Towards Rational Design of Metal-Organic
Frameworks for Sensing Applications: Efficient
Calculation of Adsorption Characteristics in Zero
Loading Regime.
Lev Sarkisov
Institute for Materials and Processes, School of Engineering, University of Edinburgh, EH9 3JL, UK
Lev.Sarkisov@ed.ac.uk
RECEIVED DATE
Efficient calculation of adsorption characteristics
The Henry’s constant of adsorption, differential enthalpy of adsorption, free energy barriers between
various compartments of the porous space and selectivity are important characteristics of a porous
material. These characteristics are directly related to the performance of the porous material in a
sensing application and can be used as preliminary criteria for computational screening of the
candidate porous materials. All these properties are linked to each other through well established
statistical-mechanical relations. In this article we demonstrate that the finely discretized representation
of the simulation cell offers a particularly convenient way to exploit these relations and, for rigid
molecules in rigid porous materials, the majority of these characteristics can be calculated from a
single simulation run. We apply the methodology to calculate the Henry’s constants and other
1
characteristics for several small organic and aromatic molecules in two metal-organic frameworks,
IRMOF-1 and MIL-47(V). We further provide predictions for TNT adsorption in these structures and
discuss the implications of our findings in the context of sensing applications.
Simulation, Henry’s constant, MOF, isosteric heat, explosive, warfare chemical
I. Introduction
In the era of global terrorism, quick, reliable and low-cost detection of explosives and warfare
chemicals in various settings, such as an airport terminal, is vital. Gravimetric quartz crystal
microbalance
(QCM)
and
surface
acoustic
wave
(SAW)
sensor
devices,
as
well
as
microelectromechanical (MEMS) systems, such as microcantilevers, are considered as promising
technologies1,2. The principal component in these systems is a functional coating. Binding of an
analyte molecule to this coating, or thin film, generates a signal which, upon amplification and
analysis, leads to a positive detection. Ideally, the coating and the final device must be able to sense
very low levels of chemicals and should be able to discriminate the toxic or explosive chemicals from
other similar but benign compounds to avoid unnecessary (and very costly) false alarms. Recent
advances in the field of porous materials with molecularly engineered pores open new opportunities
for the development of highly functional coatings with selectivity and specificity sufficient to produce
a measurable signal when dealing with explosive and warfare chemicals in concentrations requiring an
unambiguous detection (parts per billion and even parts per trillion in some cases).
Indeed, several families of porous materials have been recently discovered, where individual pores
or cages can be tuned to be complementary in shape and size to specific molecules. Metal organic
frameworks (MOFs) are crystalline, highly porous materials, formed by metal clusters linked with
organic molecules. In these structures the size and the shape of the cages and channels can be finely
tuned through the judicious selection of the organic linkers. A recent example of using MOFs for
2
sensing is provided by Allendorf and co-workers who developed microcantilever arrays covered with
thin films of MOFs and capable of detecting traces of water, methanol and ethanol in the gas phase3.
In another example, Biemmi and co-workers prepared MOF films on the gold electrode of a QCM and
investigated sorption of water4. For a general review of MOF synthesis and applications, including
sensing we refer the reader to the article by Meek and co-workers5. Luminescent MOFs, which could
provide further opportunities for sensing applications, have been reviewed by Allendorf and coworkers6. Molecularly imprinted polymer (MIP) is another example of a material with highly tunable
pores. In MIPs, polymerization takes place in the presence of the template species. Removal of the
template creates binding sites in the polymer with structure complementary to the template molecule,
thus inducing biomimetic molecular recognition functionality. This functionality of MIPs can be
exploited in separations, catalysis, drug delivery and, obviously, sensing applications. For example,
Bunte and co-workers recently explored detection of explosive vapors with MIP-coated QCM7,8.
The rich arsenal of organic chemistry implies a virtually inexhaustible number of potential MOFs
and MIPs. Not surprisingly, it is a prolific area of research, with thousands of structures already
synthesized and with the number of new structures synthesized every year outpacing our current
capability to test them in real applications. Experimental screening of novel materials for detection of
warfare chemicals poses a particular challenge due to the hazardous nature of the adsorbates. Here
molecular simulation may play a pivotal role, by providing a safe and efficient alternative. Molecular
simulations can be used as a preliminary screening tool to identify the most promising porous
materials for further experimental investigation, as has been recently proposed and demonstrated by
Haldoupis et al.9,10, and Snurr and co-workers11,12. At the same time, fundamental insights gained from
simulations at the microscopic level may inspire new, not yet synthesized materials, as well as
synthetic protocols and post-synthetic modification strategies.
Although a number of simulation studies focusing on MOF adsorption of relatively simple species,
such as hydrogen, nitrogen, carbon dioxide and methane, has emerged in recent years13, adsorption of
3
a more complex species (aromatics and their derivatives) is substantially less explored. Recent
examples of research in this area include a study by Finsy and co-workers, who explored low coverage
adsorption and enthalpies of linear and branched alkanes, as well as cyclohexane and benzene in MIL47(V)14. The same MOF was used by Castillo et al., to evaluate separation of xylenes15. In application
to explosives and warfare chemicals, Xiong et al. recently investigated interaction of hexahydro-1,3,5trinitro-1,3,5-triazine (RDX) with several isoreticular networks16-18. In the work of Greathouse and coworkers seven frameworks and a range of adsorbates, including xylenes, polycyclic aromatic
compounds, RDX, trinitrotoluene (TNT) and two nerve agents were considered, with a view to
identify some general adsorption trends and assess the overall suitability of these materials for sensing
in the relevant low-pressure regime19.
The standard simulation tool to study adsorption in rigid porous structures is a Monte Carlo
simulation in the grand canonical ensemble (GCMC). This method allows one to generate a full
adsorption isotherm to be compared to experiments, to other models or to provide a range of insights
into the process, and this is the method predominantly used in the aforementioned simulation studies.
However, calculation of a complete adsorption isotherm, exploring the range of pressures where the
porous material is saturated with the adsorbate, is not necessary for the initial assessment and ranking
of the materials for sensing applications. At very low pressures, the initial linear behavior of an
adsorption isotherm is characterized by the Henry’s constant. Together with the differential enthalpy
of adsorption, the Henry’s constant describes the affinity of the material towards a particular adsorbate
and the ratio of two Henry’s constants for two different adsorbates at the same temperature
characterizes the selectivity of the porous material. The initial screening of the porous materials for a
particular sensing application can be based on just these characteristics, namely the Henry’s constant,
the differential enthalpy of adsorption, and complemented by the selectivity analysis. An additional
benefit of this approach comes from the differential enthalpy of adsorption and the Henry’s constant
being related to each other, and therefore offering a possibility to extract these properties from a
4
limited number of calculations. The well established Widom insertion method has been traditionally
used to calculate the Henry’s constant20, whereas the variation of the logarithm of this property with
the reciprocal temperature provides a well known route to the differential enthalpy of adsorption.
There is another issue with the conventional GCMC simulations. In this method the trial attempts to
insert and delete an adsorbate molecule take place throughout the simulation volume, without taking
into account mutual connectivity and accessibility of the regions of the porous space to each other. As
a result, molecules may be introduced in pores, or cages, that are either completely inaccessible to the
adsorbate molecule, or their access is associated with substantial energy barriers, and therefore is
kinetically limited. The important role of steric restrictions in the windows between the cages and the
free energy barriers associated with them has been well recognized in the zeolite community. For
example, it was a careful analysis of the zeolite topology and how it is linked to the entropic and
enthalpic contributions to the free energy of adsorption that allowed Smit and co-workers to explain a
number of effects, associated with adsorption and transport in zeolites, such as incommensurate
diffusion of normal alkanes21-25. A recent example in the MOF field, where these effects manifested
themselves, is provided by Lamia and co-workers, who investigated adsorption of propane, propylene
and isobutane in the CuBTC framework, and concluded that in order for the simulations to be
consistent with the experimental data, small tetrahedral pockets in the CuBTC structure should be
inaccessible for isobutane and excluded from the Monte Carlo sampling26. One could argue that for
larger molecules such as TNT, the actual accessibility of the cages and channels in a metal-organic
framework should play an even greater role in the overall performance of the material. Thus, the
conventional Monte Carlo simulations must be accompanied with an analysis that can evaluate the
accessibility of the porous structure to molecules of various sizes and shapes and, ideally, characterize
the free energy pathways within the structure.
In this article we propose to calculate several key properties of porous materials, such as the Henry’s
constant and differential enthalpy of adsorption, as well as selectivity with respect to a particular pair
5
of adsorbates, using fine discretization of the simulation space. The principal advantage of this
approach compared to the conventional Widom insertion method is that in addition to the global
properties of the material, averaged over the whole simulation cell, some local characteristics of the
structure can be revealed and explored. Specifically, we exploit the relationships between the Henry’s
constant, the configurational integral and Helmholtz free energy to calculate the variation of the free
energy as experienced by an adsorbate molecule moving along a selected reaction coordinate within
the porous structure. We also calculate a property defined as the local selectivity to understand what
regions of the porous structure are responsible for the overall behavior of the material.
To illustrate the approach we concentrate on two metal organic frameworks, IRMOF-127 and MIL47(V)28. Interaction of IRMOF-1 with a broad range of volatile organic compounds, including normal
alkanes and aromatics, has been recently studied in a series of experiments by Luebbers et al.29 Their
results provide the key reference dataset for the comparison in this work. MIL-47(V) has been selected
for this study as this material features pores with sizes that closely match the molecules of interest, as
will be discussed in the Results section, and therefore it may exhibit promising affinity and selectivity
characteristics. The current approach is formulated for rigid porous materials and rigid adsorbate
molecules. In the Discussion section we explore the routes to extend the methodology to flexible
adsorbing species. For the purposes of the present work, out of various adsorbate species, investigated
by Luebbers and co-workers, we select a smaller group of molecules, which are sufficiently simple
and can be treated as rigid molecules.
II. Theory
The starting point for the derivation of the key formulae employed in this study is a slightly rearranged expression for the Henry’s constant obtained by June et al.30 (formula A.10 in the original
publication):
6
RT  s K H 
Z S (1, T ,VS ) V
Z IG (1, T ,V ) VS
(1)
where R and T are the gas constant and temperature as usual,  s is the density of the porous material,
K H is the Henry’s constant, Z S (1, T ,VS ) is the configurational integral of a single adsorbate molecule
in a sample of porous material of volume VS , Z IG (1, T ,V ) is the ideal gas configurational integral for a
single molecule in a system of some volume V . For a rigid molecule of arbitrary geometry, the
configurational integral Z S (1, T ,VS ) involved in eq 1 can be expressed as following:
Z S (1, T , VS )   e U s ( , r ) / kT ddr
where k is the Boltzmann constant,
(2)
U s ( , r )
is the potential energy of interaction of a single
adsorbate molecule with the structure of the adsorbent, and the Boltzmann factor based on this energy
is integrated over all possible orientations  of the molecule and positions of its center of mass r.
The ideal gas configurational integral Z IG (1, T ,V ) , where
Z IG (1, T ,V )  8 2V
U s ( , r )  0
for all  and r, reduces to:
(3)
Hence, the expression in eq 1 can be simplified:
RT  s K H 
Z S (1, T ,VS ) Z S (1, T ,VS )

