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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Structure and Dynamic Behavior of Na-Crown Ether Complex in the Graphite Layers Studied by DFT and H NMR 1

Kazuma Gotoh, Shinya Kunimitsu, Hanyang Zhang, Michael M Lerner, Keisuke Miyakubo, Takahiro Ueda, Hyung-Jin Kim, Young-Kyu Han, and Hiroyuki Ishida J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02965 • Publication Date (Web): 02 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018

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The Journal of Physical Chemistry

Structure and Dynamic Behavior of Na-Crown Ether Complex in the Graphite Layers Studied by DFT and 1H NMR Kazuma Gotoh,*†‡ Shinya Kunimitsu,† Hanyang Zhang§, Michael M. Lerner§, Keisuke Miyakubo∥, Takahiro Ueda∥, Hyung-Jin Kim∇, Young-Kyu Han∇and Hiroyuki Ishida† †

Graduate School of Natural Science and Technology, Okayama University, 3-1-1

Tsushima-naka, Okayama 700-8530, Japan ‡

Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University,

Nishikyo-ku, Kyoto 615-8245, Japan §

Department of Chemistry, Oregon State University, Corvallis, OR 97331-4003, USA

∥

Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka

560-0043, Japan ∇

Department of Energy and Materials Engineering and Advanced Energy and Electronic

Materials, Dongguk University-Seoul, Seoul 100-715, Korea

1 ACS Paragon Plus Environment

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ABSTRACT Diffusion of alkali metals in graphite layers is significant for the chemical and electrochemical properties of graphite intercalation compounds (GICs). Crown ethers co-intercalate into graphite with alkali metal (Na and K) cations and form ternary GICs. The structures and molecular dynamics of 15-crown-5 and 18-crown-6 ether coordinating to Na+ or K+ in GICs were investigated by DFT calculations and 1H solid state NMR analyses. DFT calculations suggest a stacked structure of crown ether - metal complex with some offset. 1H NMR shows two kinds of molecular motions at room temperature; isotropic rotation with molecular diffusion, and axial rotation with fluctuation of the axis. The structure and dynamics of crown ether molecules in GIC galleries are strongly affected by the geometry of the crown ether molecules and the strength of the interaction between alkali metal and ligand molecules.


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1. INTRODUCTION Graphite is one of the prototypical hosts that can intercalate either cations or anions between its layers when it is reduced or oxidized, respectively.1 Because of their high electric conductivity, superconductivity,2-3 and thermoelectricity,4 graphite intercalation compounds (GICs) have attracted considerable attention from the science and engineering research communities. GICs are particularly significant for electrochemical energy storage in batteries because the binary GIC consisting of lithium and graphite (LiCx: x≥6) is employed as the negative electrode material in lithium ion batteries (LIBs).5-6 Furthermore, the potential use of GICs has been expanding in recent few years. For example, potassium GICs (KCx: x≥8) was evaluated as the anodes in potassium ion batteries,7-12 and GICs were explored in dual ion batteries, with graphite serving as both cathode and anode.13-14 For sodium-ion based batteries, binary GICs have not been considered because low-stage compounds Na (NaCx) do not form by electrochemical reduction.15-17 However, electrochemical co-intercalation and deintercalation of sodium and glyme molecules (symmetric linear glycol ethers) to form ternary GICs can be repeated over 6000 cycles at high rate, suggesting that these may provide useful electrode chemistry for sodium ion batteries.17-24 Additionally, these cells do not appear to generate a solid-electrolyte interphase (SEI) at the anode surface.25 The structure and the dynamic behavior of diglyme and sodium have been investigated using 2H solid state nuclear magnetic resonance (NMR),26 and also discussed by DFT calculation.27 Our group synthesized ternary GICs consisting of sodium, diglyme(d14), and graphite by a chemical reduction reaction, and investigated the dynamics and the coordination structure of molecules using 2H solid state NMR.



