Complementary Effects of Pore Accessibility and Decoordination on

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Complementary Effects of Pore Accessibility and De-Coordination on the Capacitance of Nanoporous Carbon Electrochemical Supercapacitors Srinivasa Rao Varanasi, Amir Hajiahmadi Farmahini, and Suresh Kumar Bhatia J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10712 • Publication Date (Web): 07 Dec 2015 Downloaded from http://pubs.acs.org on December 8, 2015

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The Journal of Physical Chemistry

Complementary Effects of Pore Accessibility and De-coordination on the Capacitance of Nanoporous Carbon Electrochemical Supercapacitors

Srinivasa Rao Varanasi, Amir H. Farmahini and Suresh K. Bhatia* School of Chemical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia

Abstract We illustrate here the interplay of de-coordination and accessible pore volume in nanosized supercapacitors, using constant voltage Gibbs ensemble based grand canonical Monte Carlo simulations for three different microporous carbon electrodes of known atomistic structure, and 1-ethyl-3methylimidazolium boron tetrafluoride (EMI-BF4) as electrolyte. We demonstrate that the counter-ion coordination number decreases with pore size and this trend is similar for the electrodes considered, despite their different structures; suggesting that the pore shape is less important to this relation, at least for the carbons examined here. It is seen that ions with low coordination and/or completely de-coordinated ions induce maximum charge, while those with higher coordination induce less, in accordance with recent MD simulation results which demonstrate that ions in high degree of confinement (DOC) induce more charge than those in low DOC. Our results indicate that electrodes with different pore volumes can exhibit similar capacitances by balancing accessibility and de-coordination effects. Thus, similar capacitance may be obtained for electrodes having low pore volume, but which can adsorb a small amount of high charge inducers (de-coordinated ions) by virtue of having suitable pore size, and those having high pore volume and adsorbing many more low charge inducers (more highly coordinated ions). Keywords: Electrochemical supercapacitor; Ion de-coordination; Ionic liquid; Confinement effects; Nanoporous carbon. *To whom correspondence may be addressed. Tel.: +61 7 3365 4263. Email: [email protected].

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1. Introduction Carbon based electrochemical supercapacitors are an important class of charge storage systems that comprise two high surface area porous carbons as electrodes and an electrolyte, either solvent based or solvent free, commonly a room temperature ionic liquid (RTIL). These systems possess high cycle life and high power, since the storage mechanism is based on the formation of electric double layers (EDLs), involving physical changes in the electrode with no chemical reaction, making the charge/discharge mechanism highly reversible and rapid (having time scale of seconds or fractions of a second)1. Supercapacitors based on RTILs have received much attention in recent years, since they are environmentally friendly and support high operating voltages, despite showing lower capacitance and high equivalent series resistance (ESR) as compared to their solvent based counter-parts (usually having acetonitrile or propylene-carbonate as solvents). However, due to their non-volatile nature and higher thermal stability, RTILs are considered greener and safer options for electrochemical supercapacitor applications2-4.

Nanoporous carbide derived carbons (CDCs), such as that from titanium carbide (denoted TiC-DC) or silicon carbide (SiC-DC), and activated carbon (AC), have been demonstrated to be suitable as electrode materials in supercapacitor applications5-10. An efficient supercapacitor demands that an electrode material possess high surface area and pores that are commensurate with the size of the electrolyte ions11-14. The enhanced capacitance observed in experiments with electrodes having sub-nanometer pores is attributed to partial or complete desolvation of counter-ions adsorbed inside the pores11-12, 15. Recent studies have shown that room temperature ionic liquids (such as those based on imidazolium cations) used in combination with CDCs, carbon nanotubes and activated carbons exhibit good 2


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electrochemical performance4, 10, 16-18. There are numerous studies in the literature reporting capacitances as high as 140 F/g based on the use of different types of porous carbons in combination with RTILs6, 15, 19-22. Greater capacitances have been achieved when the average pore size is commensurate with the size of the ion (desolvated ion in case of solvent electrolytes), indicating a possible correlation between ion size and pore size11-12,

23-24

.

However, there is a need to consider the pore size distribution (PSD), as broader PSDs may lead to invariance of capacitance over a wide range of mean pore sizes similar to that observed by Centeno et al25. To optimize materials for higher capacitance, it is important to understand the factors that are influencing the degree of ionic charge separation between electrodes and the mechanism leading to this. In situ NMR spectroscopic techniques have been developed to monitor the changes in the supercapacitor system during charge/discharge processes, promising to offer better insights into the microscopic mechanism of supercapacitor performance26-30.

Nevertheless, experimental techniques frequently have

limitations in uncovering microscopic mechanisms, as they provide information on average behavior but cannot yet track individual configurations or trajectories of ions and molecules, and theoretical analysis remains a powerful tool for understanding supercapacitor performance.

