Final Report Summary - AMCOS (Advanced Materials as CO2 Removers: A Computational Study of CO2 Sorption Thermodynamics and Kinetics)
Executive Summary:
Project Context and Objectives
The overall concept of the AMCOS project was the study of the prospect of newly synthesized materials by the Indian institutions to be used as capturers of carbon dioxide and methane. The means towards this task are various computer experiments, namely, first principles ab initio calculations, and classical statistical mechanics based molecular simulations, such as Molecular Dynamics and Monte Carlo, as well as conventional ad hoc designed experiments so that to be directly comparable to the mentioned above molecular simulation computer experiments. Moreover, in addition to the tasks of the AMCOS project, though within its context, taking advantage of the experimental techniques developed during the entire period, the dynamics of hydrogen as a sorbate molecule in these materials was also investigated.
Over the past decade a branch of organic synthesis following a reticular process, gave a vast rise to oriented design and production of new materials characterised by exceptional physicochemical properties. This strategy of synthesis engineering towards target structures, created a novel class of advanced sorbents such as the zeolitic imidazolate frameworks (ZIF), characterized by large pore sizes, high apparent surface areas and a chemically active interior.
In addition, selective modification of polymeric matrices has led to the so-called functionalized polymers (FP) which exhibit improved performance futures, for instance, the enhanced ability for adsorbing specific group of molecules. Also, functionalization processes of porous silicas by aminopolymers of low molecular weight, have developed a new category of inorganic-organic hybrid sorbents, the hyperbranched aminosilicas (HAS).
Objective of the AMCOS EU-India collaborative research project was to investigate the capability of newly synthesized or/and modified classes of the aforementioned advanced materials, for use in environmental applications such as the selective separations of carbon dioxide in flue gases and natural gas. For this purpose, the sorbate molecular dynamics and thermodynamics will be studied extensively by applying, developing and integrating state-of-the-art computational tools and experimental methodologies.
The task of NTUA under AMCOS was the statistical mechanics based modeling of the sorption thermodynamics and kinetics of various molecules in recently synthesized ZIF structures in order to investigate the evolution of the sorption equilibrium over a wide range of occupancies of carbon dioxide, and to elucidate its rate and mechanism of motion in the pores of these materials. During the current reporting period NTUA examined the ZIF-3 and ZIF-8 as representative members of the series of ZIF structures.
The simulation predictions would be then compared with the measurements of the IRCE-LYON group which is responsible for measuring the guests' mobility via Quasi-elastic Neutron Scattering experiments (QENS). Simulation and QENS, both being microscopic techniques, can provide valuable information on the sorbate molecular dynamics in the ZIFs.
UNISS has developed an easy procedural protocol to derive partial charges on ZIFs from DFT-based quantum chemical calculations. The chosen structure to test was also ZIF-3 and ZIF-8, both widely studied through physical experiments. To obtain more reliable charges, several DFT calculations on a periodic ZIF-8 were carried and crosschecked one with each other and with cluster-based DFT calculations on ZIF-8 fragments of increasing size. In quantum chemical calculations for non-periodic system GAUSSIAN, TURBOMOLE were used, whereas CPMD and cp2k packages were used for periodic systems. Both the periodic ZIF-8 lattice and its various fragments have been digitally reconstructed from the X-ray crystal data collected from the Cambridge Crystallographic Data Centre (CCDC) (see http://www.ccdc.cam.ac.uk(opens in new window) online). For periodic DFT calculations, the fitting of the quantum chemical electrostatic potential to atomic site charges is performed with the REPEAT (Repeating Electrostatic Potential Extracted Atomic) method, whereas the CHELPG and MK scheme were used for DFT calculations on fragments.
The task of LU was to provide experimental data on diffusion of adsorbate molecules in the advanced adsorbent materials. These experimental data are required to validate the corresponding computational studies of the Indian and European AMCOS partners. The adsorbent materials considered during the report period are the MOF CuBTC as test material and crystalline ZIFs. The nanoporous amorphous HAS and polymer based adsorbents were not yet been synthesized by the Indian project partners. Due to the main target of the project, which is the exploration of these materials for their suitability for CO2 separation from gas mixtures, the focus in the first report period was to study single component diffusion of carbon dioxide and alkanes (methane, ethane) in selected materials. For the purpose of the CO2 diffusion studies, the 13C pulsed field gradient (PFG) NMR technique needed to be developed which included NMR probe design and development of measurement protocols.
Simultaneously to our efforts to improve and establish 13C PFG NMR diffusion studies with absorbed carbon dioxide in MOF's and ZIFs LU possesses the opportunity to measure transient concentration profiles during uptake and desorption of guest molecules in adsorbent particles by infrared (IR) microscopy. During the report period, such diffusion measurements were successfully carried out with ZIF-8 as adsorbent and carbon dioxide and methane as well as with mixtures of both molecules as adsorbate gases.
Computer modeling and screening were performed on materials synthesized by the Indian consortium. In particular the EU consortium worked on selected materials from the Zeolitic Imidazolate Framework homologue series and from Functionalized Polymers. The basic axis of the employed methods for the analysis of the efficiency of the provided materials in capturing the guest sorbates is the computational modeling utilizing Quantum mechanical calculations and also statistical mechanics based mesoscopic and atomistic simulations of the sorption processes.
Nevertheless, the phenomena pertaining to sorption in a real process is much more complicated as adsorption on the surfaces, penetration in the interior of the materials (diffusion) along with inter-crystalline transport occurring fast or infrequently depending on the energetics of the system sorbent material / guest sorbate. That led us to develop not only methodology toward the study of the thermodynamical phase equilibrium, but also study of the kinetics of the guest system within the host material as well.
The novelty of the materials of the project and consequently the complete lack of a force field (FF) imposed a strategy in two directions towards a) creating of reasonable FFs on a Quantum Mechanical basis, and b) adopting sophisticated 'expensive' experiments measuring the aforementioned kinetic and dynamics information under comparable time and length scales, so that one to be able to compare the results obtained from the computer simulation experiments.
The principle sorbate of the work during the entire period was the Carbon Dioxide (CO2), and the central objective was the investigation of the aforementioned sorbents' performance in capturing the CO2 molecule, and also, by modeling the physicochemical processes involved for this, to explain and predict the impact of the materials' structure on the CO2 storage efficiency. In addition to this, it proved imperative the inclusion of Methane (CH4) and Hydrogen (H2) in the original target sorbates as well.
Work Performed
ZIF-8 and ZIF-3 crystals were modelled using rigid, and at the end of the project, flexible force fields. The rigid model keeps the crystal atoms fixed at their positions, identified by XRD data. Therefore, structural characteristics remain unaltered throughout the simulations. The crystal atoms interact with sorbates through both long and short range forces. We tested both the Dreiding and the Universal Force-Field (UFF) dispersion interactions parameters. Two flexible models were tested for ZIF-8 and ZIF-3. The crystal atoms are allowed to move in molecular dynamics simulations of bare frameworks. Both flexible models include bond stretches, angle bends, inversions (improper torsions), dispersion and electrostatic interactions. The Dreiding and Nilsson parameterizations were used.
For the electrostatic interactions, the same charges were used as in the rigid model. It must be also noted that the quantum mechanical calculations have given the modeling a new input for the Molecular Dynamics simulations applied to the flexible models of the metallorganic frameworks of the project. The temperature was chosen to be 258 K, according to the XRD experimental data found elsewhere. Bond lengths, angle bend, improper and proper torsion angle values were computed as statistical averages throughout the runs of 100 ns.
The obtained results showed excellent agreement with experimental values. Simulations were also carried out at a lower temperature to investigate the effect of temperature on the structural conformations for both ZIF-3.and ZIF-8 structures. After the first successful 13C and 1H PFG NMR diffusion studies of the adsorbed CO2 and CH4 in the nanoporous MOF CuBTC, which were performed in order to check the developed pulse field gradient NMR probe, it was the next task to perform these NMR diffusion measurements on the Zeolitic Imidazolate Framework ZIF-8.
The previous NMR investigations were performed at gas phase pressures below 1 bar. They showed that the adsorbed amount of CO2 and CH4 in ZIF-8 is substantially smaller than in CuBTC which rendered NMR diffusion studies impossible [1]. Therefore, it was decided to explore the possibilities to perform NMR diffusion studies at elevated gas pressures. The target of 10 bar for these measurements was discussed among the AMCOS project partners. LU extend the experimental equipment for the NMR studies accordingly enabling NMR measurements at up to 15 bar. Methane and Carbon Dioxide NMR measurements have been accomplished in ZIF-8 using this new high-pressure NMR set up.
The NMR data for the relaxation times showed that the gases are in the adsorbed state. The obtained self-diffusion coefficients are in the same order of magnitude than previously published data of IR microscopy but point towards a different loading dependence. Especially for the carbon dioxide in ZIF-8, a good agreement between the NMR experimental results and results of MD simulation provided by UNISS and NTUA were found. This points towards a successful approach and development of the computational tools developed within AMCOS. PFG NMR studies of CH4 / CO2 self-diffusion in mixtures were also performed, and show that there seems to be only a minor effect on the mobility of one species in the presence of the other species. Comparisons are now being made between the experimental and computational methods on these adsorbed binary mixture.
In situ quasi-elastic neutron scattering (QENS) experiments were performed at the Institut Laue-Langevin, in Grenoble, France, on H2, CH4 and CO2 in the two samples provided by NEERI : ZIF-8 and ZIF-3, where the linkers were deuterated. From the variation of the broadening as a function of wavevector transfer, diffusion coefficients could be derived at three different H2 concentrations. Although the quality of the spectra recorded for CO2 was not optimal, diffusivities could be extracted at 200 K, at four different loadings. The statistics obtained for CH4 were better because of the larger incoherent cross section of this molecule. Comparisons are now being made between the different methods.
Results
Statistical mechanics based simulation studies at the atomistic level of Ar, CH4, D2 and H2 sorbed in the ZIF-8 and ZIF-3 were accomplished. So far we have explored the mechanisms that govern the sorption thermodynamics and kinetics of non polar sorbates possessing different sizes and strength of interactions with the metal-organic framework, in order to understand the outstanding properties of this novel class of sorbents, as revealed by experiments published elsewhere. For this purpose we developed in-house modeling procedures involving calculations of sorption isotherms, partial internal energies, chemical potential in the fully flexible host structure various probability density functions and molecular dynamics, for the modeling of sorbed phase over a wide range of occupancies inside a digitally reconstructed unit cell of ZIF-8. The results showed a marked energetic inhomogeneity perceived by the sorbates as a consequence of the 2-methylimidazolate links in the atomic framework of the metal-organic material under study, resulting in free energy barriers which give rise to inflections in the isotherms and guide the dynamics of guest molecules.
Single component CO2 NMR studies were performed with Imidazole Functionalized Polystyrene (Im-PS) obtained from ICT Mumbai. 13C NMR spectroscopy confirmed that the CO2 is rather strongly interacting with the imidazole functional group in this polymer. In agreement with this spectroscopic characterization, 13C PFG NMR diffusion measurements at elevated gas pressure of 10 bar showed that in the adsorbed carbon dioxide has short transverse relaxation times rendering intraparticle self-diffusion studies in these f-PS samples impossible. The NMR diffusion studies yield only the long-range mobility between individual adsorbent particles via the gas phase.
During the second period of the project is presented a detailed picture of the distribution of charge density across functionalized and non-functionalized frameworks via determination of electrical dipole moment separately at metal and ligand sites. The values of dipole moments were calculated from the analysis of maximally localized Wannier function and ion centres, and from corresponding charges. Based on our dipole moment analysis we rationalized the sorption of CO2 in these materials by combined Monte Carlo simulations. The adsorption thermodynamics and the uptakes of CO2 at the low pressure range depend on the strength of solid-gas interaction, increasing in accordance to the trend of the dipole moment, in the order ZIF-3 > ZIF-2 > ZIF-8. Moreover, the location and magnitude of the dipole moment vectors across the framework are important for identifying correctly the preferred adsorption site for CO2 near the frameworks. Some other properties of these materials like mechanical and chemical stability can also be addressed through the knowledge of these dipole moments calculations.
Impact of the Results
Through the computational work it was revealed the influence of the mobility of the sorbent framework on both the equilibrium and kinetic properties of the sorbed phase by means of Molecular Dynamics computer experiments, under both isochoric- isothermal and isobaric-isothermal statistical ensembles, for several host model options, combined by Widom averaging along the entire trajectory of the host-guest system toward rigorously obtained sorbate isotherms within a fully flexible lattice. This novel methodology was adapted to the study of the Self-diffusivity and the collective (Maxwell-Stefan and Transport) diffusivities of Carbon Dioxide and Methane within the Zeolite Imidazolate Framework-8. The simulation predictions are compared with measurements from Pulsed-Field Gradient Nuclear Magnetic Resonance (PFG NMR), as well as with recently conducted Infrared Microscopy (IRM) experiments elaborated on the basis of the current modeling in the flexible ZIF-8. The modeling results predict a significant influence on the sorbate transport, exerted by the 2-methilimidazolate ligands surrounding the cage-to-cage entrances, whose apertures are commensurate with the guest molecular dimensions. Moreover, calculations of the singlet probability density distribution of the sorbate molecules at selected regions within the imidazolate framework provide a plausible explanation of the transport diffusivity as a function of sorbate occupancy, measured via IRM.
