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Microscopic model of the MOF/Polymer interface: a first step towards understanding the compatibility in Mixed Matrix Membranes Rocio Semino, Naseem A. Ramsahye, Aziz Ghoufi, and Guillaume Maurin ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.5b10150 • Publication Date (Web): 14 Dec 2015 Downloaded from http://pubs.acs.org on December 15, 2015

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ACS Applied Materials & Interfaces

Microscopic model of the MOF/Polymer interface: a first step towards understanding the compatibility in Mixed Matrix Membranes Rocio Semino†, Naseem A. Ramsahye*†,‡, Aziz Ghoufi┴, Guillaume Maurin† † Institut Charles Gerhardt Montpellier UMR 5253 CNRS, Université de Montpellier, Place E. Bataillon, 34095 Montpellier Cedex 05, France. ‡ Institut Charles Gerhardt Montpellier, UMR CNRS 5253 UM2 ENSCM UM1, ENSCM, 8 rue de l’Ecole Normale, 34296 Montpellier Cedex 05, France ┴

Institut de Physique de Rennes, IPR, UMR CNRS 6251, 263 Avenue du Général Leclerc,

35042 Rennes, France.

Abstract An innovative computational methodology integrating Density Functional Theory calculations and forcefield-based molecular dynamics simulations was developed to provide a first microscopic model of the interactions at the MOF surface/Polymer interface. This was applied to the case of the composite formed by the polymer of intrinsic microporosity, PIM-1, and the zeolitic imidazolate framework, ZIF-8, as a model system. We found that the structure of the composite at the interface is the result of both the chemical affinity between PIM-1 and ZIF-8, and the rigidity of the polymer. Specifically, there is a preferential interaction between the -CN groups of PIM-1 and the NH terminal functions of the organic linker at the ZIF-8 surface. Additionally, the resulting conformation of the polymer gives rise to interfacial microvoids at the vicinity of the MOF surface. The porosity, rigidity and density of the interfacial polymer were analyzed and compared to those for the bulk polymer. It was shown that the polymer still feels the impact of the MOF surface even at long distances above 15-20 Å. Further, both the polydispersity of the polymer and the flexibility of the MOF surface were revealed to only slightly affect the properties of the MOF/interface. This work, which delivers 1 ACS Paragon Plus Environment


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a microscopic picture of the MOF surface/polymer interactions at the interface, would lead, in turn, to the understanding of the compatibility in MOF-based mixed-matrix membranes.

Keywords: MOF/Polymer Interface, Microscopic Model, Molecular Dynamics, Density Functional Theory, Mixed-Matrix Membranes

I. INTRODUCTION The characterization of the surface structure and the exploration of the interfacial interactions between external crystal surfaces and either liquid or gas molecules, or other solids are of utmost importance to understand and further control the crystal growth mechanism of a range of nanomaterials as well as their surface reactivity.1 The Mixed-matrix membranes (MMMs) which incorporate porous solids as fillers into a polymer matrix integrates a solid/solid interface that is expected to dictate the feasibility and the stability of such hybrid composites. While the performances of zeolites and Metal-Organic Framework (MOFs)-based MMMs have been intensively explored for a series of gas and liquid mixtures,2-11 a deep understanding of the interfacial interactions between the two components is still lacking. In this context, an essential prerequisite is a detailed atomic level model of the porous solids’ surface as well as that of the polymer. The construction of a polymer model can be readily achieved by the use of diverse range of established computational strategies, including a Monte Carlo based scheme12 and in silico polymerization such as the one developed by Abbot et al.13 In contrast, this is not the case for the MOF materials. Indeed, although many computational studies of adsorption and diffusion phenomena in MOF pores are available in the literature,14-18 there is a dearth of articles in which the external crystal surface of this class of porous solids is considered. To date, only a few experimental19-22 and theoretical23-25 studies have appeared in this field. Chizallet et al. first23,24 reported ab initio cluster/periodic

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calculations to reveal the acidity/basicity of the surface sites of the zinc-based zeolitic imidazolate framework ZIF-8 and their catalytic activities for the transesterification of diverse alcohols, and their models largely corroborated the experimental work of Tian et al.22 More recently, Schmid et al.,25 employed first-principles-derived forcefield and Density Functional Theory (DFT) calculations to identify the most stable surface termination of HKUST-1 and the driving force for the growth mechanism. To the best of our knowledge, here we report the first microscopic model that allows the study of the interactions at the MOF/polymer interface, developed using a hybrid computational methodology integrating quantum- and forcefield-based simulations. A first step consisted of constructing 3D periodic slab models of the MOF surfaces that are likely to dominate the crystal habit, which were then geometry-optimized using DFT calculations, paying particular attention to the nature of the terminal functional groups as well as on the structure and texture of the MOF surface. In tandem to this, we have generated a reliable model of the polymer at the atomic level. Once the two components have been created, a significant effort has been further deployed to devise a robust route implying forcefield-based molecular dynamics for the construction of reliable models for the MOF/polymer interface. Three model systems were considered, in order to assess the impact of the MOF surface flexibility, and the polydispersity of the polymer model, in terms of the number and size of the chains. Finally, the properties of this interface such as the nature of the interactions, surface coverage, conformation and rigidity of the polymers that all together play a key role in the stability of the composite have been explored. The computational procedure is summarized in Figure 1.



