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Multiscale Modeling of the HKUST-1/Poly(vinyl alcohol) Interface: From an Atomistic to a Coarse Graining Approach Rocio Semino,*,† Johannes P. Dürholt,‡ Rochus Schmid,*,‡ and Guillaume Maurin† †

Institut Charles Gerhardt Montpellier UMR 5253 CNRS, Université de Montpellier, Place E. Bataillon, 34095 Montpellier Cedex 05, France ‡ Computational Materials Chemistry Group, Lehrstuhl für Anorganische Chemie 2, Ruhr-Universität Bochum, Bochum, Germany S Supporting Information *

ABSTRACT: We present a computational multiscale study of a metal−organic framework (MOF)/polymer composite combining micro- and mesoscopic resolution, by coupling atomistic and coarse grained (CG) force field-based molecular dynamics simulations. As a proof of concept, we describe the copper paddlewheel-based HKUST-1 MOF/poly(vinyl alcohol) composite. Our newly developed CG model reproduces the salient features of the interface in excellent agreement with the atomistic model and allows the investigation of substantially larger systems. The polymer penetrates into the open pores of the MOF as a result of the interactions between its OH groups and the O and Cu atoms in the pores, suggesting an excellent MOF/polymer compatibility. Polymer structure is affected by the MOF surface up to a distance of ∼2.4 times its radius of gyration. This study paves the way toward understanding important interfacial phenomena such as aggregation and phase separation in these mixed matrix systems.

1. INTRODUCTION Composites assembling polymers and MOFs have been signaled as an alternative solution for a wide range of membrane-based liquid and gas separation processes since they combine the high permeability, easy processability, and low costs of polymer membranes with the excellent thermodynamic separation performance and high chemical stability of MOFs.1−4 However, the performance of these MOF/polymer mixed matrix membranes (MMMs) is often not as good as expected, mostly due to a poor affinity between the two components that might lead to a nonselective void formation at the interface and even to phase separation at high MOF loadings.5−7 In this context, a thorough investigation of the features of the MOF/polymer interface is crucial to further control the feasibility of advanced MMMs with optimized MOF/polymer compatibility. A first step in this direction was recently proposed by some of us in a joint computational− experimental exploration of the ZIF-8/PIM-1 and ZIF-8/PIMEA-TB interfaces7,8 (PIM stands for Polymers of Intrinsic Microporosity).9 An atomistic modeling strategy, integrating density functional theory calculations and force field-based molecular dynamics (MD) simulations, has been devised to construct and further analyze MOF/polymer interfaces8 in terms of interacting sites, MOF surface coverage and conformational arrangement of the polymer. Microscopic voids were identified at the interface of both composites7,8 as a consequence of specific intermolecular MOF/polymer interactions, the morphology of the MOF surface, and the © 2017 American Chemical Society

high rigidity of the polymers. This interplay was also evidenced for the ZIF-8/poly(vinyl alcohol) (PVOH) interface using differential scanning calorimetry and tensile test measurements.10 Even though these atomistic simulations lead to valuable insights, some relevant properties still cannot be computed due to system size restrictions. Besides a recent investigation on the macroscopic mechanical properties of composite materials by a finite element approach,11 no study has focused so far on the characterization of these systems at the intermediate, mesoscopic scale. This calls for the development of novel CG models which would allow for the computation of properties of the MOF/polymer interface that are inaccessible through standard atomistic simulations, such as the extent to which there is interfacial polymer as opposed to the bulk, and the extent and mechanism of aggregation of MOF nanoparticles in a polymer matrix. The basic principle of the CG approach is to group several atoms into a single interacting site called “bead”. This implies discarding certain degrees of freedom from the modeled system, so care should be taken of keeping those which are expected to impact the target properties. By reducing the total number of particles, force field-based MD simulations become much less computationally expensive and larger systems and longer time scales become tractable.12−14 Although CG models Received: July 18, 2017 Revised: September 6, 2017 Published: September 7, 2017 21491

