Large Out-of-Plane Deformations of Two-Dimensional Covalent

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Large Out-of-Plane Deformations of Two-Dimensional Covalent Organic Framework (COF) Sheets Haoyuan Li, and Jean-Luc Bredas J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01762 • Publication Date (Web): 08 Jul 2018 Downloaded from http://pubs.acs.org on July 8, 2018

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The Journal of Physical Chemistry Letters

Large Out-of-Plane Deformations of Two-Dimensional Covalent Organic Framework (COF) Sheets Haoyuan Li and Jean-Luc Brédas* School of Chemistry and Biochemistry Center for Organic Photonics and Electronics (COPE) Georgia Institute of Technology Atlanta, Georgia 30332-0400

E-mail: [email protected]

KEYWORDS: covalent organic frameworks, mechanical properties, out-of-plane deformations, cross correlations, COF-5

1 Environment ACS Paragon Plus

The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT

Flexibility and deformability are important factors influencing the assembly and application of two-dimensional covalent organic frameworks (2D COFs). On the one hand, the formation of stable, extended 2D sheets is a prerequisite for the fabrication of high-quality 2D crystals. On the other hand, characterizing these properties will eventually provide a path towards the inclusion of electron-vibration couplings when evaluating their electronic properties such as their band structures. Here, atomistic molecular dynamics simulations are used to investigate the mechanical properties of 2D COF sheets, taking the prototypical COF-5 as a representative example. Large out-of-plane deformations are found, about 400% higher than those encountered in graphene. In addition, structural defects lead to significantly larger twists and deformations, which underlines the challenges in fabricating stand-alone, large-size 2D COF sheets. Stacking, on the other hand, effectively reduces the out-of-plane deformations and suppresses the role of defects, two aspects beneficial to the lateral extension of 2D COF sheets.

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Two-dimensional covalent organic frameworks (2D COFs) are an emerging class of materials with attractive properties.1-5 They form via precise assembly of monomer units through covalent bonds and usually contain nm-sized pores. As graphene analogs, they are much lighter and more tailorable, with promising applications in catalysis, molecular separation, or electronic devices.614

Unlike bulk materials, strictly 2D materials are unstable in nature and tend to deform in three-

dimensional (3D) space;15 for instance, the average out-of-plane displacement of graphene sheets is reported to be 0.7 Å, with a coherence length around 10 nm.15,16 In this context, it is important to characterize the flexibility and deformability of 2D COFs. Indeed, stand-alone, stable 2D COF sheets are a prerequisite for fabricating high-quality, truly 2D crystalline structures, which remains as one of the most challenging objectives in COFrelated studies.17-20 Also, gaining an understanding of the modes and extent of deformation of 2D sheets can eventually give access to the impact of electron-vibration couplings, a critical information in the evaluation of the electronic and charge transport properties.21,22 However, the experimental determination of the mechanical properties of 2D COF sheets remains difficult given the challenges in synthesizing high-quality 2D crystalline structures. Thus, here, we investigate the flexibility and out-of-plane deformations of 2D COFs through atomistic molecular dynamics (MD) simulations. Since our goal is to gain first an understanding of the intrinsic properties of the 2D COF sheets, the simulations are carried out under vacuum conditions. We take COF-5 (Scheme 1) as a representative example,1 as it is the first reported 2D COF and has emerged in recent years as a model system of choice.23-26



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Scheme 1. Illustration of the chemical structure of COF-5 and a vacancy defect.

The protocols for the MD simulations and the parameterization process have been described in our previous work;24 thus, we only briefly recall them here: The MD simulations were carried out with the OPLS-AA force field27 using the GROMACS package (version 5.1.2).28 In all simulations, a cubic box with periodic boundary conditions is used, with a size that is sufficiently large to prevent any interactions with the images of the 2D COF sheet. Long-range electrostatic interactions were treated with the smooth particle-mesh Ewald (PME) method29. The system was heated from 0 K to 298 K over 5 ns with a velocity rescaling thermostat30. A production run of 100 ns was then carried out, in which the Nose-Hoover thermostat

31-33

is used, with a weak

coupling factor of 0.5 ps. The time step is 1 fs. Coordinates were output every 1 ps. The effect of global translational and rotational movements is removed prior to analyses.34


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Since laboratory-fabricated 2D COF sheets are usually on the order of several tens of nanometers,23 we have modeled a series of COF-5 sheets that range from ≈10 nm to ≈90 nm. Hereafter, hi denotes the out-of-plane displacement of monomer unit i and Ai, its maximum value over the entire course of the simulation; have, which averages over all monomer units and the entire MD trajectory, represents the average out-of-plane displacement at any position of the sheet at any given time, while Aave corresponds to the average distance the sheet can reach (away from the reference plane) in the out-of-plane direction. The root mean square fluctuation (RMSF) of monomer unit i is expressed as:

