Molecular Dynamics Simulations of Ether-Modified Phosphonium Ionic

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C: Energy Conversion and Storage; Energy and Charge Transport

Molecular Dynamics Simulations of Ether-Modified Phosphonium Ionic Liquid Confined in between Planar and Porous Graphene Electrode Models Guilherme Ferreira Lemos Pereira, Rafael Guimaraes Pereira, Mathieu Salanne, and Leonardo José Amaral Siqueira J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01821 • Publication Date (Web): 16 Apr 2019 Downloaded from http://pubs.acs.org on April 17, 2019

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The Journal of Physical Chemistry

Molecular Dynamics Simulations of Ether-Modified Phosphonium Ionic Liquid Confined in between Planar and Porous Graphene Electrode Models Guilherme Ferreira Lemos Pereira,† Rafael Guimarães Pereira,† Mathieu Salanne,‡ and Leonardo José Amaral Siqueira,† †Laboratório de Materiais H´ıbridos, Departamento de Qu´ımica, Instituto de Ciências Ambientais, Qu´ımicas e Farmacêuticas, Universidade Federal de São Paulo, Rua São Nicolau, 210 Diadema-SP-CEP 09913-030 – Brazil. ‡Sorbonne Université, CNRS, Physico-chimie des e´lectrolytes et nanosystèmes interfaciaux, PHENIX, F-75005, Paris, France E-mail: [email protected]

Abstract

of P atom of phosphonium cations. With both porous electrode the ions of the same charge are mostly adsorbed in front of each other across the graphene plane due to high image charges of carbon atoms of the electrode in between the ions. In the electrode of narrower pore, the capacitance varies with the applied voltage, which impacts the overall energy density of the electrode.

Phosphonium-based ionic liquids with short alkyl chains present low viscosity besides their relative high electrochemical stability. These properties make them good candidates for electrolytes of electrochemical doublelayer capacitors (EDLC). We performed molecular dynamics (MD) simulations of 2-(methoxy)-ethyl-triethylphosphonium [P222,2O1 ] bis(trifluoro-methanesulfonyl)imide [NTf2 ] ionic liquid confined in planar and nanoporous graphene electrode. The electrodes were simulated with a constant potential model, which allow the carbon charges to fluctuate. In spite of the ether function in the longer chain of phosphonium, the ions are organized in layers of alternated charge close to the surface of planar electrodes. The differential capacitance on the negative electrode is lower than in the positive electrode, which reflects the larger size of phosphonium cations. In nanoporous carbons, ˚ there is a monolayer inside the pores of 8.2 A, ˚ there are of ions, whereas in larger pores (12 A) one layer of N atom of anion and two layers

1 Introduction Supercapacitors or electrochemical doublelayer capacitors (EDLC) and batteries are energy storage devices. Both families share similar set-ups, as they are formed by two electrodes separated by an electrolyte. However, the mechanism by which they store energy is distinct. While batteries store energy by means of redox reactions during the charging/discharging cycles, supercapacitors store energy without any chemical process, that is through the adsorption of ions on the surface of the electrodes. Consequently, supercapacitors have much higher power (rate to delivery or accumulate energy) and longer

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lifetime than batteries, but they have lower energy density. 1,2 The energy density of a supercapacitor depends on the maximal cell voltage (Umax ) and the specific capacitance (C, in F/g), 1 i.e.,

