of equimolar
gas mixtures at 3258C and 1 bar. For H2/N2, H2/CH4 and
H2/C3H8 mixtures, the separation factors were measured to
be 10.2, 11.0 and 59.7, which exceed the corresponding
Knudsen coefficients (3.7, 2.8 and 4.7). The ZIF-95
membrane shows by far the highest H2/CO2 selectivity
among reported MOF and zeolite membranes. As shown in
Figure 8, the performance of ZIF-95 membrane surpasses
Robeson’s upper bound.[74] This study suggests that
hydrothermally stable and highly permselective ZIF-95
membrane is potentially interesting for H2 purification.
Furthermore, a hydrophobic Zn(bdc)(ted)0.5 membrane was tested for H2/CO2 separation.[43] Attributed to
the preferential adsorption affinity for CO2, the membrane
displays a high H2/CO2 permselectivity. For equimolar H2/
CO2 mixture at 1808C and 1 bar, H2 permeance of 2.65
£ 1026 mol m22 s21 Pa21 and H2/CO2 selectivity of 12.1
were obtained, which is promising in the potential
application of H2 purification. The effects of H2O and
CH3OH were examiend by experimental and simulation
techniques. Both H2 permeance and H2/CO2 selectivity are
almost unchanged by H2O, indicating that the pore in Zn
(bdc)(ted)0.5 is not blocked by H2O. In contrast, notable
decreases are detected in both H2 permeance and H2/CO2
selectivity in the presence of CH3OH. Specifically, H2
permeance decreases to 2 £ 1026 mol m22 s21 Pa21 and
100
H2/CO2 selectivity
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Molecular Simulation
ZIF-7 membrane20
ZIF-8 membrane21
ZIF-22 membrane23
ZIF-69 membrane33
ZIF-90 membrane22
MIL-53 membrane34
HKUST-1 membrane35
ZIF-95 membrane
10
MOFs
Polymers
36
Upper bound 1991
37
Upper bound 2008
1
1
10
100
1000
10,000 1,00,000
H2 permeability / Barrers
Figure 8. H2/CO2 selectivity versus H2 permeability in MOF
and polymer membranes.[42]
J. Jiang
H2/CO2 selectivity decreases to 8.1. Due to the high
hydrophobicity of Zn(bdc)(ted)0.5, CH3OH is strongly
adsorbed and subsequently blocks the diffusion of rarely
adsorbed H2, leading to the decrease in H2 permeance, and
consequently the decrease in H2/CO2 selectivity.
7 cluster, CO2 diffusion is slowed down. Specifically, the
diffusion coefficient of CO2 in PBI/ZIF-7 is approximately
30% of that in PBI. H2 and CO2 permeabilities in PBI/ZIF-7
membranes are greater than in neat PBI. Particularly, the
higher the ZIF-7 loading, the greater is the permeability, and
a slight enhancement in permselectivity.
Polymer/MOF membranes. To improve the mechanical
strength of polymer membranes, inorganic fillers such as
zeolites and metal oxides are added to form mixed-matrix
membranes (MMMs). However, inorganic fillers do not
have good interfacial compatibility with polymer matrices,
leading to a less ideal performance for gas separation.
Recently, nano-sized ZIF-7 was dispersed into polybenzimidazole (PBI) to fabricate MMMs for H2 purification,
and enhanced H2 permeability and H2/CO2 permselectivity
were reported.[75] Both PBI and ZIF-7 contain the same
organic unit namely benzimidazolate, such that PBI/ZIF-7
membranes could have a good interfacial compatibility. To
facilitate a clear and deep microscopic understanding, we
conducted atomistic simulation for H2/CO2 separation in
PBI/ZIF-7 membranes.[44] Figure 9(a) demonstrates a
membrane consisting of PBI and a two-cage ZIF-7 cluster.
The void size distributions in pure PBI and PBI/ZIF-7
membranes are shown in Figure 9(b). With increased ZIF-7
˚ ) increases,
loading, the percentage of large voids (.3 A
˚ ) decreases. This
while the percentage of small voids (0–3 A
is attributed to the increased free volume (empty cage) upon
adding ZIF-7 cluster. The modulus in PBI/ZIF-7 membrane
gradually increases with increased ZIF-7 loading; thus, the
mechanical strength is enhanced. This is a major advantage
of MMMs over polymer membranes, which would allow
MMMs to be practically used at high pressures. The
solubility coefficients of both H2 and CO2 in PBI/ZIF-7
membranes increase with increased ZIF-7 loading. While H2
diffusion is not significantly affected by the presence of ZIF-
Ionic liquid/MOF membranes. There has been a
considerable interest in using supported ionic liquids
(ILs) for carbon capture.[76,77] However, most studies to
date have used either organic polymers or inorganic
zeolites as supports with limited permeability.
We have proposed IL/MOF membranes and demonstrated their use for CO2/N2 separation at room temperature.
[45–47] In IRMOF-1-supported 1-n-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]), bulky
[BMIM]þ cation resides in the open pore of IRMOF-1,
whereas small [PF6]2 anion is located in metal cluster
corner and possesses a strong interaction with the framework. [PF6]2 anion is the most favourable site for CO2
adsorption. With increasing IL ratio in the membrane, CO2/
N2 selectivity increases.[45] Moreover, ILs with four
different anions including [PF6]2, tetrafluoroborate
[BF4]2, bis(trifluoromethylsulphonyl)imide [Tf2N]2 and
thiocyanate [SCN]2 were examined.[46] Among the four
anions, [Tf2N]2 has the weakest interaction with IRMOF-1.