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Figure 1. Workflow of the integral methodology developed for the generation of the MOF/polymer interface and its characterization. As an illustration, this procedure has been applied to the ZIF-826/PIM-127 (Polymer of Intrinsic Microporosity) composite. PIM-1 has been widely studied in the membranes community for diverse applications including pervaporation,28 organic solvent nanofiltration29 and gas separation membranes.30 The relatively small-pore zinc-based MOF, ZIF-8, has also been extensively investigated in the forms of powders and pure inorganic membranes owing to the flexibility of its framework that authorized the separation of a range of molecules.31 Binary composites combining ZIF-8 with PIM-132 as well as with other polymers,33-36 have been already reported to show performances even more promising than the MOF alone for gas separation applications. This paper is organized as follows. Section II.1 and II.2 summarize the PIM-1 and ZIF-8 surface constructions. Section II.3 presents the methodology we developed for the generation 4 ACS Paragon Plus Environment

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of the MOF/polymer interface. The characterization of the resulting interfaces is detailed in Section III, organized in three subsections: interactions between the polymer and the MOF, free volume distribution and rigidity of the polymer at the interface. Our main conclusions and perspectives are summarized in section IV.

II. METHODOLOGY 1. Polymer Generation The construction of the polymer was performed using the in silico polymerization approach developed by Abbot et al. as implemented in the Polymatic code.13 The choice of this polymer building strategy was motivated by the fact that it has been proven to be appropriate for building amorphous ladder backbone polymers, such as PIM-1 among others;37-39 however, note that our global methodology does not imply the use of any particular polymer construction scheme. For the sake of completeness, a short summary of this methodology is reported in Supporting Information (SI). We mainly followed the implementation of Larsen et

al.,39 with complementary implementations: (i) rather than relying on a random process to generate the initial configuration for the polymerization, a system consisting of 230 monomers (scheme given in Figure S1c) was equilibrated. Indeed, since the polymerization leads to a poly-disperse mixture, this initial number of monomers is selected to allow the construction of one long chain of ~100 monomers, among other shorter chains; (ii) instead of using a cubic simulation box, the monomers were initially distributed in an orthorhombic cell of dimensions 50 Å x 50 Å x 150 Å. The x and y dimensions of the simulation box were chosen to be similar to those of the MOF surface, while the z length was taken as three-fold this value, since an anisotropic system, with z >> x,y, is needed for further adding the MOF surface to generate the interface. The equilibration was performed by



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Molecular Dynamics runs (MD) in the NVT, NPT and NPnT ensembles successively, at temperature T = 300 K and pressure P and Pn both equal to 1 bar, Pn being the normal pressure to the plane interface. A snapshot of the monomers box is depicted in Figure S1d. Periodic boundary conditions were applied in the three directions. (iii) after this initial equilibration, the box length was enlarged along the z-axis by the addition of two empty boxes of 50 Å x 50 Å x 125 Å, so that the final dimensions of the box were 50 Å x 50 Å x 400 Å. This additional stage before the polymerization process allows for the local monomer density to be high enough to provide a good initial condition for the polymerization in terms of the proximity of the monomers, and, at the same time, low enough to allow for the formation of long chains without overlaps respectively. (iv) finally, a further step after the polymerization consisted in “capping” the so-generated polymers in order to avoid unphysical artifacts due to the presence of high-energy sites. Larsen et al.39 have used neutral steric blocking groups for this purpose. Here, a more realistic “capping” was considered and consisted of considering F and H atoms, to mimic the scenario in play for the experimentally synthesized polymer.27 This allows a more reliable microscopic description of the polymer/MOF interface. The polymerization resulted in a polydisperse mixture. Two samples of polymers were selected: (i) one long chain of 102 monomers, and (ii) a system formed by 10 chains each containing between 10 and 20 monomers. The latter resembles the PIM-1 representation proposed by Larsen et al.,39 in terms of number and size of the chains, while the former corresponds to a similar total number of monomers however assembled in a single chain, in order to propose a more realistic model of the polymer and to reduce the effect of chain ends. The MD simulations of the polymer in the different ensembles mentioned above were performed with the LAMMPS package,40 as implemented in the Polymatic code.13 The temperature and pressure were regulated by means of the Berendsen thermostat and barostat


