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Molecular Dynamic Simulations of Ionic Liquid's Structural Variations from Three to One Layers inside a Series of Slit and Cylindrical Nanopores Ke Ma, Xue-wei Wang, Jan Forsman, and Clifford E. Woodward J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 02 Jun 2017 Downloaded from http://pubs.acs.org on June 4, 2017

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The Journal of Physical Chemistry

Molecular Dynamic Simulations of Ionic Liquid’s Structural Variations from Three to One Layers inside a Series of Slit and Cylindrical Nanopores Ke Ma ,∗,† Xuewei Wang ,‡ Jan Forsman ,§ and Clifford E. Woodward

∗,∥

† School of Materials Science and Engineering Tianjin University of Technology Tianjin 300384, P. R. China ‡ School of Materials Science and Engineering, Tianjin University of Technology, Tianjin 300384, China ¶ Tianjin Key Laboratory for Photoelectric Materials and Devices, Tianjin University of Technology, Tianjin 300384, China § Theoretical Chemistry, Chemical Centre, Lund University P.O.Box 124, S-221 00 Lund, Sweden ∥ School of Physical, Environmental and Mathematical Sciences University of New South Wales, Canberra at the Australian Defence Force Academy Canberra ACT 2600, Australia E-mail: [email protected]; [email protected]

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Abstract We apply molecular dynamic simulations to describe [C2 mim+ ][T f2 N − ] ionic liquids and its mixtures with solvents confined inside carbon nanopores. Both slit and cylindrical pores are modelled to determine the influence of pore geometry on the electric double layer (EDL) structure and capacitance. Two types of solvents are selected to dilute the ionic liquids in order to establish the effect of solvent polarity. The number of cations, anions and solvents are chosen to be consistent with their densities in the bulk state. We focus on the structural changes of ionic liquids and their relation to the oscillation in capacitance as a function of varying nanopore size. Structural transitions are analyzed from 1 layer to 2 layers and 3 layers within the confinement of the nanoscale pores. Compared with slit pores, the capacitance oscillates more strongly for cylindrical pores where ions form two peaks instead of combining into a single peak in the middle of the pore. The addition of solvent does not give rise to a larger capacitance despite the solvent’s closer approach to the electrode.

Introduction Owing to its porous structure and large specific surface area, nanoporous carbon serves as a promising electrode material for electric double layer capacitors (EDLC). When immersed in ionic liquids (IL) electrolytes, the capacitance is potentially enhanced when ions and nanopores have a similar size. 1,2 Theoretical studies reveal that the correlation between capacitance and pore size displays a non-linear oscillation. 3,4 However, realistic porous carbon often contains pores of various sizes. Thus, complex porous structures make it difficult to determine pore size distributions and subsequently extract the relations between pore size and capacitance. An important component to the understanding and rational utilization of supercapacitors in applications such as electric vehicles, is to obtain insight into ion packing inside nanopores and the subsequent effect on charge storage capacity. Molecular simulations have been 2 ACS Paragon Plus Environment