Project Context and Objectives:
Project context and main objectives: A summary description
The overall concept of the AMCOS project is the study of the prospect of newly synthesized materials by the Indian institutions to be used as capturers of carbon dioxide and methane. The means towards this task are various computer experiments, namely, first principles ab initio calculations, and classical statistical mechanics based molecular simulations, such as Molecular Dynamics and Monte Carlo, as well as conventional ad hoc designed experiments so that to be directly comparable to the mentioned above molecular simulation computer experiments. Moreover, in addition to the tasks of the AMCOS project, though within its context, taking advantage of the experimental techniques developed during the entire period, the dynamics of hydrogen as a sorbate molecule in these materials was also investigated.
The computer modeling is utilized mainly for the study of the CO2-sorbent interactions along with the mobility of a wider class of guest molecules in the various host systems pertaining to the advanced materials considered in the Technical Annex, such as the zeolitic imidazolate frameworks (ZIFs) and the functionalized polymers; the hyperbranched aminosilica (HAS) were not eventually considered even in the final part of the project because their synthesis by the Indian groups proved to be problematic. The focus of the project is the selective separation and finally the storage of CO2 and secondary CH4 from unary or binary mixtures towards environmental and energy resource related applications.
Complimentary to modeling, highly sophisticated experimental techniques (e.g. quasi-elastic neutron scattering (QENS) and pulsed field gradient nuclear magnetic resonance (PFG NMR)), are designed in order to measure the thermodynamics and molecular mobility of the sorbed phase. Moreover, these experiments serve as a precious validation tool for the computer modeling output.
Project Results:
Description of the main S & T results and foregrounds
At the current final stage of the report, the majority of the scientific and technological results are already published in journals edited by the most prestigious and large scientific societies, like the American Chemical Society (ACS), the American Physical Society (APS) and the American Institute of Physics (AIP). The DOI codes of the publications have been uploaded in the publication field of the SESAM webpage.
In this section, the most important results concerning the modeling and also the experimental findings as well as the foreground of the work as emerged from the combined computational study and the conjugate measured quantities, will be summarized.
1) Factors influencing the CO2 storage capacity in Metalorganic Frameworks
Over the past decade organic synthesis gave a vast rise to oriented design and production of new classes of metal-organic crystalline materials based on framework types which resemble zeolites. This strategy of synthesis engineering1 towards target structures created materials such as the metal-organic frameworks (MOFs), which mainly because of their high uptake capacities to hydrogen, methane and carbon dioxide have become one of the most popular class of porous materials. Although their thermal stability, a key characteristic for a technologically important sorbent, can be considered moderate compared to zeolites, the reticulated process of their synthesis makes them superior compared to the conventional aluminosilicate crystals. The resulted this way organic zeolite analogues, are characterized by large pore sizes, high apparent surface areas and a chemically active interior, which provide them with exceptional properties as sorbents being capable of hosting large amounts of sorbate molecules of a broad span of sizes. The great success of these crystalline solids as molecular binders is due to processes which involve appropriate linking of selected molecular blocks together, by building them on geometrically well defined morphologies. Moreover, the high availability of these compounds for further chemical modification of their linking units can lead to the creation of a whole series of homologues possessing various pore widths.
Another recent advance in the aforementioned reticulation strategy is the synthesis of a subcategory of MOFs, termed as zeolitic imidazolate frameworks (ZIFs), wherein transition metals replace T-atoms and imidazolate or imidazolate-type links replace oxygen bridges in the conventional aluminosilicate structures. Systematic chemical modification of their substituents has also created a series of homologous ZIF structures characterized by high chemical and thermal stability, based on framework types of either known zeolite topologies such as sodalite, RHO, MER or even predicted structures.
Scientists from the field of theory and simulation have given insight into molecular dynamics of the sorbed phase in a variety of MOF and COF structures. On the contrary, despite the source of papers reporting experimentally measured high uptake capacities regarding either hydrogen, or the greenhouse gases methane and carbon dioxide in several zeolitic imidazolate structures, fewer works have dealt with modeling in ZIFs so far.
Our computer simulation methodology relies upon classical physics with interparticle interactions being calculated through potential functions such as the Lennard-Jones potential. For hydrogen we employed the quantum mechanical potential function of Feynman-Hibbs for all interactions of the guest-host system. At this point we should notice that a good force field must be capable of capturing the essential physicochemical properties of a system, but it rarely yields accurate results with respect to real experiments; this is especially true for metal-organic materials due to complexity of their atomic framework. Full-scale ab initio quantum mechanical calculations on a certain material can serve as a reasonable basis towards more sophisticated potential functions; development of such a force field is well beyond the scope of this article since we study small non polar molecules and polarizability effects can be neglected. In this study we employed the two generic force fields mentioned above, which have been used successfully in the MOFs and isoreticular MOFs (IRMOFs) modeling No adjustment of potential parameters with respect to sorption experiments in order to match the measured points have been made in this work.
1.1 Modeling of the CO2 storage in ZIFs
1.1.1 Pilot study
At the first period of the project we started the sorption equilibria experiments prior to carbon dioxide for argon, methane and hydrogen, in the ZIF-8, as a pilot study, by means of Grand Canonical Monte Carlo (GCMC) stochastic simulations using the Metropolis algorithm for the importance sampling of the configuration space.
1.1.2 Actual modeling of Carbon Dioxide (and Methane)
This part of the work aimed at exploring the influence of the mobility of the sorbent framework on both the equilibrium and kinetic properties of the sorbed phase by means of Molecular Dynamics (MD) computer experiments under isochoric- isothermal and isobaric-isothermal statistical ensembles for several host model options, combined by Widom averaging along the entire trajectory of the host-guest system toward rigorously obtained sorbate isotherms within a fully flexible lattice. The methodology is adapted to the study of the Self-diffusivity and the collective (Maxwell-Stefan and Transport) diffusivities of Carbon Dioxide (CO2) and Methane (CH4) within the Zeolite Imidazolate Framework-8 (ZIF-8). The simulation predictions are compared with measurements from Pulsed-Field Gradient Nuclear Magnetic Resonance (PFG NMR), as well as with recently conducted Infrared Microscopy (IRM) experiments elaborated on the basis of the current modeling in the flexible ZIF-8. The modeling results reveal a significant influence on sorbate transport exerted by the 2-methilimidazolate ligands surrounding the cage-to-cage entrances, whose apertures are commensurate with the guest molecular dimensions. Moreover, calculations of the singlet probability density distribution of the sorbate molecules at selected regions within the imidazolate framework provide a plausible explanation of the transport diffusivity as a function of sorbate occupancy, measured via IRM.
The actual study aimed at exploring the influence of the structural dynamics of ZIFs, having pores of width commensurate with the guests' size, on both the equilibrium and mobility properties of sorbates by means of Molecular Dynamics, thus, avoiding dependence on stochastic methodologies toward sorbed phase equilibria, under the necessary assumption of a rigid ZIF model.
Concerning the computational part of this study, it must be noted that the size and strength parameters for the nonbonded interactions between the framework atoms, as well as the constants of the harmonic and torsion potentials at the bonded groups were all received from the DREIDING generic type force field.
Then, we followed a twofold strategy in applying the values for the various potential functions:
(i) In the NH NG V T case, by making use of them without any kind of reparameterization with respect to measurements of the present work or to relevant experiments found elsewhere, and also, with no adulteration with values from other known force fields.
(ii) In the NH NG P T case, by setting the crystallographic equilibrium values in all potentials mentioned in the preceding paragraph, and moreover, increasing the force constants from their original values by an order of magnitude for the stretching potential along the bond Zn - N, and the angle bending in the Zn - N - C1 and Zn - N - C2. This type of adjustment proved to be the optimum selection in the isobaric-isothermal ensemble to preserve the unit cell volume, causing a maximum reduction up to 3.94 %, however. The latter parameters set was selected among a long series of NH P T Molecular Dynamics runs of the bare ZIF-8. On the contrary, employment of the DREIDING values results in unphysical contraction of the ZIF cages.
The first option was adopted for the isochoric-isothermal MD computer experiments; whereas the latter was chosen to enable us a more realistic modeling of the presented physical experiments by allowing volume fluctuations in the guest-framework system under constant pressure, temperature and chemical potential as imposed on by the Gibbs thermodynamic equilibrium rules.
A comparative set of results of the thermodynamics of the CO2 and CH4 phase equilibria in the ZIF via the NH NG V T and NH NG P T Molecular Dynamics computer experiments for various types of flexible structures, as a function of sorbate fugacity obtained from the excess chemical potential ìex, were examined; ìex was calculated through the Widom method.
The results show considerable augmentation of the diffusivity values for both sorbates with respect to the cases where the mentioned above dihedral angle is hindered. Moreover for methane, it is demonstrated that quasi-free motion of the organic link gives rise to a steeper transition that occurs at earlier occupancies, in agreement with the IRM measurements.
That is to say, application of a nonzero torsion potential to the ligand makes methane molecules remain behind the windows until the chemical potential increases at some higher value of pressure, so that eventually to overcome the free energy barrier and land to the next cage. Whereas, the limiting case of a quasi-freely moving link (weaker hindrance, hence, lower free energy at the window which means lower cavity-to-window free energy barrier), causes transition at an earlier stage, namely, at lower chemical potentials.
Comparison between the IRM measured diffusivities at infinite dilution (equal to self-diffusivities), and the MD computations at the same region, show acceptable agreement; the isobaric MD data are about one order of magnitude lower for the reasons discussed in the preceding lines. It is interesting that within this regime the strongly adsorbed CO2 moves faster than CH4, whereas as sorbate occupation increases further, the CH4 diffusivity curve rises and eventually exceeds the values of CO2 being in agreement with the IRM experiments.
1.2 Hydrogen storage
The possibility of the hydrogen molecule capture by the novel materials was also examined. The problem of simulating processes involving equilibria and dynamics of guest sorbates within zeolitic imidazolate frameworks (ZIF) by means of molecular dynamics (MD) computer experiments is of growing importance because of the promising role of ZIFs as molecular 'traps' for clean energy applications. A key issue for validating such an atomistic modeling attempt is the possibility of comparing the MD results, with real experiments being able to capture analogous space and time scales to the ones pertained to the computer experiments. In the present study, this prerequisite is fulfilled through the quasi-elastic neutron scattering technique (QENS) for measuring self-diffusivity, by elaborating the incoherent scattering signal of hydrogen nuclei. QENS and MD experiments were performed in parallel to probe the hydrogen motion, for first time in ZIF members.
The predicted and measured dynamics behaviour show considerable concentration variation of the hydrogen self-diffusion coefficient in the two topologically different ZIF pore networks of this study, the ZIF-3 and ZIF-8. Modeling options such as the flexibility of the entire matrix versus a rigid framework version, the mobility of the imidazolate ligand, and the inclusion of quantum mechanical effects in the potential functions, were examined in detail for the sorption thermodynamics and kinetics of hydrogen and also of deuterium, by employing MD combined with Widom averaging towards studying phase equilibria. The latter methodology ensures a rigorous and efficient way for post-processing the dynamics trajectory, thereby avoiding stochastic moves via Monte Carlo simulation, over the large number of configurational degrees of freedom a non-rigid framework encompasses.
In the previous section studies on a ZIF-8 flexible model showed that different modeling options such as the charge distribution and the extend of the mobility of the organic ligand, vastly influence the transport properties of carbon dioxide and even more the mobility and equilibrium of the bulkier methane molecule.10 In the present study we investigate the influence of the framework dynamics of two ZIF structures, the ZIF-3 and ZIF-8 (varying in the structural topology, the pore network and the type of the organic ligand), on the equilibrium and mobility properties of hydrogen and deuterium. Both sorbent materials were synthesized and characterized at the National Environmental Engineering Research Institute in Nagbur. The work includes combined QENS measurements and molecular dynamics computer experiments of the hydrogen self-diffusivity when sorbed within the two ZIF materials. The QENS measurements were performed at the Institut Laue-Langevin in Grenoble. Equilibrium MD computations were conducted for hydrogen and deuterium in fully flexible ZIF models.
The advantage of combining QENS and MD in this work is that comparable time and length scales of the molecular motion in the two techniques can be directly correlated for the calculation of self-diffusivity. More precisely, the large scattering cross-section of protons is essentially incoherent corresponding almost exclusively to the motion of individual protons, and thus the self-diffusion coefficient of the sorbed hydrogen can be extracted as a function of concentration in the host materials.11 On the other hand, through the MD simulations the produced trajectories of the sorbate guest molecules within the host matrices were elaborated in order to compute the self-diffusion coefficient via the Einstein's equation.