DOI: 10.1021/acs.jpcc.7b07090 J. Phys. Chem. C 2017, 121, 21491−21496

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The Journal of Physical Chemistry C

been transferred to the dispersion damped Buckingham potential employed in MOF-FF. Since 1-2 and 1-3 are not excluded from the Coulombic sum, both bond and angle terms of the force field have been reparametrized using the MOF-FF methodology. For this, a PVOH dimer was used as a reference system. Gaussians with a very small σi of 0.01 Å were employed for PVOH in order to reproduce the original point charge behavior. The quality of the model was assessed by comparing its density and simulated X-ray diffraction pattern with experiment (see Figure S2). A polydisperse polymer was generated using an in silico polymerization25 procedure. Polydispersity was introduced with the aim of providing a more realistic model of the polymer. The effects of polydispersity in MOF/polymer interfaces were discussed for the ZIF-8/PIM-1 system in our previous publication.8 The model consisted of 118 polymer chains with a number of monomers ranging between 10 and 37, large enough to impede the interaction between the periodic images of the HKUST-1 surface when they are brought into contact. Radial distribution functions have shown that hydrogen bonds between the OH groups in the PVOH monomers are the main interactions holding the different chains together, and also intrachain interactions of this kind were observed (see Figure S3). Further details regarding the polymer model can be found in Section I.I.II in the SI. In order to allow the polymer to equilibrate26 adapting its configuration to the chemical functions and morphology of the MOF surface, seven short heating/cooling and one long compression/decompression, NVT and NPnT MD cycles were performed with temperatures of 600 and 300 K and pressures ranging from 1 to 1000 bar (Pn is the pressure normal to the surface slab, further details are provided in the SI and in ref 8). Once the interface was built, a representative description of its microscopic features was obtained by analyzing several independent 10 ns long trajectories in the NVT ensemble with a time step of 1 fs. Berendsen thermostat and barostat27 were used with relaxation times of 0.1 and 0.5 ps respectively for the NVT and NPnT simulations. As a second step, we developed a CG force field for the system, in order to study the HKUST-1/PVOH interface at longer length scales, and we validated it by comparing some observables with those coming from atomistic simulations. A system of identical size to the atomistic interface was considered with the purpose of developing the CG model (development stage, see blue chart in Figure 1). CG representations for HKUST-1 and PVOH were combined, using a strategy analogue to that applied for the construction of the atomistic interface. The HKUST-1 model was derived following the same procedure as for the first CG model developed previously for MOFs,19 but with a less coarse mapping in order to enhance the chemical details of the model interface (see Figure S4). The degree of coarsening, defined as the total number of atoms normalized by the total number of beads that represent them, is ∼2.6 for the MOF. The PVOH CG model was adapted from a representation proposed in the literature,28 consisting of one bead per monomer (degree of coarsening: 7) with Buckingham potentials for the van der Waals interactions and springs between connected beads. This adaptation was made in order to improve the description of the structure of the polymer by improving the fitting of the experimental density and reproducing the radial distribution functions between the centers of mass of the monomers obtained with the atomistic polymer (see Section I.II.II of the

have been extensively applied to study polymers and related membranes,15−18 to the best of our knowledge none of them has described MOF/polymer composites. Following the recent achievements by some of us in building a CG model19 of the benzenetricarboxylic (BTC) Cu paddlewheel HKUST-1 MOF,20 in this paper we report the derivation of the first CG model for a MOF/polymer interface and the multiscale characterization of its properties. As a proof of concept, the HKUST-1/PVOH system was considered for two main reasons: (i) the flexibility of PVOH combined with the relatively large porosity of HKUST-1 is expected to favor a good compatibility between them; and (ii) PVOH has been already successfully integrated with a MOF in an MMM, i.e. ZIF-8.10

2. COMPUTATIONAL METHODS A workflow of our multiscale methodology is shown in Figure 1.

Figure 1. Workflow of the multiscale approach developed in this study, and the information gained at the different levels: atomistic simulations (orange), CG model development (blue), CG production runs (green).

