Supplementary Information

Molecular understanding of charge storage and charging dynamics in supercapacitors with MOF electrodes and ionic liquid electrolytes

Sheng Bi1,2, Harish Banda3, Ming Chen1,4, Liang Niu1, Mingyu Chen1, Taizheng Wu1, Jasheng Wang1, Runxi Wang1, Jiamao Feng1, Tianyang Chen3, Mircea Dincă3, Alexei A. Kornyshev2,*, and Guang Feng1,*

Table of Contents

Part 1. Structure optimization of MOFs and pore size calculation..................................................2

Part 2. Constant potential implementation and differential capacitance.........................................6

Part 3. Charge and ions inside different-sized MOFs......................................................................9

Part 4. Comparison of MOFs Ni3(HHB)2 and Ni3(HAB)2.............................................................15

Part 5. Charging dynamics under different working voltages and temperatures...........................17

Part 6. Verification of different models of electrolyte and electrode.............................................19

Part 7. Experiments on supercapacitors with Ni3(HITP)2 solely as electrodes..............................23

Part 8. Simulink circuit simulation of a practical cell-size EDLC................................................30

Part 9. Performance comparison of RTIL-based EDLCs..............................................................33

1State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology (HUST), Wuhan 430074, China. 2Department of Chemistry, Faculty of Natural Sciences, Imperial College London, Molecular Sciences Research Hub, White City Campus, W12 0BZ, London, United Kingdom.

3Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, 02139, United States.4Shenzhen Research Institute of HUST, Shenzhen, 518057, China.*e-mail: a.kornyshev@imperial.ac.uk; gfeng@hust.edu.cn

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Part 1. Structure optimization of MOFs and pore size calculation

Supplementary Figure 1 | Partial charge distribution on the studied MOFs. a, Ni3(HHB)2. b, Ni3(HITP)2. c, Ni3(HITN)2.

The atomistic structures of MOFs were obtained based on experimental measurements. The

geometry optimization of each MOF was derived from density function theory (DFT)

calculations (Supplementary Figure 1), using in Vienna ab-initio simulation package (VASP)1.

The Perdew-Burke-Ernzerhof (PBE)2 exchange-correlation functions of generalized gradient

approximation (GGA) with Grimme’s D2 dispersion correction3 were employed in DFT

calculations. The projector augmented wave (PAW) method4 with a cutoff energy of 500 eV was

used to describe the interaction between nuclei and electrons. The periodic images of atoms were

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used in all three directions. A convergence criterion for the electronic self-consistent loop of 10-5

eV was adopted. The spin-polarized effect was taken into account for accuracy description of the

total energy for MOFs system. After testing, the Γ-centered k-point meshes of 3×3×11, 2×2×6,

and 1×1×8 were adopted for the structure optimization of Ni3(HHB)2, Ni3(HITP)2 and

Ni3(HITN)2, respectively.

The lattice parameters are shown in Supplementary Table 1. Dense k-points were set as

9×9×33, 6×6×18, and 3×3×24 for the calculation of density of states (DOS) and partial atomic

charges (Supplementary Figure 1) of MOFs Ni3(HHB)2, Ni3(HITP)2 and Ni3(HITN)2, which

were obtained via DDEC6 charge analysis as implemented by Manz and co-workers.5, 6, 7

Characterizations, such as gravimetric and volumetric surface area, pore volume, and mean

pore size of these three MOFs were calculated using Zeo++ software8 with a nitrogen probe

radius of 1.86 Å. These structural properties of three studied MOFs are shown in

Supplementary Table 2.

Key parameters of MD simulation systems, such as the number of cation-anion pairs in the

simulation box, the length of electrode as well as the size of simulation box, are given in the

Supplementary Table 3.

Supplementary Table 1. Lattice parameters for three different MOFs.

MOF name a (Å) b (Å) c (Å) α (o) β (o) γ (o)

Ni3(HHB)2 12.986 12.986 3.218 90 90 120

Ni3(HITP)2 21.897 21.897 3.444 90 90 120

Ni3(HITN)2 30.268 30.550 3.476 90 90 120

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Supplementary Table 2. Structural properties for three different MOFs.

MOF name Surface area(m2 g-1, m2 cm-3)

V(cm3 g-1)

ρMOF

(g cm-3)d MOF (nm)

l(nm)

PMOF

Ni3(HHB)2 622.19, 1015.42 0.1247 1.632 0.81 0.20 0.20

Ni3(HITP)2 1153.23, 1072.22 0.4652 0.930 1.57 0.40 0.43

Ni3(HITN)2 1473.38, 967.43 0.8673 0.657 2.39 0.59 0.57

V means the pore volume per mass of the MOF;ρMOF is the mass density of the MOF;d MOF is the pore diameter of the MOF;l represents the volume-to-surface rate of the MOF pore (i.e., the pore volume divided by its surface area);PMOF denotes the porosity of the MOF (i.e., the ratio of accessible pore volume to the total volume of the MOF).

Supplementary Table 3. The number of cation-anion pairs, the box size of simulation system and the length of MOF electrode.

MOF name Number of cation-anion pairs Box size: X, Y, Z (nm) Electrode length (nm)

Ni3(HHB)2 1326 2.5972, 4.49848, 40 5.471

Ni3(HITP)2 2075 4.3794, 3.79268, 40 5.855

Ni3(HITN)2 2090 3.0268, 5.29354, 40 5.909

It is worth to notice that MOF Ni3(HITP)2 has been found to have a bulk electrical

conductivity of 5,000 S m-1 (Ref. 27), whereas the other two (Ni3(HHB)2 and Ni3(HITP)2) have

yet been synthesized. Therefore, we performed DFT calculations on these three types of MOFs

in AA stacking; their density of states (DOS) revealed that all these MOFs are conductive

(Supplementary Figure 2). Among our DFT results, calculations of MOF Ni3(HITP)2 are well

consistent with previous calculations,9, 10 while the other two MOFs Ni3(HHB)2 and Ni3(HITN)2

are not reported to date.