1.2.1 Computer Experiments
The ZIF-3 and ZIF-8 crystals were reconstructed in atomistic level using data from single crystal X-ray diffraction analysis, following the procedure described in a previous work In both structures, each zinc ion is tetrahedrally coordinated by four nitrogen atoms (ZnN4); the bridging groups in the structures are the imidazolate (IM) and the 2-methyl-imidazolate (mIM) in the ZIF-3 and ZIF-8, respectively. As discussed in the preceding section the ZIF-3 possesses a three channel pore system with two types of intersections, whereas the ZIF-8 constitutes a 3-D network of cages with a connectivity value eight.
The sorption thermodynamics computations were carried out by means of molecular dynamics experiments so that the imidazolate framework flexibility to be efficiently captured and the equilibrium pressure of the sorbed phase to be rigorously calculated following a phase space averaging procedure. Subsequently, the use of various modeling options indicates that the flexibility of the host matrix is of little importance, and also, omitting the quantum mechanical contribution in the potential function tends to overestimate the low temperature isotherms of hydrogen in both materials.
On the contrary to equilibrium properties, the framework mobility proved to influence significantly the kinetics of hydrogen in both sorbents, and particularly in the ZIF-8, wherein molecules experience tighter fitting as they pass through its hexagonal windows, being in addition subject to the hindrance exerted to them by the linkers' methyl groups. The simulated self-diffusivities as a function of loading approach the QENS measured values, when the quantum mechanical correction according to Feynman and Hibbs is applied to all dispersion interactions involved in the host-guest system. Moreover, the quasi-free rotation of the gate-like ligand of the ZIF-8 results in diffusivities approaching further the experimental data.
Potential Impact:
Description of the Potential impact
During the project years a number of novel ideas concerning the efficient modeling of sorption thermodynamics (responsible for fluid storage and capture), and molecular dynamics (responsible for the delivery of the captured fluids), were generated and subsequently presented in international conferences and also published in journals of the first rank. In the following lines a description of the impact that the project brought by to the scientific field environmental and clean energy engineering is provided in detail.
1. Estimation of Partial Charges in Small Zeolite Imidazolate Frameworks from Density Functional Theory Calculations
Force-field-based calculations (Monte Carlo or molecular dynamics) rely on a reduced description of the system electronic density by means of atomic partial charges. In our study, we explored different approaches to derive them for zeolite imidazolate frameworks. The usual approach to compute partial charges for molecular systems is based on ab initio calculations on small clusters, followed by a fitting of the quantum chemical electrostatic potential. Among the many methods, we chose the Merz-Kollman sampling scheme, which has been shown to give reliable results; we also found that, for computing partial charges, density functional theory calculations yield values comparable to the ones obtained with Hartree-Fock and perturbative methods.
Partial charges computed for molecules give a fair description of the electronic density of the isolated system, which is considered to be slightly perturbed in the condensed phase; thus, values calculated for the isolated systems are transferred to liquid/solid simulation with a negligible loss of accuracy. This approximation does not hold for crystal systems such as ZIFs; in fact, every atom/molecule in the supramolecular structure feels the crystalline environment, which should be somehow included in the description. Thus, for example, computing partial charges on the cluster formed by one zinc atom coordinated by four methylimidazolium molecules would make sense if we were interested only in the zinc charge. On the other hand, if we need to know the charges on N, we should consider a symmetric structure around the molecule.
To this end, we have explored two different methodological approaches to compute partial charges on ZIF-8 from first principles calculations. The first approach has been based on the building up of isolated clusters resembling the structure and symmetry of the crystal. We have observed that, in order to obtain converged results, the size of the cluster should be around 400 to 500 atoms, which renders this approach extremely computationally expensive. The second method is based on evaluating the REPEAT charges on the periodic crystal structure. In order to define an operative protocol to compute partial charges on ZIF-8 (which would be extended to similar materials), we compared the results obtained with two different functionals and six pseudopotentials. We found that ultrasoft Vanderbilt pseudopotentials give larger errors compared to norm-conserving Troullier_Martins or Goedecker_Teter_Hutter pseudopotentials. The results obtained with both PBE and BLYP functionals are in fair agreement, hinting that the computed properties are well described with the two of them. The convergence of results has been checked against the value of the pseudopotentials' cutoff. In the case of plane wave calculations, the partial charges converge at 150 Ry for the wave function cutoff, while for amixed plane wave and Gaussian basis sets treatment, we found a density cutoff of 700 Ry to be the ideal choice. In passing, we notice that the values obtained for Zn and N are in agreement with those from recent studies on ZIFs and on systems of biological interest.
The values of REPEAT charges are also in agreement with those computed, at a much higher computational cost, on large isolated clusters. Given the reliability of the method, and considering its relatively low computational overhead, in the second part of the article, we looked into the fluctuations of charges, by propagating the system with DFT-based molecular dynamics simulations of the periodic structure. REPEAT charges have been computed for many configurations of three zeolite imidazolate frameworks, slightly differing among them in the structure and substituents: ZIF-8, ZIF-2, and ZIF-3.
or ZIF_8, both Car_Parrinello and Born_Oppenheimer molecular dynamics simulations show that the value obtained in single point calculations are in agreement with the average value during the time evolution of the system. The common feature to the three ZIFs studied is that the fluctuations in the charges of every atom are small. To our knowledge, this represents the first study of atomic partial charges where the fluctuations are taken into account; our results justify the choice of using the point charge approximation for these kinds of materials, given that the fluctuations are negligible. Nevertheless, if highly charged or polarizable absorbates interact with the framework, the inclusion of polarization could be important in the description of physical chemical properties of ZIFs.
2. Force Field for Molecular Dynamics Computations in Flexible Frameworks
In this section, a novel force field for molecular dynamics simulations of fully flexible ZIF-8 has been presented. The structure parameters computed with this force field (such as bond length and angle and window size) are in good agreement with experimental values. Besides, our force field reproduces correctly the thermal and pressure stability of ZIF-8 crystal structure. Reliable diffusivities of CO2 were obtained with our fully flexible force field and our charge model. These results have been compared to charge models available in the literature, explaining the discrepancies on the basis of point charge influence on the movement of guest CO2 molecules via control of the window size and of the sorbate free energy landscape. Subsequently, we studied the weight that various simulation details, regarding the system modeling, have on the self-diffusivity, isolating the importance of charges, framework shape and framework flexibility on the accuracy of the final diffusivity result. After these investigations, we conclude that the force field developed during AMCOS is suitable to study the dynamic properties of sorbed CO2 molecules within the flexible structure of ZIF-8. The diffusivity of other sorbates will be the subject of upcoming work, together with the characterization of the window opening mechanism and the application of coarse-graining techniques (cellular-automata) to the system dynamics. The portability of our force field to other ZIF structures (e.g. ZIF-3 and ZIF-90) will also be investigated in the next period.
3. Speeding up simulation of diffusion in zeolites by a parallel synchronous kinetic Monte Carlo algorithm
A parallel kinetic Monte Carlo algorithm, originating from the synchronous algorithm of Martinez et al., has been applied to the study of benzene diffusion in zeolite NaX. We have shown that, despite the presence of a rollback procedure in the algorithm, high efficiencies can be reached by exploiting the local nature of the molecule-molecule interactions inside the zeolite, allowing the need of rollbacks to be minimized through a proper spatial decomposition. In the present form the algorithm is still approximate, but the correct tuning of the domains size leads to obtaining results with the desired accuracy. We believe that the algorithm outlined here is applicable in general with little modification to other types of zeolites. Even better performances are expected to be found for other zeolites like the Linda Type A (LTA) family, ZSM5, or for zeolitic imidazolate frameworks (ZIF) because of the absence of shared sites between communicating cages. Adsorbate-adsorbate interactions does not extend significantly outside the cages, thus permitting an ideal domain decomposition. As for other similar methods, the efficiency of the algorithm is very sensitive to the value of the communication/calculation ratio that can be easily controlled by changing the size or the shape of the domains.
4. A parallelizable block cellular automaton for the study of diffusion of binary mixtures containing CO2 in microporous materials
We tested our cellular automaton method in the case of binary mixtures diffusing in zeolite ZK4 and compared the results with MD data, showing its ability to cope with more than one diffusing species giving good qualitative agreement with this well established and fully microscopically detailed technique. We stress that these results are based on heuristically determined parameters aiming mainly to explore the range of possibilities of the method and, nonetheless, in the case of non-trivial behaviour such as the segregation-effect, we found that the CA gives a better agreement with MD than the robust and successful MS method used by Krishna and coworkers.
It would be obviously desirable to have a rigorous algorithm for defining the right input parameters for the automaton, extracting them from atomistic simulation. But even at this stage our tests demonstrate that the model is able to display a range of interesting behaviours and to capture on a coarse-grained level the basic mechanisms of diffusion in zeolites. Validation via comparison with other theoretical approaches is important as this justifies a further effort intended to exploit the intrinsic parallel nature of CAs for a drastic extension of the space and time scales usually accessible to the available simulation techniques for diffusion in zeolites. Using parameters obtained from MD and MC studies as an input, our BCA model is a promising tool for a future investigation of zeolite and Zeolitic Imidazolate Frameworks (ZIFs) membranes and whole microcrystal, both in and out of equilibrium.
5. The central cell model: A mesoscopic hopping model for the study of the displacement autocorrelation function
In this work, we laid down the basis of a simple computational framework, the CCM, aimed to be specific for the study of the motion on the mesoscopic scale of a single particle in a system of connected cavities in the presence of other diffusants, in conditions of thermodynamic equilibrium. Our model is local and discrete in both space and time, and in the numerical applications we have shown here it has been constructed starting from the algorithm of a lattice-gas model for diffusion in microporous material.
We have shown that, although being not possible for the CCM to sample all the information obtainable by a full lattice-gas, a CCM simulation provides an accurate reproduction of the memory effects in the self-diffusion (and thus, of the diffusion isotherm) at a minimum computational cost. The way the CCM is constructed suggested how to carry on a mean-field study of the self-diffusion process produced by the particular evolution rule adopted.
This has led to two approximated mathematical expressions for self-diffusion. The first one, more general, can be applied with data coming straight from the CCM simulation. The second one, more case-specific and derived by assuming fast local equilibration, is theoretical and yields a more accurate approximation the weaker the correlations and the lower the loadings are. Interpretation of the discrepancies between the self-diffusivity trends obtained from the numerical simulations and their two different mean-field approximations helped to understand how, and how strongly, memory effects can emerge depending on the very general features of the model parametrization.
The obtained results suggest the CCM approach to be suitable for other theoretical studies, e.g. the time correlations in the local density, as well as for direct applications in the field of the molecular coarse graining. For example, the CCM approach could be further extended to the sampling of both the adsorption and the self-diffusion isotherm through a single simulation when the lattice-gas rule includes an explicit cell-to-cell interaction potential which makes (in principle) impossible do derive the equilibrium probability distribution of states a priori. This could be done by performing a grand-canonical Monte Carlo on the border cells while keeping the core evolving with the prescribed dynamic lattice-gas rule in the canonical ensemble. Also, an even more intriguing extension of the CCM approach could be made in the field of hybrid MC-MD schemes aimed to realistically mimic the bulk effects in the motion of a tagged guest in an atomistic simulation.
6. Development and Optimization of a New Force Field for Flexible Aluminosilicates, Enabling Fast Molecular Dynamics Simulations on Parallel Architectures
In this work, a new force field has been developed enabling fast molecular dynamics simulations in flexible aluminosilicates and, thus, extending the time and space scales accessible to classical MD simulations. The structures here investigated are silicalite, Na A, Ca A, Na Y, and Na X, chosen to ensure a good degree of force field portability, allowing an extension to affine structures with minimal effort. We adopted a CHARMM-type functional form which allows, using the NAMD package, the simulation of a 1 ns trajectory per wall clock hour in systems consisting of about 4000 atoms, running over 16 cores of small Beowulf clusters. The new force field has been optimized by carefully tuning the simulated structures and IR spectra to experimental data. The resulting parametrization allows correct modeling of the system dynamics, without introduction of spurious deformations. Moreover, the structural stability of model Na A over a wide range of temperatures and pressures has been successfully tested.
This work is a starting point for future studies of sorbed molecules in zeolites, especially for the development of more reliable coarse-grained models which will further expand the accessible time and space simulation scales.
7. Atomistic Simulation Studies on the Dynamics and Thermodynamics of Non Polar Molecules within the Zeolite Imidazolate Frameworks
We have accomplished and reported statistical mechanics based modeling of the sorption thermodynamics and dynamics of selected non polar molecules in the ZIF-8. Our aim was firstly to investigate the evolution of the sorption equilibrium in this material, over a wide range of occupancies for Ar, CH4 and H2 up to saturation, and secondly to elucidate the mechanism of molecular motion under the complicated force field exerted by the zinc atoms and the 2-methyl-imidazolate groups which form the void space of the organic zeolite analogue framework under study. For this purpose we digitally reconstructed the ZIF-8 unit cell and then examined the applicability of generic force fields found in literature for the description of atomic-level interactions between sorbate molecules and framework atoms.