 e U s ( ,r ) / kT
2
Z IG (1, T ,VS )
8 VS
(4)
7
where Z IG (1, T ,VS ) is now the configurational integral for one ideal gas molecule in volume VS and
the last property in the brackets corresponds to the value of the Boltzmann factor averaged over all
possible orientations and positions of the adsorbate molecule in a sample of the porous structure of
volume VS . This property is usually calculated using the Widom insertion scheme20. The ratio of the
two configurational integrals in eq 4 naturally suggests a link between the Henry’s constant and the
free energy. Indeed, this relation can be constructed as:
 RT ln( RT  s K H )   RT ln Z S (1, T ,VS )  RT ln Z IG (1, T ,VS ) 
 AS (1, T ,VS )  AIG (1, T ,VS )
(5)
which describes the Helmholtz free energy change associated with transferring a single molecule of
adsorbate from the ideal gas system of volume VS to a sample of porous structure of the same volume.
The selectivity of the porous structure with respect to two different adsorbates X and Y can be
expressed as the ratio of the two Henry’s constants in the low loading regime:
S XY 
K H , X (T )
K H ,Y (T )
(6)
The variation of the logarithm of the Henry’s constant with the reciprocal temperature provides a
well known route to the isosteric heat of adsorption, or more appropriately, to the differential enthalpy
of adsorption31,32:
  ln K H 
h   R 