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employed to study ionic liquids inside confined spaces. 5,6 Feng et al. conducted systemic comparisons between planar, cylindrical and spherical surfaces, where curvature plays an important role in determining the EDL structure. 7,8 The electrodic charge is established imposing constant potential boundary conditions on the porous carbon electrode. 6,9 When the electrode voltage increases, the charging mechanism is complicated by a combination of three mechanisms: the adsorption of counter-ions, the desorption of co-ions and the exchange between counter-ions and co-ions inside and outside the pore. 5,10 As experimental measurements are difficult due to a lack of precise control over pore size, theoretical approaches have been employed to examine the influence of pore size. 4,11 Kornyshev et al. studied the increase of capacitance for subnanometer pores which were attributed to a superionic state emerging in metal-like pores. 12 Ion−ion interactions inside pores become exponentially screened, which allows an easier packing of ions of the same type. 10,13 As the electrode voltage increases, a sudden expulsion of co-ions occurs accompanied by an enhancement of the capacitance 10 . Classical density functional theory has also been employed to study this system, accounting for steric exclusion and ion-ion correlation terms in the free energy functionals. 14–16 Wu et al. observed the oscillatory variation of capacitance with pore size, and predicted enhanced oscillation with larger curvature for spherical shell-like electrodes. 17 The capacitance oscillation is attributed to the affect of adsorbed ions on the EDL. 4 Furthermore, ionophobic nanopores 18 provide an alternative method to increase the energy storage in nanopore EDL. For metallic nanopores, ion−ion interactions are strongly mediated by image charges induced on the inner pore surface. 10 For carbon electrodes, the ion-electrode interaction cannot be ignored either. 19,20 Yan et al. studied the π − π interaction between imidazolium cations and a graphite surface. 19,21 The specific adsorption of imidazolium cations asymmetrically increases the differential capacitance at negative electrodes. The use of nanoporous carbon, such as Carbide-derived carbon (CDC) or activated carbon, as an EDLC electrode is advantageous because of high specific surface area. However,



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an issue facing nanoporous carbon is that the nanoporous structure could potentially slow down the dynamics of electrolyte ions. IL dilution with solvents has proved a reliable method to improve the ionic mobility for IL electrolytes. 22,23 Solvent-induced changes in structural and dynamic properties have been the subject of many studies. On the one hand, diluting the IL with organic solvents reportedly leads to a significant increase of differential capacitance for an open circuit potential. 24 At a glassy carbon interface, the minimum differential capacitance of an IL electrolyte reaches a maximum with increasing solvent concentration. 24 This effect is stronger for highly polar solvents such as acetonitrile than for less polar solvents such as 1, 2 − dichloroethane. Similarly, a higher dipole moment is preferred for capacitance performance inside pores. 17 The oscillatory dependence of capacitance on the pore size can be mitigated by the addition of solvents. 17 On the other hand, the overall capacitance is only moderately affected by the acetonitrile concentration in an IL mixture, according to MD studies. 23 This observation is rationalized as being a tradeoff between lower ion concentration and cation-anion separability upon diluting the IL. It remains to be seen how a polar solvent will affect highly associated cations and anions, 25,26 based on the microscopic structure at the nanopore interface. Since the pore geometry of practical porous materials is difficult to model, the more regular geometries of a slit and cylinder are selected for qualitative comparisons. Studying density profiles inside porous structures generally requires long simulations and a large bulk environment. The simulations are sensitive to initial configurations, 27 given the difficulties for ion migration into and out of the pore. 28 When the size of the nanopore becomes comparable to the size of the ions, the ions can either form a compact double layer within the pore or be excluded, leaving the pore empty. As has been done in recent classical density functional studies, 11,17 we model the in-pore space using both slit and cylindrical geometries composed of carbon atoms. Rather than modeling a full bulk component in contact with the pore, the numbers of ion (and solvent) molecules within the nanopores are chosen to give the same density as in a chosen bulk. The ion density inside the pore is not expected to be the


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same as the bulk of the ionic solution but this approach provides a convenient zeroeth order approximation to proper electrochemical equilibrium. However, it should be pointed out that effects such as electrostriction, due to solvent and ionic attractions to the surface charges of the pore, may lead to changes to the in-pore densities at true equilibrium. On the other hand, competing effects such as the reduction in configurational entropy in the presence of surfaces will also act to counter electrostriction. Furthermore, it is also not clear that true equilibrium will actually exist in real experimental systems, especially where IL diffusion may be slow in narrow pores. Here we wish to study the structural changes across a series of nanopores are investigated as well as their connections with capacitance oscillation. Our work differs from previous theoretical studies in a number of different ways. For example, a number of these studies use coarse-grained molecular models, 9,29 while ours employ all-atom model. On the other hand, other all-atomistic studies did not consider the role played by solvent, 30 or compare pore geometries.