CO2/N2 selectivity increases in the order of
[Tf2N]2 , [PF6]2 , [BF4]2 , [SCN]2. This hierarchy
largely follows the trend of binding energy between CO2
and anion estimated by ab initio method. [BMIM][SCN]/
IRMOF-1 outperforms polymer membranes and polymersupported ILs in CO2 permeability, and its performance
surpasses Robeson’s upper bound as demonstrated in
Figure 10. In addition, both hydrophobic ZIF-71 and
hydrophilic Na-rho-ZMOF with identical topology and
similar pore size were used as supports, and hydrophilic
(a)
(b)
20
pure PBI
PBI/1-cage ZIF-7
PBI/2-cage ZIF-7
15
Percentage
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524
PBI/3-cage ZIF-7
10
5
0
0
1
2
3
4
Void size (Å)
5
6
7
Figure 9. (Colour online) (a) A membrane of PBI/2-cage ZIF-7 cluster. (b) Void size distributions in pure PBI and PBI/ZIF-7
membranes.[44]
Molecular Simulation
1000
[BMIM][SCN]/ZMOF
Polymer-SILs
Upper Bound
PCO / PN
2
100
2
ILs/IRMOF-1
10
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[BMIM][SCN]/ZIF-71
1
0.0001
0.01
1
100
4
10
PCO2 (barrer)
Figure 10. (Colour online) CO2/N2 permselectivity versus CO2
permeability in IL/MOF membranes. The red circles are
experimental data in polymer membranes and the line is
Robeson’s upper bound. Also illustrated are the data in polymersupported ILs.[47]
support was found to be superior to hydrophobic counterpart.
[47] These simulation studies reveal that IL/MOF membranes are potentially intriguing for CO2 capture, and could
trigger experimental efforts.
3.2
Hydrocarbon separation
Hydrocarbons are predominantly used as combustible
fuels and raw materials in chemical industry. Extensive
simulation efforts have been conducted for hydrocarbons
in zeolitic materials,[78] whereas the studies in MOFs
are few.
3.2.1
Alkanes
We simulated the adsorption and separation of linear and
branched alkanes in IRMOF-1 at 300 K.[48] For pure
linear alkanes (C1 to C5), a long alkane is more
preferentially adsorbed than a short counterpart at low
pressures, while the reverse is true at high pressures. At
zero loading, the adsorption properties including isosteric
heat, Henry’s constant and adsorption entropy exhibit
linear relationships with alkane carbon number. For pure
branched alkanes (C5 isomers), a linear isomer is more
strongly adsorbed than its branched analogue. The
adsorption capacities in IRMOF-1 are substantially greater
than in silicalite and carbon nanotube bundle. For a fivecomponent mixture of C1 to C5 linear alkanes, the
adsorption of long alkane first increases and then decreases
with increasing pressure, while the adsorption of short
alkane continually increases and progressively replaces
525
the long alkane at high pressures due to size entropy effect.
For a three-component mixture of C5 isomers, the
adsorption of each isomer increases with increasing
pressure, and the branched isomer is less adsorbed due to
configurational entropy effect.
The adsorption and diffusion of alkane isomer
mixtures (C4 and C5) were examined in catenated and
non-catenated MOFs (IRMOF-13, IRMOF-14, PCN-6 and
PCN-60 ) at 300 K.[49] As observed in IRMOF-1,[48]
competitive adsorption also occurs here with a greater
extent of adsorption for a linear isomer. An inflection is
seen in the isotherm as a result of sequential adsorption at
multiple favourable sites. Compared with non-catenated
counterparts, IRMOF-13 and PCN-6 exhibit larger loading
at low pressures because of constricted pores and stronger
affinity; however, the reverse is true at high pressures due
to smaller pore volume. Adsorption selectivity in the four
MOFs is comparable with that in silicalite and carbon
nanotube. As seen from the density contours in Figure 11,
nC4 is preferentially adsorbed close to the metal oxide
clusters in IRMOF-14, whereas inside the octahedral
pockets in PCN-60 . The diffusivity of alkane decreases
with the degree of branching because a slender isomer
diffuses faster. In the presence of constricted pores,
diffusivity in catenated MOFs is smaller than in noncatenated counterparts. However, the diffusion selectivity
is larger in catenated MOFs. This study provides insightful
microscopic mechanisms for the adsorption and diffusion
of alkane isomers in MOFs, and reveals that both
adsorption and diffusion selectivities can be enhanced by
catenation.
3.2.2 Xylenes
Xylenes are essential C8-aromatics derived from crude oil.
The separation of xylene isomers ( p-, m- and o-xylenes) is
practically important but challenging because of their
similar physical properties. For example, the boiling points
of p-, m- and o-xylenes are 138.4, 139.1 and 144.48C, and
their kinetic diameters are 0.67, 0.71 and 0.74 nm,
respectively.[79]
We performed a non-equilibrium MD simulation to
examine liquid chromatographic separation of xylene
isomers in MIL-101.[50] MIL-101 acts as a stationary
phase while hexane as a mobile phase, which was the case
in the experiment.[80] Figure 12 plots the transport
velocity of xylene versus external force aext acting on the
mobile phase. The velocity of each isomer rises linearly
with increasing a ext. The elution order follows
p-xylene . m-xylene . o-xylene, which is independent
of aext and in good agreement with experiment. For p-, mand o-xylenes, the interactions with MIL-101 (DEframework)
increase from 2 24.6, 2 27.0 to 2 29.0 kJ/mol. Nevertheless, the interactions with hexane (DE solvent)
J. Jiang
Figure 11.