Molecular modelling techniques such as molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as promising tools to elucidate the molecular underpinnings of the electrochemical behavior of supercapacitor materials31-36. Theoretical and molecular simulation studies by Kornyshev and co-workers37-43 have revealed several interesting features of supercapacitors combining carbon electrodes with ionic liquid electrolytes. For instance, charging dynamics in ionophobic pores is relatively fast compared to ionophilic 3



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ones, thereby providing an opportunity to optimize the electrodes for enhanced energy as well as power densities38. These authors have shown that electrodes with monodispersed pore size distributions (PSDs) deliver higher energy densities than those with polydispersed PSDs40. It has also been demonstrated that pores with atomically rough surfaces exhibit substantial capacitance enhancement as compared to those with smooth surfaces44. MD simulation studies reveal that local structure of the carbon electrode has large influence on the charging of carbon atoms in the electrode, possibly by the distinct organization of electrolyte. Thus, contrasting electrochemical performance of different TiC-DC carbon structures having similar pore size distribution has been predicted31. The poor performance of TiC-DC prepared at 1200 °C as compared to TiC-DC prepared at 950 °C is due to the presence of small graphitic domains that facilitate over- screening effects, such as those occurring in graphitic pores31. More disordered carbon structures deliver better electrochemical performance than the less disordered ones possessing graphitic domains45. MD simulation studies by Merlet et al46 demonstrate that the ions adsorbed in high degree confinements induce counter-charge on the electrode atoms more effectively than those in the low degree confinements, and such ions lose most of their solvation/coordination shell neighbors, leading to partial/complete desolvation or de-coordination. Hence, it is important to consider the microstructure of the electrode pores in addition to surface area, average pore size and pore size distribution, while optimizing electrodes for superior electrochemical performance.

In the present study, we perform Gibbs ensemble based grand canonical Monte Carlo simulations for three distinct microporous carbon structures, activated carbon (ACF-15), SiCDC and TiC-CDC, as electrodes and a RTIL, 1-ethyl-3methylimidazolium boron tetrafluoride (EMI-BF4), as electrolyte. Our simulations and analysis of the microscopic structure and 4


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energetics of the ions in the carbons reveal comparable values of capacitance in these distinct structures, despite significant differences in pore volume, and demonstrate this behavior to arise from to two complementary factors, namely, pore accessibility and de-coordination in nano-confinement. Our results explain how these two factors complement each other in order to deliver similar capacitances in the electrodes examined.

2. Computational details: Electrode models: We have considered three different microporous carbon structures independently as electrodes, namely, activated carbon fibre (ACF-15), SiC-DC and TiC-DC. Atomistic models of these materials have been developed using hybrid reverse Monte Carlo (HRMC) simulation as reported elsewhere47-49. We have taken three unit cells of ACF-15 along the zaxis (total of 3486 atoms), one unit cell of SiC-DC (2998 atoms) and one unit cell of TiC-DC (2570 atoms) as electrodes in their respective systems. The choice of three unit cells has been made for ACF-15 so as to ensure roughly equal number of carbon atoms (i.e. approximately equal mass) for all electrodes. The electrodes have been kept 10 nm apart along the z-axis while periodic boundary conditions have been imposed along x and y axes.

Electrolyte model and intermolecular potential: The ionic liquid has been modelled using a coarse grained four site model proposed by Roy et al50, in which each imidazolium cation is represented by three connected sites whereas BF4 anions are represented as single sites. Each site in the electrolyte ions is treated as a LennardJones (LJ) sphere with a point charge placed on it. The potential parameters have been taken from the work of Merlet et al51 (see supplementary information). The charge on each carbon 5



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atom of the electrodes is modelled as a Gaussian distribution centered on the atom, following Vatamanu et al.52 and earlier studies53-54. The total interaction energy of the system, comprising two carbon electrodes and ionic liquid electrolyte is given by52:

Φ to ta l = Φ L J + Φ E

(1)

Where Φ LJ ΦE =

∑

i , j ,i ≠ j

 σ ij = ∑ 4 ε ij    r  i , j ,i ≠ j   ij qi q j 4 π ε r ε 0 rij

−

1 2

∑

  

i , j ,i ≠ j

    q i q j e rfc ( γ rij ) + 4 π ε r ε 0 rij

12

 σ ij −  rij 

  

6

(2)

∑ i

q i2 γδ ( i , G )

π

(3)

Here rij is distance between two atoms (or ions) i, j = 1, 2, qi is partial charge on atom (or ion) i, σij, εij are Lennard-Jones (LJ) parameters for the i-j interaction, εo is permittivity of vacuum, εr is relative permittivity and 1/γ is width of the Gaussian distribution. The first term in eqn. (1) is the contribution from all the LJ interactions (eqn. (2)), excluding those between electrode atoms. The second term (eqn. (3)) is the contribution from electrostatic interactions. The second and third terms in eqn. (3) arise due to the Gaussian nature of the electrode charges. The delta function in eqn. (3) is zero for point charge and one for Gaussian charge distribution. The first term in eqn. (3) has been calculated using the modified Wolf method5558

. The convergence parameter in the Wolf method has been adjusted between 1-2 nm-1,

depending upon the simulation cut-off to ensure the electrostatic energies to converge to those obtained by Ewald summation approach. The cut-off length for all the interactions has been set to be 14.75 Å, 20 Å and 17.5 Å for ACF-15, SiC-DC and TiC-DC respectively, corresponding to half of the smallest dimension of the simulation cell. The specific width of the Gaussians (1/γ) is chosen to be 0.2 Å, ensuring the short range approximation to the second term in eqn. (3) is valid within the cut-off.52. LJ interactions between the atoms of the electrodes have not been considered, as the intramolecular degrees of freedom of the porous 6