Model We choose the commonly studied imidazolium-based ionic liquids: 1-ethyl-3-methyl imidazolium as cation, or [C2 mim+ ], and bis-(trifluoromethylsulfonyl)imide as anion, or [T f2 N − ]. The slit nanopores are composed of double graphene layers in parallel, while the cylindrical pore is made up of single-wall carbon nanotubes. A series of armchair carbon nanotubes from (6, 6) to (15, 15) are included to cover a range from L = 0.82nm to L = 2.03nm. A total of ten pore sizes are obtained from the diameters of the nanotubes, as shown in Table 1. Table 1: Ten pore diameters for both slit or cylindrical pore, determined from the diameter of armchair carbon nanotube. CNT Type Pore Size (nm)

(6,6) 0.82

(7,7) 0.95

(8,8) 1.08

(9,9) 1.22

(10,10) 1.36

(11,11) 1.49

(12,12) 1.63

(13,13) 1.76

(14,14) 1.9

(15,15) 2.03

The cation [C2 mim+ ] and anion [T f2 N − ] models are illustrated in Figure 1, along with 5 ACS Paragon Plus Environment


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the solvent acetonitrile (ACN) and 1, 2 − dichloroethane (DCE). Figure 1 also illustrates the cylindrical and slit pore in which the IL or IL mixtures are confined .

Figure 1: Illustration of the [C2 mim+ ][T f2 N − ] ionic liquids model, the acetonitrile (ACN) and 1, 2 − dichloroethane (DCE) solvent model. The neat IL or IL mixture are confined in cylindrical or slit nanopore. Shown above are four pore sizes for both slit and cylindrical pores, as determined from the diameter of (7, 7), (9, 9), (11, 11), (14, 14) carbon nanotube. The dimension of simulation box is set to 49.34 Å×51.28 Å×50Å for slit pores, and 30 Å ×30 Å ×147.57 Å for cylindrical pores.

The sizes of the simulation volumes are as follows. The slit pore is composed of two 49.34 Å×51.28 Å parallel graphene layers, while the cylindrical or CNT pore is of length 147.57 Å for all pore sizes. Two levels of electrode charge densities are selected in order to determine the integral capacitance. At L = 0.82nm, a charge density of +0.253C/m2 is used for positively charged cylindrical and slit pores, which gives a total charge of +6|e| for the (6, 6) CNT pore electrode and +2|e| for the slit pore. Likewise, −0.253C/m2 is set for negatively charged CNT and slit electrodes. The total excess charges on the pores are then maintained regardless of the pore sizes. When the electrode charge is varied, we maintained the same overall density of ions (and solvent), as obtained from bulk simulations using an NPT ensemble. In this procedure, the number of cations, anions, and solvent molecules when applicable, in the pore are adjusted to achieve electroneutrality for the whole system by appropriately exchanging anions and cations, which have similar molar volumes. As the pore size grows, the number of ions and solvent molecules are determined based on the molar 6 ACS Paragon Plus Environment

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volumes of neat IL, IL+ACN mixture (20% IL molar concentration) and IL+DCE mixture (25% IL molar concentration). The final molecular numbers for both slit and cylindrical pores are listed in Table 2. Table 2: Across the Ten Pore Sizes, Number of Counter-ions, Co-ions (and Solvents) inside Slit or Cylindrical Pore Pore Size (nm) Neat IL inside CNT Ncounter−ion Nco−ion Neat IL inside Slit Ncounter−ion Nco−ion IL-ACN inside Slit Ncounter−ion Nco−ion NACN IL-DCE inside Slit Ncounter−ion Nco−ion NDCE