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with relaxation times of 0.1 ps and 0.5 ps repectively.41 The energy of the system was considered as the sum of bonded and non-bonded contributions. The former includes harmonic potentials to model the stretching and bending modes, as well as cosine-based functions for dihedrals and improper dihedrals torsions. The potential parameters for these contributions were obtained from the GAFF force field.42 The non-bonded contributions were expressed as the sum of Coulombic and Lennard-Jones (LJ) 12-6 site-site potentials. The LJ parameters were taken from TraPPe,43 and crossed-interactions were computed by applying the Lorentz-Berthelot mixing rules.44 Each CHx (x=1,2,3) group in the polymer was considered as one particle (the united atom approach) in order to reduce the simulation time. Non-bonded parameters to describe the polymer are listed in Table S1 of the Supporting Information (SI). The electrostatic potential (ESP) derived partial charges, q, were computed by DFT calculations with PBE functional,45 and DNP basis set,46 using the Dmol3 47 module in Materials Studio.48 These calculations were performed on the monomer, the dimer and the two possible trimers, to test the transferability of the charges to larger polymer chains, which was found to be acceptable. These atomic charges are reported in SI (table S1). Electrostatic interactions were calculated by means of the Ewald sum while a cutoff of 15 Å was set for the LJ interactions.

2. MOF Surface Construction The construction and the geometry optimization of the MOF surface models were achieved by following the methodology described for zeolites49 and recent work on HKUST-1.25 The bulk ZIF-8 material was first geometry optimized at the DFT level, using the Quickstep module of the CP2K software.50 In these simulations both the positions of the atoms of the framework and the unit cell parameters were fully relaxed. The PBE functional45 was used along with a combined Gaussian basis set and plane wave pseudopotential strategy as



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implemented in the code. A triple zeta Gaussian-type basis set (TZVP-MOLOPT basis set provided with the code)51 was considered for all atoms, except for the metal centers, where double zeta functions were employed (DZVP-MOLOPT).51 The pseudopotentials used for all of the atoms were those derived by Goedecker, Teter and Hutter.52 These calculations included the semi-empirical dispersion corrections as implemented in the DFT-D3 method, derived by Grimme.53 A comparison of the initial and optimized cell parameters is given in Table S2. The resulting optimized structure was then used to identify sets of Miller indices that would result in a favorable surface cut, via the Bravais-Friedel-Donnay-Harker (BFDH) method.54-56 Such an approach is useful for a rapid screening of different crystal faces and allows one to focus on the faces most likely to be important in the material's crystal habit. Following this analysis, slab models of the [100] and [011] surfaces were then constructed, considering three dimensional periodic boundary conditions using the Materials Studio software.48 These models were of 96.8 Å in length along the z direction (8 times the cell size). Indeed, we

performed the energy calculation for surface slabs of different size, and we found that the energy converge for the system built up with 4 unit cells. This surface slab length also ensures that no interaction between the surfaces could take place in the z direction. We have further doubled the size for the final model used to perform the force field simulations. In addition to this, a vacuum gap of at least 15 Å was applied in the z axis, in order to avoid any interactions between the slab and its periodic images in this direction. Cleaving such a surface often leaves a net dipole in the z direction, which if left in the model, can result in an interaction of the dipole moment across the vacuum gap, and can distort the adjacent surface.57 This dipole was eliminated by “rebuilding” the surface. In the current case, this meant moving certain atoms from the top to the bottom of the slab in order to obtain the same features on both surfaces of the model, resulting in a mirror plane of symmetry at the center of the z axis.57 An


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exposed surface cut using the BFDH method often results in under-coordinated sites which, in reality, would be susceptible to reactions with solvents present in the synthesis medium. In the case of our model, a dissociative adsorption of water was considered, resulting in the attachment of an -OH group and a –H atom to the surface, as shown in Figure 2, analogous to the surface terminations of ZIF-8 proposed by Tian et al. as a result of their experimental study,22 as well as the computational modelling work of Chizallet et al.24 The final surface models were then geometry-optimized using the Quickstep module of the CP2K code,50 using the same level of theory and parameters as the optimization of the bulk ZIF-8 model. In order to select a MOF surface for the development of our mixed matrix membrane model from the two surface cuts that were considered, a surface energy of each of these two models were then calculated using the following expression,

=

– ∗ !!"# $% &

Equation 1

where A is the area of the surface slab, Esurface slab and Ebulk are the energies of the surface slab and bulk models, respectively, and n refers to the number of bulk cells used to make the surface slab. Esolvation corresponds to the energy of dissociative adsorption of solvent molecules24,49. The [011] surface was subsequently chosen for development of our hybrid MOF-polymer model, since this was the surface with the lowest energy (3.31 J m-2 and 3.65 J m-2 for the [011] and [100] surfaces respectively. Further details are given in SI).