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that mesoporous electrodes were necessary to allow the ions to fill the pores without changes in the solvation shell of the ions. Based on the fact that graphene provides large accessible surface, graphene based-electrodes have been proposed as suitable material Z Umax for electrode with higher capacitance. 19–22 E= UC (U )dU, (1) However a large discrepancy of the results 0 has been reported so far: For example, we where U is the applied voltage (in V). It can cite the EDLC obtained with microwave can be enhanced with the use of (i) porous exfoliated graphene oxide (MEGO) as electrodes (high active area) and (ii) the proper electrodes and 1-ethyl-3-methyl-imidazolium choice of electrolyte, which should have high bis(trifluoromethanesulfonyl)amide (EMIelectrochemical stability to provide cell with NTf2 ) as electrolyte that provides capacitance the highest possible operating voltage. as high as 130 F/g, 23 whereas a supercapacitor Concerning the electrolyte, since the seminal made of holey graphene with EMI-NTf2 also work of McEwen et al., 3 in which they as electrolyte yields only 45 F/g. 24 These observed that ionic liquids (room-temperature striking differences might be related to the molten salts) are relevant electrolytes, many oxidation degree of graphene that influences investigations considering ionic liquids (IL) the electrode-electrolyte interactions, as as electrolyte for EDLC have been done. 4–11 pointed out by previous molecular simulations Due to its high electrochemical window, of ionic liquids confined in between graphene allowing wide operating voltage of 3.6 oxide electrodes. 25,26 V, the IL N-butyl-N-methyl-pyrrolidinium Theories and molecular simulations of bis(trifluoromethanesulfonyl)imide ([Pyr][NTf2 ]) electrolytes have played a crucial role to the is one the most investigated as electrolyte understanding of the EDLC properties. Firstly, for EDLC. However, [Pyr][NTf2 ] provides Kondrat and Kornyshev have introduced the low power because of its high viscosity and, concept of superionic state to account for the consequently, low ionic conductivity at room fact that ions of the same sign may be in temperature. This drawback can be overcome contact inside highly confined nanopores. 27,28 with the modification of alkyl chain with an Merlet et al. 6 performed MD simulations using ether function, which decreases the viscosity, realistic models of carbide-derived-carbon enhancing the ionic conductivity. 12–15 electrodes (CDC) and demonstrated that such ILs formed by phosphonium cations with porous materials yields higher capacitance small alkyl chains yields IL with lower than planar electrodes because the former viscosity and higher ionic conductivity than prevents the overscreening effect and provides ammonium analogues. 16 Rennie et al. 17 denser packing of the counter-ions inside the showed that ILs containing ether function pores due to the screening by the pore walls can perform better as electrolyte for EDLC of the ions Coulomb interactions. A joint than their alkylated analogues, as they present experimental-computational study showed a higher specific capacitances, in addition to a reduction of the Coulomb ordering of ionic reduced cell resistance. liquids confined in carbon nanopores when Regarding the electrode properties, it is wellthe pores accomodates only single layer of known that electrode-electrolyte interactions ions, proving the existence of superionic play important role, for example, the size state. 29 In addition, Previous MD simulations matching between the ion and the pore of of ionic liquids confined in slits showed that the carbon electrode generally leads to a the narrower the pore size, the higher the significant increase of the capacitance. 4,5,18 capacitance. 10 The limit of the maximum This finding changed the traditional view capacitance is reached when the pore size ACS Paragon Plus Environment

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allow only one layer of adsorbed ions. Recently, Mendez-Morales et al. 30 performed MD simulations of coarse-grained model for imidazolium based ionic liquid confined in between slit-like electrode and showed that ions of the same charge have the tendency to adsorb in front of each other across the graphene plane under strong confinement ˚ This structuring is due (pore size of 7 A). to the formation of highly localized image charges on the carbon atoms of the electrode, which are between the ions. In wider pores ˚ such correlation is completely lost (10 A) due to the formation of bilayer of ions inside the pores. Given the larger volume of phosphonium cation and absence of MD simulation of this class of IL on the surface of electrodes, we performed MD simulations of an phosphonium-based confined in between planar and porous electrode held under constant potential with the aim to compare the effect of the size of cation to the organization of the ions under confinement and the interplay between the structure and capacitance.

(a)

(b)

Figure 1: Snapshot of the simulation box (a) for the planar and (b) for the porous electrode. Black spheres: Electrode; Red spheres: Oxygen; Yellow spheres: Sulfur; Pink spheres: Fluorine; Dark Blue spheres: Nitrogen; Light Blue spheres: Carbon; Olive spheres: Phosphorus.

2 Computational details The computational details of the bulk simulations, for which the GROMACS software 31–34 has been used, is described in the supporting information. LAMMPS package 35 was used to conduct Molecular Dynamics simulations of 300 ion pairs of 2-(methoxy)-ethyl-triethylphosphonium [P222,2O1 ] bis(trifluoro-methanesulfonyl)amide [NTf2 ] placed between two carbon electrodes of different geometry (planar and porous) as depicted in Figure 1. The starting configurations were built with PACKMOL. 36 The porous electrodes investigated here are composed by pores of width of 8.2 ˚ and 12 A. ˚ Although these structures A are simplified compared to the realistic nanoporous carbons, 6,37 the simulations allow to understand the potential impact of pore size on the system performances. The charges of carbon atoms on the electrode were allowed to fluctuate by imposing a