0.82 (6,6) 8 2

0.95 (7,7) 12 6

1.08 (8,8) 16 10

1.22 (9,9) 22 16

1.36 (10,10) 29 23

1.49 (11,11) 36 30

1.63 (12,12) 45 39

1.76 (13,13) 55 49

1.9 (14,14) 66 60

2.03 (15,15) 77 71

32 24

40 32

48 40

56 48

64 56

72 64

80 72

88 80

96 88

104 96

16 8 64

20 12 80

24 16 96

28 20 112

32 24 128

36 28 144

40 32 160

44 36 176

48 40 192

52 44 208

16 8 64

20 12 76

24 16 88

28 20 100

32 24 112

36 28 124

40 32 136

44 36 148

48 40 160

52 44 172

Molecular dynamic (MD) simulations were carried out using the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) program. 31 The OPLSAA all-atom force field 32,33 was chosen for the ionic liquids and solvent model. A more refined force field specifically for imidazolium cations is used. 34 The temperature is controlled by the Nose-Hoover thermostat method. Spherical cutoffs of 12 Å is used for the Lennard-Jones and Coulomb interactions, Finally, we note that in the simulations, the positions of all constituent carbon atoms of the nanopores were frozen. NPT simulations are conducted first to determine the bulk molar volumes of neat IL and IL solution with solvents. The NVT simulations of the pore systems were first equilibrated for 2ns at 700K, followed by a 2ns equilibration at 333K. With a timestep of 1f s, production runs continued for 4ns at 333K. Trajectories were recorded every 2ps for computing structural properties. In the Results section below, we first look at neat ILs confined inside both slit and cylindrical nanopores, and then studied the IL+solvent mixture inside slit pores.



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Results and Discussion In-pore Structure by Number Density Using the center of mass as the position coordinate for ions, number densities are plotted for cations in Figure 2(a) and anions in Figure 2(b) inside ten positively charged slit pores, as listed in Table 1. In the direction perpendicular to the page, closest to the reader is the pore with largest size L = 2.03nm, while farthest from the reader is the smallest pore of L = 0.82nm. The linear size of the cations and anions is approximately 0.7nm. Therefore, 60.0

60.0

(a) Cation

(b) Anion

40.0

40.0

3

3

(#/nm )

(#/nm )

20.0

20.0

L (nm)

L (nm)

0.82

0.82

0.95

0.95

1.08

1.08

1.22

1.22

1.36

1.36

1.49

1.49

1.63

1.63

1.76

1.76

1.90

1.90

2.03

0.0

0.5

1.0 (nm)

1.5

2.03

0.0

2.0

0.5

1.0 (nm)

1.5

2.0

Figure 2: Number density distribution of (a) cations and (b) anions, across the positive slit pore with pore size ranging from L = 0.82nm to L = 2.03nm (listed in Table 1). In the direction perpendicular to the paper, pore sizes grows from L = 0.82nm for the most inside pore, to L = 2.03nm for the pore closest to the reader. The charge density on the slit pore is +0.253C/m2 . In the diagrams the laterally placed flat rectangles are a guide to the eye for the pore limits. The color gradient helps distinguish the specific position inside the pore, i.e. thicker color means a closer position to the center of pore.

the series of nanopores covers the range of pore size from L = 0.82nm ≈ 1 layer, to L = 2.03nm ≈ 3 layers. Next we will summarize the general principles governing the structural changes with decreasing pore sizes. The usual structure of alternating layers of cations and anions becomes less apparent as the nanopore becomes narrower, as indicated in Figure 2. The structural transitions that counter-ions and co-ions undergo are summarized as follows: 8 ACS Paragon Plus Environment

