Thermal Conductivity of 3D Boron-Based Covalent Organic

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Thermal Conductivity of 3D Boron-based Covalent Organic Frameworks from Molecular Dynamics Simulations Yazhou Liu, Yanhui Feng, Zhi Huang, and Xinxin Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b04891 • Publication Date (Web): 14 Jul 2016 Downloaded from http://pubs.acs.org on July 19, 2016

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The Journal of Physical Chemistry

Thermal Conductivity of 3D Boron-based Covalent Organic Frameworks from Molecular Dynamics Simulations Yazhou Liu †, Yanhui Feng *, †, ‡, Zhi Huang †, ‡, Xinxin Zhang †, ‡ † School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China ‡ Beijing Key Laboratory of Energy Saving and Emission Reduction for Metallurgical Industry, University of Science and Technology Beijing, Beijing 100083, China

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ABSTRACT

Covalent organic frameworks (COFs) have been widely investigated for use in gas storage and separation, while their thermal properties have been scarcely studied. In the study reported in this paper, the thermal conductivities of 3D boron-based COFs were investigated for the first time using molecular dynamics simulations (MD) employing the Green-Kubo method. The predicted thermal conductivities of COF-102, COF-103, COF-105 and COF-108 were on the order of 0.1 W/(m⋅K) at 300K. The thermal conductivity decreased by up to 47% with the increase in temperature from 200 to 500K. This resulting low thermal conductivity was due to the short mean free path of the phonon in the COFs, which was deduced to be 2.7-9.2 nm. The lowfrequency phonon modes below 50 THz contributed mostly to heat conduction. By analyzing the phonon vibrational density of states and overlap energy between per two bonded atoms, it was revealed that the connection between phenylene rings in COF-102 and COF-103 weakens the phonon coupling and then harms the energy flow, as did the connection between phenylene and triphenylene rings in COF-105 and COF-108. In addition, COF-105 had the lowest total overlap energy between all atoms, leading to the minimum thermal conductivity in the four COFs. This study provided a quantitative prediction of the thermal conductivities of COFs and microscopic insight into the mechanism of heat transfer.

KEYWORDS Thermal conductivity, COFs, Molecular dynamics simulation, Vibrational density of states, Overlap energy


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1. INTRODUCTION Covalent organic frameworks (COFs) are an emerging class of crystalline materials, which are composed of light elements, typically H, B, C, N, Si and O that are linked via strong covalent bonds. Two-dimensional (2D) COFs (termed COF-1 and COF-5) and three-dimensional (3D) COFs (termed COF-102, COF-103, COF-105, and COF-108) were first synthesized by Yaghi’s group in 20051 and 20072. Similar to the so-called metal organic frameworks (MOFs)3, COFs have highly ordered internal structures, high porosity, good thermal stability and large surface areas, which make them particularly useful for applications such as gas adsorption. Compared with the MOFs, the molecular frameworks of COFs are composed of light elements that act to lower the relative weight of the structure. The synthesis of the COF materials can be tailored so that the material’s architecture including pore size, volume, and functionality can meet the demands of a particular application. COFs have been considered to be promising candidates for many potential applications such as gas storage, photo electricity and catalysis. In 2010, E. Klontzas et al.4,5 investigated newly designed 3D COFs (COF-102-2, COF-102-3, COF-102-4, and COF-102-5) for enhanced hydrogen storage capacity. In 2015, Fang et al.6 developed 3D porous crystalline polyimide COFs for drug delivery by choosing tetrahedral building units of various sizes. To date, most experimental and simulation studies on COFs have focused primarily on synthesis, gas adsorption7-9 and gas storage.10,11However, the physical properties of COFs have been barely studied. Zhao et al.12 conducted a computational study on the thermal expansion behavior of COFs and found that COFs exhibit negative thermal expansion, similar to MOFs.13 B. Lukose et al.14 performed theoretical studies on 3D COFs, including COF-102, COF-103, COF-105 and COF-108, and used density functional based methods to explore their structural,