As a first step, an atomistic interface model was built by assembling equilibrated MOF and polymer microscopic models through a series of force field-based MD simulations (see Figure 1, orange).8 HKUST-1 was represented by its most stable [111] surface with acetate terminations as a slab model21 of size 75 Å × 65 Å × 40 Å, using the ab initio derived force field MOF-FF.22 The potential energy expression in MOF-FF has been derived from the MM3 force field.23 A dispersion damped Buckingham potential was used for the treatment of long-range van der Waals interactions. Instead of point charges, spherical Gaussian charge distributions were employed to compute the Coulombic interactions. Note that all interatomic Coulombic interactions were taken into account, including 1-2 and 1-3 interactions. PVOH was modeled as a flexible collection of atoms by an adaptation of the CHARMM force field (see Figure S1).24 For this purpose, the 12-6 Lennard-Jones potential employed in CHARMM for the long-range van der Waals interactions has 21492


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Figure 2. Snapshot of the atomistic HKUST-1/PVOH interface. Color code for the MOF atoms: carbon (black), oxygen (red), hydrogen (white), copper (ochre). For clarity purposes, all polymer atoms are shown in gray, light gray represents region A and dark gray region B.

SI and Figure S5). The CG models were combined to create the CG MOF/polymer interface, using a single simulation box of the same dimension as that for the atomistic simulations but with a total number of particles significantly reduced from ∼20,000 to ∼4,000 and a series of NVT and NPnT MD cycles was performed as mentioned above. The robustness of the methodology was tested by verifying the consistency of the results with respect to the choice of the maximum temperature and pressure for the interface generation simulations (see SI). We tuned the HKUST-1/PVOH CG intermolecular interactions to reproduce three key properties obtained from the atomistic simulations: density profile, radial distribution functions, and both the average and distribution of the radius of gyration for PVOH. Further details on the methodology refinement and its validation are given in Results and Discussion. Finally, we applied our CG model to larger systems (production stage, see green chart in Figure 1). In these systems, the thickness of the HKUST-1 slab model was kept as before, but the size of the polymer phase was multiplied by a factor of 7, allowing an increase of the z-dimension of the system from 55 Å (initial atomistic interface model) to 185 Å.

Figure 3. Site−site pair correlation functions: OHKUST‑1 − HCPVOH (left upper panel), CuexternalHKUST‑1 − HC/OH1PVOH (right upper panel), CumiddleHKUST‑1 − HC/OH1PVOH (left bottom panel), from the atomistic interface model. Labels for the polymer atom types can be found in Figure S12. A scheme of the HKUST-1 slab, indicating the different layers of Cu atoms (external, middle, and internal) is also shown. Color codes are those of Figure 2.

3. RESULTS AND DISCUSSION A simple glance at the atomistic structure of the interface shows that PVOH penetrates into the HKUST-1 surface up to the first pore layer (see Figure 2). The chain ends of PVOH can sometimes circumvent the steric hindrance created by the BTC units and access the top of the second pore layer, due to the tbo topology exhibited by HKUST-1 (see Figure S11). To continue our analysis, we computed radial distribution functions for the polymer sites versus the inner pore sites in the MOF (oxygen and copper), the corresponding results are presented in Figure 3. The OH groups of PVOH strongly interact both with the O and Cu atoms that conform the paddlewheel with characteristic distances of 2.5 and 2.7 Å,

respectively. It is also of interest to know if the strength of these interactions changes with the depth of the polymer penetration. With this in mind, we defined some spatially restricted radial distribution functions, where we distinguished the different layers of Cu atoms (see the scheme in Figure 3). The Cu atoms closest to the terminations of the slab are labeled “external”. Those located at the bottom of the first pore layer and those at the middle of the second pore layer are termed “middle” and “internal”, respectively. The interactions of both H and O atoms in the polymer (labeled HC and OH1, respectively) with Cu atoms appear to be slightly stronger when passing from the 21493