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(1) at L = 2.03nm ≈ 3 layers, both counter-ion and co-ion manage to fit in 3 broad layers, including layers close to the surfaces and a layer in the middle of the pore. Within the layers close to the surfaces, the counter-ion has a major peak closest to the pore surface, together with a minor peak closer to the center. Between these major and minor peaks of the counter-ion is a co-ion peak, giving alternating co-ion and counter-ion layering. (2) going from L = 2.03nm ≈ 3 layers to L = 1.36nm ≈ 2 layers: both counter-ion and co-ion display 2 broad layers close to the pore surfaces. This occurs together with a vanishing middle layer due to the steric exclusion. (3) going from L = 1.36nm ≈ 2 layers to L = 0.82nm ≈ 1 layer: both the counter-ion and co-ion’s surface layers are suppressed due to the diminishing space, while the middle layer has built up. That is, counter-ions and co-ions transfer from surface layers to a central layer as the pore size decreases. Notwithstanding their cooperative structural transitions, the counter-ion distribution is consistently more structured than that of the co-ion, as demonstrated by the higher and narrower peaks near the pore electrode.

Curvature Effect The confinement by cylindrical pores gives rise to qualitatively different structural properties for counter-ions and co-ions compared with the slit geometry, as shown in Figure 3. Overall, the number density profiles display more pronounced peaks than in the slit. At a diameter of 0.82nm both counter-ion and co-ion end up with 2 highly structured layers across the pore which corresponds to cylindrical density profiles closely associated with the CNT surface. The two layers as shown do not merge into a broad and smooth central layer as seen in slit pores. For the CNT such a central density profile would correspond to region of charge distributed axially, through the center of the pore. That this does not occur is due to the stronger attraction to the pore surfaces in the cylindrical pore, given the concave geometry of the pore surfaces. 9 ACS Paragon Plus Environment


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60.0

200.0

(a) Cation

(b) Anion 160.0

40.0 120.0 3

3

(#/nm )

(#/nm )

80.0 20.0

40.0

L (nm)

L (nm)

0.82

0.82

0.95

0.95

1.08

1.08

1.22

1.22

1.36

1.36

1.49

1.49

1.63

1.63

1.76

1.76

1.90

1.90

2.03

0.0

0.5

1.0 (nm)

1.5

2.03

0.0

2.0

0.5

1.0 (nm)

1.5

2.0

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200.0

(d) Anion

(c) Cation 160.0

40.0 120.0 3

3

(#/nm )

(#/nm )

80.0 20.0

40.0

L (nm)

L (nm) 0.82

0.82

0.95

0.95

1.08

1.08

1.22

1.22

1.36

1.36

1.49

1.49

1.63

1.63

1.76

1.76

1.90

1.90

2.03

0.0

0.5

1.0 (nm)

1.5

2.03

0.0

2.0

0.5

1.0 (nm)

1.5

2.0

Figure 3: Across the cylindrical pore, number density distribution of (a) cations and (b) anions inside positive electrode; and (c) cations and (d) anions inside negative electrode at ten pore sizes from L = 0.82nm to L = 2.03nm. The total excess charges on electrode is equal to +6|e| on positive pore and −6|e| on negative pore. For each pore, flat line is drawn to indicate the confinement of pores on the left and right. The color gradient helps distinguish the specific position inside the pore, i.e. thicker color means a closer position to the center of pore.

Interestingly, for negative pores at the two largest diameters ofL = 1.9nm to L = 1.76nm, the cation (counter-ion) builds up a substantial secondary cylindrical layer of charge as shown inFigure 3(c). A corresponding phenomenon occurs to a significantly lesser extent with the


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positive pore (and the anionic distribution). This inner layer of charge acts to reduce the EDL screening of the pore charges and lowers the capacitance, as seen in Figure 4, and to be discussed in the next section.