constant potential method implemented in LAMMPS code, 35,38–40 which ensures an appropriated description of the surface polarization by the ions along the simulations. A vacuum region was added in the zdirection and the Yeh-Berkowitz condition for slab correction 41 was used to mimic 2D periodic boundary condition. Simulations were performed at several applied potential differences between the two electrodes, ∆Ψ= (0, 1, 2, 4 and 6 V) for setup (a) and (0, 1, 2 and 4 V) for setup (b). The simulations were conducted in the NVT ensemble with a time step of 2 fs at 400 K. The systems were first equilibrated for 40 ns at zero constant charge on each electrode. In order to speed up the charging process in the case of setup (b), equilibrations runs of 10 ns, in which the charge on each carbon atom of the electrode was 0.0125e, 0.025e and 0.048e, were performed before applying potential differences, ∆Ψ, of 1, 2, and 4 V, respectively. Considering that constant potential simulations demand higher computational times, we employed a united atom model in order to speed up the simulations. In the united atom model, the CH3 and CH2 groups were treated as single bodies. The inter and intramolecular parameter used in the simulations together with their respective


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equations are available in tables S6-S10 of the supplementary material. A scaled-charge model (scaling factor=0.8) was employed in order to predict satisfactory transport propreties (diffusion coefficients, viscosity and ionic conductivity). 42–44

with the same charge of a given surface) arises close to the first layer of ion. This layered ˚ from the surface structure extends up to 30 A in their case and is called charge overscreening. Following this work, a vast amount of MD simulations of ionic liquids at planar surfaces were performed considering different ionic liquids and their results confirmed the appearance of charge overscreening. 37,38,48–60 The introduction of ether function in the side chain of quaternary ammonium based ionic liquid could be expected to somewhat alter this scenario. However, as for previous simulations, a strongly layered (overscreening) structure is observed; 48 this finding indicates the large strength of the Coulombic interaction between the charge surface and the ions. Given that phosphonium cations are larger than quaternary ammonium cations, the Coulombic interaction might be weakened and the presence of ether oxygen (with negative partial charge) could be able to change the ions layering on the surface of charged surfaces. Figure 2 depicts the (atomic) number density profiles of [P222,2O1 ] [NTf2 ] ionic liquid at planar electrode interfaces as a function of the voltage applied to the electrodes. When the difference potential is 0 V (upper panel), the ion density profiles are symmetric close to the surfaces because both the ions can adsorb; however the adsorbed layer of cations is narrower than the anion layer. At ∆Ψ = 2 V (middle panel), the counter-ions are attracted to the surface, whereas the co-ions are pushed away, allowing the formation of alternated ion layers close to the electrodes. Note, however, that in the positive electrode there is a considerable amount of cation inside the layer of anions adsorbed on the surface of the electrode, which indicates a large asymmetry in the adsorption properties of the two ions. At ∆Ψ = 6 V, the layered structure is further enhanced. It is worth mentioning the presence of two shoulders in the first peak of the cation density profiles, close to the electrode surfaces, ˚ and 160 A. ˚ These shoulders at around 13 A are due to the oxygen atoms of ether function that are attracted or repelled by positive or

3 Results and Discussion 3.1

Bulk Properties

Phosphonium-based ionic liquids whose cations contain ether function have been previously investigated experimentally and computationally. 15–17,45 Whereas their structural properties have been properly described by means of molecular dynamics simulations, their simulated transport properties have not. It has been well accepted that non polarizable model of ionic liquids with reduced charges, i.e. charges normalized by 0.8, are able to predict quantitatively transport properties of ionic liquids. 42–44 Table 1 shows the diffusion coefficients, viscosities and ionic conductivities calculated with this potential at 400 K. The experimental values of the transport properties were obtained from the extrapolation to 400 K of the respective VTF equations obtained by Martins et al. 15 Although slightly overestimated, the calculated transport properties using the scaled-charge model are in good agreement with the experimental values. It is important to mention that the diffusion coefficients were correct for size-system effects as proposed by Yeh and Hummer. 46

3.2

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Interface simulations

3.2.1 Planar Electrodes In a molecular dynamics simulation study of molten salts at interface with planar electrodes, Lanning and Madden 47 showed that the number of counter-ion adsorbed on the surface is larger than that needed to neutralize the surface charge. Thus, in order to neutralize the charge of the first layer of ions adsorbed on the surface, a second layer of co-ions (ions


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Table 1: Experimental 15 and calculated diffusion coefficients (D), viscosity (η) and ionic conductivity (σ) at 400 K. In parenthesis are the standard deviations.The diffusion coefficients were corrected for system-size effects. 46 (10-6 Simulations Experiments 15

D+ D η σ 2 -1 -6 2 -1 cm s ) (10 cm s ) (cP) (mS cm-1 )

4.3 (0.3) 2.9

4.5 (0.5) 3.4

negative electrodes, respectively.