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Supplementary Figure 2 | Density of states (DOS) of three studied MOFs. a, Ni3(HHB)2. b, Ni3(HITP)2. c, Ni3(HITN)2. The red (blue) lines represent spin-up (spin-down) states. The Fermi level is marked by a vertical dot line.

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Part 2. Constant potential implementation and differential capacitance

The applied electrical potential between two electrodes (see Fig. 1 in the main text) is maintained

constant by the constant potential method (CPM), as it allows the fluctuations of charges on

electrode atoms during the simulation.11, 12, 13 Apparently, this approach is more realistic than

often used constant-charge simulations (based on a uniform and fixed partial charge distribution

on the electrode surface), as it takes into account the electronic polarizability of the electrode and

the image force effects. Unlike carbon nanotube or nanoslit (where a constant potential approach

may work fairly well),14, 15 the conductive MOFs typically have a 3D rough and inhomogeneous

surface,16, 17 so that the local redistribution of charges on the electrode due to interaction with

electrolyte could not be neglected. Because the studied MOFs are very conductive, at

equilibrium the MOF-scaffold will be equipotential. We mimic this by tuning the charge on each

atom of MOF electrodes, iterating them from the DFT-obtained partial charges, as listed in

Supplementary Figure 1. Owing to the interaction with electrolytes, the charges on MOF

electrode would adjust the rearranging charge distribution of the electrolyte, for each given

electrode polarization. But what is important is that the rearrangement of the electronic charge

follows inertialessly the rearrangements of the ionic distribution. Such approximation may not

generally hold for materials with very poor electronic conductivity, but they should certainly be

valid for the highly electronical conductive studied MOFs. This should be true for Ni3(HITP)2;

and most likely also for the two other studied MOFs. In addition, the enhanced screening of ion-

ion electrostatic interactions in a metallic nanopore (the concept of superionic state) could only

be correctly captured by CPM,18, 19 and many works20, 21, 22, 23, 24 have emphasized the necessity of

CPM when modeling the charging dynamics process. In this study, we use a methodology

originally proposed by Siepmann et al.25 and refined by Reed et al.26 to achieve the constant

potential on the electrode surface. This technique has already been implemented in the

simulations of carbon based supercapacitors.12, 27 Especially for the porous carbon electrode,

CPM could predict the EDL capacitance which agrees quantitatively with experiments.12

Although CPM method is much more expensive in computation, it is vital to the study the

microstructure of the electrolyte in such confinement and ion transport dynamics, as well as for

comparing the simulated energy storage performance with experiments. Specialized optimization

and parallelization are adopted here for accelerating the MD simulations. With this CPM

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technique, the charges of the MOF electrode could be obtained on the fly of simulation running.

Supplementary Figure 3 shows that electrode charge distribution along the pore surface is

homogeneous everywhere, except for pore-entrance sections (the first two MOF pieces).

Supplementary Figure 3 | Charge distributions on MOF electrode. a, Electrode charge along the pore axis. The applied electrical potential between positive and negative electrode is fixed at 4 V. Snapshots of ions inside the pores of negative and positive electrodes are, respectively, shown in the top and the bottom parts of the Figure. In the middle Figure, dashed grey lines indicate the position of each MOF sheet; red and blue regions represent the entrance part and the central part of the MOF pore. b, Charge on each MOF atom of electrodes under different voltages.

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In our MD simulation, we implemented constant potential method to mimic the applied voltage

between the two electrodes; our modified code could on-the-fly output the amount of charge of

each atom on MOF electrode during the simulation runs. We performed simulations under a

series of applied voltages. Upon the surface area of MOFs is determined, we are able to obtain

the areal surface charge density (σ) as a function of the electrode potential (ϕ). Specifically, σ is

the charged accumulated on the electrode, calculated per surface area of the electrode; electrode

potential ϕ is defined as the potential drop between an electrode and the bulk of the electrolyte

(see Fig. 1a in the main text), relative to its value at zero charge potential of the electrode. The

differential capacitance (C) is therefore calculated by taking derivatives of the MD-obtained σ-ϕ

curves (Supplementary Figure 4).

Supplementary Figure 4 | Demonstration of obtaining differential capacitance. a, The relation between surface charge density (σ) and potential on the electrode (ϕ). b, The differential capacitance (C).

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Part 3. Charge and ions inside different-sized MOFs

Supplementary Figure 5 | In-plane, 2D maps of charge and ion distributions of [EMIM][BF4] inside a pore of a studied MOF (pore diameter 0.81 nm). Each map is based on the simulation data averaged along the pore axis. Columns correspond to three (indicated) electrode potentials (given relative to PZC). a, 2D charge distributions. b-c, 2D number density distributions of cations (b) and anions (c). For better visibility, results for neighbouring pores are not displayed, and in the central pore the areas where no ions could access are shown in white.

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Supplementary Figure 6 | In-plane, 2D maps of charge and ion distributions of [EMIM][BF4] inside a pore of a studied MOF (pore diameter 2.39 nm). Each map is based on the simulation data averaged along the pore axis. Columns correspond to three (indicated) electrode potentials (given relative to PZC). a, 2D charge distributions. b-c, 2D number density distributions of cations (b) and anions (c). For better visibility, results for neighbouring pores are not displayed, and in the central pore the areas where no ions could access are shown in white.