Capacitance The electrostatic potential ψ(z) is computed from the charge distribution across the EDL inside the pore, i.e. from z = 0 to z = L, according to Poisson’s equation. The total electrode potential (relative to the bulk) at the pore surface is denoted as Ψ(surf ),. The electrode potential is obtained as the sum of the Donnan potential ψDonnan , and EDL potential at the pore surface (ψ(0) at z = 0) as given in Eq.(1):

Ψ(surf ) = ψDonnan + ψ(0)

(1)

Under an incompressibility assumption, consistent with our treatment of the electrochemical equilibrium, the Donnan potential can be obtained using the following approximate expression ( the derivation details are provided in the supporting information),

ψDonnan

v u 1 ∫L u n+ (z)exp(βeψ(z)) dz 1 = − log t 1L∫ L0 βe n− (z)exp(−βeψ(z)) dz L

(2)

0

in which e is the elementary charge, and β =

1 kT

where k is Boltzmann constant, and T

is temperature. To quantify the capacitance of the model, we calculate the the integral capacitance defined in Eq.(3). The integral capacitance per unit area is computed using the positive surface charge density σ+ and the negative surface charge density σ− , as shown in Eq.(3): C=

σ+ − σ− Ψ+ (surf ) − Ψ− (surf )

(3)

Figure 4 compares the capacitance between slit and cylindrical pores across a range of pore sizes. Inside CNT pores, the capacitance oscillates with pore size to a larger extent than 11 ACS Paragon Plus Environment


10

Integrated Capacitance C (µF/cm 2 )

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CNT Slit

8

6

4

2

0 0.5

1.0

1.5 Pore Size (nm)

2.0

Figure 4: Capacitance comparison between slit and cylindrical pores for neat IL across a range of pore sizes.

planar pores. This is consistent with the increased structuring seen in the CNT, compared with slits. The capacitance minimum at L = 1.08nm for slit pores coincides with an irregular rise of the middle layer for counter-ions, which can be seen more clearly from the view shown in Figure 5(b). Instead of becoming wider and lower in magnitude, as happens from L = 0.82nm to L = 0.95nm, the counter-ion peak becomes more concentrated into a higher central peak from L = 0.95nm to L = 1.08nm. This is caused by steric exclusion due to co-ions. Coinciding with this rise in the counter-ion density, co-ions build up a minor peak in the layers adjacent to the surfaces, as can be seen in Figure 5(a). These irregular variations of counter-ion in the middle layer, and co-ion in the surface layers give rise to a thicker EDL and larger electrode potential, which in turn leads to the slit capacitance minimum at L = 1.08nm shown in Figure 4. A similar effect is seen in cylindrical pores, at a diameter of 1.08nm, where the counter-ion density close to the surface appears to form a secondary density peak which becomes pushed toward the center of the pore due to the excluding effects of co-ions, whose density also grows close to the pore surface, see Figure 3.


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60.0

60.0

40.0

40.0

(a) Cation

(b) Anion 3

3

(#/nm )

(#/nm )

20.0

0.8 .0 2 0.9 5 1.0 8 1.2 2 1.3 6 1.4 9 1.6 3 L ( 1.7 nm 6 1.9 ) 0 2.0 3

20.0

0.8 .0 2 0.9 5

0

0.0 0.5 1.0 (nm)

1.5

0

1.0 8 1.2 2 1.3 6 1.4 9 1.6 3 L ( 1.7 nm 6 1.9 ) 0 2.0 3

0.0 0.5 1.0 (nm)

2.0

1.5 2.0

Figure 5: Across the positive slit pore, side view of number density distribution of (a) cations and (b) anions, at a range of pore sizes from L = 0.82nm to L = 2.03nm. The charge density on electrode is +0.253C/m2 . For each pore, flat line is drawn to indicate the confinement of pores on the left and right. The color gradient helps distinguish the specific position inside the pore, i.e. thicker color means a closer position to the center of pore.

Figure 6 shows the number density profiles for co-ions and counter-ions inside the slit and cylindrical pores of L = 1.63nm. As illustrated in the slit pore of Figure 6 (a) & (b), cations display a central layer as co-ions, but their density shifts to become the closest layer to the pore surface, when they act as counter-ions. The major and minor peak of the anion layers close to the pore surfaces also switch positions in response to the change in the electrode charge (from positive to negative). Therefore, the capacitance maximum for the slit at L = 1.63nm can be attributed to the significant polarization of both co-ions and counter-ions in response to changes in the electrode charge.