We opted for DREIDING force field after comparing the simulation predictions for the sorbates studied in this work, with measured isotherms under the same conditions found elsewhere.
The partial molar configurational internal energy was calculated for Ar, CH4 and H2 as a function of their loading in the metal-organic framework at 87, 240 and 77 K respectively, via grand canonical Monte Carlo. Because the computed quantity is related to the covariance of the potential energy and number of particles at a certain loading and temperature, it can map the strength of sorbate-sorbate and sorbate-sorbent interactions over the full sorbate loading range; the results showed a higher perception of energetic inhomogeneity of argon in comparison with methane and hydrogen. One- and two-point probability density functions calculated by post-processing the equilibrated configurations produced from Monte Carlo, provided a further insight into the distribution of adsorption centres inside the ZIF-8 framework. Moreover, interpretation of these results on the basis of free energy distribution offered a plausible explanation of the mobility of the sorbed phase as a function of its chemical potential inside the metal-organic framework.
Although for hydrogen and argon the agreement between simulated and measured isotherms is satisfactory, the freezing of the degrees of freedom of the organic links in our model, may cause the sitting transition step of the predicted isotherm of argon to appear earlier than the one observed experimentally. It was also showed that such inflections during the sorption and kinetics procedure involve crossing of free energy barriers located at positions near the six-ring window faces; therefore, the bonding flexibility at these areas may influence these barriers and hence the dynamics of guest molecules even at low temperatures. The inflexibility of the model ZIF-8 unit cell can also be responsible for the over-prediction of the sorption thermodynamics of the bulkier molecule of methane, with respect to measured values found elsewhere.
The molecular mobility of Ar at 87 K and H2 at 77 K inside the metal-organic sorbemt was estimated by virtue of equilibrium molecular dynamics in the canonical ensemble. Although the self-diffusivity of argon at 87 K is too low to be of any practical importance, we observed its displacement over a broad range of occupancies, in conjunction with the preceding thermodynamics findings, in order to understand the kinetic behaviour of the sorbed phase with respect to the calculated spatial partitioning of the sorbate probability density inside this new class of materials.
In view of the quantum nature of hydrogen at 77 K, we employed the path integral formulation for the quantum mechanical description of the intermolecular interactions which leads to the quadratic Taylor expanded pairwise potential function, as follows from the work of Feynman and Hibbs. Their work states that paths located at a certain state point in the configuration space are enveloped inside a Gaussian width; for low temperatures and atomic masses, the distribution around this position becomes widespread, hence a classical description is not adequate any more. The self-diffusivity of hydrogen in the ZIF-8 at 77 K as revealed by our molecular dynamics simulations, showed a marked difference between the values obtained from the classical and quantum mechanical description of the energetics. The predicted self-diffusivity presents a shallow maximum as a function of occupancy due to the loading dependent free energy barrier which separates the adsorption sites located close to the hexagonal windows, and around the cavity centre of the ZIF-8 unit cell.
At this point we should stress that the rigidity of the model ZIF-8 framework should put one under serious consideration when simulation is carried out at high temperatures, or/and guests whose size is commensurate with the effective size of critical paths for diffusion in the framework, are involved. These issues are mainly associated with the rotation of the pendant alkyl or other groups of the imidazolate-type link as well as with possible torsional motions of the organic links themselves, which become much pronounced with rising temperature. As a consequence, these phenomena may affect the dynamics of guest molecules inside the pore matrix, leading to unrealistic transport coefficients.
8. Analysis of the impact of sorbent mobility on the sorbed phase equilibria and dynamics: A study of methane and Carbon Dioxide within Imidazolate Frameworks
The scope of this part of the project is to contribute for first time in levelling the role of atomic framework flexibility, or rigidity, on the thermodynamics and transport properties of the sorbed phase in the rapidly growing class of porous coordination polymers, the imidazolate frameworks. In the absence of strict quantum mechanical descriptions toward an ad hoc parameterization of the particular ZIF, we properly adapt methodologies relying on statistical mechanics via a generic force field, giving no consideration to adjust parameter values of the potential functions with respect to the experimentally measured mass transport quantities of the present work, neither in the isochoric nor in the isobaric molecular dynamics; for the latter simulation option only, we adjusted the ZIF-8 inter-atomic distances in the lattice to their crystallographic values in an attempt to preserve the unit cell volume.
The effect of the mobility of the imidazolate ligands acting as 'saloon doors' which surround the critical for transport hexagonal windows, along with the charge distribution on the ZIF-8 atoms, proves to be of key importance for the guest dynamics. The results show successful qualitative agreement between the experiments and simulations for both equilibrium and nonequilibrium transport coefficients of methane and carbon dioxide, obtained by Pulsed-Field Gradient NMR, Infrared Microscopy, and Molecular Dynamics combined by an interactive Widom averaging procedure for the computation of the sorbed phase equilibria. Moreover, the calculated singlet probability density distribution at the vicinity of the windows intervening in the cage-to-cage paths, provides an explanation of the diffusivity trend of the two sorbate guests as revealed by both the IRM experiments and MD modeling.
9. Probing the hydrogen equilibrium and kinetics in Imidazolate Frameworks via Molecular Dynamics and Quasi-elastic Neutron Scattering Experiments
The work presented at the final stage of AMCOS is concerned with the kinetic behaviour of hydrogen and deuterium, acting as sorbate molecules, within two crystalline metal-organic structures, known as zeolitic imidazolate frameworks, the ZIF-3 and ZIF-8; the materials belong to the tetragonal and cubic crystal systems respectively and they also grow into different pore networks. Two kinds of experiments, quasi-elastic neutron scattering and molecular dynamics computer simulation, were conducted in parallel in order to track the motion of the sorbate molecules. Both QENS and MD have the advantage of capturing analogous length and time scales of the diffusing hydrogen molecules in the host materials being able to provide comparable self-diffusion coefficients.
In the current work, this simultaneous study is of particular usefulness because for first time such a comparison is performed in ZIFs' members, and also because the QENS experimental technique, apart from its individual importance in probing the sorbate motion, it does contribute as a benchmark to the validation and further development of our modeling work.
The sorption thermodynamics computations were carried out by means of molecular dynamics experiments so that the imidazolate framework flexibility to be efficiently captured and the equilibrium pressure of the sorbed phase to be rigorously calculated following a phase space averaging procedure. Subsequently, the use of various modeling options indicates that the flexibility of the host matrix is of little importance, and also, omitting the quantum mechanical contribution in the potential function tends to overestimate the low temperature isotherms of hydrogen in both materials.
On the contrary to equilibrium properties, the framework mobility proved to influence significantly the kinetics of hydrogen in both sorbents, and particularly in the ZIF-8, wherein molecules experience tighter fitting as they pass through its hexagonal windows, being in addition subject to the hindrance exerted to them by the linkers' methyl groups. The simulated self-diffusivities as a function of loading approach the QENS measured values, when the quantum mechanical correction according to Feynman and Hibbs is applied to all dispersion interactions involved in the host-guest system. Moreover, the quasi-free rotation of the gate-like ligand of the ZIF-8 results in diffusivities approaching further the experimental data.
The calculated elements of the hydrogen diffusion tensor within the ZIF-3 in the form of mean squared displacements along the principal directions of the unit cell, are in agreement with the results from the singlet probability computations along the three pore channels of the material, thus explaining the variation of the diffusivity as a function of the hydrogen concentration.
Our analysis about the tensor concentration dependence presented above, is based on the density, and hence free energy, evolution, of the guest sorbed phase in the anisotropic interior of ZIF-3. On the absence of experimental data from specialized techniques able to probe the spatial variation of mass transport, such as the Interference Microscopy, only simulation can provide such information. Furthermore, phenomena that may be related to the structural topology of the material which are likely to affect the resistance to mass transport at various directions within the host matrix, as can be found for instance in some zeolite crystals, do deserve attention.
Dissemination activities:
Peered review articles
- E.Pantatosaki G.Megariotis A.Pusch C. Chmelik, F. Stallmach, G. K. Papadopoulos, J. Phys. Chem. C (2012), 116, 201207.
- St. Schlayer , A.-K. Pusch, F.e Pielenz, St. Beckert, M. Peksa, C. Horch , L. Moschkowitz, W.-D.h Einicke, F. Stallmach: X-Nuclei NMR Self-Diffusion Studies in Mesoporous Silica Foam and Microporous MOF CuBTC, Materials 2012, 5, 617-633.
- A.-K. Pusch, T. Splith, L. Moschkowitz, S. Karmakar, R. Biniwale, M. Sant, G. B. Suffritti, P. Demontis, J. Cravillon, E Pantatosaki, F. Stallmach: NMR studies of carbon dioxide and methane self-diffusion in ZIF-8 at elevated gas pressures, Adsorption (submitted May 2012, manuscript no. ADSO-S-12-00169).
- E. Pantatosaki, G. Megariotis, A.-K. Pusch, C. Chmelik, F. Stallmach, G. K. Papadopoulos J. Phys. Chem. C 116, 201 (2012).
- Federico Giovanni Pazzona, Giuseppe Baldovino Suffritti, and Pierfranco Demontis, Journal of Chemical Theory and Computation, 2011, 7, 15751582.
- F. G. Pazzona,a) A. Gabrieli, A. M. Pintus, P. Demontis, and G. B. Suffritti, J. Chem. Phys. 134, 184109 (2011).
- Federico G. Pazzona,a) Pierfranco Demontis, and Giuseppe B. Suffritti, J. Chem. Phys. 137, 154106 (2012).
- Andrea Gabrieli, Marco Sant, Pierfranco Demontis, and Giuseppe B. Suffritti, J. Phys. Chem. C , in press.
- Andrea Gabrieli, Pierfranco Demontis,* Federico G. Pazzona, and Giuseppe B. Suffritti, Physical Review E 83, 056705 (2011).
- Alberto M. Pintus, Federico G. Pazzona, Pierfranco Demontis,a) and Giuseppe B. Suffritti, J. Chem. Phys. 135, 124110 (2011).
- Federico G. Pazzona,* Pierfranco Demontis, and Giuseppe B. Suffritti, J. Phys. Chem. C 2013, 117, 349-357.
- Bin Zheng, Marco Sant,* Pierfranco Demontis, and Giuseppe B. Suffritti, J. Phys. Chem. C 2012, 116, 933938.
Oral and Poster presentations
- A.-K. Pusch: 13C NMR Studies of Carbon Dioxide Diffusion in MOF CuBTC (talk), 11th Dutch-German IRTG workshop 'Diffusion in porous materials', Eibenstock, 23rd March 2010.
- F, Stallmach, St, Beckert, St, Hertel, C, Horch, A,-K, Pusch, M., Wehring: NMR Studies of the Mobility of Carbon Dioxide and Hydrocarbons in Nanoporous Coordination Polymers (poster P33), 10th Bologna Conference on Magnetic Resonance in Porous Media (MRPM 10), 12th to 16th September 2010 Leipzig, Germany (see http://www.mrpm.org/originalsites/MRPM10/book_of_abstracts.pdf(opens in new window) p. 87).
C. Horch, A.-K. Pusch, P. A. J. Donkers, F. Stallmach:: Low-Field High-Pressure NMR Porosimetry (poster P41), 10th Bologna Conference on Magnetic Resonance in Porous Media (MRPM 10), 12th to 16th September 2010 Leipzig, Germany (see http://www.mrpm.org/originalsites/MRPM10/book_of_abstracts.pdf(opens in new window) p. 93).
- F. Stallmach: (invited talk), NMR studies of host-guest interaction in porous materials, Nagpur, India, November 2010.
- A.-K. Pusch, C. Horch, F. Stallmach: NMR studies of diffusion and adsorption in the Metal Organic Framework CuBTC (poster), EU-India Workshop on Environmental materials, Nagpur, Indis, November 2010.
- A.-K. Pusch, S. Schlayer,F. Stallmach: 1 3C NMR diffusion studies with CO2 adsorbed at MOF CuBTC (poster), 23. Deutsche Zeolithtagung, Erlangen, Germany, 02-04 March 2011.
- A.-K. Pusch, S. Schlayer, F. Stallmach: 13C NMR Diffusion studies with CO2 adsorbed in Advanced Materials, (talk) 13th Dutch-German IRTG workshop 'Diffusion in porous materials', Leipzig, O4th April 2011.
- F. Stallmach: Transport and storage of gases, liquids and electrolytes in porous media studied by NMR (invited talk), BASF SE, Ludwigshafen, Germany, 23 March 2012.
- A.-K. Pusch, S. Schlayer, T. Splith, R. Biniwale, G. Papadopoulos, F. Stallmach: NMR studies of carbon dioxide and methane selfdiffusion in ZIF-8 at elevated pressures (talk), 6th Pacific Basin conference on Adsorption Science and Technology (PBAST-6), Taipei, Taiwan, 20-23 May, 2012.
- G. K. Papadopoulos: (invited talk), Computer Modeling of host-guest interaction in porous media, Nagpur, India, November 2010.
- G. K. Papadopoulos: (invited talk), Multiscaling Simulations of Diffusion Processes in MOFs, Leipzig 2011.