δi =

1 N

N

∑ (h (n) − i

hi

)

2

(1)

n =1

where N is the total number of snapshots (100,000) and n is the snapshot label. We consider both defect-free, isolated 2D COF sheets and defect-containing COF sheets. While the defect-free models provide a basic understanding of the mechanical properties of 2D COF sheets, in reality defects are difficult to avoid. Here, we focus on a specific type of defect – vacancy, which means that a connection site is not occupied by a monomer unit (Scheme 1). Such features have been observed under scanning tunneling microscope.35 Recently, we have developed a kinetic Monte Carlo (KMC) model that was found to describe well the formation of COF-5;24 while defects were not the focus of our original work, vacancy defects are indeed present in the simulated crystals. The defect-containing structures used in the present study are thus directly generated from the KMC simulations. To obtain a stand-alone 2D COF sheet with vacancy defects, we have isolated the middle layer from a COF-5 crystal generated from our



KMC model. Finally, we also consider stacked (both defect-free and defect-containing) 2D COF sheets. Defect-free isolated 2D sheets: For the smallest sheet (8 macrocycles, 10 nm × 10 nm), we find that the monomer units can shift over 1 nm in the out-of-plane direction (Figure 1a). The magnitude of this out-of-plane deformation is calculated to increase with the size of the sheets; for instance, when the sheet dimension doubles to ≈20 nm, the out-of-plane motion is enhanced by about 50 %. Thus, larger 2D COFs are found to be more flexible. For the largest system we were able to investigate (95 nm × 84 nm, 946 macrocycles), monomer units can move up to 13 nm in the out-of-plane direction (Aave = 4.2 nm). It is important to note that, overall, COF-5 sheets have much larger (ca. 400% higher) out-of-plane deformations compared to graphene sheets with similar sizes, which is consistent with their more porous structure.16


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Figure 1. (a) Out-of-plane deformation as a function of the size of the sheet; (b) out-of-plane deformation of the central layer as a function of the number of stacked layers.



Defective isolated 2D sheets: When we compare Figure 2a for a perfect sheet to Figure 2b depicting a defective sheet, it is clear that the latter has significantly larger deformation and twists, so much so that its structure can no longer be considered as truly 2D. In this context, direct growth of large-size single-layer 2D COFs from homogeneous conditions can be difficult to achieve due to the almost unavoidable presence of defects in the growth process, which is expected to disrupt the 2D structure. In fact, our previous KMC simulations have shown that stand-alone, large-size 2D sheets are not produced from monomers; instead, oligomers start stacking early and the nuclei are in fact multi-layer structures.24


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Figure 2. MD simulations of (a) a perfect single-layer COF-5 sheet; (b) a sheet taken from the middle layer of a crystal from the KMC simulations; (c) the whole crystal. The system was heated from 0 K (left panels) to 298 K (right panels) over 5 ns.



Impact of stacking: 2D COFs generated under homogeneous solution conditions often form stacked sheets rather than isolated single layers. We find that stacking effectively stabilizes 2D COF sheets, since (i) it reduces the out-of-plane deformations (Figure 1b) by about 50% when considering the central sheet of a five-layer stack; and (ii) it suppresses the large deformations and twists found in defective sheets (Figure 2c). Thus, in contrast to conventional wisdom, an important outcome of our simulations is to underline that stacking is expected to have a positive role in the lateral extension of the COFs through stabilization of the 2D structures, which could make it an essential step under homogeneous reaction conditions. We note that these results also mean that, when reducing the number of layers, the flexibilities of COF-5 sheets increase. Similar to the case of monolayers, increasing the lateral size of stacked COF-5 sheets leads to larger out-of-plane deformations (see Figure S1 in the Supporting Information, SI). In addition, since 2D COF-5 sheets can pack differently from the fully cofacial stacking shown in Figure 2b, we have also investigated two-layer stacks where the top layer slides over the bottom one. Interestingly, while the degrees of average out-of-plane deformations remain similar to that of a fully cofacial two-layer stack, the unstacked regions are seen to deform more significantly compared to the stacked regions (see Figures S2 and S3 in SI). Patterns of out-of-plane motions: The out-of-plane motions of two monomer units located at different positions in a stand-alone COF-5 sheet of 16 nm × 15 nm are summarized in Figure 3. The monomer units move in a quasi-periodic manner (Figure 3b). Fourier analysis of these motions indicates multiple modes involved in the out-of-plane motions (Figures 3c and 3d); the strongest two peaks correspond to the main deformation mode, whose frequency is found to be on the order of several GHz. Furthermore, we find that this motion is modulated by the size of the sheet; increasing the sheet size reduces the associated frequency (see Figure S4 in SI).