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(b) negative slit

(c) positive CNT

(d) negative CNT

Figure 6: Comparison of number density distribution for cation and anion at pore size L = 1.63nm, between (a) positive slit, (b) negative slit, (c) positive CNT pore, and (d) negative CNT pore. Dashed vertical lines represent the position of nanopore confinement.

In contrast, the already structured counter-ion and co-ion profiles inside CNT pores only swap the peak positions of the layers closest to the surface, as can be seen in Figure 6 (c) and (d). This moderate polarization response is unable to deliver strong EDL screening of the electrode charge changes and the capacitance in CNT pores is lower at L = 1.63nm accordingly.


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IL Mixture with Solvents In addition to the results above for neat ILs, we investigated the impact of adding a highly polar solvent, acetonitrile (ACN) and the less polar solvent, dichloroethane (DCE) to the ionic liquid to make electrolyte solutions in contact with slit pores. 60.0

60.0

(a) Cation

(c) Solvent ACN

40.0

40.0

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1.5

L (nm)

L (nm)

0.82

0.82

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0.95

1.08

1.08

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1.22

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(#/nm )

20.0

20.0

L (nm)

L (nm)

2.0

1.5

40.0

(#/nm )

1.5

1.0 (nm)

(f) Solvent DCE

3

1.0 (nm)

0.5

60.0

(e) Anion

40.0

0.5

20.0

0.82

(d) Cation

0.0

(#/nm )

20.0

L (nm)

1.0 (nm)

3

(#/nm )

20.0

0.5

40.0

3

(#/nm )

0.0

60.0

(b) Anion

L (nm)

0.82

0.82

0.95

0.95

1.08

1.08

1.08

1.22

1.22

1.22

1.36

1.36

1.36

1.49

1.49

1.49

1.63

1.63

1.63

1.76

1.76

1.76

1.90

1.90

2.03

2.03

0.0

0.5

1.0 (nm)

1.5

2.0

0.82 0.95

1.90 2.03

0.0

0.5

1.0 (nm)

1.5

2.0

Figure 7: Across the positive slit pore, number density distribution of (a) cations, (b) anions, (c) ACN solvents for IL+ACN mixture; and (d) cations (e) anions (f) DCE solvents for IL+DCE mixture, at a range of pore sizes. The charge density on pore electrode is +0.253C/m2 .

Figure 7 (c) and (f) shows that both solvents occupy the closest layers to the pore surfaces. The number density profiles are similar for ACN and DCE. This is manifested in similar behaviour for the capacitance curve of both mixtures as a function of the pore size, as shown in Figure 8.



10

Integrated Capacitance C (µF/cm 2 )

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IL IL+ACN IL+DCE

8

6

4

2

0 0.5

1.0

1.5 Slit Pore Size (nm)

2.0

Figure 8: Capacitance comparison between neat IL, IL+ACN mixture and IL+DCE mixture across a range of slit pore sizes.

Figure 8 demonstrates that the IL+solvent mixture leads to a less oscillatory capacitance with pore size than the neat IL. The solvent layers closest to the surfaces show no sign of diminishing with increasing pore size, particular for L greater than 1.36nm. The layer-bylayer structural transition in neat ILs are indeed “softened” by the presence of the solvents as shown in in Figure 7 (a) & (b) & (d) & (e), especially at larger pore sizes where broader peaks of low density are observed. At L = 0.95nm, the IL+ACN mixture improves the capacitance most when compared with the neat IL. Figure 9 demonstrates the normalized number density profiles and total charge densities brought about by the addition of ACN solvents. Here the number density distribution ρ(z) across the pore is normalized by ρave , which is obtained as by averaging the species density over the width of the pore. The higher capacitance in the IL+ACN solution seems to result from a reduced negative charge peak at around d = 3.4Å (in the negative pore) as is shown in Figure 9(b). From Figure 9 (a) we see that the position of this reduced charged peak is also the site of a solvent peak, which appears to support the fact that the intra-molecular polarization of the added ACN solvent contributes to the overall 16 ACS Paragon Plus Environment