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Supplementary Figure 7 | In-pore ion density and orientation distributions. a, Axial distributions of the ion number. b, Typical snapshots of ions inside the negatively and positively charged MOF pores (colours of ions same as in Fig. 1d). The pore side view of snapshots in negative electrode shows ions, separately, in the central and surface regions defined in Fig. 2b in the main text.

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Supplementary Figure 8 | Distributions of ion density and ion orientation in pores of 0.81 nm MOF electrodes. The axial number density of ions (red solid lines for cations and blue dashed lines for anions), angular distribution of cations, and typical snapshots of ions inside the MOF pores at electrode potential -2 V (a), 0 V (b), and +2 V (c).

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Supplementary Figure 9 | Distributions of ion density and ion orientation in pores of 2.39 nm MOF electrodes. The axial number density of ions (red solid lines for cations and blue dashed lines for anions) and the angular distribution of cations inside the MOF pore at electrode potential -2 V (a), 0 V (b), and +2 V (c). Note that the in-pore distribution of cations and anions has layered structure. The analysis of the distribution of angular orientation was performed, separately, for cation located in the central region (near the pore axis) and in the surface layer.

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Supplementary Figure 10 | Variation of in-pore ion population as a function of electrode potential. a-c, The number densities of cations (red solid) and anions (blue dashed) in the 0.81 nm (a), 1.57 nm (b), and 2.39 nm (c) MOFs, respectively. d-e, The population of cations (red solid) and anions (dashed blue) in the central (i.e., near axis of the pore, light blue shaded area) and surface regions (i.e., near the pore wall, light red shaded area) for MOFs with pore diameter of 1.57 nm (d) and 2.39 nm (e).

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Part 4. Comparison of MOFs Ni3(HHB)2 and Ni3(HAB)2

With the same modeling process for Ni3(HHB)2, Ni3(HITP)2, and Ni3(HITN)2 (see

Supplementary Part 1), we obtained the molecular model for MOF Ni3(hexaaminobenzene)2

(Ni3(HAB)2), based on experimental measurements.28 We then adopted Zeo++ software8 to

evaluate the accessible volume of MOF Ni3(HAB)2, and found that MOF Ni3(HAB)2 has smaller

in-pore space than MOF Ni3(HHB)2 (see Supplementary Table 4).

Supplementary Table 4. Accessible volume for Ni3(HAB)2 and Ni3(HHB)2.

MOF name V (cm3 g-1)

Ni3(HAB)2 0.0619

Ni3(HHB)2 0.1247

Supplementary Figure 11 | In-plane, 2D maps of charge and ion distributions of [EMIM][BF4] inside pores of Ni3(HAB)2. a, 2D charge distributions of RTIL in Ni3(HAB)2. b, 2D number density distributions of cations in Ni3(HAB)2. c, 2D number density distributions of

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anions in Ni3(HAB)2.

MD simulations of MOF Ni3(HAB)2 in [EMIM][BF4] electrolyte were performed to explore

the in-pore structure and its capacitance. As seen from the 2D map of charge and ion

distributions in Ni3(HAB)2 (Supplementary Figure 11) and Ni3(HHB)2 (Supplementary

Figure 5), it demonstrates that Ni3(HAB)2 has less room than Ni3(HHB)2 for ions to access.

Again, it means the pore size of Ni3(HAB)2, as seen by ions, is effectively smaller than that of

Ni3(HHB)2. The differential gravimetric capacitance obtained from MD simulations of MOF

Ni3(HAB)2 in Supplementary Figure 12a was found to be clearly smaller than MOF Ni3(HHB)2

(Figure 3b in the main text), due to the smaller in-pore room for ions to access.

We took MOF Ni3(HAB)2, synthesized with the same approach in previous work,28 as

electrode materials and then curried out the cyclic voltammetry (CV) measurements on 2-

electrode cell with [EMIM][BF4] electrolyte. The CV curve exhibits a capacitance of 17 F g-1

from (Supplementary Figure 12b), which is close the capacitance predicted by MD simulation

(~12 F g-1 under a working voltage of 1.2 V, see Supplementary Figure 12a). Previously, MOF

Ni3(HAB)2 was shown to be very promising as an electrode when using an aqueous electrolyte

with small ions, having highly reversible redox behaviors.29 However, the results herein suggest

MOF Ni3(HAB)2 may not be suitable as an electrode material for most of the IL-based electrical

double layer capacitors, as its pores are too small for ions of a typical IL to fit in (even small

[BF4]- anions have difficulties to access them, see the comparison of Supplementary Figure 11c

with Supplementary Figure 5c).

Supplementary Figure 12 | a, Differential capacitance obtained from MD simulations. b, Cyclic

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voltammograms of Ni3(HAB)2 in pure [EMIM][BF4]; scan rate 1 mV s-1.

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Part 5. Charging dynamics under different working voltages and temperatures

Supplementary Figure 13 | Charging process at different temperature. a-c, Time evolution of charge density, per unit surface area of the pore, after a cell voltage of 4 V was applied between two electrodes, displayed by the positive electrode, for MOFs with pore size of 0.81 nm (a), 1.57 nm (b) and 2.39 nm (c) at temperatures of 300, 325, 350, 375, and 400 K. In each sub-Figure, dashed lines represent the curves by fitting MD-results into the transmission line model (TLM) sketched in below Supplementary Figure 14a.