 (1/ T )  Na
(7)
8
where Na corresponds to the amount adsorbed. In experiments, it is the excess amount adsorbed that
is measured, whereas in simulations the absolute amount adsorbed is calculated. In principle, an
appropriate conversion from the absolute to excess values must be applied in order to compare the
differential enthalpy and other properties obtained in simulations to those in experiments31,32.
However, at very low pressures and loadings (the regime of interest here), the difference between the
excess and absolute amounts adsorbed is negligible.
Similar expressions for the Henry’ constant, free energy differences and selectivity can be obtained
for any arbitrary sub-region of the simulation cell. Specifically, here we consider a simulation cell,
divided into small cubelets of volume VS . For each cubelet i, Z S ,i (1, T , VS )   e U s ( ,r ) / kT ddr is
i
the configurational integral obtained by integration of the Boltzmann factor over all orientations of a
single molecule and over translational degrees of freedom r for the molecule’s center of mass,
corresponding to the space of the selected cubelet i (to distinguish it from a similar expression for the
whole space VS , the first integral in the expression above is accompanied by index i). The expression
in eq 4, formulated for the specific cubelet i becomes:
RT  s K H ,i 
Z S ,i (1, T , VS ) Z S ,i (1, T , VS )

 eU s ( , r ) / kT
2
Z IG (1, T , VS )
8 VS
ri ,
i
(8)
where K H ,i can be viewed as a local Henry’s constant representing properties of a particular cubelet
and eU S ( , r ) / kT
ri ,
i
is the average Boltzmann factor for cubelet i, which can be obtained from the
Widom insertion procedure, applied to this particular cubelet. Superscripts ri ,  reflect over what
degrees of freedom the averaging is performed. This local information can be used to estimate the free
energy change as the molecule moves from cubelet i to cubelet j:
9
AS ,i (1, T , VS )  AS , j (1, T , VS ) 
 e U S ( , r ) / kT
 Z S ,i (1, T , VS ) 

  RT ln 
   RT ln  U ( , r ) / kT
S
Z
(
1
,
T
,

V
)

S 
 S , j
 e
ri ,
i
r j ,
j




(9)
Similarly to the local Henry’s constant, we can also formulate the local selectivity:
S XY , i 
e U S ( , r ) / kT
e
ri ,
(10)
X ,i
U S ( , r ) / kT ri ,
Y ,i
which is the ratio of the two average Boltzmann factors obtained for two different species X and Y
within the same cubelet i.
It is easy to show (see Supporting Information) that the global properties of the adsorbate are
directly linked with the local properties of individual cubelets:
RT  s K H 
1
Ncubelet