Project website: http://comse.chemeng.ntua.gr/amcos/(opens in new window)
Project Context and Objectives
The overall concept of the AMCOS project was the study of the prospect of newly synthesized materials by the Indian institutions to be used as capturers of carbon dioxide and methane. The means towards this task are various computer experiments, namely, first principles ab initio calculations, and classical statistical mechanics based molecular simulations, such as Molecular Dynamics and Monte Carlo, as well as conventional ad hoc designed experiments so that to be directly comparable to the mentioned above molecular simulation computer experiments. Moreover, in addition to the tasks of the AMCOS project, though within its context, taking advantage of the experimental techniques developed during the entire period, the dynamics of hydrogen as a sorbate molecule in these materials was also investigated.
Over the past decade a branch of organic synthesis following a reticular process, gave a vast rise to oriented design and production of new materials characterised by exceptional physicochemical properties. This strategy of synthesis engineering towards target structures, created a novel class of advanced sorbents such as the zeolitic imidazolate frameworks (ZIF), characterized by large pore sizes, high apparent surface areas and a chemically active interior.
In addition, selective modification of polymeric matrices has led to the so-called functionalized polymers (FP) which exhibit improved performance futures, for instance, the enhanced ability for adsorbing specific group of molecules. Also, functionalization processes of porous silicas by aminopolymers of low molecular weight, have developed a new category of inorganic-organic hybrid sorbents, the hyperbranched aminosilicas (HAS).
Objective of the AMCOS EU-India collaborative research project was to investigate the capability of newly synthesized or/and modified classes of the aforementioned advanced materials, for use in environmental applications such as the selective separations of carbon dioxide in flue gases and natural gas. For this purpose, the sorbate molecular dynamics and thermodynamics will be studied extensively by applying, developing and integrating state-of-the-art computational tools and experimental methodologies.
The task of NTUA under AMCOS was the statistical mechanics based modeling of the sorption thermodynamics and kinetics of various molecules in recently synthesized ZIF structures in order to investigate the evolution of the sorption equilibrium over a wide range of occupancies of carbon dioxide, and to elucidate its rate and mechanism of motion in the pores of these materials. During the current reporting period NTUA examined the ZIF-3 and ZIF-8 as representative members of the series of ZIF structures.
The simulation predictions would be then compared with the measurements of the IRCE-LYON group which is responsible for measuring the guests' mobility via Quasi-elastic Neutron Scattering experiments (QENS). Simulation and QENS, both being microscopic techniques, can provide valuable information on the sorbate molecular dynamics in the ZIFs.
UNISS has developed an easy procedural protocol to derive partial charges on ZIFs from DFT-based quantum chemical calculations. The chosen structure to test was also ZIF-3 and ZIF-8, both widely studied through physical experiments. To obtain more reliable charges, several DFT calculations on a periodic ZIF-8 were carried and crosschecked one with each other and with cluster-based DFT calculations on ZIF-8 fragments of increasing size. In quantum chemical calculations for non-periodic system GAUSSIAN, TURBOMOLE were used, whereas CPMD and cp2k packages were used for periodic systems. Both the periodic ZIF-8 lattice and its various fragments have been digitally reconstructed from the X-ray crystal data collected from the Cambridge Crystallographic Data Centre (CCDC) (see http://www.ccdc.cam.ac.uk(opens in new window) online). For periodic DFT calculations, the fitting of the quantum chemical electrostatic potential to atomic site charges is performed with the REPEAT (Repeating Electrostatic Potential Extracted Atomic) method, whereas the CHELPG and MK scheme were used for DFT calculations on fragments.
The task of LU was to provide experimental data on diffusion of adsorbate molecules in the advanced adsorbent materials. These experimental data are required to validate the corresponding computational studies of the Indian and European AMCOS partners. The adsorbent materials considered during the report period are the MOF CuBTC as test material and crystalline ZIFs. The nanoporous amorphous HAS and polymer based adsorbents were not yet been synthesized by the Indian project partners. Due to the main target of the project, which is the exploration of these materials for their suitability for CO2 separation from gas mixtures, the focus in the first report period was to study single component diffusion of carbon dioxide and alkanes (methane, ethane) in selected materials. For the purpose of the CO2 diffusion studies, the 13C pulsed field gradient (PFG) NMR technique needed to be developed which included NMR probe design and development of measurement protocols.
Simultaneously to our efforts to improve and establish 13C PFG NMR diffusion studies with absorbed carbon dioxide in MOF's and ZIFs LU possesses the opportunity to measure transient concentration profiles during uptake and desorption of guest molecules in adsorbent particles by infrared (IR) microscopy. During the report period, such diffusion measurements were successfully carried out with ZIF-8 as adsorbent and carbon dioxide and methane as well as with mixtures of both molecules as adsorbate gases.
Computer modeling and screening were performed on materials synthesized by the Indian consortium. In particular the EU consortium worked on selected materials from the Zeolitic Imidazolate Framework homologue series and from Functionalized Polymers. The basic axis of the employed methods for the analysis of the efficiency of the provided materials in capturing the guest sorbates is the computational modeling utilizing Quantum mechanical calculations and also statistical mechanics based mesoscopic and atomistic simulations of the sorption processes.
Nevertheless, the phenomena pertaining to sorption in a real process is much more complicated as adsorption on the surfaces, penetration in the interior of the materials (diffusion) along with inter-crystalline transport occurring fast or infrequently depending on the energetics of the system sorbent material / guest sorbate. That led us to develop not only methodology toward the study of the thermodynamical phase equilibrium, but also study of the kinetics of the guest system within the host material as well.
The novelty of the materials of the project and consequently the complete lack of a force field (FF) imposed a strategy in two directions towards a) creating of reasonable FFs on a Quantum Mechanical basis, and b) adopting sophisticated 'expensive' experiments measuring the aforementioned kinetic and dynamics information under comparable time and length scales, so that one to be able to compare the results obtained from the computer simulation experiments.
The principle sorbate of the work during the entire period was the Carbon Dioxide (CO2), and the central objective was the investigation of the aforementioned sorbents' performance in capturing the CO2 molecule, and also, by modeling the physicochemical processes involved for this, to explain and predict the impact of the materials' structure on the CO2 storage efficiency. In addition to this, it proved imperative the inclusion of Methane (CH4) and Hydrogen (H2) in the original target sorbates as well.
Work Performed
ZIF-8 and ZIF-3 crystals were modelled using rigid, and at the end of the project, flexible force fields. The rigid model keeps the crystal atoms fixed at their positions, identified by XRD data. Therefore, structural characteristics remain unaltered throughout the simulations. The crystal atoms interact with sorbates through both long and short range forces. We tested both the Dreiding and the Universal Force-Field (UFF) dispersion interactions parameters. Two flexible models were tested for ZIF-8 and ZIF-3. The crystal atoms are allowed to move in molecular dynamics simulations of bare frameworks. Both flexible models include bond stretches, angle bends, inversions (improper torsions), dispersion and electrostatic interactions. The Dreiding and Nilsson parameterizations were used.
For the electrostatic interactions, the same charges were used as in the rigid model. It must be also noted that the quantum mechanical calculations have given the modeling a new input for the Molecular Dynamics simulations applied to the flexible models of the metallorganic frameworks of the project. The temperature was chosen to be 258 K, according to the XRD experimental data found elsewhere. Bond lengths, angle bend, improper and proper torsion angle values were computed as statistical averages throughout the runs of 100 ns.
The obtained results showed excellent agreement with experimental values. Simulations were also carried out at a lower temperature to investigate the effect of temperature on the structural conformations for both ZIF-3.and ZIF-8 structures. After the first successful 13C and 1H PFG NMR diffusion studies of the adsorbed CO2 and CH4 in the nanoporous MOF CuBTC, which were performed in order to check the developed pulse field gradient NMR probe, it was the next task to perform these NMR diffusion measurements on the Zeolitic Imidazolate Framework ZIF-8.
The previous NMR investigations were performed at gas phase pressures below 1 bar. They showed that the adsorbed amount of CO2 and CH4 in ZIF-8 is substantially smaller than in CuBTC which rendered NMR diffusion studies impossible [1]. Therefore, it was decided to explore the possibilities to perform NMR diffusion studies at elevated gas pressures. The target of 10 bar for these measurements was discussed among the AMCOS project partners. LU extend the experimental equipment for the NMR studies accordingly enabling NMR measurements at up to 15 bar. Methane and Carbon Dioxide NMR measurements have been accomplished in ZIF-8 using this new high-pressure NMR set up.
The NMR data for the relaxation times showed that the gases are in the adsorbed state. The obtained self-diffusion coefficients are in the same order of magnitude than previously published data of IR microscopy but point towards a different loading dependence. Especially for the carbon dioxide in ZIF-8, a good agreement between the NMR experimental results and results of MD simulation provided by UNISS and NTUA were found. This points towards a successful approach and development of the computational tools developed within AMCOS. PFG NMR studies of CH4 / CO2 self-diffusion in mixtures were also performed, and show that there seems to be only a minor effect on the mobility of one species in the presence of the other species. Comparisons are now being made between the experimental and computational methods on these adsorbed binary mixture.
In situ quasi-elastic neutron scattering (QENS) experiments were performed at the Institut Laue-Langevin, in Grenoble, France, on H2, CH4 and CO2 in the two samples provided by NEERI : ZIF-8 and ZIF-3, where the linkers were deuterated. From the variation of the broadening as a function of wavevector transfer, diffusion coefficients could be derived at three different H2 concentrations. Although the quality of the spectra recorded for CO2 was not optimal, diffusivities could be extracted at 200 K, at four different loadings. The statistics obtained for CH4 were better because of the larger incoherent cross section of this molecule. Comparisons are now being made between the different methods.
Results
Statistical mechanics based simulation studies at the atomistic level of Ar, CH4, D2 and H2 sorbed in the ZIF-8 and ZIF-3 were accomplished. So far we have explored the mechanisms that govern the sorption thermodynamics and kinetics of non polar sorbates possessing different sizes and strength of interactions with the metal-organic framework, in order to understand the outstanding properties of this novel class of sorbents, as revealed by experiments published elsewhere. For this purpose we developed in-house modeling procedures involving calculations of sorption isotherms, partial internal energies, chemical potential in the fully flexible host structure various probability density functions and molecular dynamics, for the modeling of sorbed phase over a wide range of occupancies inside a digitally reconstructed unit cell of ZIF-8. The results showed a marked energetic inhomogeneity perceived by the sorbates as a consequence of the 2-methylimidazolate links in the atomic framework of the metal-organic material under study, resulting in free energy barriers which give rise to inflections in the isotherms and guide the dynamics of guest molecules.
Single component CO2 NMR studies were performed with Imidazole Functionalized Polystyrene (Im-PS) obtained from ICT Mumbai. 13C NMR spectroscopy confirmed that the CO2 is rather strongly interacting with the imidazole functional group in this polymer. In agreement with this spectroscopic characterization, 13C PFG NMR diffusion measurements at elevated gas pressure of 10 bar showed that in the adsorbed carbon dioxide has short transverse relaxation times rendering intraparticle self-diffusion studies in these f-PS samples impossible. The NMR diffusion studies yield only the long-range mobility between individual adsorbent particles via the gas phase.
During the second period of the project is presented a detailed picture of the distribution of charge density across functionalized and non-functionalized frameworks via determination of electrical dipole moment separately at metal and ligand sites. The values of dipole moments were calculated from the analysis of maximally localized Wannier function and ion centres, and from corresponding charges. Based on our dipole moment analysis we rationalized the sorption of CO2 in these materials by combined Monte Carlo simulations. The adsorption thermodynamics and the uptakes of CO2 at the low pressure range depend on the strength of solid-gas interaction, increasing in accordance to the trend of the dipole moment, in the order ZIF-3 > ZIF-2 > ZIF-8. Moreover, the location and magnitude of the dipole moment vectors across the framework are important for identifying correctly the preferred adsorption site for CO2 near the frameworks. Some other properties of these materials like mechanical and chemical stability can also be addressed through the knowledge of these dipole moments calculations.
Impact of the Results
Through the computational work it was revealed the influence of the mobility of the sorbent framework on both the equilibrium and kinetic properties of the sorbed phase by means of Molecular Dynamics computer experiments, under both isochoric- isothermal and isobaric-isothermal statistical ensembles, for several host model options, combined by Widom averaging along the entire trajectory of the host-guest system toward rigorously obtained sorbate isotherms within a fully flexible lattice. This novel methodology was adapted to the study of the Self-diffusivity and the collective (Maxwell-Stefan and Transport) diffusivities of Carbon Dioxide and Methane within the Zeolite Imidazolate Framework-8. The simulation predictions are compared with measurements from Pulsed-Field Gradient Nuclear Magnetic Resonance (PFG NMR), as well as with recently conducted Infrared Microscopy (IRM) experiments elaborated on the basis of the current modeling in the flexible ZIF-8. The modeling results predict a significant influence on the sorbate transport, exerted by the 2-methilimidazolate ligands surrounding the cage-to-cage entrances, whose apertures are commensurate with the guest molecular dimensions. Moreover, calculations of the singlet probability density distribution of the sorbate molecules at selected regions within the imidazolate framework provide a plausible explanation of the transport diffusivity as a function of sorbate occupancy, measured via IRM.
