Enhancing the Capacitive Performance of Electric-Double-Layer ...
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Enhancing the Capacitive Performance of Electric-Double-Layer Capacitors with Ionic-Liquid Mixtures
C. Lian1,2, K. Liu1, K. L. Van Aken3, Y. Gogotsi3, D. J. Wesolowski4, H.L. Liu2, D.E. Jiang5, and J.Z. Wu1* 1
Department of Chemical and Environmental Engineering, University of California, Riverside, CA 92521, USA 2
State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237, P. R. China
3
Department of Materials Science and Engineering and A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, PA 19104, USA 4
5
*
Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Department of Chemistry, University of California, Riverside, CA 92521, USA
Corresponding author. Tel: (951) 8272413; Email: [email protected]
1
I. Charge inversion In the electric double layer (EDL) of ionic liquids, the ion distributions reflect strong electrostatic correlations and excluded-volume effects owing to the direct Coulomb interactions (without a medium) and high ion concentrations. The strong correlation effects may lead to oscillatory variations of the local electrical potential and the local charge density. The opposite states of the local and the electrode charges are often referred to as charge inversion or “overscreening”. Quantitatively, we may describe charge inversion in terms of the dimensionless integrated charge distribution function, which in a planar geometry is given by,
q(z) = Q+ ∑ Zi i
∫
z
0
dz ' ρ i (z ')
where q(z) describes an overall charge from the electrode surface up to position z:
Figure S1. Integrated charge distribution functions for x=0, 0.25, and 1 near a surface of the surface charge density 0.1 C/m2 for the ionic mixture discussed in the main text. 2
Figure S1 presents the integrated charge distribution functions, respectively, for x=0, 0.25, and 1. We see that the oscillatory integrated charge density is reduced when the amount of small anions in the bulk is increased. Because the surface has the same electrical charge, it is clear that the strong charge segregation at the surface arises from the size asymmetry or the difference between the molecular excluded volumes of cations and anions. II. Cyclic voltammetry To study the concentration effect experimentally, we performed cyclic voltammetry (CV) measurements for onion-like carbon (OLC) electrodes in contact with EMI-BF4-TFSI mixtures of different anion compositions. Figure S2 shows the experimental cyclic voltammograms at slow and fast scan rates for different compositions of the ionic liquids. From these curves, it is clear that the capacitance is purely from the electric double layer.
x=0 x=0.1 x=0.2 x=0.5 x=0.8 x=1
20
x=0 x=0.1 x=0.2 x=0.5 x=0.8 x=1
5 mV/s 40
Capacitance (F/g)
Capacitance (F/g)
40
0
-20
20
500 mV/s
0
-20 0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
Voltage (V)
0.5
1.0
1.5
2.0
2.5
3.0
Voltage (V)
Figure S2. Cyclic voltammograms for a capacitor containing EMI-BF4-TFSI mixtures of different anion compositions (x) at scan rates: (a) 5 mV/s and (b) 500 mV/s .
3
As discussed in the main text (Eq.8), we calculated the capacitance values shown in Figure 3b by taking the integral of the discharge curve from the current vs. voltage voltammograms and normalizing by the scan rate according to the following equation: =
2
where C is the gravimetric capacitance (F/g), v is the scan rate (V/s), m is the mass of one electrode, and I is the current.
4
Enhancing the Capacitive Performance of Electric-Double-Layer Capacitors with Ionic-Liquid Mixtures
C. Lian1,2, K. Liu1, K. L. Van Aken3, Y. Gogotsi3, D. J. Wesolowski4, H.L. Liu2, D.E. Jiang5, and J.Z. Wu1* 1
Department of Chemical and Environmental Engineering, University of California, Riverside, CA 92521, USA 2
State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237, P. R. China
3
Department of Materials Science and Engineering and A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, PA 19104, USA 4
5
*
Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Department of Chemistry, University of California, Riverside, CA 92521, USA
Corresponding author. Tel: (951) 8272413; Email: [email protected]
1
I. Charge inversion In the electric double layer (EDL) of ionic liquids, the ion distributions reflect strong electrostatic correlations and excluded-volume effects owing to the direct Coulomb interactions (without a medium) and high ion concentrations. The strong correlation effects may lead to oscillatory variations of the local electrical potential and the local charge density. The opposite states of the local and the electrode charges are often referred to as charge inversion or “overscreening”. Quantitatively, we may describe charge inversion in terms of the dimensionless integrated charge distribution function, which in a planar geometry is given by,
q(z) = Q+ ∑ Zi i
∫
z
0
dz ' ρ i (z ')
where q(z) describes an overall charge from the electrode surface up to position z:
Figure S1. Integrated charge distribution functions for x=0, 0.25, and 1 near a surface of the surface charge density 0.1 C/m2 for the ionic mixture discussed in the main text. 2
Figure S1 presents the integrated charge distribution functions, respectively, for x=0, 0.25, and 1. We see that the oscillatory integrated charge density is reduced when the amount of small anions in the bulk is increased. Because the surface has the same electrical charge, it is clear that the strong charge segregation at the surface arises from the size asymmetry or the difference between the molecular excluded volumes of cations and anions. II. Cyclic voltammetry To study the concentration effect experimentally, we performed cyclic voltammetry (CV) measurements for onion-like carbon (OLC) electrodes in contact with EMI-BF4-TFSI mixtures of different anion compositions. Figure S2 shows the experimental cyclic voltammograms at slow and fast scan rates for different compositions of the ionic liquids. From these curves, it is clear that the capacitance is purely from the electric double layer.
x=0 x=0.1 x=0.2 x=0.5 x=0.8 x=1
20
x=0 x=0.1 x=0.2 x=0.5 x=0.8 x=1
5 mV/s 40
Capacitance (F/g)
Capacitance (F/g)
40
0
-20
20
500 mV/s
0
-20 0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
Voltage (V)
0.5
1.0
1.5
2.0
2.5
3.0
Voltage (V)
Figure S2. Cyclic voltammograms for a capacitor containing EMI-BF4-TFSI mixtures of different anion compositions (x) at scan rates: (a) 5 mV/s and (b) 500 mV/s .
3
As discussed in the main text (Eq.8), we calculated the capacitance values shown in Figure 3b by taking the integral of the discharge curve from the current vs. voltage voltammograms and normalizing by the scan rate according to the following equation: =
2
where C is the gravimetric capacitance (F/g), v is the scan rate (V/s), m is the mass of one electrode, and I is the current.
4