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Figure 2: a) and b) The cut from the bulk ZIF-8, exposing the [011] face of ZIF-8. In Figure a, the blue plane is that with Miller indices of [100], and the pink one corresponds to [011]. The panels b) and c) show the cut plane (dashed line) and the [011] surface of ZIF-8, respectively. The atoms shown as spheres are those from the dissociative adsorption of water. The following color code is used for the atoms: Zn – light blue, N – dark blue, C – grey, H – white, O – red.

In our subsequent work in simulating the MOF/polymer interface, molecular dynamics simulations were performed considering the MOF fixed, as well as the case where the MOF was treated using a flexible model. In order to take the framework flexibility into account, the 10 ACS Paragon Plus Environment

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flexible forcefield parameters and the atomic partial charges, published by Zheng et al.,58 calculated using the Merz-Singh-Kollman (M-K) model,59,60 were applied to the surface slab model. The forcefield parameters for the attached -OH groups and –H atoms were taken from the AMBER61 database, following the same strategy as Zheng et al.58 The atomic charges for these latter atoms were calculated with Gaussian03,62 using the PBE functional45 and the 631G(d,p) basis set.46 For our models, both the Electrostatic Potentials fitting using a gridbased method (CHELPG) scheme63 and the M-K method59,60 were tested, and were found to give very similar values for the atomic charges. The whole set of force field potential parameters, as well as the atomic partial charges are given in SI (tables S2-S7).

3. Generation of the MOF/polymer Interface Three kinds of sample models representing the composite interface were studied; their principal characteristics are summarized in Table 1. Details on the polydispersity of system 3 are given in SI (see Figure S2). Table 1. Model systems descriptions. System PIM-1 characteristics

ZIF-8 characteristics

1

One chain, 102 monomers

Fixed surface

2

One chain, 102 monomers

Flexible surface

3

10 chains, 10-20 monomers each Fixed surface

In order to build the interface, we performed a series of three stages involving several MD simulations each, in order to merge the polymer and the MOF surface: (i) First, we equilibrated the polymer using the 21 MD steps scheme proposed by Hofmann et

al.64 and implemented by Larsen et al. in their study.39 Within this scheme, seven cycles of three MD simulations were performed: (1) NVT, T = 600 K, (2) NVT, T = 300 K and (3)



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NPT, T = 300 K (see Table 2). The value of the pressure in the NPT simulations was gradually increased, passing from the first to the third cycle up to Pmax = 50 kbar, and then was reduced stepwise, until it reached the final value of P = 1 bar. In order to choose Pmax, we have tested four different values: 1, 10, 30 and 50 kbar. We observed that the density obtained for the polymer converged to a constant value for Pmax > 10 kbar, as reported by Larsen et al. for pure PIM-1.39 Since we have added void boxes in the z direction of the monomers box prior to the polymerization, the resulting polymer was loosely packed in the z direction. When the box lengths were allowed to change isotropically in the NPT simulations, the packing was adjusted in the xy planes, while it still remained loose in the z direction (see Figure 3a and 3b). (ii) Secondly, the so-obtained polymer was brought into contact with the MOF in the same simulation box. To achieve this, the polymer coordinates were unwrapped in the z direction, and the box was added on top of the MOF box so that the z direction of the polymer is perpendicular to the MOF surface. Then, a new set of 21 MD steps was performed, but this time, the third simulation of each of the seven cycles was performed in the NPnT ensemble: the MOF acts as a “piston” on the polymer, as the system compresses and expands itself only in the z direction. The coordinates of the atoms representing the MOF framework were kept fixed during the whole process. The interaction between the polymer and the MOF was taken as a summation of Coulombic and LJ potentials contributions, with cross interaction parameters computed according to the Lorentz-Berthelot mixing rules.44 All of the simulations were performed using a modified version of DLPOLY code,65 to include the possibility of using the NPnT ensemble. After this stage, a well-packed polymer is obtained, with a typical volume of 50 Å x 50 Å x 50 Å, in contact with the MOF surface (see Figure 3c).