Project Context and Objectives:
Project context and main objectives: A summary description
The overall concept of the AMCOS project is the study of the prospect of newly synthesized materials by the Indian institutions to be used as capturers of carbon dioxide and methane. The means towards this task are various computer experiments, namely, first principles ab initio calculations, and classical statistical mechanics based molecular simulations, such as Molecular Dynamics and Monte Carlo, as well as conventional ad hoc designed experiments so that to be directly comparable to the mentioned above molecular simulation computer experiments. Moreover, in addition to the tasks of the AMCOS project, though within its context, taking advantage of the experimental techniques developed during the entire period, the dynamics of hydrogen as a sorbate molecule in these materials was also investigated.
The computer modeling is utilized mainly for the study of the CO2-sorbent interactions along with the mobility of a wider class of guest molecules in the various host systems pertaining to the advanced materials considered in the Technical Annex, such as the zeolitic imidazolate frameworks (ZIFs) and the functionalized polymers; the hyperbranched aminosilica (HAS) were not eventually considered even in the final part of the project because their synthesis by the Indian groups proved to be problematic. The focus of the project is the selective separation and finally the storage of CO2 and secondary CH4 from unary or binary mixtures towards environmental and energy resource related applications.
Complimentary to modeling, highly sophisticated experimental techniques (e.g. quasi-elastic neutron scattering (QENS) and pulsed field gradient nuclear magnetic resonance (PFG NMR)), are designed in order to measure the thermodynamics and molecular mobility of the sorbed phase. Moreover, these experiments serve as a precious validation tool for the computer modeling output.
Project Results:
Description of the main S & T results and foregrounds
At the current final stage of the report, the majority of the scientific and technological results are already published in journals edited by the most prestigious and large scientific societies, like the American Chemical Society (ACS), the American Physical Society (APS) and the American Institute of Physics (AIP). The DOI codes of the publications have been uploaded in the publication field of the SESAM webpage.
In this section, the most important results concerning the modeling and also the experimental findings as well as the foreground of the work as emerged from the combined computational study and the conjugate measured quantities, will be summarized.
1) Factors influencing the CO2 storage capacity in Metalorganic Frameworks
Over the past decade organic synthesis gave a vast rise to oriented design and production of new classes of metal-organic crystalline materials based on framework types which resemble zeolites. This strategy of synthesis engineering1 towards target structures created materials such as the metal-organic frameworks (MOFs), which mainly because of their high uptake capacities to hydrogen, methane and carbon dioxide have become one of the most popular class of porous materials. Although their thermal stability, a key characteristic for a technologically important sorbent, can be considered moderate compared to zeolites, the reticulated process of their synthesis makes them superior compared to the conventional aluminosilicate crystals. The resulted this way organic zeolite analogues, are characterized by large pore sizes, high apparent surface areas and a chemically active interior, which provide them with exceptional properties as sorbents being capable of hosting large amounts of sorbate molecules of a broad span of sizes. The great success of these crystalline solids as molecular binders is due to processes which involve appropriate linking of selected molecular blocks together, by building them on geometrically well defined morphologies. Moreover, the high availability of these compounds for further chemical modification of their linking units can lead to the creation of a whole series of homologues possessing various pore widths.
Another recent advance in the aforementioned reticulation strategy is the synthesis of a subcategory of MOFs, termed as zeolitic imidazolate frameworks (ZIFs), wherein transition metals replace T-atoms and imidazolate or imidazolate-type links replace oxygen bridges in the conventional aluminosilicate structures. Systematic chemical modification of their substituents has also created a series of homologous ZIF structures characterized by high chemical and thermal stability, based on framework types of either known zeolite topologies such as sodalite, RHO, MER or even predicted structures.
Scientists from the field of theory and simulation have given insight into molecular dynamics of the sorbed phase in a variety of MOF and COF structures. On the contrary, despite the source of papers reporting experimentally measured high uptake capacities regarding either hydrogen, or the greenhouse gases methane and carbon dioxide in several zeolitic imidazolate structures, fewer works have dealt with modeling in ZIFs so far.
Our computer simulation methodology relies upon classical physics with interparticle interactions being calculated through potential functions such as the Lennard-Jones potential. For hydrogen we employed the quantum mechanical potential function of Feynman-Hibbs for all interactions of the guest-host system. At this point we should notice that a good force field must be capable of capturing the essential physicochemical properties of a system, but it rarely yields accurate results with respect to real experiments; this is especially true for metal-organic materials due to complexity of their atomic framework. Full-scale ab initio quantum mechanical calculations on a certain material can serve as a reasonable basis towards more sophisticated potential functions; development of such a force field is well beyond the scope of this article since we study small non polar molecules and polarizability effects can be neglected. In this study we employed the two generic force fields mentioned above, which have been used successfully in the MOFs and isoreticular MOFs (IRMOFs) modeling No adjustment of potential parameters with respect to sorption experiments in order to match the measured points have been made in this work.
1.1 Modeling of the CO2 storage in ZIFs
1.1.1 Pilot study
At the first period of the project we started the sorption equilibria experiments prior to carbon dioxide for argon, methane and hydrogen, in the ZIF-8, as a pilot study, by means of Grand Canonical Monte Carlo (GCMC) stochastic simulations using the Metropolis algorithm for the importance sampling of the configuration space.
1.1.2 Actual modeling of Carbon Dioxide (and Methane)
This part of the work aimed at exploring the influence of the mobility of the sorbent framework on both the equilibrium and kinetic properties of the sorbed phase by means of Molecular Dynamics (MD) computer experiments under isochoric- isothermal and isobaric-isothermal statistical ensembles for several host model options, combined by Widom averaging along the entire trajectory of the host-guest system toward rigorously obtained sorbate isotherms within a fully flexible lattice. The methodology is adapted to the study of the Self-diffusivity and the collective (Maxwell-Stefan and Transport) diffusivities of Carbon Dioxide (CO2) and Methane (CH4) within the Zeolite Imidazolate Framework-8 (ZIF-8). The simulation predictions are compared with measurements from Pulsed-Field Gradient Nuclear Magnetic Resonance (PFG NMR), as well as with recently conducted Infrared Microscopy (IRM) experiments elaborated on the basis of the current modeling in the flexible ZIF-8. The modeling results reveal a significant influence on sorbate transport exerted by the 2-methilimidazolate ligands surrounding the cage-to-cage entrances, whose apertures are commensurate with the guest molecular dimensions. Moreover, calculations of the singlet probability density distribution of the sorbate molecules at selected regions within the imidazolate framework provide a plausible explanation of the transport diffusivity as a function of sorbate occupancy, measured via IRM.
The actual study aimed at exploring the influence of the structural dynamics of ZIFs, having pores of width commensurate with the guests' size, on both the equilibrium and mobility properties of sorbates by means of Molecular Dynamics, thus, avoiding dependence on stochastic methodologies toward sorbed phase equilibria, under the necessary assumption of a rigid ZIF model.
Concerning the computational part of this study, it must be noted that the size and strength parameters for the nonbonded interactions between the framework atoms, as well as the constants of the harmonic and torsion potentials at the bonded groups were all received from the DREIDING generic type force field.
Then, we followed a twofold strategy in applying the values for the various potential functions:
(i) In the NH NG V T case, by making use of them without any kind of reparameterization with respect to measurements of the present work or to relevant experiments found elsewhere, and also, with no adulteration with values from other known force fields.
(ii) In the NH NG P T case, by setting the crystallographic equilibrium values in all potentials mentioned in the preceding paragraph, and moreover, increasing the force constants from their original values by an order of magnitude for the stretching potential along the bond Zn - N, and the angle bending in the Zn - N - C1 and Zn - N - C2. This type of adjustment proved to be the optimum selection in the isobaric-isothermal ensemble to preserve the unit cell volume, causing a maximum reduction up to 3.94 %, however. The latter parameters set was selected among a long series of NH P T Molecular Dynamics runs of the bare ZIF-8. On the contrary, employment of the DREIDING values results in unphysical contraction of the ZIF cages.
The first option was adopted for the isochoric-isothermal MD computer experiments; whereas the latter was chosen to enable us a more realistic modeling of the presented physical experiments by allowing volume fluctuations in the guest-framework system under constant pressure, temperature and chemical potential as imposed on by the Gibbs thermodynamic equilibrium rules.
A comparative set of results of the thermodynamics of the CO2 and CH4 phase equilibria in the ZIF via the NH NG V T and NH NG P T Molecular Dynamics computer experiments for various types of flexible structures, as a function of sorbate fugacity obtained from the excess chemical potential ìex, were examined; ìex was calculated through the Widom method.
The results show considerable augmentation of the diffusivity values for both sorbates with respect to the cases where the mentioned above dihedral angle is hindered. Moreover for methane, it is demonstrated that quasi-free motion of the organic link gives rise to a steeper transition that occurs at earlier occupancies, in agreement with the IRM measurements.
That is to say, application of a nonzero torsion potential to the ligand makes methane molecules remain behind the windows until the chemical potential increases at some higher value of pressure, so that eventually to overcome the free energy barrier and land to the next cage. Whereas, the limiting case of a quasi-freely moving link (weaker hindrance, hence, lower free energy at the window which means lower cavity-to-window free energy barrier), causes transition at an earlier stage, namely, at lower chemical potentials.
Comparison between the IRM measured diffusivities at infinite dilution (equal to self-diffusivities), and the MD computations at the same region, show acceptable agreement; the isobaric MD data are about one order of magnitude lower for the reasons discussed in the preceding lines. It is interesting that within this regime the strongly adsorbed CO2 moves faster than CH4, whereas as sorbate occupation increases further, the CH4 diffusivity curve rises and eventually exceeds the values of CO2 being in agreement with the IRM experiments.
1.2 Hydrogen storage
The possibility of the hydrogen molecule capture by the novel materials was also examined. The problem of simulating processes involving equilibria and dynamics of guest sorbates within zeolitic imidazolate frameworks (ZIF) by means of molecular dynamics (MD) computer experiments is of growing importance because of the promising role of ZIFs as molecular 'traps' for clean energy applications. A key issue for validating such an atomistic modeling attempt is the possibility of comparing the MD results, with real experiments being able to capture analogous space and time scales to the ones pertained to the computer experiments. In the present study, this prerequisite is fulfilled through the quasi-elastic neutron scattering technique (QENS) for measuring self-diffusivity, by elaborating the incoherent scattering signal of hydrogen nuclei. QENS and MD experiments were performed in parallel to probe the hydrogen motion, for first time in ZIF members.
The predicted and measured dynamics behaviour show considerable concentration variation of the hydrogen self-diffusion coefficient in the two topologically different ZIF pore networks of this study, the ZIF-3 and ZIF-8. Modeling options such as the flexibility of the entire matrix versus a rigid framework version, the mobility of the imidazolate ligand, and the inclusion of quantum mechanical effects in the potential functions, were examined in detail for the sorption thermodynamics and kinetics of hydrogen and also of deuterium, by employing MD combined with Widom averaging towards studying phase equilibria. The latter methodology ensures a rigorous and efficient way for post-processing the dynamics trajectory, thereby avoiding stochastic moves via Monte Carlo simulation, over the large number of configurational degrees of freedom a non-rigid framework encompasses.
In the previous section studies on a ZIF-8 flexible model showed that different modeling options such as the charge distribution and the extend of the mobility of the organic ligand, vastly influence the transport properties of carbon dioxide and even more the mobility and equilibrium of the bulkier methane molecule.10 In the present study we investigate the influence of the framework dynamics of two ZIF structures, the ZIF-3 and ZIF-8 (varying in the structural topology, the pore network and the type of the organic ligand), on the equilibrium and mobility properties of hydrogen and deuterium. Both sorbent materials were synthesized and characterized at the National Environmental Engineering Research Institute in Nagbur. The work includes combined QENS measurements and molecular dynamics computer experiments of the hydrogen self-diffusivity when sorbed within the two ZIF materials. The QENS measurements were performed at the Institut Laue-Langevin in Grenoble. Equilibrium MD computations were conducted for hydrogen and deuterium in fully flexible ZIF models.
The advantage of combining QENS and MD in this work is that comparable time and length scales of the molecular motion in the two techniques can be directly correlated for the calculation of self-diffusivity. More precisely, the large scattering cross-section of protons is essentially incoherent corresponding almost exclusively to the motion of individual protons, and thus the self-diffusion coefficient of the sorbed hydrogen can be extracted as a function of concentration in the host materials.11 On the other hand, through the MD simulations the produced trajectories of the sorbate guest molecules within the host matrices were elaborated in order to compute the self-diffusion coefficient via the Einstein's equation.
