The reduction of greenhouse gas emissions are crucial when adequately tackling the climate change problem. These emissions, for which CO2 and CH4 are the main perpetrators, can be efficiently reduced by adsorbing these harmful gas molecules inside a host material (see Figure 1), after which these gases can either be separated or sequestered. Several potential host materials are being studied, but it is safe to say that nanoporous materials, and within this class, metal-organic frameworks (MOFs), are viable materials to fulfill this aim. MOFs are scaffold-like structures obtained by linking inorganic bricks by organic ligands, obtaining a nanoporous yet crystalline structure (see Figure 1). The large internal surface of these materials makes them excellent candidates for the aforementioned gas storage applications, since they optimize the affinity between the guest and the host material. Moreover, a lot of these MOFs exhibit linker flexibility which may vary the pore size or even merge adjacent porous channels, critically influencing the adsorption of guest molecules in these framework materials. To computationally characterize a MOF’s potential for guest adsorption, it is hence paramount to incorporate this flexibility in an adequate way. However, most contemporary studies neglect this flexibility by sampling in the grand canonical ensemble with a rigid framework, which is computationally more efficient but is a very severe approximation, even in the less flexible MOFs [1]. As a result, methodologies to incorporate this flexibility are well-received in the community [2].

Goal

The aim of this thesis is to overcome the rigid framework approximation in a systematic way by constructing an advanced molecular simulation scheme. This hybrid scheme will be composed of two contributions: a molecular dynamics (MD) contribution in which the Newtonian equations of motion are integrated, and a Monte Carlo (MC) contribution which can be used to insert or remove guest molecules. As such, both the ‘true’ dynamics, and hence the flexibility, of the MOF will be described (in the MD part), while allowing the number of guest molecules to change (in the MC part), something that is impossible in a pure MD simulation. To develop this scheme, ideas can be borrowed from MD and MC codes that were recently implemented in our in-house Pythonic molecular simulations engine, Yaff. However, these ideas will need to be combined in an ingenious way to arrive at a reliable MC/MD hybrid scheme, for instance ensuring that detailed balance is satisfied.

Many hybrid MC/MD schemes exist, and the student is encouraged to assess the accuracy and computational efficiency of a variety of these schemes. To that end, the student should implement such schemes in our in-house software, Yaff, and compare results with results obtained with the MC/MD code RASPA [4]. Herein, we will propose two such schemes to guide the mind (see Figure 2). In a first scheme, an MD simulation of an empty MOF is performed for a sufficiently long time, and several snapshots of the MOF are taken during this run. These different snapshots are expected to be representative for the flexibility of the host material. Afterwards, a separate MC simulation is started for each snapshot. During these MC simulations, we try to add guest molecules to the host material (or remove them from the host material), something that will only succeed when the guest-host interactions are favorable. When averaging over all these snapshots, the average amount of guest adsorption in the MOF can be obtained [3]. In a second scheme, a short MD simulation is initiated, after which we try to add or remove a guest molecule via an MC step. After this MC step, whether successful or not, we again perform an MD simulation, possibly with a different number of guest molecules. As such, we will obtain a sequence of alternating MD and MC steps, so that guest molecules can be removed or added during the hybrid simulation. The average amount of guest molecules is then again obtained by averaging over the whole MD/MC run [4]. While this second scheme represents more the ‘true’ phenomenon of guest adsorption in a MOF, special attention should be paid to ensure detailed balance during the MD run [5] –something the student will become familiar with early in the thesis.

The goal of this thesis subject is hence threefold. First, the student needs to get acquainted with the physical fundamentals of Monte Carlo and molecular dynamics techniques, which lay on the basis of any molecular simulation. Second, these two techniques need to be combined and implemented following for instance the two schemes outlined above. Hence, it is expected the student also looks forward to implement their own software code to extend the existing molecular engine. The computational efficiency and accuracy of the proposed schemes can then be compared with an external MC/MD code, RASPA [4], which is currently used at the Center for Molecular Modeling (CMM). Lastly, using this new methodology, the adsorption of for instance CO2 and CH4 in several MOFs will be assessed to give an indication of the best-performing MOFs in class for the reduction of greenhouse gases.

Aspects

Physics aspect: The interaction between guest molecules and the host material will play a dominant role in this thesis subject. Moreover, the student will explore the fundamentals of molecular simulations.
Engineering aspect: The aim of this thesis is to obtain well-performing materials for the adsorption of greenhouse gases, contributing to the quest to curb climate change.