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Supplementary Figure 14 | Charging process for three studied MOFs at different electrode voltages. a, Schematics of the transmission line model. The electrical current runs along a set of resistors (R). Current is blocked at the end of the line, but it can charge a chain of capacitors. b-d, Time evolution of charge density, per unit surface area of the pore, after a jump-wise change of the applied cell voltage from 0 to 1, 2, and then 4 V between the two electrodes, shown for the positive electrodes with pore diameters of 0.81 nm (b), 1.57 nm (c) and 2.39 nm (d) at a temperature of 400 K. MD-results are shown against the curves fitted to the transmission line model (green dashed lines). e-f, Intrinsic relaxation time (blue dashed line) and the ionic conductivity (red solid line) of ionic liquids in MOF pores at different potentials applied between the two MOFs electrodes with pore diameters of 0.81 nm (e), 1.57 nm (f), and 2.39 nm (g).

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Part 6. Verification of different models of electrolyte and electrode

6.1 Comparison of MD simulations with ionic liquid in different models

To verify that the coarse-grain model of [EMIM][BF4] is good enough in our simulations, all-

atom model30 has been adopted to simulate the same ionic liquid in Ni3(HITP)2. Simulation setup

is the same as that with the coarse-grain model (see Methods in the main text).

All-atom model, shown in Supplementary Figure 15, does reveal more details than the

coarse-grained model; however, they reveal very similar findings in terms of both the

equilibrium properties and structures and charging dynamics. From the in-plane, 2D maps of

charge and ion distributions (Supplementary Figure 16), these two models both demonstrate

layered structures. This is further verified by in-pore ion density distribution (Supplementary

Figure 17a-b) and the analysis of ion orientation (Supplementary Figure 17c). The same refers

to dynamics process (Supplementary Figure 18); these two models lead to almost overlapping

charging curves, with very similar total charge on fully charged electrode (relative difference is

within 4%). Those comparisons evidence that the adopted coarse-grained model can correctly

characterize [EMIM][BF4] in MOF confinement.

It should be noticed that the simulation with the coarse-grain model could save much more

computational resource and the time than using the all-atom model, since there are about 20,000

atoms in an MD system with the coarse-grain model while the total number is about 60,000 with

the all-atom model.

[EMIM]+ [BF4]-

Supplementary Figure 15 | All-atom model of RTIL [EMIM][BF4].

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Supplementary Figure 16 | In-plane, 2D maps of charge and ion distributions of [EMIM][BF4] inside a pore of a studied MOF, using all-atom force field. Each map is based on simulation data averaged along the pore axis (pore diameter is 1.57 nm). Columns correspond to three (indicated) electrode potentials (0 V means PZC, see the main text). a, 2D charge distributions. b-c, 2D number density distributions of cations (b) and anions (c). For better visibility, results for neighboring pores are not displayed, and in the central pore the areas where no ions could access are shown in white. This is to be compared with Fig. 2 in the main text.

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Supplementary Figure 17 | In-pore ion density and orientation distributions using all-atom force field for [EMIM][BF4]. a, Axial distributions of the ion number. b, Radial ion distributions. c, Angular distribution of cations located in central and surface regions of the MOF pore. This is to be compared with Fig. 3 in the main text.

Supplementary Figure 18 | Comparison of charging process based on coarse-grained model and all-atom model of RTIL [EMIM][BF4]. Q∞ represents the total charge on fully charged electrode, and that obtained from all atom model is very similar with that from coarse-grained model (the relative difference is within 4%).

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6.2 Comparison of MD simulations with electrode MOF in different stacking models

To verify the effect of layer to layer stacking in MOF on the capacitive performance, we adopted

an AB stacking, reported to be slipped-parallel with 1/16-th of a unit cell displacement along

both a and b from layer to layer,31 to compare with the AA stacking (i.e., no displacement and

rotation between layers) of MOF used in main text. Thus, we took the model of AB-stacking

MOF electrode (Supplementary Figure 19a) in additional modeling. Using Zeo++ software8,

we calculated the specific surface area and pore size as 1184.44 m2 g-1 and 1.48 nm, respectively,

which are close to the MOF electrode in AA stacking (i.e., 1153.23 m2 g-1 and 1.57 nm in

Supplementary Table 2).

We then performed MD simulations with such AB-stacking Ni3(HITP)2 electrodes. In

comparison with the previous charging curve from AA-stacking MOF simulations, such tiny

parallel slip (0.137 nm) introduces a negligible difference on both capacitance (surface charge in

equilibrium) and charging process (Supplementary Figure 19b).

Supplementary Figure 19 | Comparison of charging dynamics of modeling Ni3(HITP)2 in different stacking models. a, Model of MOF in AB stacking. b, Charge on MOF electrode as a function of time.

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Part 7. Experiments on supercapacitors with Ni3(HITP)2 electrodes

Supplementary Figure 20 | N2 adsorption isotherm of different Ni3(HITP)2 at 77 K. The specific surface areas were computed from these isotherms as 556, 641, and 732 m2 g-1.

Supplementary Figure 21 | a-c, Scanning electron micrograph (SEM) of Ni3(HITP)2 in specific surface areas (SSAs) of 556 m2 g-1 (a), 641 m2 g-1 (a), and 732 m2 g-1 (b). One can see that the MOF with higher SSA exhibits the larger rob-like crystallite. d, High-resolution transmission electron microscopy (HRTEM) image of Ni3(HITP)2 showing a hexagonal pore packing. Inset of d is the Fourier transform of the image in the red box.