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electrode structures are assumed to be frozen. Hence there are only electrostatic interactions between the fluctuating electrode charges. While the electrochemical dilatometry studies on carbon electrodes have shown that there can be charge-induced microscopic structural changes in the electrode due to pumping of electrons in and out, and also due to insertion of electrolyte ions inside smaller pores, inclusion of such effects is beyond the scope of the present work. Image interactions have not been treated explicitly in our simulations. The cross interaction parameters between dissimilar atoms have been calculated using standard Lorentz-Berthelot mixing rules. All the simulations have been performed in vacuum (ϵr = 1). Simulation procedure Pore characterization of electrode materials: Pore size distributions (PSDs) of the carbon models have been determined using the spherical probe geometric approximation technique proposed by Gelb and Gubbins59,60. The method makes use of the Metropolis Monte Carlo algorithm to insert random points into the unit cell. The center to center distance of a successfully inserted probe molecule with any atom of the network must be always larger than ߪ௦௢௟௜ௗି௣௥௢௕௘ to ensure no overlap occurs. Once statistically adequate sampling of the phase space was achieved, the porosity is calculated based on the number of accepted moves divided by total number of insertion attempts. For the PSD, the acceptance of a successful trial insertion is followed by a random walk away from its original point which is repeated in many different random directions. This way the maximum diameter of a spherical probe which simultaneously encompasses the original insertion point and does not overlap any network atom is determined. The pore sizes are calculated from the Connolly surface which is defined to be the surface traced by the exterior of the probe particle while rolling over the pore wall. 7



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Constant voltage Gibbs ensemble based GCMC simulations: After characterizing the pore structure of the electrode materials, we have performed Gibbs ensemble based constant voltage grand canonical Monte Carlo simulations on porous carbon electrodes, following the recent algorithm of Punnathanam35, as

implemented by us

elsewhere36. The grand canonical partition function at constant voltage is given by:

Ξ (µ , Φ ,V , T ) =

∞

∞

∑ σ

∑ eβ µ

A = −∞

[ N + Φ θt ]

Q ( N ,θ t ,V , T )

(4)

N =0

where Q ( N ,θ t ,V , T ) =

N

∑

N1 A = 0

N

∑

Q AC ( N 1 A , N1C , N , θ t , V , T )

(5)

N1 C = 0

where QAC ( N1 A , N1C , N ,θt ,V , T ) =

(qV )2 N ..... e− βU ds 2 N N1A ! N1C ! N2 A ! N2C ! ∫ ∫

(6)

and the probability density distribution is given by:

f (s2N , N1A ,N1C ,N2A ,N2C ,θt ) ∝

(qV)2N βµN βΦθt −βU e e e N1A!N1C!N2A!N2C!

(7)

Here, µ, Φ, V and T are chemical potential, applied voltage, volume and temperature respectively. θt is the total charge on the electrode, β is (kBT)-1 and q is eβµ. The number of cations and anions in each of the electrodes are N1C, N2C and N1A, N2A respectively, where 1, 2 are the indices of the electrodes. Imposing the following condition ensures charge neutrality in the overall system:

N1 A + N 2 A = N1C + N 2C = N

(8)

There are six different Monte Carlo moves (formulated using Eqn. 6) performed during the simulation, namely, translation, insertion, deletion, charge plus ion transfer (CPIT), ion 8


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transfer (IT) and charge transfer (CT). In a translation move, an ion is chosen randomly from a randomly selected electrode and moved by a small distance (determined by the maximum allowed acceptance, 35%), and rotated (in case of EMI+) by a small angle with respect to a randomly selected axis passing through the center of mass of the selected ion. In an insertion (or deletion) move, an ion pair is created in a randomly chosen electrode at random positions (similarly an ion pair is selected for deletion in a deletion move). In a charge plus ion transfer move (CPIT), an ion (cation or anion) is chosen randomly from a randomly selected electrode and transferred to the other electrode, and

a charge equivalent to the ion’s charge is

added/subtracted to/from the origin/destination electrode respectively. By doing this, the CPIT move preserves the charge neutrality of each of the electrodes. In an ion transfer (IT) move, an ion (cation or anion) is selected randomly from a randomly chosen electrode and transferred to the other electrode. Unlike the CPIT move, no charge compensation on the respective electrodes is performed, and therefore this move does not preserve charge neutrality of the individual electrodes, although overall charge neutrality is preserved following eqn (8). In a charge transfer move (CT), a small amount of charge is transferred between electrodes. The transferred charge is shared only between randomly chosen 500 or half the number of atoms, whichever is smaller, in the destination electrode, which ensures non-uniform charge distribution among the atoms in the destination electrode. All these moves are accepted or rejected according to Metropolis scheme, and the acceptance probability for any move is:

 f new  acc PMC  move = min 1,  f old 

9


(9)