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Figure 3: a) side and b) upper views of a configuration of the 102 monomers long polymer chain after the first stage of the surface generation process. c) Snapshot of one of the polymer/MOF interface configurations corresponding to the case of rigid ZIF-8 (system 1) after the second stage of the process. The polymer carbon atoms are rendered in cyan, the oxygen atoms in red and the nitrogen atoms in blue, while the atoms of the MOFs are depicted by the color code described in Figure 2. (iii) Finally the last stage consisted of the MD production runs over 10 ns, in the NVT ensemble, at 300 K. Since the 21 MD steps high-pressure stages can influence the final conformations of the polymer at the MOF surface, several independent runs were generated for analysis (see SI). The initial conditions for these runs were generated in two different



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ways: (i) by applying 10 heating / cooling MD cycles with different temperatures and durations to the selected polymer chains at the first stage of the interface generation process, before adding the MOF, and (ii) by performing Biased Potential Dynamics (BPD)66 on the polymer/MOF system and choosing configurations with different polymer end-to-end distances. The BPD approach was performed using the DLPOLY code,63 with the Hamelberg bias potential.67,68 This technique is based on the addition of a boost potential to the real potential energy of the system, so that the energy of local minima is raised, in principle without affecting the energy of the maxima and saddle points.66 This technique has been extensively used for studying systems with slow relaxation times69 including proteins and amorphous solids,70-72 as well as suggested for the study of polymers.73 In this work, we present results from BPD simulations using

'

"

= 0.2, 0.3 and 0.35, which are typical

values,67,68 and a () associated to a thermal energy of 8000 K, which was necessary in order to achieve an efficient sampling of the configurational space. More details regarding this technique and its implementation are provided in SI.

Table 2. Details of the thermodynamic conditions for the 21 MD steps used in the process of the interface generation. Step Ensemble

T (K) P(kbar)

Length (ps)

1

NVT

600

50

2

NVT

300

50

3

NPT*/NPnT**

300

4

NVT

600

50

5

NVT

300

100

6

NPT*/NPnT**

300

1 (0.02 Pmax)

30 (0.6 Pmax)


50

50

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7

NVT

600

50

8

NVT

300

100

9

NPT*/NPnT**

300

10

NVT

600

50

11

NVT

300

100

12

NPT*/NPnT**

300

13

NVT

600

5

14

NVT

300

10

15

NPT*/NPnT**

300

16

NVT

600

5

17

NVT

300

10

18

NPT*/NPnT**

300

19

NVT

600

5

20

NVT

300

10

21

NPT*/NPnT**

300

50 (Pmax)

25 (0.5 Pmax)

5 (0.1 Pmax)

0.5 (0.01 Pmax)

0.001

50

5

5

5

800

* First and ** Second stages

III. RESULTS AND DISCUSSION A. PIM-1/ZIF-8 Interfacial Structure Our chosen model for ZIF-8 surface can be schematically described as a “zig-zag” where the outermost atoms are the NH groups of the imidazole linkers, and the innermost are the OH groups directly bonded to the Zn atoms (see Figure 4a). These two MOF surface sites are potential attractive sites for the -CN groups and/or the O atoms of the heterocycle of PIM-1. To confirm this, the radial distribution functions (RDF) between different MOF-polymer atom pairs have been first calculated from the MD trajectories. Figure 5a reports the corresponding



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data in the case of the long chain PIM-1 interacting with the rigid ZIF-8 surface. This series of RDF indicates that the polymer arranges in such a way to form a preferential interaction between its nitrogen atom of the cyano function and the –NH group of the MOF surface leading to a mean characteristic (NH)ZIF-8 - (N)PIM-1 distance ~2.57 Å. In addition to this, the aliphatic carbons of PIM-1 in some cases can be located in the vicinity of (NH)ZIF-8 with corresponding mean distances of ~ 3.09 Å. This scenario is encountered when the L-shape vertex of the polymer (see Figure 4b) falls into the troughs formed by the “zig-zag” MOF surface as shown in Figure 6b. The interactions between the (OH)ZIF-8 group and the PIM-1 sites are found to be much less specific, due to the fact that these hydroxyl groups are less exposed to the polymer phase compared to (NH)ZIF-8 (see Figures S10 and S11). An illustration of the resulting geometry of the polymer attached at the MOF surface is provided in Figure 6. Further, Figure S9 evidences that the nature of the PIM-1/ZIF-8 interactions is only slightly affected when the flexibility of the MOF is taken into account. One can however notice that some local reorientation of the MOF surface reduces the interaction between the methyl groups and the (NH)ZIF-8 functions (see Figure S9a bottom panel). The (NH)ZIF-8 . . . (N)PIM-1 is the most predominant interaction, as was observed for the one chain PIM-1 / rigid ZIF-8 system (see Figure S9a top panel). In addition, the consideration of the polymer sample containing the small chains emphasizes that the polydispersity of the polymer chain does not have a significant impact in the nature of the preferential interactions with the MOF surfaces (see Figure S9b). More significant changes might be observed for MOFs with a pore size large enough to allow a partial penetration of the polymer into the pores which is indeed not the case for the selected composite system where the dimensions of the PIM-1 monomer exceed the pore aperture of ZIF-8, ~4 Å. Note that, even though the effect of the flexibility of the MOF surface at the structure of the interface were found to be almost negligible,


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flexibility would have to be considered for further studies of gas adsorption/diffusion at the interfaces.