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Supplementary Figure 22 | Enhanced crystallinity. a, PXRD patterns of Ni3(HITP)2 in different surface areas. b, The full width at half of the maximum (FWHM) of the diffraction peaks at 2θ = 5° changes with specific surface area. The simulated PXRD, shown as a reference, is based on the crystal structure of Ni3(HITP)2. The increase of the intensity of diffraction peaks at 2θ = 5° (a) and the decrease of FWHM (b) indicate the enhanced MOF crystallinity.

Supplementary Figure 23 | Capacitive measurement of a symmetrical supercapacitor cell. a, Electrode made of Ni3(HITP)2 with Ni foam as collector. b, Electrode made of pure Ni foam. Both types of electrodes have a very similar size. The scan rate is 5 mV s-1. CV curves exhibit that the charge contribution from Ni foam can be neglected.

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Supplementary Figure 24 | Cyclic voltammograms of Ni3(HITP)2 with different crystallinity in a three-electrode cell with ionic liquid [EMIM][BF4]. a, MOF electrode with specific surface area of 556 m2 g-1 showing lower crystallinity. b, MOF electrode with specific surface area of 732 m2 g-1 showing higher crystallinity. The scan rate is 10 mV s-1.

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Supplementary Figure 25 | Stability test of voltage window of MOF Ni3(HITP)2. a, MOF electrode with specific surface area of 556 m2 g-1. b, MOF electrode with specific surface area of 732 m2 g-1. The scan rate is 30 mV s-1.

We have now performed multi-cycle CV measurements for different samples of MOF

Ni3(HITP)2 electrodes (Supplementary Figure 25). We started with the sample that displayed

specific surface area of 732 m2 g-1 and highly ordered PXRD pattern (showing higher

crystallinity), and found that no Faradaic activity occurred within a 2.8 V window from -0.9 V to

+1.9 V (Supplementary Figure 24b). This MOF electrode has continuously shown steady

performance during 2000 cycles (there is some minor degradation within 500 cycles, but it

stabilizes after that, see Supplementary Figure 25) for a symmetric voltage window of -0.7 V to

+0.7 V, i.e., within 1.4 V window.

Sample’s crystallinity plays an important role here. Indeed, we also investigated the sample that

has lower specific surface area (556 m2 g-1) and less perfect PXRD pattern (both indicate lower

crystallinity). This sample can continuously work stably over 2000 cycles but only within a

narrower voltage interval of 1.0 V, from -0.5 V to +0.5 V (Supplementary Figure 25b). This

suggests that the voltage interval of stable performance, at least for the explored MOF

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Ni3(HITP)2 electrodes, could be expanded by synthesis strategies that enhance their specific

surface area and crystallinity.

Supplementary Table 5. Specific surface area, specific-mass capacitance and areal capacitance of Ni3(HITP)2 in RTIL [EMIM][BF4] obtained at a scan rate of 10 mV s-1. Values in brackets are for a scan rate of 5 mV s-1.

Specific surface area (m2 g-1) Gravimetric capacitance (F g-1) Areal capacitance (μF cm-2)

556 58 (66) 10.4 (11.9)

641 70 (75) 10.9 (11.7)

732 76 (84) 10.4 (11.5)

Supplementary Figure 26 | Resistance analyses for two-electrode cells with MOF and carbon electrode materials. Galvanostatic charge and discharge curves at current densities of 0.5 A g-1. The electrodes were made of MOF (Ni3(HITP)2) and activated carbon (YP-50F) compressed on Ni foam without any binders or addictives. The mass loading is ~4 mg cm-2. Inset shows how to determine the ESR from the potential drop at the beginning of a constant current discharge.

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Supplementary Figure 27 | Nyquist plot for EDLCs of MOF Ni3(HITP)2 pellet in ionic liquid [EMIM][BF4]. Electrochemical impedance spectroscopy of a real 2-electrode cell was performed for EDLCs with the electrode of MOF Ni3(HITP)2 pellets in [EMIM][BF4], from 10 mHz to 200 KHz. The inset shows a zoom-in of the high and middle-frequency region.

With the electrochemical impedance spectroscopy (EIS) measurement, we obtained the

experimental Nyquist plot of a real 2-electrode cell, based on the electrode of MOF Ni3(HITP)2

pellets in ionic liquid [EMIM][BF4]. From the Nyquist plot in Supplementary Figure 27, the

ESR is evaluated as 8.9 Ω cm2, which is close to that from the galvanostatic charge-discharge

measurement (8.6 Ω cm2) as well as to the theoretical one (6.4 Ω cm2) obtained from intersection

of the vertical line and the X axis (see Fig. 6a in main text).

Moreover, unlike the theoretical Nyquist plot shown in the main text (Fig. 6a), experiment

shows (i) an inclined but not ideally vertical line at low frequency and (ii) a semi-circle loop in

the high and middle-frequency region. In the low frequency domain, the experimental EIS curve

deviates from the vertical line of simulation result, and such deviation is expected. A recent

research suggests that this would be a result of the RTIL’s low conductivity, in which they

showed that such deviation becomes more significant as the conductivity of the RTIL

decreases.32 The discrepancy in high and middle-frequency region may be attributed to the

contact resistance between MOF pellets and current collector.33

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Part 8. Simulink circuit simulation of a practical cell-size EDLC

Supplementary Figure 28 | Schematics of the conceived two-electrode symmetrical cell and circuit diagram in Simulink. a, Size parameters of the practical cell-size system with MOF pellet electrodes (upper panel) and a picture of the cell measured in experiments (lower panel). The mass loading of MOF pellets is 5.9 mg cm-2. b, Equivalent circuit model of the cell-size system (hereafter is named EDLC module). c, Ragone plot measurement circuit by constant power load test via DC-DC converter module. The equivalent circuit model consists of two RC transmission line models for positive and negative electrode respectively, as well as the resistor of separator (R sep). Each capacitor (C cell) or resistor (Rcell) has the same value, so that the entire transmission line model consists of many repeating RC sections (here we use 6 sections, which has been tested to be large enough; further increasing the number of sections has negligible effects on results). The Ragone test circuit is designed by attaching a boosting DC-DC converter to the EDLC module, so that the output voltage of the EDLC module is boosted and maintained at 4V. By manipulating the power load of the circuit, we get the available energy of the tested EDLC module at different constant active power request.