4.1 3.8

42.5 30.2

are repelled from the surface as the potential on the electrode increases, as depicted in Figure 3. Above ∆Ψ = 4 V, there is not any anion adsorbed on the negative electrode, whereas the opposite electrode still has small density of cation atoms (oxygen atoms).

Figure 3: Number density profiles of the ions close to negative and positive electrode. Integrating these density profiles densities provides the number of the ions adsorbed on the surface of each electrode, Figure 4. Lets ˚ as a reference point on the consider z = 11 A left electrode to obtain the number of ions adsorbed on the surface because there is no anion present at this position when the applied potential difference is 4 V or higher. Similarly, ˚ for the right side, the reference point is 158 A. Table 2 presents the number of ions adsorbed on the electrodes surfaces, the total charge of the adsorbed ions, and the total charge on the electrodes, which was obtained by average values of charge on each electrode after charges have converged as depicted in Fig. S3 of Support Information. At ∆Ψ = 0 V, the number of cations adsorbed is slightly larger

Figure 2: Number density profiles of the two ions of the ionic liquid adsorbed at planar electrode interfaces with ∆Ψ = 0, 2, and 6 V at 400 K. Figure 3 shows a zoom of the ion density profile close to the electrodes at different potentials. Because of the molecular nature of the ions, there are peaks of atom on the electrode surfaces. Note that the higher the potential applied to the electrode, the larger the density of counter-ions adsorbed on the each surface. On the other hand, the co-ions


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than the number of anion, which provides an excess charge of +0.6e close to surfaces of the electrodes. Charging the electrodes from ∆Ψ = 0 to 1 V, two anions adsorbed on the surface of the left electrode are replaced by two cations. On the left electrode, occurs the adsorption of three new anions, but without replacement of cations. Further charging of the electrodes, from ∆Ψ = 1 to 2 V, two cations swap with two anions on the negative electrode, whereas in positive electrode, only one cation leaves the surface, which is replaced by two anions. As a consequence, at ∆Ψ = 4 V, only cations are adsorbed on the surface of negative electrode. On the other side, there are still some cations on the surface of positive electrode. Further charging to ∆Ψ = 6 V does not lead to further adsorption of cations, indicating that the surface of the negative electrode is saturated at this stage. Although the NTf2 anion is rather voluminous, the number of anions adsorbed on the surface of positive electrode is larger than number of cations adsorbed on the negative electrode.

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the effective ion accumulation (EIA) factor, Rz [ ρcounter ion (s ) ρco ion (s)]ds EI A(z) = 0 σ /e (2) where z is the distance from the electrode surface, σ is the absolute average of the charges in the electrode, e is the electron charge, and ρcounter ion and ρco ion are the number density of counter-ion and co-ion, respectively. Figure 5 shows the effective ion accumulation factor calculated at ∆Ψ = 1, 2, 4, and 6 V for negative (left panel) and positive (right panel) electrodes. The electrode charge is exactly screened at the distances where EIA reaches 1.0. The main feature observed in EIA is the fact that the overscreening is larger at low voltages. The oscillations observed in EIA of the negative electrode calculated at ∆Ψ = 1 V ˚ away from the electrode extend up to 40 A ˚ from surface while they fade away at ca. 30 A the surface of the positive electrode.

jj

Figure 5: The effective ion accumulation (EIA) factor as function of ∆Ψ as defined in eq. (1).

Figure 4: Number of ions adsorbed in the first layer close to the planar surface of the electrodes.

The differential capacitance of each interface depends on the surface charge on the electrode and on the potential drop across the interface. The surface charge is simply calculated by summing the charges of each carbon atom (see Figure S3 of Support Information) of the electrode, and divide the obtained value by the ˚ surface area of one graphene layer (L x = 32.2 A ˚ The potential drop is and Ly = 34.4 A). obtained from the electrostatic potential

For all the applied voltages, there are residual charges due to the excess of counter-ions adsorbed on the surface of the electrodes, which is responsible for the charge overscreening. As proposed by Feng et al., 61 an interesting method to characterize the overscreening of electrode is to determine


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Table 2: Number of ions adsorbed in the first adjacent plane to the electrode surfaces, total charge of the corresponding ionic layer (Qion (e)), total charge on the electrodes (Qele (e)), and ∆Q = Qion Qele (e). ∆Φ 0V 1V 2V 4V 6V