Figure 4. Schematic representation of (a) the ZIF-8 surface and (b) the PIM-1 “monomer”. The atom color code is the same as in Figures 2 and 3.

To further confirm that the so-obtained MOF/polymer geometries correspond to a global minimum on the potential energy surface, we analyzed the trajectories generated by BPD runs in complement to the MD simulations which evidenced a slow dynamics of PIM-1 due the well-known rigid character of this polymer, Figure 5b reveals that the nature of the MOF/polymer interactions issued from the BPD runs turns out to be very similar to that obtained from the MD analysis. This observation unambiguously confirms that the (NH)ZIF8

- (N)PIM-1 interactions predominantly govern the composite interface.



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Figure 5. Radial distribution functions for the pairs (NH)ZIF-8

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. . .

xPIM-1 = N (top), O

(middle) and methyl (bottom) calculated for the long chain PIM-1/ rigid ZIF-8 surface. a) results obtained from 4 different MD runs, b) results obtained from 2 different BPD runs (magenta and green) and from the average over the 9 MD runs for the sake of comparison (black).


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Figure 6. Illustration of a) (NH)ZIF-8 . . . (N)PIM-1 interaction and b) (NH)ZIF-8 . . . (Methyl)PIM1.

Color codes are the same as in Figures 2 and 3.

B. Free Volume Distribution of the Polymer Phase As a further step, the analysis of the pore size distribution (PSD) of the voids for the PIM-1 phase was performed. As a preliminary step, we cut the polymer phase in the composites at different z values, and thus generated slices that are mainly xy planes, with a height of z = 3 Å. extremes of the MOF surface to the other. Figure 7 shows a representation of these slices for the top part of the MOF surface, for a representative configuration of the one chain PIM-1/ rigid ZIF-8 system (see Figure S12 for results for the other systems).



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Figure 7. Snapshots of xy planes of the polymer phase of z = 3 Å width. z = 0 Å corresponds to the polymer layer adjacent to the MOF surface and z = 24 Å represents the middle of the polymer phase. One can observe that the z density of polymer atoms increases when moving away from the ZIF-8 surface, until it converges towards an almost constant value. Two regions in the interfacial layer can be clearly identified: a region represented by the first 4 pictures, on the one hand; and another region described by the rest of the pictures. The first zone labeled as region A, is characterized by a very low polymer density, in close proximity to the MOF surface, of 9-15 Å width, characterized by “interfacial microvoids” and some polymer penetration into the MOFs “pockets”. This phenomenon is illustrated by the snapshot provided in Figure 8b. The second zone, labeled as region B, is more bulk-like. In complement to this, a more quantitative analysis was undertaken. Figure 8a reports the density plot of both polymer and MOF atoms as a function of the z axis. When one scans the domain [z=0 Å to z= whole box length along the z axis (141 Å in this case)], a first region can be defined where only the polymer is present, and its atomic density oscillates around an equilibrium value (see black line). Above z~13 Å, the atomic density of the polymer drops until z~24 Å and then we enter a region where only the MOF is present (see red curve), until 20 ACS Paragon Plus Environment

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z~119 Å. Above this limit, the polymer atomic density starts to increase until it reaches once again a constant value. Note that there is a region of overlap, where the atomic densities of both components do not totally vanish. This is due to the penetration of the polymer in the troughs of the MOF surface, as illustrated in Figure 8b. The limits of the region A can be defined as follows: (i) the z-value for which the polymer density starts to oscillate around its equilibrium value, and (ii) the z-value for the outer Zn atoms, which is almost the same as the value where the polymer atomic density vanishes. An illustration of this so-defined region is provided in Figure 8b, where it is highlighted and superimposed with the rest of the system. The average length of region A in the z-axis was found to be 12.3, 13.6 and 13.9 Å for the systems 1, 2 and 3 respectively (see Table 1). This interfacial width is within the same order of magnitude as that usually found for interfaces involving MOFs and zeolites.74,75