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where fnew and fold represent probability density distributions (see Eqn. (6)) for the states after and before the moves respectively. Further details of the Monte Carlo moves and their acceptance criterion can be found elsewhere35-36. The simulations are initiated starting with empty electrodes with a zero charge on each carbon atom. The voltage has been set at 2V. The system is equilibrated for 20,000 Monte Carlo (MC) cycles, comprising about 5 million MC moves. The number of Monte Carlo moves in each cycle is equal to the total number of ions in the system, while the minimum number of MC moves in each MC cycle is set to be 100. A production run of about 60,000 MC cycles is performed during which the coordinates of the ions and charges on the electrode atoms are stored at the end of each MC cycle for subsequent analysis. All the simulations have been performed at a temperature of 300 K and a bulk activity of 0.001nm-3. At this activity, bulk simulations on the ionic liquid model, provided a number density of 3.61 ion pairs/nm3, which is very close to what is expected from the density values given by Merlet et al51 (3.86 ion pairs/nm3). All Monte Carlo moves have been given equal priority. 3. Results and discussions Pore characterization: Prior to performing Gibbs ensemble based grand canonical Monte Carlo simulations, we have characterized the pore structure of the three porous carbon electrodes using the spherical probe geometric approximation technique, with three different hard sphere probes of diameters 2.64 Å, 5.84 Å and 4.51 Å representing He, EMI+ and BF4respectively. Figures 1a, 1b and 1c illustrate the resulting pore size distributions. The PSDs indicate that the three structures possess a broad distribution between 0-8Å, for all the three probes. It is seen that the specific pore volume of ACF-15 is relatively higher than that of other two structures, up to the maximum pore size (10.5 Å). In this pore range (0-10.5 Å), the 10


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specific pore volume of SiC-DC is somewhat lesser than that of ACF-15. However, it possesses pores larger than 10.5 Å and up to 13.5 Å, absent in ACF-15 and TiC-DC. TiC-DC possesses two narrow peaks between 8.6 and 10.4 Å, lying at 9 Å and 10 Å respectively. It is seen that the specific pore volume is smaller for TiC-DC in comparison to the other two carbons, though the latter two structures may compete with each other depending on the probe size. The values of specific pore volume for the three structures with different probes have been tabulated in Table 1. The specific pore volume of ACF-15 is slightly higher than that of SiC-DC. The difference between these two is 0.055, 0.011 and 0.04 cc/g/Å respectively with Helium, EMI+ and BF4- probes. Possibly, this variation between different probes is due to the fact that He and BF4- could probe the smaller pores around 5 Å and EMI+ could not. Most of the pore volume in SiC-DC is contributed from the pores in the range 9-13 Å while in ACF-15 0.20

it is mostly from

(a) He

ACF-15 SiC-DC TiC-DC

pores between 8-

0.15

PSD (cc/g/Å)

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10.5 Å. 0.10

0.05

0.00 1

2

3

4

5

6

7

8

9

10

11

12

13

pore size (Å)

11


14

15


0.20

(b) EMI+


PSD (cc/g/Å)

0.15

0.10

0.05

0.00 4

5

6

7

8

9

10

11

12

13

14

15

pore size (Å) 0.20

(c) BF4-


0.15

PSD (cc/g/Å)

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0.10

0.05

0.00 4

5

6

7

8

9

10

11

12

13

14

15

pore size (Å)

Figure 1: Pore size distributions of ACF-15, SiC-DC and TiC-DC with hard sphere probes of size comparable to (a) He, (b) EMI+ and (c) BF4-. We also note that the cation is represented as a single sphere of effective size of 5.84Å, though it is a combination of three connected sites in the actual coarse grained model (see supplementary information). Hence, the cation may see a slightly different PSD than that shown in Figure 1b, and the difference in the accessibility of ACF-15 and SiC-DC in the constant voltage simulations may be slightly different from that predicted from the PSD and specific pore volumes. However, the specific pore volumes (Table 1) using three different 12


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probes indicate that the apparent accessibility of TiC-DC is much smaller than that of ACF15 and SiC-DC, and this order may not alter during the constant voltage simulations.

Table 1: Specific pore volume of ACF-15, SiC-DC and TiC-DC calculated using spherical probe approximation technique with three different probes.

Carbon

Specific pore volume (cc/g) using different size probes He EMI+ BF4(2.64 Å) (5.84 Å) (4.51 Å)

ACF-15

0.615

0.459

0.54

SiC-DC

0.560

0.448

0.50

TiC-DC

0.335

0.190

0.256

Charge storage capability and mechanism: Following characterization of the pore structure of the three electrode materials, we have conducted Gibbs ensemble based grand canonical ensemble simulations on three different systems comprising ACF-15, SiC-DC and TiC-DC as electrodes with EMI-BF4 electrolyte. These three carbon structures are distinctly different with respect to carbon density, PSD and specific pore volume (c.f. Figure 1 and Table 1). The gravimetric and volumetric charge densities per electrode are tabulated in Table 2. The integral capacitance has been calculated from: Cint = σ / ∆V

(10)

where σ is the charge density accumulated on one of the electrodes, which can be either gravimetric or volumetric. We note that it is important to consider both volume and mass of the electrodes while optimizing the electrode materials for supercapacitor applications.