(Colour online) Density contours of nC4 in (a) IRMOF-14 and (b) PCN-60 .[49]
decrease slightly from 2 37.3, 2 36.9 to 2 36.5 kJ/mol.
Consequently, p-xylene interacts the most weakly with
MIL-101 and the most strongly with hexane, and has the
fastest transport velocity. The opposite is in o-xylene,
which has the slowest velocity. The DDE ( ¼ DEsolvent 2
DEframework) are 2 12.7, 2 9.9 and 2 7.5 kJ/mol, respectively, for p-, m- and o-xylenes. The DDE decreases in the
order of p-xylene . m-xylene . o-xylene, which is
consistent with the elution order. The difference in DDE
among the three xylene isomers is greater than that in
DEframework and DEsolvent. This implies that the separation
of xylene isomers is attributed to the cooperative solute –
framework and solute – solvent interactions. Analysis of
radial distribution functions suggests that o-xylene is the
closest to MIL-101, while p-xylene resides the farthest
away. This is consistent with the energetic analysis that oxylene interacts the most strongly with MIL-101, as
attributed to its largest polarity among the three xylene
isomers.
4
3
v (m/s)
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526
2
p-xylene
m-xylene
o-xylene
1
0.03
0.04
0.05
aext (nm/ps2)
Figure 12. Transport velocity of xylene versus external force
acting on mobile phase.[50]
3.3
Alcohol adsorption and biofuel purification
Depletion of fossil fuels and increased CO2 concentration
due to the combustion of fossil fuels have sparked a
considerable interest worldwide to develop renewable
energy resources such as biofuel. Compared with
conventional fuels, biofuel is environmentally benign
and carbon neutral with less emission of gaseous
pollutants. As-produced biofuel contains a large amount
of water and alcohol (e.g. ethanol), and it is a prerequisite
to separate water/alcohol mixture to produce fuel-grade
biofuel. The separation alone is estimated to account for
60 –80% of biofuel product cost [81]; thus, highly efficient
biofuel purification is indispensable. A few experimental
studies examined alcohol adsorption and biofuel purification in MOFs; nevertheless, simulation effort is rare.
3.3.1 Alcohol adsorption
Combining experiment and simulation, we investigated
methanol adsorption in Zn(bdc)(ted)0.5 and the simulated
isotherm is in good agreement with the experiment [40]. In
two MOFs (hydrophobic ZIF-71 and hydrophilic rhoZMOF) with identical topology and similar pore size, the
adsorption of methanol and ethanol was examined.[51]
The isotherms in Na-rho-ZMOF are type I, attributed to
the high affinity of non-framework Naþ ions and ionic
framework. In ZIF-71, the framework – adsorbate affinity
is relatively weaker and type V adsorption is observed. The
predicted ethanol adsorption in ZIF-71 matches fairly well
with available experimental data.
We further simulated the adsorption of a series of
normal alcohols (C1 –C4) in ZIF-8.[53] Particularly, the
effects of force fields and framework charges on alcohol
adsorption were assessed. Although these effects have
been, to a certain extent, examined for the adsorption of
small gas molecules in ZIF-8, it is unknown or very
Molecular Simulation
10
10
8
8
N (mmol/g)
(b) 12
N (mmol/g)
(a) 12
6
exp.
UFF
AMBER
DREIDING
4
2
0
0
5
10
15
P (kPa)
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6
4
exp.
cluster charges
periodic charges
2
20
527
0
0
5
10
15
20
P (kPa)
Figure 13. (Colour online) (a) Effect of force fields on methanol adsorption. (b) Effect of framework charges on methanol adsorption.
‘cluster’ and ‘periodic’ indicate that the framework charges were estimated on the basis of cluster and periodic models, respectively.[53]
limited on how they would affect alcohol adsorption.
Figure 13 shows the adsorption isotherms of methanol in
ZIF-8 at 308 K predicted by three force fields UFF,
AMBER and DREIDING, as well as experimentally
measured. With increasing pressure, the isotherm can be
characterised into three regimes. At low pressures,
adsorption extent is small corresponding to cluster
formation at the favourable adsorption sites in ZIF-8. At
intermediate pressures, cage filling occurs with a sharp
increase in uptake. Finally, saturation is gradually
approached at high-pressure regime. Among the three
force fields, the uptake decreases in the order of
UFF . AMBER . DREIDING. The predictions of
DREIDING match the best with the experiment;
particularly, the saturation loading is close to the measured
value, although the loadings at low pressures are
overestimated. The predictions using ‘cluster’ and
‘periodic’ charges are close except at intermediate
pressures, and both match well with the experiment. This
suggests that the interactions between methanol and ZIF-8
framework are dominated by the LJ potential, and the
Coulombic potential plays a secondary role. The
adsorption of ethanol, propanol and butanol in ZIF-8 was
also simulated and compared with the experimental data.