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Figure 8. a) Density of polymer (black line) and MOF atoms (red line) as a function of the z coordinate for a representative configuration of PIM-1/rigid ZIF-8 system. The blue dashed lines represent the limits of regions A and B (see text). b) Snapshot of the interface, where the atoms that belong to region A are opaque, and the rest are transparent. One characteristic that could be investigated in order to assess if region B corresponds to a bulk-like polymer is the density. The average simulated densities of the polymer restricted to

region B are (0.89 + 0.04) g cm-3, (0.82 + 0.05) g cm-3 and (0.92 + 0.04) g cm-3, for systems 1, 2 and 3 respectively (see Table 1), where the error bars were computed as the standard deviation of the data. Both the flexibility of the framework and the increase of the number of polymer chains together with a reduction in their size do not produce statistically significant changes, since the error bars of the densities for all systems show superposition. These density values are ~10 % lower than the one that was previously reported for the bulk polymer (0.98 g cm-3) using the same computational approach to build PIM-1.39 It could be argued that such a lower density value might result from a deficient equilibration scheme for the particular system of interest. To check this, a second 21 MD steps cycle was performed on one of the system 1 configurations and the difference in the obtained density with respect to that of the first equilibration scheme was of 2%, which is not statistically significant since the error is ~5%. Indeed, the so-obtained lower density compared to the value for the bulk PIM-1 is related to a genuine characteristic of the polymer phase, most probably due to a different geometry of the polymer backbone imposed by the anchoring sites present at the MOF surface. It can thus be concluded that the influence of the MOF surface extends further than

region A, even at distances greater than 20 Å from the surface. As a further step, the analysis of the pore distribution in the polymer phase was undertaken separately for region A and region B, by two different computational strategies. The first one, known as the v_connect approach,76 consists of measuring the volume for each of the “pores” which is plotted as a distribution of sphere radius values (see SI). Since one considers the 22 ACS Paragon Plus Environment

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“pore” volume regardless of its shape, large interconnected void networks are computed as only one “pore”. The second approach is based in the method developed by Bhattacharya and Gubbins,77 in which the PSD is the statistical distribution of the largest sphere that can be fitted at some point in the space without any overlap with the polymer atoms. This methodology assumes spherical shape of the “pores”, and in doing so, a large interconnected network of void space is considered as several different “pores”. The corresponding data are reported in Figure 9 for the PIM-1/rigid ZIF-8 system.

Figure 9. Histograms for the pore size distribution computed for a representative configuration of PIM-1/rigid ZIF-8 system according to (i) the v_connect methodology, for positronium (black) and nitrogen (red) sized probes, weighted by pore number (top) and by



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free volume fraction (middle) and to (ii) the sphere fitting method (bottom). Region A (left) and region B (right).

One first observes that the distribution of the number of pores as a function of the equivalent radius calculated using the v_connect methodology with probes of the size of positronium and nitrogen atoms(Figure 9 top) is relatively broad for both regions A and B. The number of pores with a given equivalent radius is shown to decrease when the radius is increased. The difference between the two regions is the range of radius covered: while for region B we find pores up to * + ~ 4 Å, region A exhibits additional larger pores, * + ~ 6.5 Å, that can be associated with “interfacial microvoids” that can be observed from Figure 3c. This feature is confirmed by the free volume fraction plotted as a function of the equivalent radius (Figure 9 middle). The larger pores for region A are few, but represent an important volume fraction, of about ~40% and ~25% when the probe molecule is positronium, and nitrogen respectively. The presence of the “interfacial microvoids” is also confirmed by the PSD computed by the sphere fitting method (Figure 9 bottom). The distribution range is almost the same than for the v_connect graphs, which supports that the voids are not highly interconnected. Contrary to the case of bulk PIM-1,78 no mesopores can be detected, the pore sizes are restricted to the micropores region, for both regions A and B. This observation confirms that even at long distances ~ 15-20 Å from the MOF surface, the polymer still feels the influence of the MOF due to the conformational change it undergoes at the interface. This is also reflected in the average value of the equivalent radius weighted by the free volume fraction obtained with the positronium probe * + ~ 4.1 Å which slightly deviates with the experimental value reported by PALS for the bulk polymer (4.8 Å).79-80 Similar analyses were performed for systems 2 and 3 (see Figures S13 and S14). The resulting distributions are very similar to that reported in


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Figure 9, the sole exception is that the maximum radius of region A voids is slightly larger, typically around 6.5-7 Å, in these cases.

C. Rigidity of the Polymer Phase As a further step, the stiffness of the interfacial polymer was characterized by computing the distribution of two typical dihedral angles of the backbone. The analysis performed separately for region A and region B led to similar observations and consequently, Figure 10 reports the histograms for the global polymer phase. Figure 10a reports the θC-C-O-C profile for the bonds at an ether-O atom averaged over all the MD trajectories for the PIM-1/rigid ZIF-8 system. This angle represents a measure of the degree of flexibility of the “planar” part of the molecule as proposed by Heuckel et al.78 Compared to the behavior for the bulk polymer,78 the two peaks centered around +180o are narrower and the shoulders at +150o are no longer present. This suggests that there is a lower degree of out-of-plane oscillation for the ladder backbone of the interfacial PIM-1 than for the bulk polymer. The second dihedral angle φC-CC-C

that involves the spiro carbon atoms is an observable of the flexibility of the “L” vertex of

the polymer. Figure 10b shows that the interfacial polymer exhibits a single broad peak for this angle ranging from -95o to -15o with the presence of a maximum at -54o. This profile significantly deviates with the broad bimodal distribution between -10o and -110° and two maxima at -35o and -75o previously reported for the bulk polymer.78 This observation confirms that the interfacial polymer exhibits a higher degree of rigidity than the bulk one, and supports the conclusion that the conformation of the PIM-1 at the MOF/polymer interface is quite different compared to the situation for the bulk polymer.



