Electrical Double Layer Capacitance of CurvedGraphite Electrodes

Jannes Seebeck,† Peter Schiffels,‡ Sabine Schweizer,¶ Jorg-Rudiger Hill,§,¶ andRobert Horst Meißner∗,†,‖

†Institute of Polymers and Composites, Hamburg University of Technology, Denickestraße15, 21073 Hamburg, Germany

‡Fraunhofer-Institut fur Fertigungstechnik und Angewandte Materialforschung IFAM -Klebtechnik und Oberflachen, Wiener Straße 12, 28359 Bremen, Germany

¶Scienomics GmbH, Burgermeister-Wegele-Straße 12, 86167 Augsburg, Germany§Materials Design SARL, 42, Avenue Verdier, 92120 Montrouge, France‖MagIC – Magnesium Innovation Centre, Institute of Materials Research

Helmholtz-Zentrum Geesthacht, Max-Planck Str. 1, 21502 Geesthacht, Germany

E-mail: robert.meissner@tuhh.de

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This document is the Accepted Manuscript version of a Published Work that appeared in finalform in Journal of Physical Chemistry C (copyright American Chemical Society) after peerreview and technical editing by the publisher. To access the final edited and published work seehttps://pubs.acs.org/doi/10.1021/acs.jpcc.9b10428

Abstract

To improve the understanding of the relationbetween electrode curvature and energy storagemechanisms, a systematic investigation of thecorrelation between convex and concave elec-trode surfaces and the differential capacitanceof an electrochemical double layer capacitorusing molecular dynamics simulations is pre-sented. Each electrode consists of three layersof curved graphene sheets with a convex andconcave surface to which the constant potentialmethod was applied. The differential capaci-tance shows a fluctuating behavior with respectto the curvature radius of the convex and con-cave areas of the electrode. The reasons iden-tified for this are differences in the geometricarrangement and solvation of the adsorbed ionsas well as a steric hindrance prohibiting furthercharge accumulation. Since the total differen-tial capacitance is calculated as a weighted av-erage of contributions from concave and convexsurfaces, the influence of individual curvatureson the total capacitance is significantly reducedfor the total electrode surface.

Introduction

Electrochemical double layer capacitors(EDLCs) or supercapacitors are promising en-ergy storage devices characterized by a highpower density, short charging times and a longservice life. However, their disadvantage is arelatively low energy density compared to tra-ditional batteries.1 The energy storage mecha-nism in an EDLC is based on an electrostaticfield formed at the interface between a conduc-tive electrode and an electrolyte, the so-calledHelmholtz double layer, with a separation ofcharge in the order of a few Angstroms – sev-eral orders smaller than in a conventional ca-pacitor. By using organic electrolytes2,3, whichprovide a low viscosity and higher ionic con-ductivity as compared to ionic liquids at room

temperature, EDLCs can be operated in a verylarge electrochemical window.4–7 In additionto the electrolyte composition, the efficiency ofthe EDLC is strongly determined by the elec-trode material. In particular the chemical andphysical properties of carbon-based materials,such as the high specific surface area, the goodelectric conductivity, the high chemical stabil-ity and the wide operating temperature range,make them suitable candidates for electrodes.2,8

In order to develop new carbon materials withincreased capacitance, it is thus crucial to un-derstand how carbon structures affect chargestorage mechanisms.2,4,5

Capacitances as a function of the mean poresize of several porous carbon-based structureswere previously determined experimentally aswell as from simulations.9–16 By limiting theelectrolyte contact only to the convex part ofan electrode, e.g., by using the outer surfacesof fullerenes or carbon nanotubes (CNT), a re-duction in capacitance was observed.17–19 Inall these studies, however, only the influenceof either purely concave or convex geomet-ric structures were investigated. In complexporous structures, e.g., amorphous carbons onthe contrary, influences from different geome-tries are always intertwined. Hence, it is prac-tically impossible to allow rigorous conclusionsabout influences of edges, pores, curvatures andtheir combination on the differential capaci-tance from simulations of amorphous carbonsalone. Thus, this work attempts to investigateindividual contributions of convex and concaveelectrode curvatures to the differential capaci-tance of the entire electrode and establish a linkto more complex porous structures.

Computational Details

The calculations were carried out withinthe framework of molecular dynamic simula-tions using the Large-scale Atomic/MolecularMassively Parallel Simulator (LAMMPS)20.