N cubelet
e U S ( ,r ) / kT
i 1
ri ,
(11)
i
where N cubelet is the number of cubelets. If the size of the cubelet is sufficiently small (much smaller
than the characteristic size of the adsorbate molecule), each e U S ( ,r ) / kT
ri ,
i
term can be approximated
by neglecting the translational degrees of freedom within the cubelet and considering only the
orientational ones:
eU S ( , r ) / kT
ri ,
i
 eU S ( , r ) / kT

i
(12)
10
In practice, this is implemented by placing the center of mass of the molecule into the center of the
selected cubelet and generating several orientations of the adsorbate molecule to obtain the average
property on the right in eq 12. This approximation becomes more accurate as the size of the cubelet
decreases and is exact in the limit of infinitely small cubelets.
One can view the employed procedure as a numerical integration of the component of the
configurational integral associated with the translational degrees of freedom of the center of mass of
the molecule while integration over the orientational degrees of freedom is obtained from the
stochastic Monte Carlo (in other words, Widom) method. We note here that similar numerical
integration could be also applied to the orientational degrees of freedom involved in eq 8. Details of
the selected procedure would depend on the required accuracy and computational efficiency.
III. Methodology
As a case study, we consider two metal organic framework structures, IRMOF-127 and MIL-47(V)28,
interacting with several adsorbate molecules, ranging in size from chloroform to TNT (Figure 1). The
abbreviations for the species are defined in the caption for Figure 1. These species are selected as they
are reasonably simple, can be considered as rigid structures and, with the exception of TNT, have the
corresponding reference experimental data in IRMOF-1 at 473 K29. Interaction of a single molecule
with the atoms of the structure involves van der Waals and Coulombic components. The van der
Waals interactions are described using the Lennard-Jones potential. Lennard-Jones parameters in this
study for both MOFs and adsorbates are obtained from the UFF force field (see Supporting
Information)33. Partial charges on the atoms of metal-organic frameworks are taken from the work of
Yazaydın et al.34 In that study partial charges were obtained from the B3LYP density functional
theory35-37 calculations on individual structural fragments of the frameworks using the ChelpG
method38. Here we use the same level of theory as in the reference study to obtain partial charges on
adsorbate molecules. All density functional calculations are carried out using Gaussian 0939.
11
The adsorbate-adsorbent Coulombic interactions are calculated using a variant of the Wolf pairwise
summation method, proposed by Fennell and Gezelter40:
 erfc (r ) erfc (Rc )





r
Rc
qi q j 
,
uCoul (r ) 
2 2


40  erfc (RC ) 2 exp( RC ) 


(
r

R
)