3.3.2 Biofuel purification
For biofuel purification, we simulated the separation of
ethanol/water liquid mixtures in Na-rho-ZMOF and Zn4O
(bdc)(bpz)2 at both pervaporation (PV, 508C) and vapour
permeation (VP, 1008C) conditions.[52] In hydrophilic Narho-ZMOF, water is preferentially adsorbed over ethanol
due to its strong interaction with non-framework Naþ ions
and ionic framework, and the adsorption selectivity of
water/ethanol is higher at a lower composition of water.
With increasing water composition, the diffusion selectivity of water/ethanol increases. In contrast, ethanol is
adsorbed more in hydrophobic Zn4O(bdc)(bpz)2 as
attributed to the favourable interaction with methyl
groups, and the adsorption selectivity of ethanol/water is
higher at a lower composition of ethanol. With increasing
ethanol composition, the diffusion selectivity of ethanol/
water increases slightly. The permselectivities in the two
MOFs at both PV and VP conditions are largely
determined by adsorption selectivity. In Na-rho-ZMOF,
the maximum permselectivity is about 12 at VP condition,
and Na-rho-ZMOF is preferable for biofuel dehydration.
In Zn4O(bdc)(bpz)2, the maximum permselectivity is 75 at
PV condition, and Zn4O(bdc)(bpz)2 is promising for
biofuel recovery. This study provides microscopic insight
into the separation of water/ethanol mixtures in hydrophilic and hydrophobic MOFs at both PV and VP
conditions, and suggests that hydrophobic MOF is superior
to hydrophilic counterpart for biofuel purification.
Subsequently, simulation was conducted to screen
hydrophobic MOFs including ZIF-8, 60, 71, 90, 96,
towards high-performance purification of dilute biofuel at
room temperature.[54] As shown in Figure 14, the
simulated isotherm of ethanol for ethanol/water mixture
in ZIF-8 matches fairly well with the experiment. Among
the five MOFs, ZIF-8 is predicted to possess the highest
ethanol/water selectivity.
3.4 Water treatment
With increasing population, water scarcity has been a
global concern and how to supply sufficient fresh water is
a topical issue. On the other hand, a substantial amount of
contaminants such as heavy metal ions and organic
compounds have been introduced into water. These
contaminants are toxic and carcinogenic, and thus, should
be removed to minimise health and environmental risks.
528
J. Jiang
(b) 50
(a) 7
5
4
3
2
exp.
sim.
1
0
0.00
0.01
0.02
0.03
0.04
30
20
10
0.05
0
0.00
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Xethanol
Figure 14.
3.4.1
ZIF-8
ZIF-60
ZIF-71
ZIF-90
ZIF-96
40
Sethanol/water
Nethanol (mmol/g)
6
0.01
0.02
0.03
Xethanol
0.04
0.05
(Colour online) (a) Adsorption of ethanol/water in ZIF-8 and (b) ethanol/water selectivity.[54]
Water desalination
More than 95% of water on the earth is seawater, which
could supply abundant fresh water after economical
desalination. A few desalination techniques such as
reverse osmosis (RO) and thermal distillation have been
developed for seawater.[82] In particular, RO accounts for
half of the installed desalting capacity worldwide.[83]
Nevertheless, the capital cost of current RO technology is
high and needs to be improved prior to propagation.
Membrane materials in RO play a pivotal role in desalting
performance, and extensive studies have been reported
towards the development of novel membranes ranging
from polymeric membranes, carbon nanotubes to biological water channels (aquaporin).[84 –87]
From non-equilibrium MD simulation, we demonstrated that ZIF-8 membrane could potentially act as an RO
membrane. ZIF-8 was chosen because of its chemical/
thermal stability and remarkable resistance to water and
organics. This is largely due to the hydrophobic cages in
ZIF-8 and the strong tetrahedral ZnN4 clusters assembled
by metals and linkers. The simulation system is
schematically shown in Figure 15. Under external pressure,
water desalination occurs through the ZIF-8 membrane,
Figure 15. (Colour online) Water desalination through ZIF-8
membrane.[55]
whereas Naþ and Cl2 ions cannot transport due to the
sieving of small apertures in ZIF-8. The flux of water
permeating the membrane scales linearly with external
pressure. From temperature-dependent flux, the activation
energy of water is estimated to be 24.4 kJ/mol. Because of
surface interaction and geometrical confinement, water
molecules in the ZIF-8 membrane experience less
hydrogen bonding compared with bulk water. In addition,
the life time of hydrogen bonding in the membrane is
considerably longer. This simulation study suggests that
ZIF-8 might be potentially useful for water desalination.
3.4.2
Removal of toxic ions
As mentioned earlier, toxic ions in water should be
removed for water treatment. In this context, we conducted
simulation for the exchange of Pb2þ ions with Naþ ions in
Na-rho-ZMOF at 298 K.[56] Pb2þ was chosen because it is
toxic and a common contaminant after water transporting
through lead-bearing household pipelines. Figure 16 shows
the simulation system at different durations. Initially, Pb2þ
and Cl2 ions reside in solution and Naþ ions are in rhoZMOF framework. Upon starting simulation, Pb2þ ions
rapidly move into the framework while Naþ ions move out.