To predict the capacitive performance of a practical cell-size MOF-based supercapacitor

(shown in Supplementary Figure 28a), Simulink circuit simulations were performed based on

the equivalent circuit model (i.e., EDLC module shown in Supplementary Figure 28b). All the

size parameters are following our experiment of the MOF pellet electrode (dcell=6.4mm), the

thickness of the electrode (LMOF=180 µm), and the thickness of the separate (Lsep=25µm). The

RC transmission line circuit (with six repeating RC sections) has been adopted to model the

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positive and negative electrodes of the cell-size system, and the separator has been modeled as a

pure resistor. Each capacitor has the same value (C cell) and each resistor has the same Rcell. These

values are calculated based on the MD-obtained area-specific capacitance (Carea) and TLM-fitted

conductivity of ions in the MOF pore (σ ) by the following equations:

C cell=Carea ×S × ρMOF × LMOF× π ( dcell

2 )2

nsets

(S1)

Rcell=1σ

×LMOF

π ( dcell

2 )2

PMOF

× 1n set (S2)

where S is the gravimetric surface area of the MOF, ρMOF is the density of the MOF, and PMOF is

the porosity of the MOF, which are obtained from MD system (Supplementary Table 2); dcell is

the diameter of the cell-size electrode (6.4 mm) and LMOF is the characteristic thickness of the

MOF electrode (180 µm for all three studied MOFs), which are taken from our experiment setup

of the two-electrode symmetrical cell (Supplementary Figure 28a); nsets is the number of

repeating RC sections in RC transmission line circuit model (nsets=¿ 6 in this work, which has

been tested to be large enough; further increasing the number of sections has negligible effects

on results)34. Parameters Carea and σ are obtained, respectively, from MD simulations and the

TLM fitting of MD-obtained charging curves. The separator has been modeled as pure RTIL

(here we simply consider that the resistance of the separator region is only contributed from

RTIL in the separator). Thus, the resistor (R sep) can be calculated as:

R sep=1

σ RTIL×

Lsep

π ( dcell

2 )2 (S3)

where σ RTIL is the conductivity of bulk RTIL [EMIM][BF4] (e.g., 1.26 S m-1 at 300 K), and Lsep is

the thickness of the separator (25 µm, cf. Supplementary Figure 28a).

The Nyquist plots of cell-size systems were obtained by the impedance measurement

simulations of EDLC module in Simulink with frequency ranging from 1 kHz down to 10 mHz.

To obtain the Ragone plots of the cell-size system, we design a boosting DC-DC circuit in

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Simulink to perform constant power load test of EDLC module (Supplementary Figure 28c).

With the help of DC-DC converter, the output voltage (V out) of EDLC module could be

maintained at a fixed value (here we set 4V), and by setting different values of loading resistor,

the power request can be manipulated. For instance, if we set Rload at 4 Ω, the power request (Preq

) would be fixed at Preq=(V ¿¿ out)2

R load=¿¿ 4 W. Then, by measuring how long the EDLC module

could supply such required power in Simulink circuit simulations, we can get the available

energy of the EDLC at this power request (i.e., Ragone plots in Fig. 6 in the main text and

Supplementary Figure 29).

Supplementary Figure 29 | Ragone plot of MOF-based supercapacitors under an applied voltage of 4 V. a-b, Gravimetric (a) and volumetric (b) Ragone plots for cell-size MOF-based supercapacitors. Blue triangles, black squares, and red dots represent results for MOFs with pore size of 0.81, 1.57, and 2.39 nm, respectively. Grey dotted lines indicate the lasting time that means how long a supercapacitor can supply the power as the one at the intersection point.

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Part 9. Performance comparison of RTIL-based EDLCs

Supplementary Table 6. Energy and power densities of porous materials for RTIL-based EDLCs.

Electrode material Electrolyte Energy density Power density Ref.Wh kg-1 Wh L-1 kW kg-1 kW L-1

Interconnected porous carbon nanosheets [EMIM][BF4] 11.4 98 35

Carbon nanofibers [EMIM][TFSI] 246 30 36

Carbon [EMIM][TFSI] 20 42 37

Porous carbon nanofiber [EMIM][TFSI] 80 0.4 38

Porous 3D graphene-based materials [EMIM][BF4] 98 137 39

Laser-scribed graphene [EMIM][BF4] 1.36 0.8 40

2D hierarchical porous carbon [EMIM][BF4] 6.0 0.47 41

Carbonized cellulose nanofibrils [BMPY][TFSI] 21 41.6 42

Hydrogen-annealed graphene [EMIM][BF4] 148.75 31.24 30.95 6.5 43

Porous carbon nanosheets [EMIM][BF4] 25.4 15 44

Porous 3D few-layer graphene-like carbon [EMIM][BF4] 44.0 152.9 45

Hierarchically porous carbon nanosheets [EMIM][TFSI] 74.4 17.5 46

porous carbons [EMIM][TFSI] 56 10 47

Conductive MOFs [EMIM][BF4] 30 20 20-46 13-30 predicted

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References

1. Kresse G, Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 1996, 6(1): 15-50.

2. Perdew JP, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77(18): 3865-3868.

3. Grimme S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry 2006, 27(15): 1787-1799.

4. Blöchl PE. Projector augmented-wave method. Physical Review B 1994, 50(24): 17953-17979.

5. Manz TA, Sholl DS. Chemically Meaningful Atomic Charges That Reproduce the Electrostatic Potential in Periodic and Nonperiodic Materials. Journal of Chemical Theory and Computation 2010, 6(8): 2455-2468.