˚ Negative electrode; z up to 11 A # Cation # Anion Qion (e) Qele (e) ∆Q 7.0 9.0 11.0 12.8 13.3

6.1 3.8 1.7 0.1 0.0

0.7 4.2 7.4 10.2 10.6

-0.04 -1.8 -3.2 -6.1 -8.3

0.66 2.4 4.2 4.1 2.3

profile, which in turn is calculated from Poisson equation:

Ψ ( z ) = Ψ q ( z0 )

1 ε0

Z

z z0

dz0

Z

z0 ∞

˚ Positive electrode; z above 158 A # Cation # Anion Qion (e) Qele (e) ∆Q 7.3 7.4 6.0 3.3 2.3

6.1 11.1 13.1 16.3 17.4

0.8 -3.0 -5.7 -10.4 -12.1

-0.04 1.8 3.8 6.6 8.7

0.76 -1.2 -1.9 -3.8 -3.4

C =

∂σs (4) ∂∆Ψ where σs is surface charge density and ∆Ψ = Ψ Ψbulk is the potential drop. Here, Ψbulk was arbitrarily set to 0 V. Figure 7 shows the surface charge density on the electrodes as function of the potential drop. The average differential capacitances were obtained from the slope of the straight lines and are presented in Table 3. In [P222,2O1 ] [NTf2 ] ionic liquid, the capacitance of the positive and negative electrode respectively are 4.2 and 3.2 µF cm-2 . Note that the capacitances calculated for [BMI][PF6 ] ionic liquid in the simulations in which a constant potential model was also employed have similar values. The larger capacitance observed for the positive electrode in [P222,2O1 ] [NTf2 ] may be related to the overscreening behavior in this electrode, which fades away at shorter distances than in the negative electrode.

dz00 ρq (z00 )

(3) where z0 is a reference point inside the left electrode, providing Ψq (z0 ) = Ψ , ρq (z) is the charge density, and ε 0 is the vacuum permittivity. Figure 6 shows the electrostatic potential profiles obtained from the MD simulations of [P222,2O1 ] [NTf2 ] at different applied voltages on the electrodes. For every ∆Ψ, the potential drop of negative electrode is always larger, in absolute value, than that obtained for the positive electrode.

Table 3: Capacitance values obtained from the linear trends observed for the negative and positive electrodes. Ionic Liquid [P222,2O1 ] [NTf2 ] [BMI] [PF6 ]

Figure 6: Poisson potential profiles across the simulation boxes for the various potential differences applied (flat electrodes). The differential capacitance electrodes is given by

for

C+ (µF cm-2 ) C- (µFcm-2 ) 4.2 3.9

3.2 4.8

3.2.2 Porous electrode

both

˚ pores Structure of the liquid in the 8.2 A Figure 8 shows the charge and ion density


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Figure 8: Density profiles of ions and charges inside the negative and positive electrodes ˚ with slit space of 8.2 A.

Figure 7: Surface charge density as a function of the potential drop across the interfaces. Red and black dots stand for negative and positive electrodes, respectively. The corresponding differential capacitances are obtained by the slope of the two curves.

and a sharp region of low negative charge density. These finding indicates that the high negative charges induced on the surface of the pore repel the oxygen atoms of ether chain of cation inward the pore. Compared to ∆Ψ = 0V, the density of negative charges on the edges of the electrode is even larger, but it does not provoke remarkable changes in the layered structure of ions from the edge of the pore toward the bulk. On the positive electrode, the pore is also mainly filled of anion at ∆Ψ = 2 V. The main difference is the presence of cations that remain close to the edge of electrode, which prevents the formation of a sharp ˚ As a density of positive charges at z 205 A. consequence, the layering of the liquid when going towards the bulk is less pronounced than in the other side of the electrochemical cell. Figure 9 shows a density map in the xz-plane of cations and anions inside and in the vicinity of the negative electrode. In order to enhance the visualization, only the ions located in one of the slits were considered and the data was averaged over the last 4 ns of the simulation. The formation of layers of alternate charges inside the slit is clearly observed at ∆Ψ = 0 V, that extends toward the bulk region of the liquid. In order to study further the arrangement of the ions inside the pores, Figure 10 shows the density map in the yz-plane calculated