1.2.1 Computer Experiments
The ZIF-3 and ZIF-8 crystals were reconstructed in atomistic level using data from single crystal X-ray diffraction analysis, following the procedure described in a previous work In both structures, each zinc ion is tetrahedrally coordinated by four nitrogen atoms (ZnN4); the bridging groups in the structures are the imidazolate (IM) and the 2-methyl-imidazolate (mIM) in the ZIF-3 and ZIF-8, respectively. As discussed in the preceding section the ZIF-3 possesses a three channel pore system with two types of intersections, whereas the ZIF-8 constitutes a 3-D network of cages with a connectivity value eight.
The sorption thermodynamics computations were carried out by means of molecular dynamics experiments so that the imidazolate framework flexibility to be efficiently captured and the equilibrium pressure of the sorbed phase to be rigorously calculated following a phase space averaging procedure. Subsequently, the use of various modeling options indicates that the flexibility of the host matrix is of little importance, and also, omitting the quantum mechanical contribution in the potential function tends to overestimate the low temperature isotherms of hydrogen in both materials.
On the contrary to equilibrium properties, the framework mobility proved to influence significantly the kinetics of hydrogen in both sorbents, and particularly in the ZIF-8, wherein molecules experience tighter fitting as they pass through its hexagonal windows, being in addition subject to the hindrance exerted to them by the linkers' methyl groups. The simulated self-diffusivities as a function of loading approach the QENS measured values, when the quantum mechanical correction according to Feynman and Hibbs is applied to all dispersion interactions involved in the host-guest system. Moreover, the quasi-free rotation of the gate-like ligand of the ZIF-8 results in diffusivities approaching further the experimental data.
Potential Impact:
Description of the Potential impact
During the project years a number of novel ideas concerning the efficient modeling of sorption thermodynamics (responsible for fluid storage and capture), and molecular dynamics (responsible for the delivery of the captured fluids), were generated and subsequently presented in international conferences and also published in journals of the first rank. In the following lines a description of the impact that the project brought by to the scientific field environmental and clean energy engineering is provided in detail.
1. Estimation of Partial Charges in Small Zeolite Imidazolate Frameworks from Density Functional Theory Calculations
Force-field-based calculations (Monte Carlo or molecular dynamics) rely on a reduced description of the system electronic density by means of atomic partial charges. In our study, we explored different approaches to derive them for zeolite imidazolate frameworks. The usual approach to compute partial charges for molecular systems is based on ab initio calculations on small clusters, followed by a fitting of the quantum chemical electrostatic potential. Among the many methods, we chose the Merz-Kollman sampling scheme, which has been shown to give reliable results; we also found that, for computing partial charges, density functional theory calculations yield values comparable to the ones obtained with Hartree-Fock and perturbative methods.
Partial charges computed for molecules give a fair description of the electronic density of the isolated system, which is considered to be slightly perturbed in the condensed phase; thus, values calculated for the isolated systems are transferred to liquid/solid simulation with a negligible loss of accuracy. This approximation does not hold for crystal systems such as ZIFs; in fact, every atom/molecule in the supramolecular structure feels the crystalline environment, which should be somehow included in the description. Thus, for example, computing partial charges on the cluster formed by one zinc atom coordinated by four methylimidazolium molecules would make sense if we were interested only in the zinc charge. On the other hand, if we need to know the charges on N, we should consider a symmetric structure around the molecule.
To this end, we have explored two different methodological approaches to compute partial charges on ZIF-8 from first principles calculations. The first approach has been based on the building up of isolated clusters resembling the structure and symmetry of the crystal. We have observed that, in order to obtain converged results, the size of the cluster should be around 400 to 500 atoms, which renders this approach extremely computationally expensive. The second method is based on evaluating the REPEAT charges on the periodic crystal structure. In order to define an operative protocol to compute partial charges on ZIF-8 (which would be extended to similar materials), we compared the results obtained with two different functionals and six pseudopotentials. We found that ultrasoft Vanderbilt pseudopotentials give larger errors compared to norm-conserving Troullier_Martins or Goedecker_Teter_Hutter pseudopotentials. The results obtained with both PBE and BLYP functionals are in fair agreement, hinting that the computed properties are well described with the two of them. The convergence of results has been checked against the value of the pseudopotentials' cutoff. In the case of plane wave calculations, the partial charges converge at 150 Ry for the wave function cutoff, while for amixed plane wave and Gaussian basis sets treatment, we found a density cutoff of 700 Ry to be the ideal choice. In passing, we notice that the values obtained for Zn and N are in agreement with those from recent studies on ZIFs and on systems of biological interest.
The values of REPEAT charges are also in agreement with those computed, at a much higher computational cost, on large isolated clusters. Given the reliability of the method, and considering its relatively low computational overhead, in the second part of the article, we looked into the fluctuations of charges, by propagating the system with DFT-based molecular dynamics simulations of the periodic structure. REPEAT charges have been computed for many configurations of three zeolite imidazolate frameworks, slightly differing among them in the structure and substituents: ZIF-8, ZIF-2, and ZIF-3.
or ZIF_8, both Car_Parrinello and Born_Oppenheimer molecular dynamics simulations show that the value obtained in single point calculations are in agreement with the average value during the time evolution of the system. The common feature to the three ZIFs studied is that the fluctuations in the charges of every atom are small. To our knowledge, this represents the first study of atomic partial charges where the fluctuations are taken into account; our results justify the choice of using the point charge approximation for these kinds of materials, given that the fluctuations are negligible. Nevertheless, if highly charged or polarizable absorbates interact with the framework, the inclusion of polarization could be important in the description of physical chemical properties of ZIFs.
2. Force Field for Molecular Dynamics Computations in Flexible Frameworks
In this section, a novel force field for molecular dynamics simulations of fully flexible ZIF-8 has been presented. The structure parameters computed with this force field (such as bond length and angle and window size) are in good agreement with experimental values. Besides, our force field reproduces correctly the thermal and pressure stability of ZIF-8 crystal structure. Reliable diffusivities of CO2 were obtained with our fully flexible force field and our charge model. These results have been compared to charge models available in the literature, explaining the discrepancies on the basis of point charge influence on the movement of guest CO2 molecules via control of the window size and of the sorbate free energy landscape. Subsequently, we studied the weight that various simulation details, regarding the system modeling, have on the self-diffusivity, isolating the importance of charges, framework shape and framework flexibility on the accuracy of the final diffusivity result. After these investigations, we conclude that the force field developed during AMCOS is suitable to study the dynamic properties of sorbed CO2 molecules within the flexible structure of ZIF-8. The diffusivity of other sorbates will be the subject of upcoming work, together with the characterization of the window opening mechanism and the application of coarse-graining techniques (cellular-automata) to the system dynamics. The portability of our force field to other ZIF structures (e.g. ZIF-3 and ZIF-90) will also be investigated in the next period.
3. Speeding up simulation of diffusion in zeolites by a parallel synchronous kinetic Monte Carlo algorithm
A parallel kinetic Monte Carlo algorithm, originating from the synchronous algorithm of Martinez et al., has been applied to the study of benzene diffusion in zeolite NaX. We have shown that, despite the presence of a rollback procedure in the algorithm, high efficiencies can be reached by exploiting the local nature of the molecule-molecule interactions inside the zeolite, allowing the need of rollbacks to be minimized through a proper spatial decomposition. In the present form the algorithm is still approximate, but the correct tuning of the domains size leads to obtaining results with the desired accuracy. We believe that the algorithm outlined here is applicable in general with little modification to other types of zeolites. Even better performances are expected to be found for other zeolites like the Linda Type A (LTA) family, ZSM5, or for zeolitic imidazolate frameworks (ZIF) because of the absence of shared sites between communicating cages. Adsorbate-adsorbate interactions does not extend significantly outside the cages, thus permitting an ideal domain decomposition. As for other similar methods, the efficiency of the algorithm is very sensitive to the value of the communication/calculation ratio that can be easily controlled by changing the size or the shape of the domains.
4. A parallelizable block cellular automaton for the study of diffusion of binary mixtures containing CO2 in microporous materials
We tested our cellular automaton method in the case of binary mixtures diffusing in zeolite ZK4 and compared the results with MD data, showing its ability to cope with more than one diffusing species giving good qualitative agreement with this well established and fully microscopically detailed technique. We stress that these results are based on heuristically determined parameters aiming mainly to explore the range of possibilities of the method and, nonetheless, in the case of non-trivial behaviour such as the segregation-effect, we found that the CA gives a better agreement with MD than the robust and successful MS method used by Krishna and coworkers.
It would be obviously desirable to have a rigorous algorithm for defining the right input parameters for the automaton, extracting them from atomistic simulation. But even at this stage our tests demonstrate that the model is able to display a range of interesting behaviours and to capture on a coarse-grained level the basic mechanisms of diffusion in zeolites. Validation via comparison with other theoretical approaches is important as this justifies a further effort intended to exploit the intrinsic parallel nature of CAs for a drastic extension of the space and time scales usually accessible to the available simulation techniques for diffusion in zeolites. Using parameters obtained from MD and MC studies as an input, our BCA model is a promising tool for a future investigation of zeolite and Zeolitic Imidazolate Frameworks (ZIFs) membranes and whole microcrystal, both in and out of equilibrium.
5. The central cell model: A mesoscopic hopping model for the study of the displacement autocorrelation function
In this work, we laid down the basis of a simple computational framework, the CCM, aimed to be specific for the study of the motion on the mesoscopic scale of a single particle in a system of connected cavities in the presence of other diffusants, in conditions of thermodynamic equilibrium. Our model is local and discrete in both space and time, and in the numerical applications we have shown here it has been constructed starting from the algorithm of a lattice-gas model for diffusion in microporous material.
We have shown that, although being not possible for the CCM to sample all the information obtainable by a full lattice-gas, a CCM simulation provides an accurate reproduction of the memory effects in the self-diffusion (and thus, of the diffusion isotherm) at a minimum computational cost. The way the CCM is constructed suggested how to carry on a mean-field study of the self-diffusion process produced by the particular evolution rule adopted.
This has led to two approximated mathematical expressions for self-diffusion. The first one, more general, can be applied with data coming straight from the CCM simulation. The second one, more case-specific and derived by assuming fast local equilibration, is theoretical and yields a more accurate approximation the weaker the correlations and the lower the loadings are. Interpretation of the discrepancies between the self-diffusivity trends obtained from the numerical simulations and their two different mean-field approximations helped to understand how, and how strongly, memory effects can emerge depending on the very general features of the model parametrization.
The obtained results suggest the CCM approach to be suitable for other theoretical studies, e.g. the time correlations in the local density, as well as for direct applications in the field of the molecular coarse graining. For example, the CCM approach could be further extended to the sampling of both the adsorption and the self-diffusion isotherm through a single simulation when the lattice-gas rule includes an explicit cell-to-cell interaction potential which makes (in principle) impossible do derive the equilibrium probability distribution of states a priori. This could be done by performing a grand-canonical Monte Carlo on the border cells while keeping the core evolving with the prescribed dynamic lattice-gas rule in the canonical ensemble. Also, an even more intriguing extension of the CCM approach could be made in the field of hybrid MC-MD schemes aimed to realistically mimic the bulk effects in the motion of a tagged guest in an atomistic simulation.
6. Development and Optimization of a New Force Field for Flexible Aluminosilicates, Enabling Fast Molecular Dynamics Simulations on Parallel Architectures
In this work, a new force field has been developed enabling fast molecular dynamics simulations in flexible aluminosilicates and, thus, extending the time and space scales accessible to classical MD simulations. The structures here investigated are silicalite, Na A, Ca A, Na Y, and Na X, chosen to ensure a good degree of force field portability, allowing an extension to affine structures with minimal effort. We adopted a CHARMM-type functional form which allows, using the NAMD package, the simulation of a 1 ns trajectory per wall clock hour in systems consisting of about 4000 atoms, running over 16 cores of small Beowulf clusters. The new force field has been optimized by carefully tuning the simulated structures and IR spectra to experimental data. The resulting parametrization allows correct modeling of the system dynamics, without introduction of spurious deformations. Moreover, the structural stability of model Na A over a wide range of temperatures and pressures has been successfully tested.
This work is a starting point for future studies of sorbed molecules in zeolites, especially for the development of more reliable coarse-grained models which will further expand the accessible time and space simulation scales.
7. Atomistic Simulation Studies on the Dynamics and Thermodynamics of Non Polar Molecules within the Zeolite Imidazolate Frameworks
We have accomplished and reported statistical mechanics based modeling of the sorption thermodynamics and dynamics of selected non polar molecules in the ZIF-8. Our aim was firstly to investigate the evolution of the sorption equilibrium in this material, over a wide range of occupancies for Ar, CH4 and H2 up to saturation, and secondly to elucidate the mechanism of molecular motion under the complicated force field exerted by the zinc atoms and the 2-methyl-imidazolate groups which form the void space of the organic zeolite analogue framework under study. For this purpose we digitally reconstructed the ZIF-8 unit cell and then examined the applicability of generic force fields found in literature for the description of atomic-level interactions between sorbate molecules and framework atoms.
We opted for DREIDING force field after comparing the simulation predictions for the sorbates studied in this work, with measured isotherms under the same conditions found elsewhere.