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Figure 3. (a) Illustration of a stand-alone COF-5 sheet with dimensions of 16 nm × 15 nm and of the positions of two representative monomer units (denoted as I and II); (b) out-of-plane displacements of I and II as a function of time; Fourier analysis of the out-of-plane motions of (c) I and (d) II, respectively.

As can be deduced from Figure 3b, the magnitudes of the out-of-plane motions vary as a function of the positions of the monomer units. To understand the out-of-plane motions over a longer range, we have also analyzed a 95 nm × 84 nm COF-5 sheet, see Figure 4a. Edges have larger deformations compared to the center and the largest deformations are seen at the four corners (root mean square fluctuations are over 300% larger compared to the inner part of the



sheet). We note that these features are also seen in smaller sheets as well as in stacks (see Figures S5 and S6 in SI).

Figure 4. (a) Root mean square fluctuation of the out-of-plane displacement for the monomer units in a 95 nm × 84 nm COF-5 sheet (96,264 atoms). The color bar represents the value of δi (Eq. 1); (b) a representative snapshot from the MD trajectories. The color bar represents the outof-plane displacement. The red arrows correspond to 30 nm.


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Figure 4b shows a representative snapshot of the simulated COF-5 sheet. The out-of-plane motions result in ripples in the two-dimensional sheet. The distances between the peaks of the ripples is around 30 nm, which is about 200% larger than those found in graphene sheets.15,16 This large value together with the large out-of-plane deformations confirm that 2D COF sheets are much more flexible compared to graphene. In order to understand coordination in the motions of the different monomer units, we have calculated the cross correlation of the out-of-plane motions, defined as:36

cij =

∆ri ⋅ ∆r j ∆ri ⋅ ∆ri

1/2

∆r j ⋅ ∆r j

(2)

1/2

where ∆ri and ∆rj represent the out-of-plane displacement vectors (relative to the average position) of monomer units i and j, respectively. The value of cij ranges between [-1,1]; a value of 1 means that the i and j monomer units always move in the same direction; -1 means motions in opposite directions; and 0 means uncorrelated movements. Figure 5a shows the cross correlation between a monomer unit near the center and the other monomer units. There are strongly coordinated motions in the central area, extending to about 9 macrocycles in each direction. In addition, the central part correlates in a negative fashion with the corners, which underlines that center and corners tend to move in opposite directions. The four corners also have coordinated motions, in particular in the diagonal direction (Figure 5b).



Figure 5. Cross correlations of the out-of-plane motions of a monomer unit (a) in the center (marked in green and by the arrow) and (b) in the bottom left corner (marked in green and by the arrow), with the other monomer units of a 95 nm × 84 nm COF-5 sheet. The color bars represent the value of cij (Eq. 2).


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Lastly, while the above discussions have focused on the intrinsic mechanical properties, it is also useful to evaluate the influences of the presence of solvent as well as of high temperature, i.e., conditions frequently used in the fabrication of COFs. We note that including solvent molecules when simulating these large, extended 2D networks is computationally very demanding. We have thus studied a COF-5 analog, based on one macrocycle (12 monomer units). Importantly, the degree of out-of-plane deformations actually remains similar when solvent molecules (4:1 mesitylene/dioxane) and a high temperature (90 °C) are both considered (see Figure S7 in SI).23 This can be rationalized by realizing that while a higher temperature and thus a higher kinetic energy can lead to larger molecular motions, the frequent collisions with the solvent molecules are expected to bring the opposite effect. In summary, in order to understand the flexibility and deformability of 2D COF sheets, we have performed atomistic molecular dynamics simulations on a representative 2D COF, COF-5. Our main findings are as follows: (i) COF-5 sheets are not flat. The out-of-plane deformations increase with the size of the sheet. For sheets with dimensions of ≈90 nm, the monomer units can move up to 13 nm (away from the reference plane) in the out-of-plane direction. (ii) Defects lead to considerably larger deformations and twist. (iii) Stacking effectively stabilizes the 2D COFs and neutralizes the influences of defects. (iv) Multiple modes contribute to the out-of-plane motions. The frequency of the major mode is on the order of several GHz and is found to decrease with the size of the sheets. (v) The extent of out-of-plane deformation varies depending on the position in the sheet. Corners and edges have larger flexibilities.