˚ at profiles in porous electrodes with 8.2 A ∆Ψ = 0 V and ∆Ψ = 2V. At null voltage, cations are much more present at the entrance of the pores than anions, which induces huge negative charges on the edges of the electrodes ˚ as depicted by the (z = 32 and z = 205 A), green line of Figure 8 (upper panel). From the entrance of the pore toward the bulk of the ionic liquid, there is a region of high densities of anions immediately close to this cation layer, followed by another layer of cations, thus giving rise to a structure characterized by the formation of ion layers of alternated charges ˚ from the edge of the that extend up to 20 A pores. Similarly, inside the pores there also are ions layers of alternated charges toward the bottom of the pore that induce opposite charges on the electrode.It is noteworthy mentioning that from the pore toward the bulk the ion structuring is very different from that found in planar electrodes at ∆Ψ = 0V. Note that both cations and anions are present at the bottom of the pore. At ∆Ψ = 2V, the negative porous electrode is mainly filled by cations, organized in four distinct layer along the z-axis. In the regions where there are anions, the charge density on ˚ the electrode is less negative. At z 32 A, there is a shoulder in the cation density profile


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Recent experimental and computational study devoted to the investigation of the ordering of ionic liquids inside carbon nanopores described the partial breaking of Coulomb interaction when the ions are confined as a single layer, this effect being enhanced in the presence of an applied electric potential. 29 In this study the authors employed scattering experiments, whose outcome results in structure factors, S(k ) (k-space correlations) that have been used to unravel the structure of ions under confinement and with applied voltage. Instead of using correlations in the k-space, we will investigate the correlations by means of radial distribution functions, g(r ), of the ions confined inside narrow carbon pores that allow only one layer of ions. Figure 11 shows the (P–P) and the (N–N) self-correlations, as well as their cross-correlations (P–N) both inside the pores and across the pores, for different applied voltage. Inside the pore (left panel), the characteristic distances for the cation-cation correlations ˚ , which range between between 7 and 11 A is reminiscent of the bulk structure. The intensity of the correlations is enhanced by the application of a voltage, in agreement with the results of Futamura et al. 29 On the contrary, the cation-anion distances are longer than in the bulk and the intensity of the peak does not change with voltage. Finally, correlations between the anions become less intense and longer-ranged when the voltage increases due to the de-filling of the pores. Across the pores, the P-P correlations ˚ appears as an intense peak around 8.4 A, which is close to the distance between the ˚ used in the simulations graphene layers (8.2 A) and shows the formation of stacks of cations from pore to pore, an effect which was already observed in a recent simulation study. 30 The N– N radial distribution function is more complex, since it displays three well-defined peaks ˚ This is due to the between 7.0 and 11.0 A. splitting in two layers of the anions. The first peak therefore corresponds to anions facing each other, one being on top of the lower pore while the other one is at the bottom of the

Figure 9: Density map of cations and anions in the xz-plane inside and in the vicinity of the negative electrode. The green rectangle represents the position of the graphene sheets. for N and P atoms of [NTf2 ] and [P222,2O1 ], respectively. These atoms were chosen because they are close to center of mass of respective ions. As one can observe, the P atoms are located in the middle of each slit, indicating a formation of single layer of cations. On the contrary, two peaks are obtained for the N atoms inside each slit, however a further examination of the trajectory shows that there are not two layers of anions but rather than that NTf2 can be adsorbed in two different ways inside the slits.

Figure 10: Density map of cations and anions in the yz-plane inside and in the vicinity of the ˚ The negative electrode with slit space of 8.2 A. green rectangle represents the position of the graphene sheets.


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in comparison to that observed in narrower pores. From the edge of both electrodes towards the bulk region of the ionic liquid, the layered structure observed in the narrower pore at ∆Ψ = 0 V is completely lost, as can be seen in Figure 12. Inside the electrodes, cations and anions are still organized in layers, but both ions are located in the same layers along the z-axis.

Figure 11: Radial distribution functions calculated for P-P, P-N and N-N correlations in given layer (inside) and between different layers (across) of the negative electrode with ˚ under different applied slit space of 8.2 A electric potential. ˚ also higher pore. The main peak at 8.4 A corresponds to anions facing each other, but which now are both either on the top or at the bottom of their relative pores. Finally, the ˚ corresponds to anions which peak at 11.0 A are stacked together but correspond to nonadjacent pores. The overall stacked structure is due to the polarization of the surface by the ions; our porous electrodes are simulated with constant potential model, so that image charges arise on the electrodes due to the charges of the ions close to them. Therefore, for example, a cation inside a given pore will induce a strong negative charge at the surface of the electrode. As a consequence, this negatively charge region will attract cations of the neighboring pore. Due to the strong correlations of ions of the same sign, the cross-correlations (P – N) across the pores ˚ with appear at larger distances around 10.5 A, a very broad peak. At ∆Ψ = 1 or 2 V, the main structural features remain the same as at null voltage. Very similar behavior has been found for the positive electrode.