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EDL screening. Therefore, capacitance is increased due to the solvent addition. 11

Figure 9: At pore size L = 0.95nm of negative slit, (a) normalized number density comparison, (b) charge density and electrostatic potential profiles comparison between neat IL and IL+ACN mixture. Electrostatic potential ψ(z) at pore surface is shifted to be zero. Dashed vertical lines represent the position of nanopore confinement.

The capacitance improvement brought in by the IL+ACN solution is reproduced by the IL+DCE mixture. Figure 10 compares the number density and charge profiles between IL+ACN and IL+DCE mixtures at L = 0.95nm.

Figure 10: At pore size L = 0.95nm of positive slit, (a) normalized number density comparison, (b) charge density and electrostatic potential profiles comparison between IL+ACN mixture and IL+DCE mixture. Electrostatic potential ψ(z) at pore surface is shifted to be zero. Dashed vertical lines represent the position of nanopore confinement.

As shown in in Figure 10 (b) IL+DCE mixtures show a larger potential drop due to 17 ACS Paragon Plus Environment


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charge density differences from d = 4.0Å to d = 6.5Å compared with the IL+ACN mixture. Around this region, the ACN solvent shows a clear peak while DCE solvent does not. The more polar ACN molecule is responsible for the differences in charge profiles (Figure 10 (b)), and a stronger EDL screening reflected by a lower potential. To understand why the capacitance is not increased by adding solvents overall, as it does in classical density functional studies, 11 we further distinguish the solvent’s contribution to charge profiles from the total, for the IL+ACN mixture at the largest slit pore of L = 2.03nm in Figure 11. It is evident that the charge density of ACN solvents resembles the total charge profiles, only within the central region of the pore. Closer to the surfaces the solvent contribution is smaller and most of the EDL screening is still accomplished by the ions in the regions close to the pore surface. Thus the width of the electric double layer in Figure 11 is not significantly reduced by including solvent.

Figure 11: Charge density comparison between total and solvent component for IL+ACN mixture inside (a) negative electrode, (b) positive electrode, at slit pore size L = 2.03nm. Red line indicates the total charge density inside the same pore with pure IL, as a reference. Dashed vertical lines represent the position of nanopore confinement.


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Conclusions We study the carbon electrode with slit and cylindrical pore geometries immersed in ionic liquids electrolytes. The structural profiles are recorded in response to varying sizes of both slit and cylindrical pores. As the slit pore size decreases from L = 2.03nm to L = 1.36nm, the middle layer of counter-ion and co-ion gradually separate into two minor peaks which later merge into two side layers. The two broad side layers further evolve into a single middle layer, as the pore size continues to decrease from L = 1.36nm to L = 0.82nm. With co-ions and counter-ions transferring back and forth between middle and side layers, the effective thickness of EDL oscillates with pore size and so does the capacitance. Curved surfaces in CNT pore exerts stronger confinement on the mobility of both co-ion and counterions. Inside a small cylindrical pore, we see two surface layers of counter-ions and co-ions (corresponding to a cylindrical density) rather than a broad central layer as seen in slit pores. IL dilution with solvent weakens the capacitance’s oscillation over varying pore sizes. But the capacitance is not substantially increased upon solvent addition for most of the studied pore sizes.

Acknowledgements This work was supported by Tianjin Natural Science Foundation (No. 16JCYBJC18000). This work was completed in part with resources provided by the School of Materials Science and Engineering, Tianjin University of Technology, China.

Supporting Information Available Donnan potential expressions, number density profiles inside cylindrical and slit pores are presented in the Supporting Information.

This material is available free of charge via the

Internet at http://pubs.acs.org/.



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