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There are many reports on the preparation of ternary GICs containing Na or the other alkali metal ions with molecular organic co-intercalates forming a solvated intercalate structure.1 Most co-intercalates have been amines or ethers, for example, ethylenediamine (en) and tetrahydrofuran, due to their ability to strongly solvate alkali metal cations and their reductive stabilities.28-42 We recently described the preparation of the ternary GICs containing crown ethers (15-crown-5 ether (15c5), 18-crown-6 ether (18c6)) and Na or K cations.43 These GICs are obtained either by reductive intercalation of an alkali metal-en complex followed by co-intercalate exchange or by the direct reaction of graphite with a crown ether, alkali metal, and an electrocatalyst. Powder X-ray diffraction, thermal analysis, and GC/MS data were combined to determine a stage-1 bilayer gallery structure for these products. However, the dynamic behavior of the intercalated metal complex, which is a key to understanding the intercalate orientation, has not been evaluated. Comparison of the coordination structure with linear ether (glymes) GICs can be valuable in elucidating the different intercalate diffusion rates in these GIC galleries. We have been exploring the dynamic structure of organic amines and ethers using 2H solid state NMR.26, 44 However, this method can only be applied to GICs synthesized using deuterated solvents. We here investigate the dynamics of 15c5 and 18c6 in Na-15c5-GIC using 1

H static NMR instead of 2H NMR. The reported compositions of Na-15c5-GIC and

K-15c5-GIC are [Na1.7(15c5)]C21 and [K1.2(15c5)]C23, indicating the mole ratios of Na and K cations to 15c5 ether are 1.7 and 1.2, respectively.43 The energies of some structures models of sodium and crown ethers in graphene layers were estimated using DFT calculation, in order to discuss the coordination structure of crown ethers to alkali metal cations.


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2. EXPERIMENTAL METHODS 2.1. Solid State NMR analyses Ternary GIC samples consisting of alkali metals and crown ethers were synthesized according to a previous report.43 We prepared Na-15c5-GIC, K-15c5-GIC, and Na-18c6-GIC by co-intercalate exchange of Na-en-GIC to form Na-15c5, K-15c5 or Na-18c6. The compositions of Na-15c5-GIC and K-15c5-GIC are estimated to be [Na1.7(15c5)]C21 and [K1.2(15c5)]C23, respectively, as has been reported previously,43 whereas the composition of Na-18c6-GIC has not been determined. For Na-18c6-GIC, two GIC phases having different gallery height (∆d) have been reported; ∆d = 0.86 nm (α), and 0.70 nm (β). We confirmed that our Na-18c6-GIC sample consists of phase α mainly, with a minor β phase component. All samples used in the present study were characterized using powder X-ray diffraction (PXRD) and elemental analyses. For 1H NMR measurement, each GIC sample was sealed into a 5.0 mmφ glass sample tube after drying under reduced pressure. 1

H NMR spectra (resonance frequency at 200 MHz) were obtained at the range between

145 K and ambient temperature using a DSX-200 spectrometer (Bruker). A solid echo pulse sequence with 4.0 µs pulse length was applied. For the calculation of the second moment (M2) value of 15c5 and 18c6 molecules, the most stable structures of 15c5 and 18c6 were estimated by DFT calculations at B3LYP/6-31G(d,p) level by Gaussian 09W. The theoretical M2 values about the rigid state and under rotation of 15c5 and 18c6 were estimated using the Van Vleck equation.45-46

23

Na magic-angle spinning (MAS) NMR spectra (resonance frequency at 132.2

MHz) were measured at room temperature using a DD2 spectrometer (Agilent Technologies) 5 ACS Paragon Plus Environment