C 

RC2
 1/ 2
RC



r  RC
(13)
where, ε0 is the electric constant, r is the distance between two partial charges qi and q j , α is the
damping parameter (here equal to 0.1), and RC is the cutoff distance, which for both Lennard-Jones
and Coulombic interactions is taken to be 12.8 Å in this work. Although this approach has been
recently employed in a number of simulation studies, to reinforce its robustness we demonstrate that it
can be used to describe adsorbate-adsorbent interactions with accuracy comparable to the conventional
Ewald summations (see Supporting Information).
A series of preliminary studies was carried out in order to assess the performance and the accuracy
of the proposed method as a function of the cubelet size and number of probed orientations. In this
series the adsorbate was IRMOF-1 and the probe molecule was carbon dioxide, modeled with the
TraPPE forcefield parameters41. For the results of these preliminary tests see Supporting Information.
As the final choice of parameters, throughout the article we consider a cubelet of 0.5x0.5x0.5 Å in
size and for each cubelet we perform 50 trial orientations of the molecule (in case of TNT we perform
500 trial orientations, unless specified otherwise). To estimate the error of the calculations, we
concentrate on TET in MIL-47(V) at 300 K, where, due to strong confinement of the adsorbate
species, the convergence of the average properties is expected to be the slowest. We perform five
independent runs with different random seed numbers (used to generate random orientations of TET),
and observe that the standard error of the mean for the Henry’s constant KH is about 3%.
12
IV. Results
In Table 1 we summarize the Henry’s constants KH in IRMOF-1 from computer simulations (in the
second column at 300 K and in the third column at 473 K) and the reference experimental study at 473
K (in the fourth column)29. This table also contains data for the differential enthalpies of adsorption
h from simulations and the reference experimental study, in columns five and six, respectively. In
the reference study three different samples of IRMOF-1 were investigated, and the data in Table 1
corresponds to Sample 2 (as designated in the original publication), for which the most extensive set of
data is available and for which the simulation results provide the best agreement. Indeed, given that no
forcefield parameter optimization was undertaken, the simulation results for the Henry’s constant
reproduce quite accurately both the overall trend and the magnitude of the reference values for the
aromatic species. At the same time, we note a substantial discrepancy between the simulations and
experiments for smaller molecules, ACH, ACT and CHL. First, we note that the simulation KH values
for ACH, ACT and CHL are inline with the data for the other small molecules, such as CO 2 (KH =0.12
[mol/kg/bar] at 473 K, in this work). Second, we try other charge models and observe that these
differences in the KH values can not be reconciled via this route (see the Supporting Information file).
Thus, we believe that the key source of this discrepancy is the structural disintegration of IRMOF-1 in
the experimental studies. The authors of the original publication noted that the stability of the IRMOF1 samples was an issue in some of the experiments29. Given this discrepancy, no further investigation
on the differential enthalpy of adsorption is pursued for ACH, ACT and CHL. For other species, this
property is calculated using eq 7 and the dependency of the logarithm of the Henry’s constant on the
variation of the reciprocal temperature is shown in Figure 2. The overall trend in the differential
enthalpy is reproduced reasonably well, with the simulations values being systematically lower
compared to the experimental values by about 20%. A notable exception is the result for TET, for
which the experimental value of the differential enthalpy does not follow the expected trend. Table 1
also contains simulation predictions for TNT in IRMOF-1. According to these results, at ambient
13
conditions (300 K), IRMOF-1 should exhibit substantial affinity towards TNT and we will attempt to
place this result in the context of sensing applications in the Discussion section. IRMOF-1 should also
exhibit high selectivity towards TNT with respect to, for example, TOL, which is a common solvent,
has similar structure to TNT, but is relatively benign (in other words, not explosive). At 300 K, the
overall STNT TOL is about 300, however at higher temperature, it drops to much lower values (of about
7.5), as calculated from eq 6. More detailed information on what regions of the porous space are
specifically responsible for this selectivity can be obtained from the local selectivity analysis, eq 10.
The information is visualized in Figure 3. This figure suggests that confinement and steric restriction
play an important role in inducing high selectivity. In particular, the regions of higher selectivity are
located either in the vicinity of the organic linkers or near the windows between the cages. Although
the centers of the cages still prefer TNT simply due to a larger number of interaction sites in the TNT
molecule and hence stronger interaction with the MOF, the selectivity towards TNT is significantly
diminished. Figure 3 also shows a reaction coordinate as a black line going through the centers of the
cages and windows of IRMOF-1. We emphasize here that the definition of the reaction coordinate is
dictated by the objectives of the analysis and a number of choices is possible. For example, it can be
defined as the minimum free energy trajectory through a specific window or a channel in the porous
structure. The reaction coordinate in Figure 3 is used for illustration. Free energy variation and
selectivity for TNT and TOL along this reaction coordinate are shown in Figure 4 at 300 K and Figure
5 at 473 K. Note the location of the two pronounced free energy minima for TNT at around 7 Å and 17
Å. These coordinates correspond to the window region between the two cages of IRMOF-1, where the
paddle-wheel aromatic linkers form a constriction. For TOL, these two minima are at slightly different