Figure 12: Density profiles of ions and charge density inside the negative and positive ˚ electrodes with slit space of 12 A. At ∆Ψ = 2V, the electrodes are mainly filled by counter-ions, but there is a considerable amount of co-ions (bottom panel of Figure 12). Note that the number of co-ions inside ˚ and the electrodes with slit space of 8.2 A same applied voltage is much lower. In this confined space, the ions are organized in layers of alternate charges along the zaxis. As a consequence of the large amount of co-ions inside the electrodes that partially screen the charges of counter-ions, the charge accumulated on the electrodes is lower if compared with that on electrode with lower space. A further illustration of the arrangement of the ions inside the negative electrode can be seen in Figure 13 that depicts the density map of cations and anions in the xz-plane ˚ with ∆Ψ = 0 and 2 V. of a slit of 12 A When the electrodes have no applied voltage, the disposition of the green ellipses drawn over the density map of anions resembles the typical charge ordering structure of bulky

˚ pores In Structure of the liquid in the 12 A the electrodes with larger porosity (slit space ˚ the structure pattern strongly changes of 12 A),


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In such environment, the NTf2 anions adopt an arrangement, in which the CF3 groups are adsorbed on the surface of graphene sheets as can be seen from the density profile of the F atoms.

Figure 13: Density map in the xz-plane of cations and anions inside and in the vicinity of ˚ the negative electrode with slit space of 12 A. The green rectangle represents the position of the graphene sheets. Figure 15: Radial distribution functions calculated for P-P, P-N and N-N correlations in given layer (inside) and between different layers (across) of the negative electrode with ˚ under different applied slit space of 12 A electric potential. For better comparison the bulk lines was multiplied by 3 in P-P and N-N correlations and by 5 in P-N correlations.

ionic liquids and molten salts. Upon the charging of the electrode, ∆Ψ = 2V, some anions quit the pores and they organize in layers of alternate charges, as anticipated in Figure 12.

At ∆Ψ = 0 V, the P-P, P-N, and N-N radial distribution functions calculated only for those atoms located in a given pore and those calculated for the bulk region present correlation peaks at the same distances, as shown by the black and blue lines of Figure 15 (inside panels). These findings, therefore, indicate that the ions inside the ˚ can adopt an slits with pore size of 12 A organization similar to that found in the bulk. However, as for the smaller pore size, we observe some cation-cation correlations across the pores, as can be seen from the ˚ in presence of the correlations around 9 A the corresponding radial distribution function. This suggests again the existence of stacked layers of phosphonium cation adsorbed on the bottom and upper face of adjacent slits.

Figure 14: Density profiles of P (cation), N and F (anion) atoms inside the negative electrode ˚ along the y-axis. with slit space of 12 A Figure 14 shows the density profiles of P, N and F atoms along a cross-section of the electrode. Disregarding the potential difference, there are two layer of P atoms and one layer of N atoms, indicating the formation of two layers of cations and one layer of anions adsorbed on the surface of graphene sheets.

Performance of the simulated supercapacitors Table 4 provides the charge accumulated


11


applied voltage within 0 and 4 V using eq.1 and using four times the total mass of the electrodes for normalization as precognized for experimental studies. 63 The results of this analysis are displayed on Figure 16. It appears that the electrode with narrower pore perform better up to applied potentials of 3.4 V, as would intuitively be expected from table 4. However, for ˚ pore size material larger potentials, the 12 A displays a better performance. This result is in remarkable agreement with the previous work from Kondrat et al., in which they obtained a similar pattern using a combination of meanfield theory and Monte-Carlo simulations of an electrolyte using a primitive model. 64 It is remarkable that this effect is recovered when simulating a realistic system using a complex all-atom model. This result is due to the different charging mechanisms in the two electrodes: Albeit the small pores allow an efficient charging at low potential through ion swapping process and efficient screening of the like-like charged ions, saturation occurs at some point after which they become hard to charge. On the contrary, the larger pores are not as efficient at low voltage but the charging continues to occur at larger voltages. Linear sweep voltammogram of [P222,2O1 ] [NTf2 ] measured at carbon electrode show that this IL has a large electrochemical window, that is, the potential window lies between -3.0 to +2.3 V using Ferrocene(Fc)/ferrocenium(Fc+ ) redox couple as reference. 16 Therefore, considering its high electrochemical stability, supercapacitors built with [P222,2O1 ] [NTf2 ] ˚ and porous electrodes with pores of 12 A could operate at potentials between 3.4 and 4.4 V in order to obtain better performances regarding energy density.