At t ¼ 0.2 ns, a large number of Pb2þ ions have moved into
rho-ZMOF, particularly near the solution/rho-ZMOF
interface. Meanwhile, Naþ ions move out and stay in
solution. A portion of Cl2 ions also move into the
framework during ion exchange. Once exchanged, Pb2þ
ions prefer staying in the framework without moving back
to solution. This induces a Donnan effect on the
distributions of Naþ and Cl2 ions between the framework
and the solution. At t ¼ 2 ns, all Pb2þ ions are exchanged
and reside in the framework. In addition, Pb2þ ions located
at the solution/rho-ZMOF interface also move into rhoZMOF.
By umbrella sampling, we estimated the potentials of
mean force (PMFs) for ions moving from solution into
Molecular Simulation
529
(a) t = 0
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PbCl2
Na-rho-ZMOF
(b) t = 0.2 ns
PbCl2
(c) t = 2 ns
Figure 16. (Colour online) Removal of Pd2þ by ion exchange in Na-rho-ZMOF: (a) t ¼ 0, (b) t ¼ 0.2 ns and (c) t ¼ 2 ns. Pb2þ: orange;
Cl2: green; Naþ: blue.[56]
rho-ZMOF. The PMF for Pb2þ is about 2 10 kBT and more
favourable than 2 5 kBT for Naþ, which contributes to the
observed ion exchange. The residence-time distributions
and mean-squared displacements reveal that all the
exchanged Pb2þ ions stay continuously in rho-ZMOF
without exchanging with other ions in solution. Upon
comparison, Naþ ions have a shorter residence time and a
larger mobility. The exchanged Pb2þ ions in rho-ZMOF
are located at the eight-, six- and four-membered rings.
Due to different confinement effects, Pb2þ ions exhibit
distinct dynamics at the three locations. Specifically, Pb2þ
ions at the eight-membered ring have the highest mobility,
while those at the four-membered ring have a negligible
mobility. Quantitative understanding is provided by this
study for ion exchange in ionic MOF and suggests that
rho-ZMOF might be an intriguing candidate for the
removal of toxic ions.
3.4.3 Removal of organics
In chemical industries, organics are required to be
removed/recovered from water. For example, dimethyl
sulphoxide (DMSO) is often mixed with water to form
biphasic medium, which is used to dissolve chemotherapeutic drug busulfan.[88]and formulate polymers, dyes
and electronics.[89] To recycle, DMSO needs to be
recovered from aqueous solution. Although distillation
technology has been applied for DMSO recovery, it is
energetically intensive.
A simulation study for DMSO recovery from aqueous
solution was reported in three hydrophobic MOFs, namely
Zn4O(bdc)(bpz)2, Zn(bdc)(ted)0.5 and ZIF-71 at 298 K.
[57] The free volumes in Zn4O(bdc)(bpz)2, Zn(bdc)(ted)0.5
and ZIF-71 are approximately 0.87, 0.79 and 0.44 cm3/g
and the porosities are 69.4%, 64.9% and 50.4%,
respectively. In the three MOFs, type I adsorption
isotherms are observed for DMSO, while H2O exhibits
type V adsorption isotherms with hysteresis. This implies a
stronger interaction of DMSO than water with the three
MOFs. The saturation capacity of DMSO is 10 mmol/g in
Zn4O(bdc)(bpz)2, drops to 8.0 mmol/g in Zn(bdc)(ted)0.5
and 4.4 mmol/g in ZIF-71. Such a hierarchy is consistent
with the decreasing order of free volume and porosity in
the three MOFs. Due to the hydrophobic nature, the three
MOFs are highly selective towards DMSO from DMSO/
H2O mixture. As shown in Figure 17, the selectivity in the
three MOFs initially increases with increasing XDMSO,
then decreases within the range of XDMSO under study. The
initial increase is attributed to the enhanced interaction of
DMSO with multiple adsorption sites in the framework.
However, the interaction strength drops when most
adsorption sites are occupied, and furthermore, smaller
H2O molecules are more easily filled into the framework;
consequently, a decrease in selectivity is seen at high
530
J. Jiang
with MIL-101, and thus transports fastest. Furthermore,
Arg forms the largest number of hydrogen bonds with water
and possesses the largest hydrophilic solvent-accessible
surface area. In contrast, Trp has the weakest interaction
with water and is the closest to MIL-101. Elucidated from
detailed energetic and structural analysis, the underlying
separation mechanism is attributed to the cooperative
solute – solvent and solute– framework interactions. The
molecular insight from this simulation study suggests that
MIL-101 might be an interesting material for the separation
of important biomolecules.
1800
SDMSO/H2O
1500
1200
900
600
300
0
0.00
0.01
0.02
0.03
0.04
0.05
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XDMSO
Figure 17. (Colour online) DMSO/H2O selectivity in Zn4O
(bdc)(bpz)2, Zn(bdc)(ted)0.5 and ZIF-71.[57]
XDMSO. The highest selectivity is predicted up to 1700 in
ZIF-71; nevertheless, the recovery capacity of DMSO in
ZIF-71 is significantly smaller than in Zn4O(bdc)(bpz)2
and Zn(bdc)(ted)0.5. From a practical point of view, Zn4O
(bdc)(bpz)2 and Zn(bdc)(ted)0.5 might be better among the
three MOFs for DMSO recovery.