locations, namely 5.5 Å and 18.5 Å, respectively. This difference in the two profiles leads to the
regions of substantial selectivity as reflected in the bottom panel of Figure 4. As shown in Figure 5, at
a higher temperature these trends are preserved, and the selectivity profile has a similar shape to that in
Figure 4, however the actual selectivity values are one order of magnitude lower at the peaks.
14
We now turn our attention to MIL-47(V). The structure of this material is shown in Figure 6 on the
left. In the direction normal to the plane of the figure, the structure features straight channels, not
connected to each other. Each channel is formed by four walls of the benzyl units, connected in the
vertices of the channel to the octahedral vanadium complexes (an additional view of the structure is
provided in the Supporting Information file). Morphological characterization tools applied to MIL47(V) indicate that these channels are accessible to spherical probes of up to about 7.25 Å in
diameter42. This value is comparable with the characteristic size of molecules such as TET and TNT.
Close match in size between the pores and the molecules under consideration is reflected in the
predicted Henry’s constants as summarized in Table 2. These constants are up to five-six orders of
magnitude higher at 300 K and up to three orders of magnitude higher at 473 K in MIL-47(V)
compared to IRMOF-1. Similarly to IRMOF-1, the absolute value of the differential enthalpy of
adsorption increases (signifying stronger interaction) from BEN to TET. In IRMOF-1 this series
finishes with TNT, however, in MIL-47(V) TNT is positioned between XYL and 3MB (as calculated
using the data in Figure 2 on the right). Tighter confinement of the adsorbing species in MIL-47(V)
also leads to some interesting selectivity behavior. Specifically, if we focus on the TNT-TOL pair, at
300 K the overall STNT TOL is about 6.6, according to the eq 6, whereas at 473 K the trend reverses
altogether and the material exhibits preference towards TOL, with STNT TOL =0.41. To understand this
behavior we carry out a more detailed analysis of the local behavior. In Figure 6, in the center and on
the right, we show a cross-section of the channels with the distribution of the local selectivity at 300 K
and 473 K, respectively. The color scheme is the same as in Figure 3. These pictures reveal that there
is only a small region of space in the center of a channel with selectivity towards TNT. The rest of the
pore space is essentially not accessible to the bulky TNT and exhibits preference towards TOL, as
indicated by the blue color ( STNT TOL < 1). Let us look at the free energy profile along the channel. To
be more rigorous, we define the reaction coordinate here as the locus of the Helmholtz free energy
minima for TNT along the channel. Again, the local selectivity is defined as the ratio of the Henry’s
15
constants for TNT and TOL along this path. These results are summarized in Figure 7 and 8 for 300 K
and 473 K, respectively. At 300K, the free energy profile has a rather smooth form for TOL and
periodic oscillating shape for TNT. The periodicity of the profile for TNT reflects the underlying
periodic crystalline structure of the channel in MIL-47(V). As the points on the free energy profile
correspond to the properties of individual cubelets and do not benefit from the averaging over all
cubelets in the system, there is some variation in the values of the free energy minima and maxima.
Nevertheless, it is clear that along the reaction coordinate there are locations exhibiting extreme
affinity and, consequently, extreme selectivity towards TNT as shown in Figure 7, lower panel. Within
these locations, the tight match between the size and structure of TNT and the surrounding channel
must have important consequences on the rotational and translational degrees of freedom of the TNT
molecule. The entropic nature of this effect manifests itself in a strong variation of the free energy
profile for TNT with temperature. As a result, at 473 K, there are now regularly spaced regions on the
reaction coordinate with selectivity towards TOL (Figure 8). Overall, at a lower temperature few
locations within the channel with very high affinity for TNT dominate the average properties of the
material and it shows selectivity towards TNT. However, at a higher temperature, MIL-47(V) prefers
TOL over TNT as seen from Table 2 and discussed earlier. We note here, however, that the suggested
preferential adsorption of TNT over TOL in MIL-47(V) at lower temperatures may never be attained
in the experiments, as transport of TNT molecules within the channels of the MIL-47(V) structure will
be clearly dominated by TNT molecules having to cross energy barriers of 10-20 kJ/mol every 3-5 Å.
V. Discussion
In the Discussion section, we would like to reflect on the scope, applicability and limitations of the
presented approach, and then place our findings in the context of sensing applications. In this article
we demonstrate that the lattice representation of the simulation cell offers a particularly convenient
16
way to calculate various important characteristics of porous materials in zero loading regime. Since the
proposed approach is intended for computational screening of promising materials for sensing
applications, it is useful to comment on its efficiency. Properties, such as the Henry’s constant of
adsorption and spatial variation of the Helmholtz free energy, can be obtained from a single
simulation. Local and overall selectivity with respect to two components is calculated from two
simulations. Currently, the differential enthalpy of adsorption requires several simulations at different
temperatures in order to apply eq 7. However, a small modification of the program, where instead of
the Boltzmann factor, the temperature independent values of the intermolecular energy are stored for
each cubelet, would also allow one to calculate the differential enthalpy of adsorption from a single
simulation. The computational efficiency of the code ranges from 103 seconds (on a single core of