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with a single pulse sequence of 2.0 µs pulse length. 1M NaCl aqueous solution was used as a reference for the chemical shift. Although differential scanning calorimetry (DSC) was performed using Pyris 1 analyzer (PerkinElmer) to observe possible phase transition in samples with the temperature range between 135 K and 298 K, no DSC signals were observed for these samples. 2.2. First-principles calculations Density functional theory calculations were performed using the Vienna ab initio simulation package (VASP).47-48 We employed the revised Perdew–Burke–Ernzerhof type exchange and correlation functional49-50 combined with the introduction of vdW-DF51 for the non-local correlation part to accurately account for the dispersion interactions. The projector augmented wave (PAW) method52 was used for the ion interaction. The Brillouin zone was sampled using a Γ-centered 3 × 3 × 3 k-point mesh, while the electronic states were smeared using the Methfessel–Paxton scheme with a broadening width of 0.2 eV. The electronic wave functions were expanded in a plane wave basis with a cutoff energy of 520 eV and the atomic relaxation was continued until the Hellmann–Feynman forces acting on the atoms were less than 0.2 eV nm–1. We treated 2p63s1 for Na, 3p64s1 for K, 2s22p2 for C, 2s22p4 for O, and 1s for H as the valence electron configuration. M (Na and K)-crown ether-GIC systems were simulated by 5 × 5 supercell including one graphene sheet consisting of 50 C atoms and M-crown ether complexes. The formation energy of M-crown ether intercalation were defined as Ef = [Etot(2M(15c5)C25) − Etot(C50) − 2Etot(M(15c5))]/2, where Etot(2M(15c5)C25), Etot(C50), and Etot(M(15c5)) are the total energy of M-(15c5)-GIC, graphene sheet, and M-crown ether complex, respectively. 6 ACS Paragon Plus Environment

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3. RESULTS 3.1. Solid State NMR Fig. 1 presents 1H NMR spectra of the Na-15c5-GIC, K-15c5-GIC, and Na-18c6-GIC samples taken between 293 K and 123 K. Although each spectrum doesn't correspond to a single Gaussian or Lorentzian curve, it was able to be fitted by two Gaussian components (Fig. 2) which correspond to two motional states of the crown ether molecule in each GIC sample. The crown ether molecules existing outside of layered structure should be quite few because of small specific surface area of graphite. The two components observed in 1H NMR are ascribed to molecules intercalated in the layered structure. The narrower components (C1) of Na-15c5-GIC (Fig. 1(a)) and K-15c5-GIC (Fig. 1(b)) having the FWHM (full width at half maximum) of ca. 10 ppm predominate at room temperature. The C1 components of Na-15c5-GIC and K-15c5-GIC decreased under 230 and 240 K, respectively, with a slight broadening, and almost disappeared at 157 K. On the other hand, the intensity of broader components (C2) of Na-15c5-GIC and K-15c5-GIC increased under 228 K with considerable broadening. Below 157 K, the spectra consisted of C2 only; the narrower component (C1) disappeared. For Na-18c6-GIC (Fig. 1(c)), C1 almost disappeared below 196 K. Only the broader component (C2) and small impurity signals around 0 ppm were observed in the range between 196 K and 146 K. The signal intensity ratio of C1/C2 and the second moment (M2) of C1 and C2, which are estimated by curve fitting, are shown in Figs. 3(a) and 3(b), respectively. The M2 values of C2 in Na-15c5-GIC and K-15c5-GIC increased from 2.0 Gauss2(G2: 10-2 mT2) to 20.8 G2 and 29.2 G2, respectively, with temperature reduction 7 ACS Paragon Plus Environment


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to 149 K. The M2 values of C2 in Na-18c6-GIC also increased from 1.9 G2 to 29.9 G2. The consecutive signal-broadening of each component by cooling suggests no first-order structural phase transition in each GIC sample; this is confirmed by the absence of any DSC transition signal.

(a)

(b)

(c)

Fig. 1 1H static NMR spectra in Na-15c5-GIC (a), K-15c5-GIC (b), and Na-18c6-GIC (c). Some sharp components included in the spectra are noise caused in NMR hardware.


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Fig. 2 Deconvolution of 1H spectra taken at room temperature to two components; narrower component (C1) and broader component (C2).



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(a)

(b)

Fig. 3 Signal intensity ratios of C1 / C2 for three GIC samples (a), and the estimated second moments (M2) of C1 and C2 for each sample.