13



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Hence, the gravimetric and volumetric charge densities are calculated using mass and volume of the dry electrodes, with ‘< >’ representing the ensemble average. The denominator, ∆V is the applied potential difference between the two electrodes. The gravimetric charge density values for ACF-15 and SiC-DC are close to each other while TiC-DC is not significantly different. The gravimetric and volumetric capacitances calculated from eqn. (10) are also given in Table 2. The capacitance values (particularly volumetric) for the activated carbon are in agreement with those reported in the literature15 (100 F/g, 50 F/cc), while those for CDCs are lower than values for similar carbons

6, 20-21

(160 F/g, 85 F/cc) , possibly due to the

narrow pore structure of our electrodes. The values of gravimetric and volumetric capacitances are quite similar to each other in all the three electrodes, as their densities are close to 1.0 g/cm3. The competing results obtained for TiC-DC, despite its lower specific volume, are counter-intuitive and quite intriguing, requiring a more detailed probe into the charging mechanism at the microscopic level.

Table 2: Values of the gravimetric charge density and capacitance, and volumetric charge density and capacitance for electrodes based on ACF-15, SiC-DC and TiC-DC. Carbon

Gravimetric charge density (C/g)

Gravimetric capacitance (F/g)

Volumetric charge density (C/cc)

Volumetric capacitance (F/cc)

ACF-15

117.63

58.815

103.16

51.58

SiC-DC

117.80

58.90

110.496

55.248

TiC-DC

101.38

50.69

120.64

60.32

We note that the charging of a porous electrode is not just filling the electrode with the electrolyte but it is mainly the (ionic) charge separation between the electrodes when an external voltage is applied. The amount of charge induced in an electrode is proportional to 14


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the difference between the number of counter-ions and co-ions in the electrode and does not depend upon the total amount of the electrolyte electro-sorbed into the electrode. The values of total number density and the difference between counter-ion to co-ion number densities are tabulated in Table 3. The number density values indicate that relatively high amount of electrolyte has been electro-sorbed into SiC-DC electrodes as compared to other two electrode materials; in agreement with the comparison of specific pore volumes estimated using neutral probes (c.f. Table 1). Figures 2a, 2b and 2c illustrate snapshots of cathodes of ACF-15, SiC-DC and TiC-DC filled with EMI-BF4 electrolyte respectively. Visual inspection of the snapshots confirms that TiC-DC is filled with relatively lower amount of electrolyte as compared to the other two. Despite lower total number density, the difference in number densities of counter-ions and co-ions in the electrodes of TiC-DC are significantly higher than in the other two, indicating greater charge separation, leading to values of charge density and capacitance comparable to those of ACF-15 and SiC-DC.

Table 3: Values of total number density (number of ions per unit volume) and the difference between the number densities of counter-ion and co-ion in the electrodes, for ACF-15, SiCDC, TiC-DC electrodes at 2V. Carbon

Total number density, ρ (nm-3)

ρcounter-ion - ρco-ion (nm-3)

ACF-15

2.348

0.728

SiC-DC

2.625

0.797

TiC-DC

1.796

0.840

Having determined the relative accessibility of the electrodes from the specific pore volumes estimated by the spherical probe geometric approximation technique using neutral probes, and the overall number density of the electrolyte electro-sorbed into the electrodes during constant voltage simulations, we have also analyzed the wetting behavior of the electrodes with respect to the counter-ion as well as the co-ion. 15



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In order to compare the wettability of porous carbon structures at the set voltage, we have defined a parameter called wetting length, which is the distance between the ion and carbon atom, within which the number of carbon atoms around a given ion type are enumerated. The fraction of carbon atoms within the wetting length from the given ion has been evaluated and its variation with wetting length is illustrated in Figure 3, for the counter-ion in cathode (cation). Figure 4 depicts that for co-ion in cathode (anion). It is seen that about 75% carbon atoms in SiC-DC have been exposed to counter-ions, while it is 70 and 60% for ACF-15 and TiC-DC respectively, at a wetting length of 0.5 nm.

Figure 2: Snapshots of ion-electrode configurations in (a) ACF-15 (b) SiC-DC and (c) TiCDC cathodes. Yellow and blue spheres represent EMI+ (three sites) cation and BF4 (one site) anions respectively. The electrodes are shown in cyan coloured bonded representation. Some of the inaccessible regions have been encircled. The fraction of carbon atoms exposed to counter-ion is always greater for SiC-DC than the other two, at all wetting lengths between 0.35 and 0.5 nm. This indicates that the carbon 16


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atoms in TiC-DC are less accessible to counter-ions of the RTIL than those in ACF-15 and SiC-DC, as evident from the PSDs depicted in Figure 1. The increase in fraction of carbons with wetting length (c.f. Figures 3 and 4) is less steep in case of TiC-DC, indicating that there are more bulky regions in TiC-DC which are not accessible to the electrolyte (marked by circles in Figure 2c), though there exist less bulkier inaccessible regions in ACF-15 (see Figure 2a) and SiC-DC (see Figure 2b). The co-ions in SiC-DC could approach carbons more closely than in TiC-DC, which might happen in larger pores of size between 1 nm and 1.3 nm (Figure 4). The fraction of carbons within 0.5 nm of wetting length from co-ions in the cathode is about 5% and 4% in SiC-DC and ACF-15 respectively, whereas it is only 2% in TiC-DC. The co-ions will induce counter charge on the nearby carbon atoms, leading to reduced charge density. From these observations, we can infer that the larger pores, particularly those above 1 nm, will accommodate more co-ions besides counter-ions, leading to reduced charge separation in ACF-15 and SiC-DC electrodes. The fraction of carbons at the shortest approachable distance (see insets in Figs. 3 and 4) is comparatively higher in TiC-DC than in the other two, indicating tighter confinement in TiC-DC and this will be reflected by the ion-electrode energy, particularly the short-range part (LJ), which will be discussed later. Besides the relative number of counter-ions and co-ions inside the electrode, the structure of coordination shells of co-ions around counter-ions will provide further insights into the charge storage mechanism. The coordination shell structure is completely modified when the ionic liquid is subjected to confinement, depending upon pore size, shape and pore size distribution.