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electronic, energetic and mechanical properties. The results demonstrated that COFs’ mechanical stability is in accordance with MOFs, and both their bulk modulus do not exceed 20 GPa. In addition, all four COFs in this reported study were semiconductors with band gaps ranging from 2 to 4 eV. Saeed Amirjalayer et al.15 predicted that the low density materials COF-105 and COF108 show bulk moduli below MOF-5. And the ctn (carbon nitride, I 43d ) networks of COF-102 and COF-103 show values for bulk modulus, which are comparable with MOF-5, emphasizing their structural stiffness. The thermal transport properties of COFs play an important role in gas adsorption, because the adsorption in nanoporous materials is an exothermic process. Consequently, it affects the heat transfer in a gas storage system and thereby affects the system temperature as well as gas storage capacity. Consequently, appropriate thermal management is required to retain energy efficiency.16Furthermore, heat transfer in nanoporous materials is also important in applications in the optical, electronic, and optoelectronic fields.17 However, to the best of our knowledge, there have been no studies reported that deal with the thermal conductivity of COFs. For comparison, however, one can consider recent work conducted on the thermal conductivity of porous MOFs. For example, in 2006, Huang et al.18 predicted the thermal conductivity of MOF-5 in the temperature range of 200-400 K using molecular dynamics. The simulated thermal conductivity was found to be low for a crystal (0.31 W/(m⋅K) at a temperature of 300 K) and showed a weak temperature-dependence. Also, Huang et al.19 measured the thermal conductivity of MOF-5 single cubic crystal (1-2 mm in size) over a wide temperature range of 6-300K, using the longitudinal and steady-state heat flow method. These author’s experimental value for the thermal conductivity was 0.32 W/(m⋅K) at 300 K. In 2013, Zhang et al.20 predicted that the thermal conductivity of Zeolitic Imidazolate Framework-8 (ZIF-8) was about 0.165 W/(m⋅K)


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using equilibrium molecular dynamics (EMD) simulation. Such a low thermal conductivity was due to the short mean free path of phonon in ZIF-8, which was estimated to be less than two unit cells. Qian et al.21 studied the thermal conductivity of a layered organic-inorganic hybrid crystal

β − ZnTe(en) . using the interatomic potential (Morse potential) derived from ab initio simulations. Because of the incorporation of organic ligands, the hybrid crystal β − ZnTe(en) .

is much more flexible than the inorganic crystal ZnTe , and the predicted thermal conductivities of the hybrid crystal were found to be one order of magnitude lower than those of inorganic

ZnTe crystal based on either experimental22 or MD simulation23 results. Wang et al.24 calculated the anisotropic thermal conductivities of water-stable MOF-74 using the Boltzmann transport equation (BTE) and the density-functional-based tight-binding method. They determined that the thermal conductivity to be 0.44 and 0.68 W/(m⋅K) at 300 K, across and along the pore directions. In addition, J. Purewal et al.25 in 2012 reported an effective thermal conductivity of around 0.1 W/(m⋅K) for low-density MOF-5 pellets made of compressed powders, which is close to the result from a later study(0.091W/(m⋅K),T=300K) conducted by Y. Ming et al..26 To improve the thermal conductivity of MOF-5, Liu et al. synthesized a series of high-density MOF-5 composites containing 0-10wt % expanded natural graphite (ENG), which enhanced the thermal conduction and found that the thermal conductivity was increased by a factor of 5. Although the thermal conductivities of some MOFs have been obtained, the relationship between thermal conductivity and microscopic structure of the materials is still not clear. Huang et al. indicated that the C1/C2 atoms act as a bottleneck in MOF-5.18 Zhang et al. considered Zn and N atoms as the key component for the transfer of energy in ZIF-8.20 However, neither of these investigators performed a quantitative analysis of the material in question. Single crystals of MOF materials can often be obtained and directly subjected to the structural identification using single crystal X-