3.5 Bio- and chiral separation and drug loading
3.5.1 Bio-separation
Bio-separation is of central importance in pharmaceutical
industry, but experimental and simulation studies are
scarcely reported for bio-separation using MOFs. In this
regard, we conducted MD simulation to investigate the
separation of amino acids (Arg, Phe and Trp) in MIL-101 at
300 K.[50] Similar to the liquid chromatographic separation of xylene isomers discussed earlier, MIL-101 is the
stationary phase and water is the mobile phase, as illustrated
in Figure 18. The three amino acids differ in structure,
molecular weight and charge. The simulation reveals that
the elution order is Arg . Phe . Trp. Among the three
amino acids, Arg is the most hydrophilic. It experiences the
strongest interaction with water but the weakest interaction
Arg
Phe
MIL-101
Trp
Figure 18. (Colour online) Separation of three amino acids
(Arg, Phe and Trp) in MIL-101.[50]
3.5.2 Chiral separation
In Mother Nature, living organisms exhibit significantly
different biological responses to chiral enantiomers. One
enantiomer may have desired pharmacological activity,
while the other is inactive or toxic.[90] The production of
pure enantiomeric compounds is crucial for health care.
However, the separation of chiral molecules is challenging,
as a pair of enantiomers display identical physical and
chemical properties. Only in asymmetric environment,
enantiomers experience different affinities and may be
separated.
Chiral separation by membrane is attractive because of
its low cost, high capacity, continuous operation and easy
scale-up. However, high-performance chiral separation
membrane materials are currently scarce. By integrating
experimental and simulation techniques, we examined the
separation of racemic mixture of R/S-methyl phenyl
sulphoxide (MPS) in an MOF membrane.[58] The MOF
namely Zn2(bdc)(L-lac)(dmf) possesses a homochiral
˚ pore, and the chiral
structure with approximately 5 A
centres of L-lactate moieties are exposed along the pore.
The membrane was prepared on ZnO support by reactive
seeding method. The porous support acted as an inorganic
source reacting with organic precursor to grow a seeding
layer for the secondary growth of MOF membrane. Thus, a
strong adhesive and uniform seeding layer was achieved to
aid in the preparation of a superior MOF membrane.
Experimentally, S-MPS was found to diffuse through the
membrane in a relatively lower velocity than R-MPS.
Parallel simulation predicted the same elution order, i.e. RMPS transports faster than S-MPS as shown in Figure 19
(a). To provide microscopic insight into the chiral
separation, the interaction energies of R-/S-MPS with the
MOF were estimated. As shown in Figure 19(b), S-MPS
has a stronger interaction (in both LJ and Coulombic
contributions) with the MOF than R-MPS. Therefore,
R-MPS is less strongly bound onto the MOF and diffuses
faster. This study potentially provides a new, sustainable
and highly efficient technique for chiral separation.
Molecular Simulation
(b) –120
40
R-MPS
S-MPS
20
–60
–30
10
0
0
0
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R-MPS
S-MPS
–90
30
∆E (kJ/mol)
Displacement (nm)
(a)
531
2
4
6
8
LJ
10
Coulombic
Total
t (ns)
Figure 19. (Colour online) (a) Displacements of R-/S-MPS in MOF as a function of simulation duration. (b) Interaction energies of R-/SMPS with MOF.[58]
3.5.3 Drug loading
The interest in using nanoporous materials for drug loading/
delivery has increased considerably. The loading capacity
and release of drug in a porous carrier are governed by a
variety of factors such as pore size, shape, connectivity and
host affinity. In conventional materials (e.g. inorganic silica,
carbonaceous materials and polymeric matrixes), drug
loading capacity is usually not sufficiently high and
encapsulated drug is difficult to be specifically released. To
achieve a high loading and a controlled release, porous
materials such as MOFs possessing large volumes and
regular structures are desired.
We report a simulation study to understand the
microscopic interactions of ibuprofen (IBU) with MIL-101
and UMCM-1.[59] IBU was chosen as a model drug because
it is commonly used for the relief of arthritis, dysmenorrhea,
acne and fever. MIL-101 and UMCM-1 possess large pore
volumes (1.96 and 2.28 cm3/g) and high surface areas (3451
and 4764 m2/g). Particularly, MIL-101 contains unsaturated
Lewis acidic metal sites by removing terminal waters in
Figure 20.
octahedral Cr3O trimmers; however, UMCM-1 does not
have. The predicted maximum loading of IBU in MIL-101 at
298 K is 1.11 g IBU/g MIL-101, which agrees fairly well
with experimentally determined 1.37. In both MIL-101 and
UMCM-1, IBU loading is four times higher than in silica
MCM-41.[91] The substantially high loading in the two
MOFs implies that they might be useful for drug delivery as a
small amount of carrier is needed for high dosage.
To assess possible bond formation between IBU and
host structure, the highest occupied molecular orbitals
(HOMOs) were calculated.[59] As shown in Figure 20, the
HOMOs are distinctly different between MIL-101 and
UMCM-1. From the frontier HOMOs, a coordination bond
appears to form between the carboxylic group in IBU and
the Cr3O metal oxide in MIL-101. The band gap is only
0.064 eV in IBU/MIL-101, significantly lower than
3.146 eV in IBU/UMCM-1. The latter is prohibitively
large and implies difficulty for IBU and UMCM-1 to form
a bond. Based on the mean-squared displacement, the
mobility of IBU in MIL-101 is substantially smaller than
(Colour online) HOMOs in IBU/MIL-101 and IBU/UMCM-1.[59]
J. Jiang
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in UMCM-1. This is attributed to the coordination bond
formation between IBU and MIL-101, which is the
primary factor for the delayed release of IBU in MIL-101
experimentally observed.