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Figure 10. Histograms for the distribution of the two dihedral angles θC-C-O-C and φC-C-C-C in the polymer calculated from the MD simulations for the PIM-1/rigid ZIF-8 system. For comparison, the values of θC-C-O-C and φC-C-C-C for the monomer in vacuum are 180° and -52° respectively.78

IV. CONCLUSIONS In this paper, we have presented a computational methodology able to build and characterize a polymer/MOF interface. First, the two components of the interface, the MOF surface and the polymer, were modeled. As a second step, the interface is generated in a three stages procedure involving Molecular Dynamics runs. We have successfully compared these results with those obtained from biased potential dynamics simulations, where the configurational space is efficiently sampled, and we have also verified that the statistics gathered from the different initial conditions leads to the same physicochemical picture of the interface. Furthermore, we have assessed the differences in the results by varying (a) the length / number of chains of the model polymer, and (b) the flexibility of the MOF surface. Overall, the three models studied lead to the same gross microscopic picture. 26 ACS Paragon Plus Environment

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The results for the application of our methodology for a model system were described for the resulting PIM-1@ZIF-8 system. The interactions between the phases in the binary composite are the result of the interplay between (i) the energetically favored proximity of the interacting sites, (ii) the rigidity of the polymer and (iii) the distribution of the MOF “pockets”. We found that there are interactions between the CN groups from PIM-1 and the NH groups of the imidazoles that “cap” the Zn atoms at the ZIF-8 surface. Moreover, the aliphatic carbons, which are located at the vertex of the “L”-shaped monomer, get into some of the “pockets” formed by the “zig-zag” shape of the surface. Due to the rigidity of the polymer at the interface, which was found to be even higher than for the bulk polymer, there are also “interfacial microvoids” between the two components. Indeed, two regions can be clearly identified in the interfacial polymer: region A, which consists of the “interfacial microvoids”, and region B, a more bulk-like polymer. Region A has a width of ~ 13 Å, with pores of radius up to 6-7 Å, that do not seem to be highly interconnected. At longer distances, the interface continues, characterized by a polymer region with lower density than that from the bulk, and a somewhat different porosity, with pore sizes up to 4-5 Å and no mesopores. Our methodology is fully transferrable to other polymer/MOF systems, and we believe it will be useful to scan the potential affinity between different polymers and MOF surfaces. The sole prerequisite in order to successfully apply this methodology is to have an adequate forcefield description of the system of interest, which should also include a flexible description of the MOF surface if the pore dimensions require it. Further directions of our research include studying the compatibility of ZIF-8 with polymers of different rigidity, other polymer/MOF interfaces with the selection of MOFs with different chemical terminations and pore aperture, and polymers of various dimensions, and comparison of our results with experimental measurements. Furthermore, we are planning to use this interface model to gain an unprecedented in-depth analysis of the H2/CO2 gas



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separation process at the microscopic scale. Such a systematic study will pave the way towards the selection of the best MOFs/polymers pairs to ensure the experimental feasibility of the corresponding hybrid membranes for further application in the areas of gas and liquid separation.

V. ASSOCIATED CONTENT Supporting information available: detailed description of the different algorithms used for building the polymer and the MOF and for validating and characterizing the MOF/polymer interface, tables with all the potential parameters, and additional graphs that further illustrate our results. This material is available free of charge via the Internet at http://pubs.acs.org. VI. AUTHOR INFORMATION Corresponding author E-mail: [email protected]

VII. ACKNOWLEDGEMENTS The research leading to these results has received funding from the European Community Seventh Program (FP7/2007-2013) under grant agreement n° 608490 (project M4CO2). The authors thank Dr. Ben Slater for very useful discussions on MOF surfaces and their terminations, Dr. Said Hamad and Dr. A. Rabdel Ruiz Salvador for initial discussions on DFT applied to MOF surfaces, and Prof. N. Steunou (Institut Lavoisier Versailles, France) for fruitful discussions on the polymer/MOF interactions. G.M. thanks Institut Universitaire de France for its support.

VIII. REFERENCES


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Polymer Interface

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