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The simulation cell consisted of two curvedgraphitic electrodes enclosing an electrolyte.The electrolyte was made of a 1.5 M 1-n-butyl-3-methylimidazolium hexafluorophos-phate ([BMI]+-[PF6]−) solution in acetonitrile(ACN) and was represented by a coarse grainedmodel as summarized by Merlet et al.3. Fig. 1shows schematically the structure of the coarsegrained molecules. The corresponding simula-tion parameters are summarized in Table 1.

Figure 1: Coarse grained model of the elec-trolyte used in the simulations. Parameters arelisted in Table 1.

For comparison of the performance, addi-tional simulations with flat graphitic electrodeswere carried out as well.

The simulation system was set up in threesteps: First, Packmol 21 was used to obtaina statistical distribution of the coarse grainedmolecules in a bulk electrolyte simulation cell.After a 0.02 ns equilibration run in the NVEensemble, followed by a 0.02 ns NVT simula-tion at 300 K, the density of the bulk elec-trolyte was adjusted by a 2 ns NPT simula-tion at 300 K and 1.0 bar using the Nose-Hooverthermostat/barostat. In all simulations thebonds of the ACN as well as bonds and an-gles of the [BMI]+ were constrained using theSHAKE algorithm, whilst for the bond angle ofACN a stiff spring was used to fix the angle to180◦. The electrostatic interactions were calcu-lated using the particle-particle particle-meshmethod (pppm) along with a cutoff radius of12 A for the short ranged potentials.

In the second step, a three layered planargraphitic model served as initial structure formodeling the wave-like electrodes. In order todefine the concave and convex radii of the mid-

dle layer in the final curved structure the lengthof the initial simulation cell perpendicular tothe zig-zag direction of the planar graphenelayers should be equal to the perimeter of acorresponding carbon nanotube (CNT) withthe same radius. The wave-like structure re-sulted from a deformation of that cell dimensionto twice the diameter of the CNT equivalent.There is a series of carbon potentials that canbe used for the simulation of carbon based elec-trode structures and are described by de Tomaset al.22. We used the LCBOP23 potential in aNVT simulation at 300 K for 0.05 ns and a fol-lowing energy minimization.

The final electrode radii for the middle layer,Rmid, as well as for the concave and convex sur-face areas which are in contact with the elec-trolyte, Rconc and Rconv, are presented in Tab. 2.

In the third step, the electrolyte has to adaptthe contour of the electrodes while a realisticbulk density in the center of the simulation boxis preserved. Thus, the curved electrodes haveto be pressed against the bulk electrolyte fromboth sides in order to represent experimentalconditions at the given temperature and con-centration according to the results of Huo etal.24. An initial displacement of the electrodeswas achieved using a NVT ensemble at 400 Kapplied to the pure ionic liquid and at 300 K forthe organic electrolyte with a simulation timeof 100 ps and a time step of 2 fs. After the ini-tial compression, the displacement of the elec-trodes was coupled to the experimentally deter-mined bulk density of 0.96 g cm−3 in the centerof the electrolyte. During the displacement ofthe electrodes the density was evaluated at eachtime step. The displacement was successivelyadjusted during the simulation in order to con-verge to the experimental density. In this case,a final error of the density of ±0.03 g cm−3 wasachieved. The final structure of an electrochem-ical cell with curved electrodes as used in oursimulations is illustrated in Fig. 2.

The determination of the differential capaci-tance was carried out in the NVT ensemble at300 K for the solvated liquid and at 400 K forthe pure ionic liquid. After an equilibration runfor 0.2 ns, the data was recorded for 3.8 ns atthe respective electrode potential. In order to

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Table 1: Coarse grained model parameters for the molecules represented in Fig. 1 asreported by Merlet et al. 3.

Site Imi Met But [PF6]− N C Meq / e 0.4374 0.1578 0.1848 -0.78 -0.398 0.129 0.269

M / g ·mol−1 67.07 15.04 57.12 144.96 14.01 12.01 15.04σi / A 4.38 3.41 5.04 5.06 3.30 3.40 3.60

εi / kJ ·mol−1 2.56 0.36 1.83 4.71 0.42 0.42 1.59

Table 2: Radii of the concave, Rconc, and con-vex, Rconv, parts of the inner layer in contactwith the electrolyte as well as the radius of themiddle layer (Rmid). Radii are obtained by fit-ting circles to convex and concave areas of theelectrode.