17



1.0 ACF-15 SiC-DC TiC-DC

0.8

cation in cathode

0.6

0.4

fraction of carbons

fraction of carbons

0.0040 0.0035 0.0030 0.0025 0.0020 0.0015 0.30

0.2

wetting length (nm)

0.0 (a)

0.30

0.35

0.40

0.45

0.50

wetting length (nm)

Figure 3: Fraction of carbon atoms wetted by the cations in the ACF-15, SiC-DC and TiCDC cathodes, as a function of wetting length.

0.06 ACF-15 SiC-DC TiC-DC

0.05

anion in cathode

0.04

0.03

0.02

fraction of carbons

fraction of carbons

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

4e-7

3e-7

2e-7

1e-7 0.33995

0.34000

0.01

0.34005

0.34010

0.34015

0.34020

wetting length (nm )

0.00

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

0.52

wetting length (nm)

Figure 4: Fraction of carbon atoms wetted by the anions in the ACF-15, SiC-DC and TiCDC cathodes, as a function of wetting length.

18


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In bulk, each cation is surrounded by about 7 anions in the first coordination shell (coordination number). However, the coordination number will be less than 7 when the ions are subjected to confinement31, 46. The coordination number obtained by integrating the first peak of the radial distribution function up to the first minimum will be an average quantity, but does not provide adequate information about the counter-ion and co-ion coordination inside the electrodes. Hence, we have calculated the distribution of coordination number of co-ions around each counter-ion within 0.63 nm (the position of first minimum of RDF between cation and anion, see Figure S5 of supplementary information) for all the three structures and in bulk as well. Figure 5 depicts the distribution of coordination number for anions around cations in cathodes of all the three porous structures at 2V, in TiC-DC with no charge on carbon atoms and in bulk. The coordination number exhibits a sharp peak at 7 in the bulk and has a broad distribution between 0 and 6 in ACF-15 and SiC-DC. It is evident that the coordination shell is effectively modified depending on the level of confinement. Unpaired counter-ions (coordination number zero) will polarize the electrode more than the paired ones. The most probable coordination number in ACF-15 and SiC-DC is 2 while it is 1 for TiC-CDC. The maximum possible coordination number is 5 and 6 in ACF-15 and SiCDC respectively, while it is 3 in TiC-DC at 2V. For SiC-DC, the lower coordination numbers (0 to 2) are marginally less probable compared to ACF-15; in contrast the higher coordination numbers (3 to 6) are marginally less probable in ACF-15. This explains why ACF-15 attains charge density nearly equal to that of SiC-DC, despite possessing lower specific pore volume compared to SiC-DC. The coordination number distribution in neutral TiC-DC is quite distinct from that in bulk, shifted towards lower coordination numbers (Figure 5), showing that the cations lose most of their coordination shell partners inside the nanoporous TiC-DC structure even in the absence of external field. This indicates that the nanoporous TiC-DC 19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

structure modifies the coordination shell significantly and facilitates effective charge separation process between the TiC-DC electrodes. The completely de-coordinated (coordination number = 0) and single coordinated (coordination number = 1) counter-ions are more probable in TiC-DC than in the other two carbons. These observations from our Monte Carlo simulations are consistent with what has previously been reported from MD simulation studies on RTILs in TiC-DC electrodes46. Counter-ions that are completely de-coordinated will polarize the electrodes more effectively than the others. Complete de-coordination will occur only when the ion size is commensurate with the pore size, and such pores seem to be more probable in TiC-DC than in ACF-15 and SiC-DC. The larger coordination shells can appear only in the larger pores, particularly those larger than 1 nm, such as those present particularly in SiC-DC. Figure 6 demonstrates the average coordination number of counterions as a function of pore size, determined by the spherical probe geometric approximation technique (see simulation procedure). It shows that the average coordination number is between 1 and 2 for pores of size between 0.7 and 0.9 nm, and 3 in 1 nm pores in all the three structures. Higher coordination numbers are found in SiC-DC in pores larger than 1 nm. The variation of coordination number appears to be similar for all three carbons, implying that the pore shape is less important to this relation at least for the carbons considered here. However, this cannot be considered generic until a systematic study is performed on a variety nanoporous carbons with varying complexity in the pore structure. Besides probing the significant de-coordination in sub-nanometer pores, it is also important to examine the amount of counter-charge induced in the electrode atoms locally by these differently coordinated counter-ions. Figure 7 illustrates the variation of charge induced by each ion on the electrode atoms with coordination number in both cathode and anode of the three carbon structures. Maximum charge, up to 1.0e, is induced by completely de20


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Page 21 of 36

coordinated ions, whereas the ions corresponding to higher coordination numbers induce very little or almost no charge on the electrode atoms.