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The Journal of Physical Chemistry C “external” to the “middle” layer from 2.7 to 2.65 Å and from 3.6 to 3.5 Å, respectively. The OH groups in the polymer were also found to interact with the acetate terminations of the MOF slab with a characteristic distance of 2.7 Å (see Figure S12). The overall picture is a strongly interacting MOF/polymer pair, with excellent compatibility. To further quantify the polymer penetration, we plotted the atomic density profile of the two species as a function of the direction normal to the surface slab in Figure 4. The polymer

To this end, we produced CG models for the MOF and the polymer and combined them by using an analog protocol to that used for generating the atomistic interfaces. The key point of this approach is to adequately parametrize the mutual HKUST-1/PVOH interactions. These were modeled by Buckingham terms with parameters calculated from those of the pure components by applying the Lorentz−Berthelot mixing rules29 as a first approximation. It was found that this model produces an excess penetration of the polymer into the second layer of the MOF surface as compared to the scenario depicted by the atomistic simulations (see Figure S6). Therefore, the CG interface model was refined by reducing the depth of the potential well for all MOF/polymer interactions. Models from 90% down to 50% of the original interaction strength were tested. The appropriate CG interface model was selected from these with the aim to reproduce three key properties from the atomistic simulations: (i) the density profile of the polymer as a function of the distance from the surface of the MOF, (ii) some relevant site-to-site radial distribution functions, and (iii) the radius of gyration of the polymer. The CG model with 60% well depth performed better than the others in terms of the general shape of the density profile, the radial distribution functions and the radius of gyration, and therefore it was selected as the most reliable CG interface model for the purpose of this study (more details can be found in Section I.III of the SI). Figures 4 and 5 illustrate the

Figure 4. Density profile for the atomistic HKUST-1 (orange) and the atomistic (black) and CG model (red) for PVOH. The latter has been multiplied by a factor of 7 to take into account the degree of coarsening.

density is zero in the [−6.5,6.5] Å interval (with z = 0 for the center of the slab), which corresponds to the second pore layer. It further increases for z = ±[6.5,18] Å (region A), up to a point where it starts to oscillate for z = ±[18,25] Å (region B). This general tendency was also identified before for the ZIF-8/ PIMs interfaces.7,8 However, there are two important distinct features for this particular MOF/polymer pair: first, the polymer density only starts to drop when PVOH penetrates the MOF and not before. This reveals that region A is associated with the penetration of the polymer into the first pore layer and that there are no microvoids at the MOF surface, as there were for the previously studied ZIF-8/PIM interfaces. Second, the drop in the density in region A is not monotonic as for the previously reported composites but shows some peaks instead (see, for example, the 12−15 Å region in Figure 4). The maxima for the polymer density coincide with the corresponding voids of the MOF, reflecting that the polymer nicely fits the structure of the MOF pores. Furthermore, the polymer density in region B oscillates around a value that is lower than the bulk density. This implies that the polymer structure in region B is still influenced by the MOF. The size of the system considered for the atomistic simulations corresponds to a total of ∼20,000 atoms of which ∼13,000 belong to the polymer phase. Typically, the impact of a filler in the polymer phase extends up to 2−3 times the radius of gyration of the polymer,15 which is in this case around 7 Å. In order to properly asses the decay of the perturbation generated by the surface we need to include polymer filling at least 3 times the radius of gyration for each side of the slab and a bulk region of the same size, ∼ 40 Å, this would imply simulation boxes of z ∼ 120 Å, which would mean a total of ∼85,000 atoms. The mere size and the necessary configurational sampling would make this extremely expensive at the atomistic scale. Thus, in order to bridge length and time scales, a more efficient approach has been devised with the derivation of a novel CG model.