Rconv / A Rconc / A Rmid / A9.77 3.55 4.0710.33 4.19 4.7510.88 4.74 5.4211.40 5.35 6.1011.95 5.79 6.7813.05 6.91 8.1414.68 8.60 10.1715.76 9.76 11.53

apply the defined electric potentials (0 V, 1 V,2 V, 3 V, 4 V and 5 V) the constant potential(CONP) method, as it is described by Wang etal.25, was used. Under the assumption that theelectrode material has an electrical conductiv-ity close to that of metals, the CONP methodcalculates the partial charge for each electrodeatom at a defined potential difference. In con-trast to the constant charge method, the resultsof a CONP simulation are more realistic.19 Fur-thermore, due to the self-consistent charge de-termination of this method, the CONP methodcan be applied to arbitrary electrode geome-tries.3 A well-established approach to calculatedifferential capacitances for flat26 electrodes ge-ometries is to solve numerically the Poissonequation along the z-axis to calculate the poten-tial drop. Due to the approximately linear be-havior of the surface charge density with regardto the potential drop the differential capaci-tance is assumed to be a constant and equalsthe averaged capacitance (see Fig. S8). Mer-

Figure 2: A model of an electrochemical cellused in the simulations. Two curved graphiticelectrodes are separated by an organic elec-trolyte. An electrical potential U is appliedby employing the constant potential method.ACN is represented as a gray transparent fluid,[BMI]+ and [PF6]− are represented by blue andred particles, respectively.

let et al.14 and Lu et al.27 used this approachfor the potential drop calculation of superca-pacitors with non-planar electrodes as well. Byusing the time average of the positive or nega-tive surface charge density 〈σ±〉 of the CONPsimulations as a function of the potential drop∆Ψ, the differential capacitance of the negativeand positive electrode can be calculated withthe equation

Cdiff =δ〈σ±〉δ∆Ψ

(1)

where the potential drop ∆Ψ is defined as thedifference of the applied potential at the pos-itive or negative electrode Ψ± and the poten-tial in the middle of the electrolyte region Ψbulk

(∆Ψ = Ψ± − Ψbulk). Ψbulk can be obtained bysolving the Poisson equation along the direction

4

which passes through both electrodes:

Ψ(z) = Ψ(z0)− 1

ε0

∫ z

z0

dz′∫ z′

−∞dz′′ρ(z′′) (2)

where Ψ(z0) = Ψ± is the boundary conditionand ρ the charge density time average of aninfinitesimal thin slab in z-direction.

Results and Discussion

A linear regression of the time-averaged surfacecharges on the electrode against the potentialdrop allows the successive determination of thedifferential capacitance of each electrode (seeSI for a detailed description of the approach).Fig. 3(a) shows the evolution of the differentialcapacitance as a function of the curvature ra-dius of the middle layer. The curvature of themiddle layer is identical in the concave and con-vex area. Thus Rmid can be used as a referencefor the capacitance of the entire electrode. Weobserved an almost constant difference in thedifferential capacitance for positive and nega-tive electrodes which can be attributed to thedifferent size of the ions. A decrease of the ca-pacitance from 4.7µF cm−2 to 4.3µF cm−2 forthe negative electrode and from 5.5µF cm−2 to4.9µF cm−2 for the positive electrode with anincrease of the radius of curvature, Rmid from4.1 A to 4.7 A is observed. The differential ca-pacitance increases by 0.4µF cm−2 for the neg-ative and 0.5µF cm−2 for the positive electrodewith a further increase in the curvature radius.Compared to flat electrodes, denoted by stars inFig. 3(a), positively charged curved electrodeshave an overall higher capacitance (with theexception at Rmid = 4.7 A). Negatively chargedcurved electrodes behave worse or equivalent tothe flat electrode equivalent. The discrepancyin capacitance between the positive and nega-tive electrode is probably a consequence of theshape disparity of the cations and anions.26,28