This study unravels the energetics and dynamics of
IBU in two mesoscopic MOFs at a molecular level.
Nevertheless, we should note that the experimental study
of IBU loading/delivery in MIL-101 was conducted in a
solvent (hexane). However, solvent was not included in
our simulation. The inclusion of solvent would screen the
interaction and reduce the accessibility between drug and
carrier. Thus, more elaborate investigation on drug
behaviour in MOFs should take solvent into account.
0.4
0.2
Stress sv (GPa)
532
0.0
–0.2
simulation
experiment
–0.4
–0.06
–0.03
0.00
0.03
0.06
strain ev
Figure 21.
ZIF-8.[60]
(Colour online) Volumetric stress versus strain in
3.6 Mechanical moduli, structural transition and
thermal conductivity
Most simulation studies in MOFs assume that the
frameworks are fixed. However, many MOFs exhibit
framework flexibility. For example, gas molecules (N2,
CH4, C2H6 and C3H8) with kinetic diameters larger than
the window size of ZIF-8 were observed to diffuse through
ZIF-8.[92 – 94] Therefore, the framework flexibility should
be incorporated to properly describe such MOFs. For the
prototype ZIF-8, we have developed force fields by
combining DFT calculation, Amber force field and
experimental crystallographic data.[60,61] The force fields
were adopted to predict the mechanical moduli, structural
transition and thermal conductivity of ZIF-8.
5.35 and 5.94 GPa upon introducing one-cage, two-cage
and three-cage ZIF-7 clusters, respectively.[44] Therefore,
the modulus in PBI/ZIF-7 membrane is gradually
enhanced with increased ZIF-7 loading.
It is noteworthy that mechanical properties are
sensitive to force field used and their accurate prediction
is a challenging task. Based on classical force fields (e.g.
DREIDING, CVFF and MM3), a few simulation studies
overestimated Young’s and bulk moduli of MOF-5 by
several folds.[98 – 100] Different force fields even gave
drastically different moduli, indicating their incapability to
quantitatively describe the mechanical properties.
3.6.1 Mechanical moduli
For solid materials, mechanical strength can be quantified
by moduli.[95] By including framework flexibility, a force
field developed for ZIF-8 was used to estimate the bulk
and Young’s moduli.[60] Figure 21 plots the volumetric
stress sv versus strain 1v in ZIF-8. The relationship of
simulated sv and 1v is approximately linear from 2 0.3 to
0.3 GPa, though the experimental stress –strain curve is
nonlinear at high pressures. The bulk modulus Ev
predicted is about 7.24 ^ 0.03 GPa, close to experimentally determined 6.52 ^ 0.35 GPa at low pressures.[96]
Similarly, the stress along c direction sc also increases
linearly with the strain 1c . On this basis, Young’s modulus
Ec is estimated to be 2.99 ^ 0.08 GPa, which agrees well
with an experimental value of 2.97 ^ 0.06 GPa.[97]
Young’s modulus in the a or b direction is nearly identical
to Ec, implying that ZIF-8 is mechanically isotropic. This
prediction is in accord with the fact that ZIF-8 is a cubic
crystal and has homogeneous atomic distribution along
three orthogonal directions.
As discussed earlier, one major advantage of MMMs
over polymer membranes is improved mechanical
strength. In PBI/ZIF-7 membranes, our simulation reveals
that the bulk modulus of PBI increases from 4.11 to 4.77,
3.6.2 Structural transition
Upon external stimuli (e.g. temperature, pressure and
sorption), some MOFs may undergo structural transition.
Understanding the fundamental mechanism of structural
transition is crucial for their potential applications in
sensing, separation, drug delivery, etc. However, it is
experimentally difficult to examine structural transition
microscopically.
By developing a hybrid MC/MD simulation method,
we successfully mimic the continuous structural transition
of ZIF-8 induced by N2 sorption at 77 K.[61] Unlike the
commonly used GCMC method in which framework is
fixed, ZIF-8 in the hybrid MC/MD method is allowed to
relax along with N2 sorption. As shown in Figure 22,
stepped sorption isotherm is predicted with three distinct
regions, which agrees well with experimental data. Three
regions correspond to a high-loading (HL) structure, a lowloading (LL) structure and the transition between HL and
LL. Upon structural transition, the cell size rises, the
orientation of imidazolate rings and the motion of framework atoms exhibit sharp changes. In addition, pronounced
changes occur in various contributions of potential energies
(including stretching, bending, torsional, van der Waals and
Coulombic). Radial distribution functions reveal strong
Molecular Simulation
N2 (molecules/uc)
50
experiment
simulation
40
30
20
10
0
10–5
10–4
10–3
10–2
10–1
100
Figure 22. (Colour online) Structural transition of ZIF-8
induced by N2 sorption.[61]
interactions between N2 and imidazolate rings. The
simulation suggests that the structural transition of ZIF-8
is caused by the reorientation of imidazolate rings, which is
attributed to the enhanced van der Waals interaction
between sorbed N2 and imidazolate rings as well as the
reduced torsional interaction in framework. This study
provides clear and quantitative microscopic understanding
for the structural transition of ZIF-8, and has an important
implication for other porous materials.