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The 1H M2 values calculated for intramolecular 1H - 1H dipole - dipole interactions in the rigid and rotating state of 15c5 and 18c6 molecules are shown in Table 1. The evaluated M2 values of C1 and C2 at 293 K in Na-15c5-GIC (Fig. 2) are 0.04 G2 and 2.0 G2, respectively. Generally, the contribution to M2 by intermolecular 1H - 1H interactions can be estimated as 0.5∼1.5 G2. Therefore, the former M2 value (0.04 G2) should be assigned to the 15c5 molecule under isotropic rotation with liquid-like diffusion of intercalates because molecular diffusion can cancel the intermolecular contribution of M2 by averaging intermolecular interactions. This result means that most of Na-15c5 complexes are moving freely in the GIC galleries. The C1of K-15c5-GIC and Na-18c6-GIC can also be explained by the diffusion of crown ether molecules because the M2 values of C1 for K-15c5-GIC and Na-18c6-GIC at room temperature (0.01 G2 for K-15c5-GIC, and 0.04 G2 for Na-18c6-GIC) are similar to those obtained for Na-15c5-GIC.

Table 1 Calculated 1H second moments (M2) of 15c5 and 18c6 molecules assuming stable molecular structures. The values only consider intramolecular interaction without intermolecular

Motional mode

M2 / G2 (intramolecular) 15c5 18c6

static

15.6

16.2

rotation around an axis perpendicular to molecular plane

4.9

2.0

isotropic rotation

0.0

0.0

contribution.



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In contrast, the M2 values of C2 for Na-15c5-GIC (2.0 G2) and K-15c5-GIC (0.50 G2) observed at 293 K are comparable with the M2 values for isotropic rotation taking account of intermolecular interactions, but are too small for the axial rotation of 15c5. The assignment of molecular motion for 15c5 will be discussed after the calculation of the stable molecular structure of the Na+-15c5 complex in the GIC galleries, because an optimized stacked structure of these complexes is necessary to evaluate the molecular motion using the M2 values. The M2 of C2 for Na-18c6-GIC (1.9 G2) corresponds with axial rotation of 18c6 (2.0 G2) without intermolecular interactions (Table 1). The M2 of C2 for Na-15c5-GIC at 149 K (20.8 G2) might become larger at lower temperature because the M2 value is not constant even in the temperature range. The observed M2 values over 20 G2 (20.8, 29.2, and 29.9 G2 for Na-15c5-GIC, K-15c5-GIC and Na-18c6-GIC, respectively) at low temperature are significantly larger than the theoretical values for the rigid state, which means that the contribution of intermolecular interactions is not negligible, especially in K-15c5-GIC and Na-18c6-GIC. The crown ether molecules are densely packed in GIC galleries, with only a short separation between intercalates.

3.2. Structure of alkali metal and 15c5 between graphene layers estimated using DFT calculation and 23Na MAS NMR Figs. 4 (a) and (b) show the structures and total energy of two possible bilayer models for Na-15c5-GIC; (a) is a bilayer model with two stacked 15c5 molecules, whereas (b) shows an offset stacked structure. The total formation energy (Ef) of each system was estimated by the following equation: 12 ACS Paragon Plus Environment

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f tot 2Na155C tot C

2tot (Na155/2 The Ef of system (b), -1.51 eV, was found to be lower than that for system (a), -1.34 eV, indicating that offset stacking is preferable for Na-15c5. The optimized gallery height (∆d) of 0.75 nm in these systems is slightly less than that observed experimentally (0.86 nm)43; however, offset stacking over the range of many molecules might result in a larger gallery height requirement. A similar result was also obtained for K-15c5-GIC (Fig. 5(a) and (b)). The formation energy of offset stacking (b) was 0.12 eV lower than for the stacked model (a). The

∆d in these systems, 0.80 nm, is also smaller than the experimental value (0.886 nm).

(a)

∆d = 0.83 nm Ef = -1.34 eV (b)

∆d = 0.75 nm Ef = -1.51 eV

Fig. 4 Structures and their total energy of two bilayer models of Na1.0(15c5)C25. (a) is a model of bilayer that two 15c5 molecules are stacked, whereas (b) considers an offset of stacking of ethers. (∆d : gallery height, Ef : total formation energy)



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(a)

∆d = 0.82 nm Ef = -1.12 eV (b)

∆d = 0.80 nm Ef = -1.24 eV

Fig. 5 Structures and their total energy of two bilayer models of K1.0(15c5)C25. (a) is a model of bilayer that two 15c5 molecules are stacked, whereas (b) considers an offset of stacking of ethers.