inside the positive porous electrodes with ˚ at different applied slit spaces of 8.2 and 12 A, voltage. Table 4: Total charge accumulated in the positive porous electrodes with slit space of ˚ at different applied electric 8.2 and 12 A, potential. ∆Ψ

˚ 12 A ˚ 8.2 A

1V 2V 4V

15.2 31.5 39.0

11.6 21.2 35.8

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Applied voltage (V)

Figure 16: Variation of the energy density of the device with the applied voltage. The black and red lines account for the pore of 8.2 and ˚ respectively. 12 A, In principle, a larger charge should correspond to better performance of the device. However, as can be seen from equation 1, the energy density is mainly impacted by the voltage-dependence of the capacitance, an effect which was already exploited by Kondrat and Kornyshev for suggesting ionophobic pores as a way to improve the performance of supercapacitors. 62 Here, the accumulation of charge Q+ with respect to the potential strongly deviates from linearity, so that the capacitance was extracted by fitting the variation with a polynomial law and differentiating the resulting function. The specific energy was then estimated for any

4 Conclusion In this work, we have studied via molecular dynamics simulations the structure and the capacitive behavior of a phosphonium-based ionic liquid put in contact with two different structures of carbon electrodes. In the case of


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Supporting Information Available

planar graphite, in agreement with previous works, the liquid forms several layers before the bulk structure is organized. The structure is shown to change significantly with the polarity of the electrode, due to the large asymmetry between the two ions. In terms of performance, the differential capacitance on the negative electrode is lower than in the positive electrode, which is due to the larger size of phosphonium cations that prevents an efficient packing. In nanoporous electrodes, the structure also differs markedly with the size of the pore. When it is narrow (e.g. of similar dimension as the ions), a single layer of ions is formed, while a multi-layer reminiscent of the bulk ˚ wide pore. structure is observed for a 12 A Upon application of a voltage, the charging is very efficient at low voltage in narrow pores, but the structure does not evolve much beyond 2 V, so that the number of accumulated electrons tend to saturate. On the contrary, in the larger pores, the charging mechanism is more monotonous. As a consequence, even if the total number of accumulated electrons may be smaller for the latter, we estimate that the energy density for large applied voltages (4 V) could overcome the one of smaller pores, in agreement with previous work from Kondrat and Kornyshev. 64 Future works should explore the possibility to combine two pore sizes in order to increase further the energy density over the whole voltage range.

All the parameters of the force field for cation and anion can be found in the Tables S1-S10 in the Support Information file. This material is available free of charge.

References B. E. Electrochemical (1) Conway, Supercapacitors: Scientific Fundamentals and Technological Applications; Kluwer Academic/Plenum Publishers, 1999; p 698. (2) Simon, P.; Gogotsi, Y.; Dunn, B. Where Do Batteries End and Supercapacitors Begin? Science 2014, 343, 1210–1211. (3) McEwen, A. B.; Ngo, H. L.; LeCompte, K.; Goldman, J. L. Electrochemical Properties of Imidazolium Salt Electrolytes for Electrochemical Capacitor Applications. J. Electrochem. Soc. 1999, 146, 1687–1695. (4) Chmiola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P.; Taberna, P. L. Anomalous Increase in Carbon Capacitance at Pore Sizes Less Than 1 Nanometer. Science 2006, 313, 1760–1763. (5) Largeot, C.; Portet, C.; Chmiola, J.; Taberna, P.-L.; Gogotsi, Y.; Simon, P. Relation between the Ion Size and Pore Size for an Electric Double-Layer Capacitor. J. Am. Chem. Soc. 2008, 130, 2730–2731.

Acknowledgement The authors gratefully acknowledge support from FAPESP (São Paulo Research Foundation) and Shell, Grant Number 2017/11631-2, and the strategic importance of the support given by ANP (Brazil’s National Oil, Natural Gas and Biofuels Agency) through the R&D levy regulation. This work used resources of the ”Centro Nacional de Processamento de Alto Desempenho em São Paulo (CENAPADSP).” This study was financed in part by the Coordenaça˜ o de Aperfeiçoamento de Pessoal de N´ıvel Superior - Brasil (CAPES) - Finance Code 001.

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