Due to the fact that the electric potentials forconvex and concave areas are the same, the po-tential drop for both is assumed to be equal.Resulting differential capacitances for individ-ual concave and convex regions of both elec-

trodes using the aforementioned assumption areshown for the negative and positive electrodein Fig. 3(b) and Fig. 3(c), respectively. Gener-ally, higher fluctuations of the differential ca-pacitance for individual curvatures comparedto the entire electrode appear. The concavepart of the negative electrode (dashed line inFig. 3(b)) shows two very clear maxima locatedat 4.7 A and 6.9 A and three minima locatedat 3.6 A, 5.4 A and 8.6 A. The convex part, onthe other hand, (dotted line in Fig. 3(b)) showsthree maxima at 9.8 A, 11.4 A and 14.7 A andfluctuates with a generally smaller amplitude.A similar behavior is observed for the posi-tive electrode (see Fig. 3(c)). However, a gener-ally higher capacitance is observed for concavepositive electrode parts compared to negativelycharged electrodes. Whereas for the convexparts of the positive and negative electrodes nopronounced difference is observable. Concaveand convex surface contributions to the differ-ential capacitance of the entire electrode de-pend on the ratio of the respective curved areato the entire electrode surface. By calculatingthe weighted arithmetic mean from the convexand concave capacitances, in which the respec-tive surface of the concave and convex part isused as weight, the exact differential capaci-tance of the full electrode is indeed ultimatelyobtained. The strong signal at Rconc = 6.9 A isthus compensated in the total electrode capac-itance by the larger surface area and lower ca-pacitance of the convex region in our particularcurved electrode model.

Individual consideration of the convex andconcave area allow a more rigorous interpre-tation of the charge storage mechanisms inthese areas, while still maintaining the linkto realistic graphitic structures apparent in,e.g., amorphous carbons.29 At a concave radiusof 3.6 A, a 75%-reduction of the solvation shellof both ion types adsorbed on the concave elec-trode part occurs (see Fig. S5) and a minimumof the differential capacitance is observed. Thisbehavior is similar to the decrease of the differ-ential capacitance observed for flat electrodeswhen it is switched to the ionic liquid equiva-lent of the organic electrolyte (Fig. S8). A fur-ther increase of the concave radius in Fig. 4 al-

5

4 6 8 10Rmid / Å

4.0

4.5

5.0

5.5

6.0

C diff

/ F

cm2

neg. electrodepos. electrode

(a)

4 6 8 10Rconc / Å

4

6

8

10

C diff

/ F

cm2

RconcRconv

10 12 14 16Rconv / Å

(b)

4 6 8 10Rconc / Å

4

6

8

10

C diff

/ F

cm2

RconcRconv

10 12 14 16Rconv / Å

(c)

Figure 3: (a) Differential capacitances of the positive and negative electrode as a function of thecurvature radius of the middle layer, Rmid (the differential capacitance of flat electrodes is given bystars) and differential capacitances of concave and convex areas of negatively (b) and positively (c)charged electrodes as a function of the curvature radii, Rconc and Rconv.

lows again more solvent molecules to enter thepocket (apparent in the increase of the solva-tion shell of the adsorbed ions, see Fig. S5),effectively reducing overscreening and eventu-ally resulting in the increase of the differentialcapacitance observed at 4.7 A. Multiple capac-itance peaks have been also observed experi-mentally in Vatamanu et al. 30 for nanoporousmaterials with different pore widths. The oc-currence of capacitance peaks for confined or-ganic electrolytes was also found in the simu-lations of Feng and Cummings 11 using a sim-ilar organic electrolyte. Following their argu-mentation, fluctuations of the differential ca-pacitance of concave pocket-shaped electrodescould be explained as follows: When increasingthe curvature radius, pocket sizes occur thathave a larger concave surface area, but do notoffer additional space for adsorbing new ions.In this case, the surface area is increased butno additional surface charges are induced (orthey are even reduced due to the geometricshape of the electrode), leading to a capaci-tance minimum. Increasing the curvature ra-dius further, additional ions can adsorb at thesurface and another capacitance maximum isobserved. However, this argumentation is notable to explain some of the features apparentin Fig. 3(b) and (c), e.g., the height and the dif-ference of the second peaks observed at a con-cave radius of 6.7 A for negative and positiveelectrodes. Thus, a more sophisticated inves-

tigation of the ionic adsorption structure andthe interplay with the solvent is required to ad-dress, e.g., the influence of the change of therelative permittivity due to adsorbed ACN be-tween the electrode and the ions on the capaci-tance. The number of ACN, [PF6]− and [BMI]+