Intel Westmere E5620 processor) for CO2 in IRMOF-1 with the parameters specified in the
Methodology section to 105 seconds for TNT in MIL-47(V) with one thousand trial orientations per
cubelet. The current version of the code has not been parallelized, however the lattice nature of the
algorithm offers an opportunity for a high degree of parallelization and much greater computational
efficiency.
As with any other simulation study, generation of quantitatively accurate predictions using the
proposed methodology depends on the available molecular forcefield. The use of the UFF to describe
both MOF and adsorbate species in this work is dictated by convenience and consistency
considerations rather by the accuracy of the forcefield. Lack of the intermolecular parameters
purposefully developed to describe adsorption in MOF materials has been widely recognized as an
important issue in the adsorption modeling community, and systematic development and calibration of
these parameters is an ongoing research17,43,44.
The current study is limited to rigid adsorbates in rigid, but not necessarily ordered or crystalline,
porous materials. Extension to flexible linear and branched molecules can be easily envisioned using
the Configurational Bias Monte Carlo method45,46 to generate trial configurations of molecules in
17
individual cubelets. We further recognize that the flexibility of MOFs will have a profound impact on
the considered properties. For example, in IRMOF-1 the aromatic paddle wheel linkers possess some
rotational freedom at ambient temperature and may assume orientations, which reduce or open the
windows between the cages, compared to the single crystalline structure studied here. Although in one
recent study by Ford and co-workers, it was observed that the flexibility of IRMOF-1 had only a minor
impact on the self-diffusion coefficients and activation energies for normal alkanes up to n-hexane and
benzene47, these effects can be more pronounced for larger molecules, such as TNT, in more restricted
spaces, such as MIL-47(V).
One approach to explore these effects is to consider several key
representative structures of a porous material. A more general strategy would be based on the
simulations in the osmotic ensemble as has been recently reviewed by Coudert and co-workers48.
These approaches will be investigated in future work.
Despite the reservations regarding the forcefield parameters, the agreement between the
experimental and simulation data is encouraging for IRMOF-1 and therefore, we would like to
conclude this article with some speculations on the applicability of IRMOF-1 and MIL-47(V) to TNT
sensing. TNT vapor pressure at 25°C has been estimated at 1.73∙10-6 kPa, or 17 ppb (mole fraction)49.
We use 1 ppb of TNT as the target detection limit. From the calculated Henry’s constants we estimate
that at 1 ppb equilibrium bulk concentration, the loading of TNT in IRMOF-1 is about 0.49 g/kg, or
0.49 ng/μg, and in MIL-47(V) it is about 81 g/kg, or 81 ng/μg. In the recent QCM studies of water
sorption on the CuBTC film, Biemmi and co-workers observed that they could confidently detect
loadings of 22 ng/cm2, with the film surface density being 45-75 μg/cm2(Ref.4). In other words, the
current technology, based on MOFs, can detect 0.3-0.5 ng of adsorbate binding per μg of a MOF.
From this perspective, both IRMOF-1 and MIL-47(V) are suitable candidates for TNT sensing (in case
of IRMOF-1 confirming earlier observations by Greathouse and co-workers19). However, other issues
may prevent the actual implementation of sensors based on these MOFs. Namely, the IRMOF-1 low
stability and propensity to disintegrate in the presence of moist air, well known to the experimental
18
adsorption community, preclude it from becoming a viable candidate. Transport constrains and low
selectivity most likely exclude MIL-47(V) from further considerations. Hence, the search for the best
MOFs for explosive detection continues, but we hope with the tools proposed in this work it will be a
much more streamlined process.
ACKNOWLEDGMENT. LS would like to thank Dr. Miguel Jorge and Dr. Tina Düren for useful
comments and suggestions. This work has made use of the resources provided by the Edinburgh
Compute and Data Facility (ECDF). (http://www.ecdf.ed.ac.uk/). The ECDF is partially supported by
the eDIKT initiative (http://www.edikt.org.uk).
Supporting Information Available. The supporting information file contains additional derivations
related to the Theory section (and specifically to eq 11), summary of the UFF interaction parameters,
results of the preliminary test runs for CO2 in IRMOF-1, and other data in the same order it is
mentioned in the article. This information is available free of charge via the Internet at
http://pubs.acs.org.
19
Figure captions
Figure 1: Computer visualization of the molecular structure of the investigated adsorbate species.
From top down and from left to right, benzene (BEN), toluene (TOL), p-xylene (XYL), 1,2,4trimethylbenzene (3MB), tetralin (TET), trinitrotoluene (TNT), chloroform (CHL), acetone (ACT),
and acetaldehyde (ACH) are shown. Carbon atoms are shown in cyan, hydrogen in grey, oxygen in
red, nitrogen in blue and chlorine in green, respectively. Chemical structures of the investigated
species are further provided in the Supporting Information file.
Figure 2: Logarithm of the Henry’s constant KH as function of the reciprocal temperature 1/T for
IRMOF-1 (on the left) and MIL-47(V) (on the right) in the range of temperatures between 300 K and
473 K.
Figure 3. Computer visualization of the IRMOF-1 structure (on the left) and local TNT-TOL
selectivity STNT TOL,i at 300 K (in the center) and at 473 K (on the right). STNT TOL,i <1 (selectivity
towards TOL) is shown in blue, 1< STNT TOL,i <10 is shown in green, 10< STNT TOL,i <100 is shown in
yellow and 100< STNT TOL,i <1000 is shown in red. The reaction coordinate explored in Figure 4 and
Figure 5 is shown as a black line in all three panels.
Figure 4. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in Figure 3) in IRMOF-1 at 300 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in Figure 3) in