We note that COF-5 has an equilibrium structure that is essentially coplanar; it is thus likely that out-of-plane deformations in 2D COFs with lower torsion-potential barriers can be larger. The important consequence is that stand-alone 2D COF sheets, which deform substantially in 3D space, are not truly “two-dimensional”. Thus, the assumption of perfectly flat sheets should be used with care. Out-of-plane deformations disrupt the periodic structure in the 2D plane and can be detrimental to properties such as charge transport. It is useful to note, however, that 2D COFs can also be fabricated through monomer deposition and direct synthesis on substrates; in this context, it will be of interest to investigate to what extent the COF sheet-substrate interactions can dampen the sheet motions. Finally, we underline that the presence of defects and the high flexibility at the sheet corners are expected to be detrimental to the lateral extension of 2D COFs. Interestingly, stacking of the sheets can actually benefit the growth of 2D COF crystals through stabilization of their structures.

ASSOCIATED CONTENT Supporting Information. Results for three-layer COF-5 stacks of different laterals sizes and two-layer stacks of different types of packing, frequency of the main out-of-plane motions as a function of the size of the sheet, root mean square fluctuations of additional COF-5 sheets, and the out-of-plane displacement of a COF-5 analog simulated under solvation.

AUTHOR INFORMATION Corresponding Author *[email protected]


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ACKNOWLEDGMENTS This work was supported by the Army Research Office, under the Multidisciplinary University Research Initiative (MURI) program, Award No. W911NF-15-1-0447, and under Grant No. W911NF-17-1-0339. REFERENCES (1) Cote, A. P.; Benin, A. I.; Ockwig, N. W.; O'Keeffe, M.; Matzger, A. J.; Yaghi, O. M., Porous, crystalline, covalent organic frameworks, Science 2005, 310, 1166. (2) Feng, X.; Ding, X. S.; Jiang, D. L., Covalent organic frameworks, Chem. Soc. Rev. 2012, 41, 6010. (3) Wu, D. C.; Xu, F.; Sun, B.; Fu, R. W.; He, H. K.; Matyjaszewski, K., Design and Preparation of Porous Polymers, Chem. Rev. 2012, 112, 3959. (4) Colson, J. W.; Dichtel, W. R., Rationally synthesized two-dimensional polymers, Nature Chem. 2013, 5, 453. (5) Ding, S. Y.; Wang, W., Covalent organic frameworks (COFs): from design to applications, Chem. Soc. Rev. 2013, 42, 548. (6) Sun, B.; Zhu, C. H.; Liu, Y.; Wang, C.; Wan, L. J.; Wang, D., Oriented Covalent Organic Framework Film on Graphene for Robust Ambipolar Vertical Organic Field-Effect Transistor, Chem. Mater. 2017, 29, 4367. (7) Miao, J.; Xu, Z.; Li, Q.; Bowman, A.; Zhang, S.; Hu, W.; Zhou, Z.; Wang, C., Vertically Stacked and Self-Encapsulated van der Waals Heterojunction Diodes Using Two-Dimensional Layered Semiconductors, ACS Nano 2017, 11, 10472. (8) Dey, K.; Pal, M.; Rout, K. C.; Kunjattu H, S.; Das, A.; Mukherjee, R.; Kharul, U. K.; Banerjee, R., Selective Molecular Separation by Interfacially Crystallized Covalent Organic Framework Thin Films, J. Am. Chem. Soc. 2017, 139, 13083. (9) Medina, D. D.; Sick, T.; Bein, T., Photoactive and Conducting Covalent Organic Frameworks, Adv. Energy. Mater. 2017, 7, 1700387. (10) Xiang, Z. H.; Cao, D. P.; Dai, L. M., Well-defined two dimensional covalent organic polymers: rational design, controlled syntheses, and potential applications, Polym. Chem. 2015, 6, 1896. (11) Pyles, D. A.; Crowe, J. W.; Baldwin, L. A.; McGrier, P. L., Synthesis of Benzobisoxazole-Linked Two-Dimensional Covalent Organic Frameworks and Their Carbon Dioxide Capture Properties, ACS Macro Lett. 2016, 5, 1055. (12) Xu, Q.; Tao, S.; Jiang, Q.; Jiang, D., Ion Conduction in Polyelectrolyte Covalent Organic Frameworks, J. Am. Chem. Soc. 2018, 140, 7429. (13) Zhao, F.; Liu, H.; Mathe, S.; Dong, A.; Zhang, J., Covalent Organic Frameworks: From Materials Design to Biomedical Application, Nanomaterials 2018, 8, 15. (14) Zhao, W.; Xia, L.; Liu, X., Covalent organic frameworks (COFs): perspectives of industrialization, CrystEngComm 2018, 20, 1613. (15) Meyer, J. C.; Geim, A. K.; Katsnelson, M. I.; Novoselov, K. S.; Booth, T. J.; Roth, S., The structure of suspended graphene sheets, Nature 2007, 446, 60.



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Large Out-of-Plane Deformations of Two-Dimensional Covalent

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