0.6

ACF-15 SiC-DC TiC-DC TiC-DC (no charge) Bulk

0.5

fraction of ions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

cation in cathode

0.3

0.2

0.1

0.0 -1

0

1

2

3

4

5

6

7

8

9

10

coordination number

Figure 5: Distribution of anion coordination number around cations in the ACF-15, SiC-DC and TiC-DC cathodes at 2V, in neutral TiC-DC and in the bulk. This analysis provides a basis to explain why these three electrodes exhibit almost similar capacitances, despite having distinct pore volumes and pore accessibilities. TiC-DC attains most of its capacitance by electro-sorbing high charge inducers (de-coordinated ions for instance with coordination number 0 or 1) whereas ACF-15 and SiC-DC attain the similar capacitance by electro-sorbing more of somewhat highly coordinated ions including the decoordinated ones. Thus, the shortcoming of weaker de-coordination effects in ACF-15 and SiC-DC is overcome by higher accessibility, and vice-versa in TiC-DC. The asymmetry in the charge induced by counter-ions in cathode (cation) and anode (anion) stems from the

21



asymmetry in the structure of cation and anion (see Figure S4 of supplementary information for coordination number distribution of anions in anode).

6


5

coordination number

cation in cathode

4

3

2

1

0 6

7

8

9

10

11

12

13

14

pore size (Å)

Figure 6: Average coordination number of cation in cathode as a function of the size of its local pore. 1.5 ACF-15 (+) SiC-DC (+) TiC-DC (+) ACF-15 (-) SiC-DC (-) TiC-DC (-)

1.0

charge induced per ion (e)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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anode

0.5

0.0

-0.5

cathode -1.0

-1.5 0

2

4

6

8

coordination number of counter-ion

Figure 7: Average charge induced by adsorbed counter-ions on their local electrode pore atoms as a function of their coordination number. Here ‘+’ and ‘-’ represent cathode and anode respectively. 22


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After analyzing the structure of the porous electrodes and coordination shells of counter-ions electro-sorbed inside the electrode, we have also analyzed energies contributed from LJ as well as electrostatic interactions. The distribution of LJ energy per ion contributed only from the ions of the RTIL inside the cathode pores for all the three porous materials are shown in Figure 8. The most probable ion-ion LJ energy per ion in TiC-CDC is around 4.0 kJ/mol, while it is -6.8 kJ/mole and -7.3 kJ/mol in ACF-15 and SiC-DC respectively. These values are much smaller in magnitude than that in the bulk (-19.5 kJ/mol),. The ion-ion LJ energy depends upon the number of immediate neighbors, essentially the coordination shells of counter-ions in this context. It indicates that the extent of clustering of ions (number of nearest neighbors) is much higher in ACF-15 and SiC-DC than in TiC-DC. The extent of clustering in ACF-15 is somewhat lesser than in SiC-DC. This difference can be attributed to the presence of larger pores, for instance, those larger than 1 nm in ACF-15 and SiC-DC. The ion-ion LJ energy in neutral (i.e. uncharged) TiC-DC is close to that in TiC-DC at 2V, and more repulsive than that of bulk, indicating that the neutral structure significantly reduces the number of coordination shell neighbors even in the absence of an external field. However, it is also crucial to understand how these ionic clusters interact with the porous structures under which they are subjected to confinement. The distributions of LJ interaction energy per ion, between ions and the electrode atoms are shown in Figure 9, in all the three structures. It shows that the LJ energy between ions and electrode atoms in TiC-DC is more negative than that in ACF-15 and SiC-DC which indicates that the ions in TiC-DC are subjected to stronger confinement than in ACF-15 and SiC-DC, also indicated by the relatively higher fraction of carbons found in TiC-DC at the shortest wetting length (see insets of Figure 3 and 4). The confinement in ACF-15 appears to be somewhat stronger than in SiC-DC, which can again be 23



attributed to their distinct pore size distributions. The ion-electrode LJ energy in TiC-DC cathode at 2V is somewhat more attractive than in neutral TiC-DC because of the changes in the electrolyte configurations and charge separation due to the external field.

ACF-15 SiC-DC TiC-DC TiC-DC (no charge) Bulk

normalised distribution function

2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 -21

-20

-19

-9

-8

-7

-6

-5

-4

-3

-2

-1

ELJ (kJ/mol)

Figure 8: Distribution of ion-ion LJ energy per ion in the ACF-15, SiC-DC and TiC-DC electrodes at 2V, in uncharged TiC-DC and in the bulk.

1.8 ACF-15 SiC-DC TiC-DC TiC-DC (no charge)

1.6


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -35

-34

-33

-32

-31

-30

-29

-28

-27

-26

-25

ELJIL-ELEC (kJ/mol)

Figure 9: Distribution of ion-electrode LJ energy per ion in the ACF-15, SiC-DC, TiC-DC electrodes at 2V, and in uncharged TiC-CDC.