components in the double layer at the positiveand negative electrode are considered in moredetail in the following to explain the capaci-tance peaks. The extent of the double layerat the positive and negative electrodes was es-timated from the first minimum of the corre-spondingly adsorbed imidazole groups for thenegatively charged electrode and [PF6]− for thepositively charged electrode. Further detailsand the ionic number density distribution fora small and large curvature can be found in theSI. In addition to the density fluctuations in z-direction, the number density within the doublelayer and along the curvature in Fig. S1 showsfurthermore a fluctuating behavior. A more de-tailed investigation of possible reasons for thisbehavior would go beyond the scope of this pa-per. However, this interesting aspect is plannedto be investigated further in the future. By us-ing this method, it is thus possible to identifya consistent double layer thickness of 5.3 A forthe positive and 5.7 A for the negative electrodeof curved graphitic structures – independent ofapplied potential and curvature. As an exam-ple, Fig. 4 and Fig. 5 show the number of ACNand [BMI]+ components as well as [PF6]− ions

6

within the Helmholtz layer of the concave andconvex areas of the negative and positive elec-trode at 3 V, with respect to the radius of cur-vature. Results for other electrode potentialsare found in the SI.

4 6 8 10Rconc / Å

01234567

n com

p / 1

nm2

MethylImidazoleButhylC(ACN)N(ACN)Me(ACN)PF6

(a)

4 6 8 10Rconc / Å

01234567

n com

p / 1

nm2

MethylImidazoleButhylC (ACN)N (ACN)Me (ACN)[PF6]

(b)

Figure 4: Number density, ncomp, of methyl,imidazole and buthyl groups of [BMI]+, N, Cand methyl groups of ACN and [PF6]− in thedouble layer of the negatively charged concave(a) as well as positively charged concave (b)electrode areas. Results are from a simulationat 3 V.

In general, number densities of ACN compo-nents show more pronounced peaks for bothelectrodes than for the ionic components. Acorrelation between ACN and ionic componentpeaks in Fig. 4(a) and (b) with the concave ca-pacitance in Fig. 3(b) and (c) is observed. How-ever, the ACN number at the negative convexarea in Fig. 5(a) shows a somewhat similar be-havior to the convex capacitance in Fig. 3(b)with increasing radii. The dependence of the

10 12 14 16Rconv / Å

01234567

n com

p / 1

nm2

MethylImidazoleButhylC(ACN)N(ACN)Me(ACN)PF6

(a)

10 12 14 16Rconv / Å

01234567

n com

p / 1

nm2

MethylImidazoleButhylC (ACN)N (ACN)Me (ACN)[PF6]

(b)

Figure 5: Number density, ncomp, of methyl,imidazole and buthyl groups of [BMI]+, N, Cand methyl groups of ACN and [PF6]− in thedouble layer of the negatively charged convex(a) as well as positively charged (b) electrodeareas. Results are from a simulation at 3 V.

number density on the curvature becomes morepronounced at higher surface charge densitiesinduced by the applied potential (see Fig. S9-S12). The fluctuations of the number densitiesof ACN components as well as the changing ra-tio of [BMI]+ components in the double layerof the electrodes with increasing curvature in-dicate a possible rearrangement and differentadsorption geometries of the ions depending onthe curvature of the electrode. Due to the loca-tion of the [BMI]+ charge centre between twoorganic side chains acting as spacers, some ad-sorption orientations of the [BMI]+ eventuallyinduce a higher charge on the curved electrodesurface than others. The change of the ad-sorption geometry and an associated structuralphase transition of the ions has been also pre-

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viously observed for flat electrodes at differentelectrode potentials.31

A more rigorous analysis of the orientationof [BMI]+ to the electrode surface is possi-ble by defining three angles, as indicated inFig. 6a: i) The angle between the line whichpasses through both the imidazole group andthe methyl group and the z-axis of the simula-tion box (green line in Fig. 6a). ii) The anglebetween the line which passes through both theimidazole group and the butyl group and the z-axis of the simulation box (red line in Fig. 6a).iii) The angle between the normal of the planein which the three components of [BMI]+ are lo-cated and the z-axis (blue line in Fig. 6a). Only[BMI]+, whose imidazole groups are in the dou-ble layer of the negative electrode, are regardedin this calculations. Fig. 6 shows exemplary theprobability density histograms of the angles cal-culated from the production run for three cur-vatures (for histograms of other curvatures seeFig. S14).