6. Manz TA, Sholl DS. Improved Atoms-in-Molecule Charge Partitioning Functional for Simultaneously Reproducing the Electrostatic Potential and Chemical States in Periodic and Nonperiodic Materials. Journal of Chemical Theory and Computation 2012, 8(8): 2844-2867.

7. Manz TA, Limas NG. Introducing DDEC6 atomic population analysis: part 1. Charge partitioning theory and methodology. RSC Advances 2016, 6(53): 47771-47801.

8. Willems TF, Rycroft CH, Kazi M, Meza JC, Haranczyk M. Algorithms and tools for high-throughput geometry-based analysis of crystalline porous materials. Microporous and Mesoporous Materials 2012, 149(1): 134-141.

9. Chen S, Dai J, Zeng XC. Metal–organic Kagome lattices M3(2,3,6,7,10,11-hexaiminotriphenylene)2 (M = Ni and Cu): from semiconducting to metallic by metal substitution. Physical Chemistry Chemical Physics 2015, 17(8): 5954-5958.

10. Foster ME, Sohlberg K, Spataru CD, Allendorf MD. Proposed Modification of the Graphene Analogue Ni3(HITP)2 To Yield a Semiconducting Material. The Journal of Physical Chemistry C 2016, 120(27): 15001-15008.

11. Feng G, Huang J, Sumpter BG, Meunier V, Qiao R. Structure and dynamics of electrical double layers in organic electrolytes. Physical Chemistry Chemical Physics 2010, 12(20): 5468-5479.

12. Merlet C, Rotenberg B, Madden PA, Taberna P-L, Simon P, Gogotsi Y, et al. On the molecular origin of supercapacitance in nanoporous carbon electrodes. Nature Materials 2012, 11(4): 306-310.

13. Vatamanu J, Vatamanu M, Bedrov D. Non-Faradaic Energy Storage by Room Temperature Ionic Liquids in Nanoporous Electrodes. ACS Nano 2015, 9(6): 5999-6017.

14. Yang L, Fishbine BH, Migliori A, Pratt LR. Molecular simulation of electric double-layer capacitors based on carbon nanotube forests. Journal of the American Chemical Society 2009, 131(34): 12373-12376.

34

425

426427428

429430

431432

433434

435436437

438439440441

442443

444445446

447448449

450451452

453454455

456457458

459460

461462463

15. Feng G, Cummings PT. Supercapacitor capacitance exhibits oscillatory behavior as a function of nanopore size. The Journal of Physical Chemistry Letters 2011, 2(22): 2859-2864.

16. Campbell MG, Sheberla D, Liu SF, Swager TM, Dincă M. Cu3(hexaiminotriphenylene)2: An Electrically Conductive 2D Metal–Organic Framework for Chemiresistive Sensing. Angewandte Chemie International Edition 2015, 54(14): 4349-4352.

17. Sheberla D, Bachman JC, Elias JS, Sun C-J, Shao-Horn Y, Dincă M. Conductive MOF electrodes for stable supercapacitors with high areal capacitance. Nature Materials 2017, 16(2): 220-224.

18. Kondrat S, Kornyshev AA. Superionic state in double-layer capacitors with nanoporous electrodes. Journal of Physics: Condensed Matter 2011, 23(2): 022201.

19. Kondrat S, Georgi N, Fedorov MV, Kornyshev AA. A superionic state in nano-porous double-layer capacitors: insights from Monte Carlo simulations. Physical Chemistry Chemical Physics 2011, 13(23): 11359-11366.

20. Merlet C, Péan C, Rotenberg B, Madden PA, Simon P, Salanne M. Simulating Supercapacitors: Can We Model Electrodes As Constant Charge Surfaces? The Journal of Physical Chemistry Letters 2012, 4(2): 264-268.

21. Reed SK, Lanning OJ, Madden PA. Electrochemical interface between an ionic liquid and a model metallic electrode. Journal of Chemical Physics 2007, 126(8): 084704.

22. Péan C, Merlet C, Rotenberg B, Madden PA, Taberna P-L, Daffos B, et al. On the Dynamics of Charging in Nanoporous Carbon-Based Supercapacitors. ACS Nano 2014, 8(2): 1576-1583.

23. Kondrat S, Wu P, Qiao R, Kornyshev AA. Accelerating charging dynamics in subnanometre pores. Nature Materials 2014, 13(4): 387-393.

24. Bedrov D, Piquemal J-P, Borodin O, MacKerell AD, Roux B, Schröder C. Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields. Chemical Reviews 2019, 119(13): 7940-7995.

25. Siepmann JI, Sprik M. Influence of surface topology and electrostatic potential on water/electrode systems. The Journal of Chemical Physics 1995, 102(1): 511-524.