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In supercapacitor systems, electrostatic energy is the main component of energy which can indicate the extent of ionic separation between the electrodes. Figure 10 illustrates the ion-ion electrostatic energy per ion for the three electrode materials. It is evident that the electrostatic energy per ion is more repulsive under confinement than in bulk, and is more repulsive in TiC-DC than in ACF-15 and SiC-DC, and is somewhat repulsive in ACF-15 than in SiC-DC. More repulsive ion-ion electrostatic energy indicates the domination of completely decoordinated or less coordinated counter-ions and increased level of confinement, indicated by rapid increase in the radial distribution function between counter-ion and co-ion before the first peak (illustrated in Figure S5 of supplementary information). The ion-ion electrostatic energy per ion in neutral TiC-DC is more repulsive than that in the bulk (Figure 10 (inset)), indicating a significant reduction of number of coordination partners of a given ion (Figure 5). The repulsive nature of electrostatic energy in TiC-DC cathode at 2V with respect to that in neutral TiC-DC is attributed to the charge separation between the electrodes (electrodes attracting more ions of counter charge).

However, the neutral pores of TiC-DC are

instrumental in breaking the coordination shell of the ions, aiding the external field to induce charge density more effectively than in other structures.

25


1.2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

distribution function


1.0

0.8

Page 26 of 36

2.0 TiC-DC (no charge) Bulk

1.5

1.0

0.5

0.0

0.6

-122 -120 -118

0.4


-72 -69

ECoul (kJ/mol)

0.2

-66

-63

0.0 -48

-44

-40

-28

-26

-24

-22

-20

-18

ECoul (kJ/mol)

Figure 10: Distribution of ion-ion Coulomb energy per ion in the ACF-15, SiC-DC, TiC-DC electrodes at 2V, uncharged TiC-DC and bulk (inset).

4. Conclusions We have performed Gibbs ensemble based grand canonical ensemble Monte Carlo simulations on ACF-15, SiC-DC and TiC-DC microporous carbons as electrodes in combination with an RTIL. Our results demonstrate that all the three structures exhibit similar gravimetric and volumetric capacitances, despite wide contrast in their pore structure. The counter-ion coordination with co-ions is greatly reduced under confinement (decoordination effect), similar to desolvation of ions in solvent based electrolytes in high confinements46.

The distribution of coordination number of counter-ions (EMI+ in the

cathode) has a broad distribution in the range 0-6 in ACF-15 and SiC-DC (compared to average coordination number of 7 in the bulk), whereas this distribution is quite narrow in TiC-DC. TiC-DC exhibits capacitance close to that of ACF-15 and SiC-DC, despite 26


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possessing almost half the amount of specific pore volume as compared to ACF-15 and SiCDC. The Lennard-Jones part of the energy between electrolyte ions is lower and that between electrolyte and electrode is higher in TiC-DC than in ACF-15 and SiC-DC, despite relatively small amount of electro-sorption in TiC-DC; this is indicative of stronger confinement experienced by the electrolyte in TiC-DC. The contribution of Coulomb energy to ion-ion interaction energy is more repulsive in TiC-DC which indicates that the counter-ions are mostly de-coordinated in TiC-DC than in ACF-15 and SiC-DC. The coordination numbers of cations are greatly reduced even in the neutral pores of uncharged TiC-DC, facilitating stronger de-coordination effects when an external voltage is applied. Completely decoordinated counter-ions induce higher counter-charge in the local electrode atoms than those with one or more co-ion neighbors, consistent with the degree of confinement effect on counter-ion coordination number and subsequent effect on local carbon atoms, observed using MD simulations by Merlet et al46. TiC-DC delivers similar capacitance as ACF-15 and SiC-DC, complementing the shortage of accessibility by electro-sorbing high charge inducing counter-ions such as those with coordination number 0 or 1 while ACF-15 and SiC-DC complement the shortage of de-coordinated counter-ions by providing accessibility to many low charge inducers (somewhat high coordinated counter-ions). Our results imply that for excellent electrochemical performance, the electrode should possess a porous structure that has maximum accessibility to the electrolyte as well as pores of size that facilitate decoordination of counter-ions. 5. Acknowledgements This research has been supported by a grant (DP150101824) from the Australian Research Council under the Discovery Scheme. We thank Dr. J. C. Palmer, University of Houston, for providing the HRMC-derived structure of TiC-DC. 27



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ASSOCIATED CONTENT Supporting Information TiC-CDC 800 model, interaction model of electrolyte, coordination number distribution of anion in anode, and radial distribution function between cation-anion in cathode. The Supporting Information is available free of charge on the ACS Publications website at DOI: .

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35



TOC Graphic 6


5

coordination number

cation in cathode

4

3

2

1

0 6

7

8

9

10

11

12

13

14

pore size (Å)

1.5 ACF-15 (+) SiC-DC (+) TiC-DC (+) ACF-15 (-) SiC-DC (-) TiC-DC (-)

1.0

charge induced per ion (e)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 36

anode

0.5

0.0

-0.5

cathode -1.0

-1.5 0

2

4

coordination number of counter-ion

36


6

8

Complementary Effects of Pore Accessibility and Decoordination on

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