3.6.3
Thermal conductivity
Adsorption/desorption in MOFs is exothermic/endothermic process. The heat released/adsorbed would affect
system temperature and process performance. For instance,
heat transfer is associated with H2 storage system and
appropriate thermal management is required to retain
energy efficiency.[101] Furthermore, heat transfer in
nanoporous materials is also substantially important for
(a) 0.20
the development of electronic, optical and optoelectronic
devices.[102] To our best knowledge, only one simulation
study was reported in the literature to examine the thermal
conductivity of MOF-5.[103]
Based on a force field we developed,[60] thermal
conductivity of ZIF-8 and corresponding mechanism were
investigated.[62] The simulated conductivity is about
0.165 W/mK. Such a low thermal conductivity is due to the
short mean free path of phonon in ZIF-8, which is estimated
to be less than two unit cells. As shown in Figure 23, the
conductivity increases from 0.165 to 0.190 W/mK with an
increasing temperature from 300 to 1000 K. The temperature
effect is attributed to the enhanced overlap in the vibrational
density of states between Zn and N atoms. The contributions
of lattice vibrations in different directions to heat flux were
examined from non-equilibrium MD simulation. It was
found that the longitudinal vibration contributes 60% to
thermal transport in ZIF-8; in contrast, transverse vibration
contributes 40%. Furthermore, the contributions from
different forces to heat flux were analysed. While the
stretching and Lennard-Jones components have 31%
contribution each, the bending and Coulombic components
contribute 17% and 21%, respectively. However, the
contribution of torsional component is nearly zero. Although
this study is focused on ZIF-8, the methodology can be
extended to other ZIFs and MOFs.
4. Summary and perspective
This manuscript summarises the comprehensive and
systematic simulation endeavours in the author’s research
group for diverse potential applications of MOFs,
including carbon capture, hydrocarbon separation, alcohol
adsorption and biofuel purification, water treatment, bioand chiral separation, drug loading, as well as mechanical
moduli, structural transition and thermal conductivity.
(b) 0.8
Zn
N
overlap
0.19
0.6
0.18
VDOS
Thermal conductivity (W/mK)
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P/P0
533
0.17
0.4
0.2
0.16
0.15
0.0
300
400
500
600
700
800
Temperature (K)
900 1000
0
10
20
30
40
50
60
Frequency (THz)
Figure 23. (Colour online) (a) Temperature effect on the thermal conductivity of ZIF-8. (b) Vibrational density of states for Zn and N
atoms and their overlap at 300 K.[62]
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534
J. Jiang
While most simulations in MOFs have been focused on
gas storage and separation, our group has initiated several
simulation studies for potential applications in liquid
separation (e.g. biofuel purification, water treatment and
bio- and chiral separation). With increasing demands for
clean water, liquid fuels and high-purity biomolecules, it is
foreseeable that more simulation studies will be conducted
for liquid separation in the near future.
A wealth of atomic-resolution and time-resolved
insights have been provided by simulation to critically
understand microscopic properties (both equilibrium and
dynamic) in MOFs. These molecular insights are not just
important complement to experiments, but essential to
secure correct interpretation of experimental data and to
test hypothetical candidates. Subsequently, MOFs can be
screened from numerous candidates in a high-throughput
manner or rationally designed by incorporating specific
functionality, with little resort to costly and lengthy
experimental testing.
Despite the considerable progress in quantitative
mechanistic understanding of MOFs, we should note that a
number of challenges exist for future simulation exploration.
(1) Most simulation studies in MOFs adopt empirical or
semi-empirical force fields. While certain success is
achieved, these force fields may lead to inaccurate
predictions as they were constructed with empirical rules.
In this regard, a general and transferable force field is highly
desirable. Nevertheless, developing such a force field for
MOFs is technically challenging because a wide variety of
metal clusters and organic linkers are involved in MOFs. (2)
Mechanical strength of MOFs is crucial for practical
applications. In gas storage and separation, as well as liquid
separation, the pressure exerted on MOF sorbents or
membranes may distort structure and deteriorate performance. It is important to understand how pressure affects
framework and pore geometry. Currently, only limited
simulation studies estimate mechanical moduli. As discussed earlier, the mechanical properties of MOFs are
sensitive to force field used and difficult to be accurately
predicted. (3) A large number of MOFs are chemically
unstable in water and organic solvents, which impedes their
practical use in moisture or liquid phase. Furthermore,
thermal stability should also be taken into account in
applications, e.g. high-temperature pre-combustion carbon
capture. Fundamental understanding in the chemical and
thermal stability of MOFs is indispensable. It is useful to
unravel by simulation the important factors that govern
stability, thus providing guidelines on the selection of
suitable building blocks to synthesise stable MOFs.
However, simulation studies on this topic are rare and
more efforts are needed.
To recapitulate, molecular simulation has played an
increasingly important role in the vibrant field of MOFs.
Significant progress has been achieved; however, challenges still exist and indeed provide new opportunities for
future simulation studies to unravel more in-depth
microscopic insights and thus provide bottom-up guidelines on the rational screening and design of novel MOFs.
For practical applications, both process requirements and
material properties should be considered. Therefore, it is
imperative to holistically synergise simulation with
process optimisation, as well as material synthesis,
towards the development of best MOFs for advanced
technological innovation.
Acknowledgements
The author gratefully acknowledges his coworkers and
collaborators for their contributions to the studies reviewed
here and the National University of Singapore, the Ministry of
Education of Singapore and the Singapore National Research
Foundation for financial support.
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