26. Reed SK, Madden PA, Papadopoulos A. Electrochemical charge transfer at a metallic electrode: A simulation study. The Journal of Chemical Physics 2008, 128(12): 124701.

27. Vatamanu J, Borodin O, Smith GD. Molecular insights into the potential and temperature dependences of the differential capacitance of a room-temperature ionic liquid at graphite electrodes. Journal of the American Chemical Society 2010, 132(42): 14825-14833.

28. Dou J-H, Sun L, Ge Y, Li W, Hendon CH, Li J, et al. Signature of Metallic Behavior in the Metal–Organic Frameworks M3(hexaiminobenzene)2 (M = Ni, Cu). Journal of the American Chemical Society 2017, 139(39): 13608-13611.

29. Feng D, Lei T, Lukatskaya MR, Park J, Huang Z, Lee M, et al. Robust and conductive two-dimensional metal−organic frameworks with exceptionally high volumetric and areal capacitance. Nature Energy 2018, 3(1): 30-36.

35

464465466

467468469

470471472

473474

475476477

478479480

481482

483484485

486487

488489490

491492

493494

495496497

498499500

501502503

30. Chaban VV, Voroshylova IV, Kalugin ON. A new force field model for the simulation of transport properties of imidazolium-based ionic liquids. Physical Chemistry Chemical Physics 2011, 13(17): 7910-7920.

31. Sheberla D, Sun L, Blood-Forsythe MA, Er S, Wade CR, Brozek CK, et al. High Electrical Conductivity in Ni3(2,3,6,7,10,11-hexaiminotriphenylene)2, a Semiconducting Metal–Organic Graphene Analogue. Journal of the American Chemical Society 2014, 136(25): 8859-8862.

32. Rennie AJR, Sanchez-Ramirez N, Torresi RM, Hall PJ. Ether-Bond-Containing Ionic Liquids as Supercapacitor Electrolytes. The Journal of Physical Chemistry Letters 2013: 2970-2974.

33. Portet C, Taberna PL, Simon P, Laberty-Robert C. Modification of Al current collector surface by sol–gel deposit for carbon–carbon supercapacitor applications. Electrochimica Acta 2004, 49(6): 905-912.

34. Pean C, Rotenberg B, Simon P, Salanne M. Multi-scale modelling of supercapacitors: From molecular simulations to a transmission line model. J Power Sources 2016, 326: 680-685.

35. Zhou D, Wang H, Mao N, Chen Y, Zhou Y, Yin T, et al. High energy supercapacitors based on interconnected porous carbon nanosheets with ionic liquid electrolyte. Microporous and Mesoporous Materials 2017, 241: 202-209.

36. Kim CH, Wee J-H, Kim YA, Yang KS, Yang C-M. Tailoring the pore structure of carbon nanofibers for achieving ultrahigh-energy-density supercapacitors using ionic liquids as electrolytes. Journal of Materials Chemistry A 2016, 4(13): 4763-4770.

37. Fuertes AB, Sevilla M. High-surface area carbons from renewable sources with a bimodal micro-mesoporosity for high-performance ionic liquid-based supercapacitors. Carbon 2015, 94: 41-52.

38. Tran C, Lawrence D, Richey FW, Dillard C, Elabd YA, Kalra V. Binder-free three-dimensional high energy density electrodes for ionic-liquid supercapacitors. Chemical Communications 2015, 51(72): 13760-13763.

39. Zhang L, Zhang F, Yang X, Long G, Wu Y, Zhang T, et al. Porous 3D graphene-based bulk materials with exceptional high surface area and excellent conductivity for supercapacitors. Scientific Reports 2013, 3: 1408.

40. El-Kady MF, Strong V, Dubin S, Kaner RB. Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors. Science 2012, 335(6074): 1326-1330.

41. Yao L, Wu Q, Zhang P, Zhang J, Wang D, Li Y, et al. Scalable 2D Hierarchical Porous Carbon Nanosheets for Flexible Supercapacitors with Ultrahigh Energy Density. Advanced Materials 2018, 30(11): 1706054.

42. Li Z, Liu J, Jiang K, Thundat T. Carbonized nanocellulose sustainably boosts the performance of activated carbon in ionic liquid supercapacitors. Nano Energy 2016, 25: 161-169.

43. Yang H, Kannappan S, Pandian AS, Jang J-H, Lee YS, Lu W. Graphene supercapacitor with both high power and energy density. Nanotechnology 2017, 28(44): 445401.

36

504505506

507508509510

511512513

514515516

517518

519520521

522523524

525526527

528529530

531532533

534535

536537538

539540541

542543

44. Chen C, Yu D, Zhao G, Du B, Tang W, Sun L, et al. Three-dimensional scaffolding framework of porous carbon nanosheets derived from plant wastes for high-performance supercapacitors. Nano Energy 2016, 27: 377-389.

45. Zhao J, Jiang Y, Fan H, Liu M, Zhuo O, Wang X, et al. Porous 3D Few-Layer Graphene-like Carbon for Ultrahigh-Power Supercapacitors with Well-Defined Structure–Performance Relationship. Advanced Materials 2017, 29(11): 1604569.

46. Liu D, Jia Z, Wang D. Preparation of hierarchically porous carbon nanosheet composites with graphene conductive scaffolds for supercapacitors: An electrostatic-assistant fabrication strategy. Carbon 2016, 100: 664-677.

47. Sevilla M, Ferrero GA, Diez N, Fuertes AB. One-step synthesis of ultra-high surface area nanoporous carbons and their application for electrochemical energy storage. Carbon 2018, 131: 193-200.

37

544545546

547548549

550551552

553554555