The estimate of Ef also considers the state of the excess Na and K cations that do not coordinate to crown ethers. Fig. 6 shows two possible arrangements for Na1.5(15c5)C25; (a) with excess Na ions isolated on the graphene layers, or (b) with Na ions coordinated by forming a Na3(15c5)2 complex. Since the Ef of (a) is lower than that of (b), the formation of Na3(15c5)2 complexes appears unlikely. This result suggests that 1.0 of Na in the composition Na1.7(15c5)C25 is coordinated by 15c5, and the excess amount (0.7) of Na cations are on the surface of graphene layers without coordinating to 15c5.

23

Na MAS NMR spectra of

Na-15c5-GIC also show two components (Fig. S1(a)). Main peaks at 8 ppm and -23 ppm are ascribed to a second-order quadrupolar component (quadrupolar coupling constant; qcc= 4.2 14 ACS Paragon Plus Environment

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MHz) of Na ion, whereas subordinate signal at +2 ∼ -5 ppm can be assigned to either Na ions at the graphene layer surface or to Na ions located in defects in the GIC. 23Na-18c6-GIC shows similar spectra (Fig. S1(b)), with a narrower qcc of the main component (qcc= 1.7 MHz) and the subordinate signal is indistinct. The anisotropy of the Na ion in Na-15c5 seems to be larger than in Na-18c6, although estimated Bader charges of Na ion in Na-15c5 and in Na-18c6 (Fig. S2) are almost the same.

(a)

∆d = 0.76 nm ∆E = 0 (b)

∆d = 0.80 nm ∆E = +0.35 eV per Fig. 6 Two possible structures and a comparison of their total energies of two bilayer models of Na1.5(15c5)C25. Na ion and 15C5 form 1:1 complex and the excess Na ion is isolate (a). Na and 15C5 form Na215C51 complex (b). The total formation energy (Ef) in (a) is 0.35 eV lower than (b).



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4. DISCUSSION 4.1. Estimation of the motion of crown ethers in GIC galleries at room temperature According to the DFT calculations described in the previous section, an offset stacking model of two Na-15C5 complexes is the most stable structure for Na+-crown ether intercalates in these GICs. Based on the structure in Fig. 4(b), M2 values for the two offset stacked Na-15c5 complexes (Na2(15c5)2) were calculated and are shown in Table 2. The static M2 of 16.7 G2, which includes intramolecular interactions and intermolecular contribution of protons between the two 15c5 molecules, is larger than the 15.6 G2 obtained for static M2 of a 15c5 molecule (Table 1). The difference in these values, 1.1 G2, is the intermolecular contribution. The difference between experimental value at low temperature (20.8 G2) and 16.7 G2 can be ascribed to other intermolecular contributions between the neighboring molecules, or to 1H nuclei on the defect sites of the graphene surface.

Table 2 Calculated 1H second moments (M2) of Na2(15c5)2 complex (offset stacking) in Fig. 4(b). Motional mode of each molecule

M2 / G2 Na2(15c5)2

static

16.7

rotation around an axis perpendicular to molecular plane

5.3

rotation around an axis with 26° fluctuation of the axis

2.0

isotropic rotation

-(*)

(*)

Improbable because two 15c5 are too close.


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Since the estimated M2 for Na2(15c5)2 complexes under axial rotation of two 15c5 molecules, 5.3 G2, is still larger than the experimental value of 2.0 G2 for C2 in Na-15C5-GIC, we assumed a rotation of 15c5 molecules around an axis perpendicular to the molecular plane with some fluctuation of the rotation axis (z direction) in order to explain the M2 value. The experimental value (2.0 G2) of M2 coincides with the simulated M2 value when the fluctuation angle of the rotation axis to x and y directions is 26°. Considering the intermolecular contribution between the neighboring molecules, the fluctuation angles should be slightly larger than 26°. This molecular motion is illustrated in Fig. 7(a). For K-15c5-GIC and Na-18c6-GIC, the M2 values of C2 (0.51 G2 and 1.9 G2) were analyzed in the same way. We obtained a similar value of K-15c5-GIC by rotation of 15c5 around an axis perpendicular to molecular plane and another axis along to the molecular plane, which is almost equivalent to isotropic rotation of the molecule. In contrast, 1.9 G2 for 18c6 is almost explainable by rotation around the perpendicular axis with slight fluctuation, even though 0.3∼0.5 G2 in 1.9 G2 should be explained as an intermolecular contribution. These motions are illustrated in Figs. 7(b) and 7(c). The activation energies of the axial rotation for C2 of Na-15c5-GIC, K-15c5-GIC, Na-18c6-GIC are roughly estimated as 11.1, 7.0, and 12.2 kJ mol-1, respectively, by calculating ∆M2 between isotropic rotation and static state.46, 53