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ray diffraction. Unfortunately, to date, no single crystal of COF materials have been successfully synthesized. Consequently, the experimental measurement on the thermal conductivity on COFs is still not practically possible. In a word, to explore the potential applications of COFs, it is important to quantitatively know their thermal properties and understand the underlying mechanism of heat transfer. In this reported study, we performed EMD simulation was performed to predict the thermal conductivity of four types of 3D COFs (COF-102, COF-103, COF-105 and COF-108). The temperature dependence of the thermal conductivity was discussed. The relative contributions of different phonon oscillation frequencies to the thermal conductivity, the phonon vibrational density of states (VDOS) and the overlap phonon energy were analyzed to determine which atoms are mismatched in density of states. The heat transfer bottleneck in the nanostructure was found using quantitative analyses. This work was intended to lead to an exploration of the thermal properties of COFs and provide some fundamental data for the efficient design of COFbased architecture. 2. MODEL AND METHODS For this study, four types of 3D COFs were chosen for simulation, namely, COF-102, COF103, COF-105 and COF-1082. Simulated powder X-ray diffraction in comparison with experimental powder spectrum suggested a ctn topology for COF-102, 103 and 105, and bor (boracite, P 43m ) topology for COF-108.2 In this work, ctn topology was used for the four types of COFs. The crystal structures for COF-102 and COF-108 are illustrated in Fig.1 (a) and (b). If the tetrahedral C atom in COF-102 and COF-108 is replaced by a Si atom, the corresponding structures are of COF-103 and COF-105.


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COF-102 and COF-103 can be synthesized by the self-condensation of tetra (4-dihydroxyborylphenyl) methane (TBPM) and tetra (4-dihydroxy-borylphenyl) silane (TBPS), respectively,

under formation of planar boroxine (B O ) rings.2 If we further perform the co-condensation of these compounds with triangular hexahydroxytriphenylene (HHTP), COF-105 and COF-108 will result. The optimized cell parameters in comparison with experimental values2 are given in Table 1. (a)

(b)

Fig.1 (a): crystal structure of COF-102; (b): crystal structure of COF-108; carbon, boron, oxygen and hydrogen atoms are represented in gray, red, green and white, respectively. If the tetrahedral C is replaced by Si, the structures are of COF-103 and COF-105, respectively. Table 1 Optimized cell parameters and experimental values of COFs with ctn (carbon nitride, I 43d

) topology. Structure

Building blocks

Cell parameters[Å] Simulation15

Experiment2

Density ρ [gcm-3]

COF-102

TBPM

27.144

27.1771(13)

0.43

COF-103

TBPS

28.353

28.2477(21)

0.39


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COF-105

TBPS+HHTP

44.596

COF-108

TBPM+HHTP

43.387

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44.886(5)

0.18 0.19

* TBPM: tetra (4-dihydroxy-borylphenyl) methane; TBPS: tetra (4-dihydroxy-borylphenyl) silane; HHTP: triangular hexahydroxytriphenylene; In 2012, S. Amirjalayer et al.15 developed a force field for boron based COFs, derived from ab initio simulations. All the simulations in this work are based on this force field. All the details about the force field can be found in our Supporting Information. The MD simulation included two different techniques, equilibrium (EMD) and nonequilibrium (NEMD) molecular dynamics. NEMD requires the imposition of a steady-state temperature gradient along the axes of interest and the thermal conductivity is calculated using Fourier’s law of heat conduction. 27 NEMD requires a relatively larger sized simulation system, to build a reproducible diffusive temperature profile. EMD has significant advantages over NEMD in that it requires much smaller simulation cells to achieve converged results. Therefore, EMD was chosen to predict the thermal conductivity of COFs in the microcanonical ensemble. In the EMD method, small fluctuations of heat current are monitored over time and the Green–Kubo relation is used to determine the thermal conductivity of these perturbations in equilibrium.28 The thermal conductivity is written using the Green–Kubo relation:20,29 k =

〈(0) ∙ ()〉

⑴

Where ! is volume; "# is the Boltzmann constant; T is temperature; is heat flux; and ⟨ ⟩

denotes time average. The heat flux was calculated by

& = '∑* )* --- +, − ∑* ---- ./ --- +, 0

⑵

---- / is the symmetric Where )* is the total energy of atom 1 ; --- is +, the velocity of atom 1 ; and . stress tensor of atom 1 defined as


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.33 ---- ./ = 2.34 .35

.34 .44 .45

.35 .45 6 .55

⑶

with @ C .78 = − 9 ∑AB& :;& "RSTU& > "RSTU& W > "RSTU& . This result indicates that larger total overlap energy between all species of atoms results in higher thermal conductivity for the material. Larger total overlap energy implies a weaker mismatch while stronger phonon coupling exists in the material, which benefits heat transport47.