Different preferred angles for [BMI]+ indicatea correlation between the adsorption orienta-tion and the curvature radius. Distinguish-ing between concave and convex area (Fig. S15and Fig. S16) illustrates that the dependenceis significantly influenced by the concave area.The stronger dependence from concave areascould also be an explanation for the more pro-nounced fluctuations of the concave differen-tial capacitance. Thus, the [BMI]+ adsorptionorientations can be correlated with the num-ber of [BMI]+ molecules adsorbing on the elec-trode surface, explaining to some extent a ca-pacitance increase by crowding.32 Some orien-tations favors a higher number of imidazolegroups in the double layer, leading to a higherinduced charge on the electrode and increaseddifferential capacitance. However, in order toanalyze this more accurately, a more sophis-ticated analysis of the double layer structureat the electrode surface is necessary. For thispurpose, free energy changes associated with achange of the ion adsorption motif with vary-ing electrode potential and curvature need tobe taken into account. Analyzing the structureof the ions and solvent at different curvaturesand electrode potentials using advanced sam-

pling techniques, e.g., umbrella sampling and aweighted histogram analysis, would enable fur-ther insights into the mechanisms of the energystorage apparent in realistic carbon electrodes.However, this goes along with an immense com-putational effort and would require flexible elec-trodes which are not (yet) possible using theCONP method in LAMMPS.

Conclusion

In this work, the influence of convex and con-cave electrode geometries, that are typicallypresent in electrode materials of modern super-capacitors, on the differential capacitance hasbeen investigated. For this purpose, MD simu-lations employing a constant potential methodwere performed on models of electrochemi-cal cells with curved graphitic electrodes anda commonly used organic electrolyte betweenthem. It was observed that the total elec-trode capacitance fluctuations origin from con-cave and convex areas of the electrode and theirindividual differences in their capacitance am-plitudes. Furthermore, the total differential ca-pacitance of the entire electrode surface is cal-culated as the weighted average of both elec-trode geometries and consequently the impactof the concave area on the total differential ca-pacitance is greater than that of the concavearea. For this reason, differential capacitancefluctuations of the total electrode is generallyattenuated. However, the higher capacitance ofthe positive electrode is due to the larger influ-ence of the concave part compared to the neg-ative electrode.

In general, a correlation of the differential ca-pacitance with the total number of ions and sol-vent in the Helmholtz layer of the electrodeswas observed. In more detail, capacitance fluc-tuations are furthermore explained by a geo-metric reorientation of the [BMI]+ and to someextent an increase or decrease of the solva-tion shell. This work aims to improve theperformance of supercapacitors by providing afundamental understanding of the energy stor-age mechanisms in curved graphitic structures.Thus, by favoring certain electrode geometries

8

(a)

0 50 100 15012 /

0.000

0.005

0.010

0.015

0.020

0.025

prob

(b)

0 50 100 15012 13 /

0.0000.0020.0040.0060.0080.0100.012

prob

(c)

Figure 6: Histograms of the probability density,ρprob, of the orientation angle between the z axisand a) the line between the imidazole and the methyl group (θ13), b) the line between the imidazoleand the butyl group (θ12) and c) the normal of the plane in which all three groups of the coarsedgrained [BMI]+ in the double layer of the negative electrode (θ12−13) are located. Results are from asimulation at 3 V. The size of the double layer was derived from RDFs between the surface carbonatoms and the imidazole groups.

in the production process of amorphous car-bons, cf. the structure of negatively curvedschwarzites33, it is expected to increase the ca-pacitance of supercapacitors with this new gen-eration electrode materials. In this context, de-sign criteria for the structure of electrode sur-faces, e.g., a favorable mean curvature radius fora specific organic electrolyte, can be developed.

Acknowledgement Funded by the DeutscheForschungsgemeinschaft (DFG, GermanResearch Foundation) – Projektnummer192346071 – SFB 986 and – Projektnummer390794421 – GRK 2462. Furthermore, the au-thors gratefully acknowledge financial supportby the German Ministry of Education and Re-search in the AktivCAPs project (grant no.03SF0430B).

Supporting Information Available: Thesupporting information provides details aboutthe solvation shell calculation as well as furthergraphic representations for comparison with thepresented data. This material is available freeof charge via the Internet at http://pubs.acs.org/.

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