(a)

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(b)

(c)

Fig. 7 Molecular motions of 15c5 and 18c6 in the Na-15c5-GIC (a), K-15c5-GIC (b), and Na-18c6-GIC (c).

4.2. Structure and motion of C2 crown ethers within GIC galleries The expected structures and their molecular motion of Na-15c5-GIC, K-15c5-GIC and Na-18c6-GIC estimated from the results of 1H NMR and DFT calculation are represented in Fig. 8. In Na-15c5-GIC (Fig. 8(a)), Na-15c5 complexes stack in pairs parallel to the encasing graphene layers with some offset. The C2 component of complexes are under axial rotation with a fluctuation of the rotation axis over 26°. In contrast, the motion of K-15c5 in K-15c5-GIC is more active than Na-15c5. The fluctuation is almost an isotropic rotation (Fig. 8(b)). In this case, a stacked structure of two complexes is unlikely because of their molecular motion. The nearly isotropic motion of K-15c5 is also supported by lower activation energy of the axial rotation for C2 of K-15c5-GIC (7.0 kJ mol-1). Indeed, our 2H NMR analyses suggest that K ions in K-piperazine-GIC and K-1,4-diazabicyclo[2.2.2]octane(dabco)-GIC are not strongly coordinated by organic molecules.44 In the present case, the 15c5 molecules under isotropic like rotation might be weakly anchored in the GIC galleries. These results imply that


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the structure and the molecular motion of intercalants are largely influenced by interactions from alkali metal cations. (a)

(b)

(c)

Fig. 8

The expected structure and the molecular motion for C2 of Na-15c5-GIC (a),

K-15c5-GIC (b) and Na-18c6-GIC (phase α) estimated from the results of 1H NMR and DFT calculation.



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For Na-18c6-GIC, although two GIC phases with different gallery heights (∆d) have been reported,43 the major component of our sample is phase α (∆d = 086 nm). In the GIC, Na-18c6 complexes can rotate around an axis perpendicular to the molecular plane with slight fluctuation at room temperature (Fig 8(c)). 18c6 is planar and symmetric, and has smaller distortion than 15c5 in the molecular structure. The structure might affect the fluctuation of the axial rotation of the molecules coordinating to alkali metal ions.

5. CONCLUSION The structures and molecular dynamics of 15c5 and 18c6 molecules coordinating to Na or K in ternary GICs were revealed by the combination of total energy estimation using DFT calculation and analyses of 1H solid state NMR spectra. DFT calculation suggested a more stable structure comprising Na-15c5 (1:1) stacked complexes stack with some offset. The excess Na or K can be ascribed to ions existing on the defect structure in graphene surface. By 1

H NMR line widths, two kinds of molecules undergoing different molecular motions were

observed at room temperature; isotropic rotation with molecular diffusion, and axial rotation with fluctuation of the axis. The rapid diffusion of crown ether - cation complex intercalates will be advantageous for electrochemical and chemical intercalation and deintercalation. The structure and dynamics of crown ether molecules in GIC galleries are strongly affected by the geometry of the crown ether molecules and the strength of the interaction between alkali metal and ligand molecules.


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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 23

Na MAS NMR spectra of Na-15c5-GIC and Na-18c6-GIC taken at room temperature,

Bader charges on Na ions in Na-15c5-GIC, Na-18c6-GIC, and Na on graphene estimated by DFT calculation.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by JSPS KAKENHI (Grant No. 17K06017), and Elements Strategy Initiative for Catalysts and Batteries (ESICB) in Kyoto University.



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