We focused on four sets of comparison, i.e. COF-102 vs. COF-103, COF-105 vs. COF-108, COF-102 vs. COF-108 and COF-103 vs. COF-105. Each set has a tiny structural difference, representing an exchange of only one tetrahedral Si atom and C atom in sets of COF-102 vs. COF-103 and COF-105 vs. COF-108. The latter had the HHTP rather than the former in sets of COF-102 vs. COF-108 and COF-103 vs. COF-105. When the tetrahedral C atom was replaced by


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a Si atom this mismatch of atoms increased and the phonon coupling was weakened. As a result, the thermal conductivities of COF-102/COF-108 were higher than those of COF-103/ COF-105. Similarly, compared with COF-102 /COF-103, energy localization worsens and phonon coupling was weakened in COF-108/COF-105 owing to the introduction of HHTP with additional thermal resistance. 0.06

C0 C1 C2 C3 C4 B O Overlap

0.00024

0.04 0.03

Overlap energy(ev)

(a)

0.05 VDOS(1/THz)

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


0.02 0.01

0.00020

COF-102

(b) COF-103 COF-108

0.00016 0.00012

COF-105

0.00008 0.00004

0.00 0

20

40 60 Frequency(THz)

80

0.00000 111

Fig.9 (a) Vibrational density of states for all species of atoms of COF-102 and their overlap at 300 K; (b) Overlap energy between all species of atoms of COF-102, COF-103, COF-105 and COF-108.

CONCLUSIONS In summary, the thermal conductivities of COF-102, COF-103, COF-105 and COF-108 were studied using equilibrium molecular dynamics with the Green-Kubo method. The relative contributions of different phonon oscillation frequencies to thermal conductivity, the phonon vibrational density of states (VDOS) and the overlap phonon energy were analyzed to estimate the heat transfer bottleneck and energy localization in the nanostructure. The main conclusions of this study are as follows: (1) The estimated thermal conductivity of four types of COFs is on the order of 0.1 W/(m⋅K) at

300K. And they were in the order of "RSTU& 9 > "RSTU& > "RSTU& W > "RSTU& . As the ACS Paragon Plus Environment

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simulated system temperature was increased from 200 to 500 K, the thermal conductivities decrease between 26.6% and 47.0% for all four COFs. (2) It is deduced that the phonon mean free paths of four COFs are less than two unit cells, i.e. 2.7-9.2 nm, similar to some MOFs. This short mean free path for phonons results in the low thermal conductivity for the COFs. The heat conduction in the COFs can be primarily attributed to the low frequency phonon modes in the range of 0-50 THz. (3) Energy localization occurs on the C2 and C3 atoms in phenylene ring of the structure, as well as on C5, C6 and C7 atoms in HHTP. The C0-C1 or Si-C1 bonds act as bottlenecks to energy transport, followed by B-O atoms. In other words, the connection section between phenylene rings in COF-102 and COF-103, and the connection between phenylene and triphenylene in COF-105 and COF-108, are detrimental to the phonon coupling and energy flow. (4) The total overlap energy in the VDOS of all the species atoms was found to be the most serious mismatched structure in COF-105, resulting in its thermal conductivity being the lowest of four COFs examined. When the tetrahedral C atom was replaced by a Si atom, the atom mismatch increased, so that the thermal conductivities of COF-102/COF-108 were higher than COF-103/COF-105. Compared with COF-102/COF-103, the energy localization and phonon coupling was weaker in COF-108/COF-105 due to the introduction of HHTP with additional thermal resistance. This study is focused on 3D boron-based COFs, but the methodology employed can be extended to other COFs. To date, reports of the thermal properties of these complex nanoporous materials have been very scarce. More fundamental and in-depth studies will facilitate the design of COFs with desired thermal properties, which will enhance their use in practical applications in the marketplace.


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ASSOCIATED CONTENT Supporting Information Validation of the simulation method, all the details about the force field in section 2 and overlap energy in section 3.6. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * Yanhui Feng. E-mail: [email protected]. Tel: 86-010-62334971

ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China (51422601 and 51436001), and the Fundamental Research Funds for the Central Universities (FRF-TP-15003C1).

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Table of Contents (TOC) Image The TOC graphic in the actual size was submitted as an attachment in File Upload.


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Thermal Conductivity of 3D Boron-Based Covalent Organic

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