Figure 5. Top panels: distribution of the radius of gyration. Bottom panels: radius of gyration for chains of N monomers. Atomistic model (black) and CG model (red).

excellent agreement between the density profile and the radius of gyration simulated using this CG model and the corresponding data calculated at the atomistic level. Subsequently, the newly derived CG model was exploited to reveal properties of the MOF/polymer system that would be computationally too costly to be obtained by atomistic simulations, namely the density profile and the variation of the average radius of gyration for the polymer, several nanometers away from the MOF surface. Figure 6 depicts the atomic density profile. The overall structure of the polymer density with oscillations of decreasing amplitude that finally converge to the bulk polymer density is similar to that found for other polymer/nanoparticle composites.30,31 Region B shows large amplitude oscillations around an average value that increases with the distance from the HKUST-1 surface, indicating a layer ordering at the interface. The boundary of region B, which marks the end of the interfacial region and the 21494


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CG strategy to study full MOF nanoparticles embedded in the polymer matrix in order to shed light on important phenomena such as aggregation and phase separation in these technologically promising composites.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b07090. Methodology and computational details, detailed description of the CG model development; atomistic and CG results (PDF)

Figure 6. Atomic density profiles as plotted in Figure 4 including the CG PVOH from the large interface simulations (green).

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beginning of the bulk polymer, can now be determined: it extends up to z = ±(37 ± 5) Å, about 17 Å away from the surface, roughly 2−3 times the polymer average radius of gyration value, consistently to what has been found for other families of polymer composites.15 Beyond this point, the density fluctuates around its bulk value (region C, bulk PVOH). As a further step, the radii of gyration for PVOH were computed. For this, the polymer chains were classified with respect to the z-coordinate of their centers of mass, into those belonging to regions A, B, and C. The average radius of gyration of the polymer in region A is of 6.9 ± 0.1 Å, smaller than for regions B and C of 7.4 ± 0.1 and 7.3 ± 0.1 Å, respectively. Since the distribution of chain sizes in the different regions is very similar (see Figure S13), this different behavior can only be attributed to a change of conformation of the polymers. Indeed, the polymer in region A is confined within the open pores at the surface of the MOF, and this forces the chains to have a more compact conformation compared to those that are free from this constraint. Propitiously, this additional information at longer scale is gained while maintaining an accurate description of the interfacial region depicted at the atomistic level.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Rocio Semino: 0000-0003-3937-7414 Guillaume Maurin: 0000-0002-2096-0450 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research leading to these results has received funding from the European Community Seventh Program (FP7/2007-2013) under Grant 608490 (project M4CO2). G.M. thanks Institut Universitaire de France for its support. This project has been supported by the Deutsche Forschungsgemeinschaft (DFG, Priority Program 1362 and Grant SCHM 1389/8-1). Further financial support from the Cluster of Excellence RESOLV (EXC 1069) funded by the DFG is gratefully acknowledged. J.P.D. is grateful for the financial support by the Fonds der Chemischen Industrie (FCI).

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CONCLUSIONS This work features the first atomistic/CG multiscale simulation study on a MOF/polymer interface. The scenario found for the HKUST-1/PVOH interface is radically different from those for the previously reported ZIF-8/PIMs interfaces:7,8 there are no interfacial voids; instead, the polymer penetrates into the first pore layer at the MOF surface. Strong intermolecular interactions hold the components together, and they are reinforced by the increase in the contact surface between the two components due to the penetration. This is a computational confirmation that a very good MOF/polymer affinity can be achieved, as it was already reported experimentally.32 Furthermore, the first CG model for these composites was developed, and it was possible to obtain from it the full picture of the MOF/polymer interface. When moving away from the MOF surface, PVOH density increases, following the structure given by the first pore layer of HKUST-1. The interface then continues with ample oscillations of the PVOH density around an increasing average value up to a distance of roughly 2.4 times the average radius of gyration from the HKUST-1 surface, in the same range as was previously found for other polymer composites.15 Beyond, the bulk behavior of PVOH is observed, marking thus the end of the interfacial region. It is noteworthy that the main interface features could be captured with reasonable accuracy using a simple CG model for PVOH with a relatively high degree of coarsening of one bead per monomer. Future directions of this work will be to extend this

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