IRMOF-1 at 300 K.
20
Figure 5. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in Figure 3) in IRMOF-1 at 473 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in Figure 3) in
IRMOF-1 at 473 K.
Figure 6. Computer visualization of the MIL-47(V) structure (on the left) and local TNT-TOL
selectivity STNT TOL,i at 300 K (in the center) and at 473 K (on the right). STNT TOL,i <1 (selectivity
towards TOL) is shown in blue, 1< STNT TOL,i <10 is shown in green, 10< STNT TOL,i <100 is shown in
yellow and 100< STNT TOL,i <1000 is shown in red. Data is generated using 1000 trial orientations of an
adsorbate molecule in each cubelet.
Figure 7. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in the text) in MIL-47(V) at 300 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in the text) in
MIL-47(V) at 300 K. Data is generated using 1000 trial orientations of an adsorbate molecule in each
cubelet.
Figure 8. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in the text) in MIL-47(V) at 473 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in the text) in
21
MIL-47(V) at 473 K. Data is generated using 1000 trial orientations of an adsorbate molecule in each
cubelet.
22
Table 1: Summary of the Henry’s constants KH in IRMOF-1 at 300 K and 473 K from simulations
(columns two and three) and from experiments29 at 473 K (column four). The table also shows the
differential enthalpies of adsorption h
in IRMOF-1 from simulations (column five) and
experiments29 (column six)a
KH [mol/kg/bar] KH [mol/kg/bar] KH [mol/kg/bar]  h
sim at 300 K
sim at 473 K
exp at 473 K23
sim
[kJ/mol]  h
exp23
BEN
1.09x103
4.76
5.75
37.06
46.7
TOL
7.06x103
12.59
13.40
43.17
54.0
XYL
60.95x103
36.32
42.30
50.64
64.0
3BM
55.41x104
109.28
129.00
58.18
72.6
TET
10.07x105
168.51
201.00
59.30
27.2
TNT
21.26x105
93.49
-
68.41(86.6119)
-
ACH
-
0.31
1.84
-
-
ACT
-
0.82
11.50
-
74.4
CHL
-
0.75
3.94
-
39.2
a
[kJ/mol]
The notation for the adsorbate species is explained in the caption for Figure 1. The table also
compares the simulation result for the differential enthalpy of adsorption h for TNT in IRMOF-1
with that from the work of Greathouse and co-workers19.
23
Table 2: Summary of the Henry’s constants KH at 300 K and 473 K and differential enthalpies of
adsorption h in MIL-47(V) from computer simulationsa
KH [mol/kg/bar] at KH [mol/kg/bar] at
 h [kJ/mol]
300 K
473 K
BEN
1.37x106
31.19x101
57.22
TOL
53.79x106
22.03x102
68.89
XYL
19.51x108
13.78 x103
80.88
3MB
62.04x109
86.87x103
91.91
TET
53.34x1010
42.37x104
95.78
TNT
35.56x107
91.18x101
87.79
ACH
-
1.36
-
ACT
-
10.76
-
CHL
-
12.24
-
a
The notation for the adsorbate species is explained in the caption for Figure 1.
24
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Figure 1: Computer visualization of the molecular structure of the investigated adsorbate species.
From top down and from left to right, benzene (BEN), toluene (TOL), p-xylene (XYL), 1,2,4trimethylbenzene (3MB), tetralin (TET), trinitrotoluene (TNT), chloroform (CHL), acetone (ACT),
and acetaldehyde (ACH) are shown. Carbon atoms are shown in cyan, hydrogen in grey, oxygen in
red, nitrogen in blue and chlorine in green, respectively. Chemical structures of the investigated
species are further provided in the Supporting Information file.
BEN
3MB
CHL
TOL
TET
ACT
XYL
TNT
ACH
29
Figure 2: Logarithm of the Henry’s constant KH as function of the reciprocal temperature 1/T for
IRMOF-1 (on the left) and MIL-47(V) (on the right) in the range of temperatures between 300 K and
16
32
14
28
12
24
XYL
10
20
3MB
16
TET
12
TNT
ln(KH)
ln(K H)
473 K.
8
6
4
8
2
4
0
0.002
0.0025
1/T
0.003
0.0035
0
0.002
BEN
TOL
0.0025
0.003
0.0035
1/T
30
Figure 3. Computer visualization of the IRMOF-1 structure (on the left) and local TNT-TOL
selectivity STNT TOL,i at 300 K (in the center) and at 473 K (on the right). STNT TOL,i <1 (selectivity
towards TOL) is shown in blue, 1< STNT TOL,i <10 is shown in green, 10< STNT TOL,i <100 is shown in
yellow and 100< STNT TOL,i <1000 is shown in red. The reaction coordinate explored in Figure 4 and
Figure 5 is shown as a black line in all three panels.
31
Figure 4. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in Figure 3) in IRMOF-1 at 300 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in Figure 3) in
IRMOF-1 at 300 K.
0
-5
A (kJ/mol)
-10
-15
-20
-25
-30
-35
-40
0
5
10
15
20
25
20
25
x (Å)
300
STNT-TOL
250
200
150
100
50
0
0
5
10
15
x (Å)
32
Figure 5. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in Figure 3) in IRMOF-1 at 473 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in Figure 3) in
IRMOF-1 at 473 K.
0
-5
A (kJ/mol)
-10
-15
-20
-25
-30
-35
-40
0
5
10
15
20
25
20
25
x (Å)
40
35
STNT-TOL
30
25
20
15
10
5
0
0
5
10
15
x (Å)
33
Figure 6. Computer visualization of the MIL-47(V) structure (on the left) and local TNT-TOL
selectivity STNT TOL,i at 300 K (in the center) and at 473 K (on the right). STNT TOL,i <1 (selectivity
towards TOL) is shown in blue, 1< STNT TOL,i <10 is shown in green, 10< STNT TOL,i <100 is shown in
yellow and 100< STNT TOL,i <1000 is shown in red. Data is generated using 1000 trial orientations of an
adsorbate molecule in each cubelet.
34
Figure 7. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in the text) in MIL-47(V) at 300 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in the text) in
MIL-47(V) at 300 K. Data is generated using 1000 trial orientations of an adsorbate molecule in each
cubelet.
A (kJ/mol)
-20
-40
-60
-80
0
5
10
15
20
25
20
25
x (Å)
4000
STNT-TOL
3000
2000
1000
0
0
5
10
15
x (Å)
35
Figure 8. Top: The Helmholtz free energy A (kJ/mol) profile along the reaction coordinate x (Å) (as
defined in the text) in MIL-47(V) at 473 K. Black line is for TNT, red line is for TOL. Bottom:
Selectivity for TNT over TOL STNT TOL along the reaction coordinate x (Å) (as defined in the text) in
MIL-47(V) at 473 K. Data is generated using 1000 trial orientations of an adsorbate molecule in each
cubelet.
A (kJ/mol)
-20
-40
-60
-80
0
5
10
15
20
25
20
25
x (Å)
60
STNT-TOL
50
40
30
20
10
0
0
5
10
15
x (Å)
36
SYNOPSIS TOC
Computer visualization of the local selectivity distribution for trinitrotoluene over toluene in IRMOF1.
37