The partial molar configurational internal energy was calculated for Ar, CH4 and H2 as a function of their loading in the metal-organic framework at 87, 240 and 77 K respectively, via grand canonical Monte Carlo. Because the computed quantity is related to the covariance of the potential energy and number of particles at a certain loading and temperature, it can map the strength of sorbate-sorbate and sorbate-sorbent interactions over the full sorbate loading range; the results showed a higher perception of energetic inhomogeneity of argon in comparison with methane and hydrogen. One- and two-point probability density functions calculated by post-processing the equilibrated configurations produced from Monte Carlo, provided a further insight into the distribution of adsorption centres inside the ZIF-8 framework. Moreover, interpretation of these results on the basis of free energy distribution offered a plausible explanation of the mobility of the sorbed phase as a function of its chemical potential inside the metal-organic framework.
Although for hydrogen and argon the agreement between simulated and measured isotherms is satisfactory, the freezing of the degrees of freedom of the organic links in our model, may cause the sitting transition step of the predicted isotherm of argon to appear earlier than the one observed experimentally. It was also showed that such inflections during the sorption and kinetics procedure involve crossing of free energy barriers located at positions near the six-ring window faces; therefore, the bonding flexibility at these areas may influence these barriers and hence the dynamics of guest molecules even at low temperatures. The inflexibility of the model ZIF-8 unit cell can also be responsible for the over-prediction of the sorption thermodynamics of the bulkier molecule of methane, with respect to measured values found elsewhere.
The molecular mobility of Ar at 87 K and H2 at 77 K inside the metal-organic sorbemt was estimated by virtue of equilibrium molecular dynamics in the canonical ensemble. Although the self-diffusivity of argon at 87 K is too low to be of any practical importance, we observed its displacement over a broad range of occupancies, in conjunction with the preceding thermodynamics findings, in order to understand the kinetic behaviour of the sorbed phase with respect to the calculated spatial partitioning of the sorbate probability density inside this new class of materials.
In view of the quantum nature of hydrogen at 77 K, we employed the path integral formulation for the quantum mechanical description of the intermolecular interactions which leads to the quadratic Taylor expanded pairwise potential function, as follows from the work of Feynman and Hibbs. Their work states that paths located at a certain state point in the configuration space are enveloped inside a Gaussian width; for low temperatures and atomic masses, the distribution around this position becomes widespread, hence a classical description is not adequate any more. The self-diffusivity of hydrogen in the ZIF-8 at 77 K as revealed by our molecular dynamics simulations, showed a marked difference between the values obtained from the classical and quantum mechanical description of the energetics. The predicted self-diffusivity presents a shallow maximum as a function of occupancy due to the loading dependent free energy barrier which separates the adsorption sites located close to the hexagonal windows, and around the cavity centre of the ZIF-8 unit cell.
At this point we should stress that the rigidity of the model ZIF-8 framework should put one under serious consideration when simulation is carried out at high temperatures, or/and guests whose size is commensurate with the effective size of critical paths for diffusion in the framework, are involved. These issues are mainly associated with the rotation of the pendant alkyl or other groups of the imidazolate-type link as well as with possible torsional motions of the organic links themselves, which become much pronounced with rising temperature. As a consequence, these phenomena may affect the dynamics of guest molecules inside the pore matrix, leading to unrealistic transport coefficients.
8. Analysis of the impact of sorbent mobility on the sorbed phase equilibria and dynamics: A study of methane and Carbon Dioxide within Imidazolate Frameworks
The scope of this part of the project is to contribute for first time in levelling the role of atomic framework flexibility, or rigidity, on the thermodynamics and transport properties of the sorbed phase in the rapidly growing class of porous coordination polymers, the imidazolate frameworks. In the absence of strict quantum mechanical descriptions toward an ad hoc parameterization of the particular ZIF, we properly adapt methodologies relying on statistical mechanics via a generic force field, giving no consideration to adjust parameter values of the potential functions with respect to the experimentally measured mass transport quantities of the present work, neither in the isochoric nor in the isobaric molecular dynamics; for the latter simulation option only, we adjusted the ZIF-8 inter-atomic distances in the lattice to their crystallographic values in an attempt to preserve the unit cell volume.
The effect of the mobility of the imidazolate ligands acting as 'saloon doors' which surround the critical for transport hexagonal windows, along with the charge distribution on the ZIF-8 atoms, proves to be of key importance for the guest dynamics. The results show successful qualitative agreement between the experiments and simulations for both equilibrium and nonequilibrium transport coefficients of methane and carbon dioxide, obtained by Pulsed-Field Gradient NMR, Infrared Microscopy, and Molecular Dynamics combined by an interactive Widom averaging procedure for the computation of the sorbed phase equilibria. Moreover, the calculated singlet probability density distribution at the vicinity of the windows intervening in the cage-to-cage paths, provides an explanation of the diffusivity trend of the two sorbate guests as revealed by both the IRM experiments and MD modeling.
9. Probing the hydrogen equilibrium and kinetics in Imidazolate Frameworks via Molecular Dynamics and Quasi-elastic Neutron Scattering Experiments
The work presented at the final stage of AMCOS is concerned with the kinetic behaviour of hydrogen and deuterium, acting as sorbate molecules, within two crystalline metal-organic structures, known as zeolitic imidazolate frameworks, the ZIF-3 and ZIF-8; the materials belong to the tetragonal and cubic crystal systems respectively and they also grow into different pore networks. Two kinds of experiments, quasi-elastic neutron scattering and molecular dynamics computer simulation, were conducted in parallel in order to track the motion of the sorbate molecules. Both QENS and MD have the advantage of capturing analogous length and time scales of the diffusing hydrogen molecules in the host materials being able to provide comparable self-diffusion coefficients.
In the current work, this simultaneous study is of particular usefulness because for first time such a comparison is performed in ZIFs' members, and also because the QENS experimental technique, apart from its individual importance in probing the sorbate motion, it does contribute as a benchmark to the validation and further development of our modeling work.
The sorption thermodynamics computations were carried out by means of molecular dynamics experiments so that the imidazolate framework flexibility to be efficiently captured and the equilibrium pressure of the sorbed phase to be rigorously calculated following a phase space averaging procedure. Subsequently, the use of various modeling options indicates that the flexibility of the host matrix is of little importance, and also, omitting the quantum mechanical contribution in the potential function tends to overestimate the low temperature isotherms of hydrogen in both materials.
On the contrary to equilibrium properties, the framework mobility proved to influence significantly the kinetics of hydrogen in both sorbents, and particularly in the ZIF-8, wherein molecules experience tighter fitting as they pass through its hexagonal windows, being in addition subject to the hindrance exerted to them by the linkers' methyl groups. The simulated self-diffusivities as a function of loading approach the QENS measured values, when the quantum mechanical correction according to Feynman and Hibbs is applied to all dispersion interactions involved in the host-guest system. Moreover, the quasi-free rotation of the gate-like ligand of the ZIF-8 results in diffusivities approaching further the experimental data.
The calculated elements of the hydrogen diffusion tensor within the ZIF-3 in the form of mean squared displacements along the principal directions of the unit cell, are in agreement with the results from the singlet probability computations along the three pore channels of the material, thus explaining the variation of the diffusivity as a function of the hydrogen concentration.
Our analysis about the tensor concentration dependence presented above, is based on the density, and hence free energy, evolution, of the guest sorbed phase in the anisotropic interior of ZIF-3. On the absence of experimental data from specialized techniques able to probe the spatial variation of mass transport, such as the Interference Microscopy, only simulation can provide such information. Furthermore, phenomena that may be related to the structural topology of the material which are likely to affect the resistance to mass transport at various directions within the host matrix, as can be found for instance in some zeolite crystals, do deserve attention.
Dissemination activities:
Peered review articles
- E.Pantatosaki G.Megariotis A.Pusch C. Chmelik, F. Stallmach, G. K. Papadopoulos, J. Phys. Chem. C (2012), 116, 201207.
- St. Schlayer , A.-K. Pusch, F.e Pielenz, St. Beckert, M. Peksa, C. Horch , L. Moschkowitz, W.-D.h Einicke, F. Stallmach: X-Nuclei NMR Self-Diffusion Studies in Mesoporous Silica Foam and Microporous MOF CuBTC, Materials 2012, 5, 617-633.
- A.-K. Pusch, T. Splith, L. Moschkowitz, S. Karmakar, R. Biniwale, M. Sant, G. B. Suffritti, P. Demontis, J. Cravillon, E Pantatosaki, F. Stallmach: NMR studies of carbon dioxide and methane self-diffusion in ZIF-8 at elevated gas pressures, Adsorption (submitted May 2012, manuscript no. ADSO-S-12-00169).
- E. Pantatosaki, G. Megariotis, A.-K. Pusch, C. Chmelik, F. Stallmach, G. K. Papadopoulos J. Phys. Chem. C 116, 201 (2012).
- Federico Giovanni Pazzona, Giuseppe Baldovino Suffritti, and Pierfranco Demontis, Journal of Chemical Theory and Computation, 2011, 7, 15751582.
- F. G. Pazzona,a) A. Gabrieli, A. M. Pintus, P. Demontis, and G. B. Suffritti, J. Chem. Phys. 134, 184109 (2011).
- Federico G. Pazzona,a) Pierfranco Demontis, and Giuseppe B. Suffritti, J. Chem. Phys. 137, 154106 (2012).
- Andrea Gabrieli, Marco Sant, Pierfranco Demontis, and Giuseppe B. Suffritti, J. Phys. Chem. C , in press.
- Andrea Gabrieli, Pierfranco Demontis,* Federico G. Pazzona, and Giuseppe B. Suffritti, Physical Review E 83, 056705 (2011).
- Alberto M. Pintus, Federico G. Pazzona, Pierfranco Demontis,a) and Giuseppe B. Suffritti, J. Chem. Phys. 135, 124110 (2011).
- Federico G. Pazzona,* Pierfranco Demontis, and Giuseppe B. Suffritti, J. Phys. Chem. C 2013, 117, 349-357.
- Bin Zheng, Marco Sant,* Pierfranco Demontis, and Giuseppe B. Suffritti, J. Phys. Chem. C 2012, 116, 933938.
Oral and Poster presentations
- A.-K. Pusch: 13C NMR Studies of Carbon Dioxide Diffusion in MOF CuBTC (talk), 11th Dutch-German IRTG workshop 'Diffusion in porous materials', Eibenstock, 23rd March 2010.
- F, Stallmach, St, Beckert, St, Hertel, C, Horch, A,-K, Pusch, M., Wehring: NMR Studies of the Mobility of Carbon Dioxide and Hydrocarbons in Nanoporous Coordination Polymers (poster P33), 10th Bologna Conference on Magnetic Resonance in Porous Media (MRPM 10), 12th to 16th September 2010 Leipzig, Germany (see http://www.mrpm.org/originalsites/MRPM10/book_of_abstracts.pdf(opens in new window) p. 87).
C. Horch, A.-K. Pusch, P. A. J. Donkers, F. Stallmach:: Low-Field High-Pressure NMR Porosimetry (poster P41), 10th Bologna Conference on Magnetic Resonance in Porous Media (MRPM 10), 12th to 16th September 2010 Leipzig, Germany (see http://www.mrpm.org/originalsites/MRPM10/book_of_abstracts.pdf(opens in new window) p. 93).
- F. Stallmach: (invited talk), NMR studies of host-guest interaction in porous materials, Nagpur, India, November 2010.
- A.-K. Pusch, C. Horch, F. Stallmach: NMR studies of diffusion and adsorption in the Metal Organic Framework CuBTC (poster), EU-India Workshop on Environmental materials, Nagpur, Indis, November 2010.
- A.-K. Pusch, S. Schlayer,F. Stallmach: 1 3C NMR diffusion studies with CO2 adsorbed at MOF CuBTC (poster), 23. Deutsche Zeolithtagung, Erlangen, Germany, 02-04 March 2011.
- A.-K. Pusch, S. Schlayer, F. Stallmach: 13C NMR Diffusion studies with CO2 adsorbed in Advanced Materials, (talk) 13th Dutch-German IRTG workshop 'Diffusion in porous materials', Leipzig, O4th April 2011.
- F. Stallmach: Transport and storage of gases, liquids and electrolytes in porous media studied by NMR (invited talk), BASF SE, Ludwigshafen, Germany, 23 March 2012.
- A.-K. Pusch, S. Schlayer, T. Splith, R. Biniwale, G. Papadopoulos, F. Stallmach: NMR studies of carbon dioxide and methane selfdiffusion in ZIF-8 at elevated pressures (talk), 6th Pacific Basin conference on Adsorption Science and Technology (PBAST-6), Taipei, Taiwan, 20-23 May, 2012.
- G. K. Papadopoulos: (invited talk), Computer Modeling of host-guest interaction in porous media, Nagpur, India, November 2010.
- G. K. Papadopoulos: (invited talk), Multiscaling Simulations of Diffusion Processes in MOFs, Leipzig 2011.
Project website: http://comse.chemeng.ntua.gr/amcos/(opens in new window)
