Supplementary Information for

“Exploring Non-Linearities of Carbon-Based

Microsupercapacitors from an Equivalent Circuit Perspective”

Danupol Boonpakdee, Cristian F. Guajardo Yevenes,

Werasak Surareungchai, and Chan La-o-vorakiat∗

∗ chan.lao@kmutt.ac.th

1

Electronic Supplementary Material (ESI) for Journal of Materials Chemistry A.This journal is © The Royal Society of Chemistry 2018

S1. POTENTIAL WINDOW SELECTION

We scanned the voltage over a wide range to find the positive potential where the upturns

due to hydrolysis reaction start to be visible (Fig S1). We chose the potential window up

to 0.8 V for most of the CV scans presented in the main text. In these measurments, MSCs

contain the same LiCl/PVA gel as described in the main text and the scan rate is set to

30 mV s−1.

0 0.2 0.4 0.6 0.8 1 1.2 1.4E (V)

0

2

4

6

Cur

rent

Den

sity

(μAc

m-2)

FIG. S1. Selecting the scan potential window to avoid the spike at high potential

S2. SYMMETRIC CV WHEN COMPLETELY SWITCHING THE POLARITY

The CVs are symmetric when the potential sweeps covers both negative and positive

potentials symmetrically. Here we have performed the measurements at various scan rates.

All could be described by a linear circuit model with three free parameters (C,Rs, Rp). (Fig.

S2)

S3. SURVEYING ASYMMETRIC CV IN LITERATURES

To point out that the asymmetric capacitance is not limited to our selection of electrode

and electrolyte but rather a general feature in other systems, we extracted 10 CV curves

from most cited articles with a keyword “micro-supercapacitor” indexed in Web of Science R©

2

Low Scan Rate CV High Scan Rate CV

Res

ista

nces

(kΩ

)

ESR EPR

(a) (b)

(c) (d)

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Potential (E)

-80

-60

-40

-20

0

20

40

60

80 0.025 Vs-1

0.050 Vs-1

0.1 Vs-1

0.3 Vs-1

0.5 Vs-1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Potential (E)

-300

-200

-100

0

100

200

300 1 Vs-1

2 Vs-1

3 Vs-1

4 Vs-1

5 Vs-1

0 1 100

20

40

60

80

100

120

0.1 1 10

10

100

1000

Cap

acita

nce

(μFc

m-2)

Scan Rate (Vs-1) Scan Rate (Vs-1)

Cur

rent

Den

sity

(μAc

m-2)

Cur

rent

Den

sity

(μAc

m-2)

FIG. S2. A completely symmetric CV when reversing the polarity of the electrode for both (a)

low and (b) high scan rate to measure (c) capacitance, (d) equivalent serial resistance (circles),

and equivalent parallel resistance (open squares). The curve fitting results from a linear equivalent

circuit model are displayed as lines.

(only electric double-layer capacitors are included and the results are as of 20 February

2018).

By trying not to over-analyze the data, we simply bisect the CVs into charing (blue) and

discharging halves (red); then we invert both current and potential axes of the discharg-

ing curve. After offsetting the current level, the two curves should overlap if the circuit

parameters are symmetric (as demonstrated by our physical equivalent circuit, simulation

and polarity-switched CVs). Our survey gives a surprising result that all of the reported

CVs process certain degree of asymmetry as in our current work, and most of the curves

behave similar to “hidden-storage” non-linearity by having a higher current amplitude of

discharging curve.

Using our equivalent circuit approach would deepen the investigation of intricate electrical

features of these MSCs beyond the conventional approach.

3

Asymmetric CV from this work

Original Inverted Conditions

1.

0.00 0.25 0.50 0.75V

5

0

5

10

A

0.00 0.25 0.50 0.75V

0

5

10

15

A main result (Fig. 4c)

Symmetric CVs from this work

Original Inverted Conditions

1.

0.0 0.5 1.0V

5

0

5

10

15

A

0.0 0.5 1.0V

0

5

10

15

20

25

A equivalent circuit simulation (Fig. 1d)

2.

0.5 0.0 0.5V

20

10

0

10

20

A

0.5 0.0 0.5V

0

10

20

30

40

50

A polarity-switched CV (Fig. 4d)

3.

0.00 0.25 0.50 0.75V

20

0

20

A

0.00 0.25 0.50 0.75V

0

20

40

60

A physical equivalent circuit (Fig. 3b)

CVs from most cited “micro-supercapacitor” articles from Web of Science R©

Original Inverted Conditions (electrode/electrolyte, scan rate [ref.])

1.

0.0 0.5 1.0V

2

0

2

4

mFc

m2

0.0 0.5 1.0V

0

2

4

6

mFc

m2

rGO/GO, 40 mV s−1 [1]

4

2.

0.0 0.5 1.0V

4000

2000

0

2000

4000

mAc

m3

0.0 0.5 1.0V

0

2000

4000

6000

8000

mAc

m3

SWNT-rGO fibres/H3PO4-PVA, 100 mV s−1 [2]

3.

0.0 0.5 1.0V

10

5

0

5

10

15

mAc

m2

0.0 0.5 1.0V

0

5

10

15

20

25m

Acm

2

rGO-CNT/KCl, 1 V s−1 [3]

4.

0.0 0.5 1.0V

0.2

0.0

0.2

mAc

m2

0.0 0.5 1.0V

0.0

0.2

0.4

0.6

mAc

m2

graphene quantum dots/Na2SO4, 1 V s−1 [4]

5.

0.5 0.0 0.5V

0.4

0.2

0.0

0.2

0.4

mA

0.5 0.0 0.5V

0.0

0.2

0.4

0.6

0.8

mA

MoS2, 200 mV s−1 [5]

6.

1.0 0.5 0.0V

0.006

0.004

0.002

0.000

0.002

0.004

A

1.0 0.5 0.0V

0.000

0.002

0.004

0.006

0.008

0.010

A Ni(OH)2 nanowire/KOH-PVA, 200 mV s−1 [6]

7.

0.0 0.5V

200

100

0

100

200

mAc

m3

0.00 0.25 0.50 0.75V

0

100

200

300

400

mAc

m3

MnOx−Au/H2SO4-PVA, 50 V s−1 [7]

5

8.

0.00 0.25 0.50 0.75V

2

0

2

mAc

m2

0.00 0.25 0.50 0.75V

0

2

4

6

mAc

m2

rGO fibers/H3PO4-PVA, 20 mV s−1 [8]

9.

0.5 0.0V

0.01

0.00

0.01

0.02

mA

0.75 0.50 0.25 0.00V

0.00

0.01

0.02

0.03

0.04

mA

rGO-SWCNT fiber/Na2SO4-PVP, 10 mV s−1 [9]

10.

0 2V

100

50

0

50

100

150

A

0 1 2 3V

0

50

100

150

200

250

A SWNT/ionic liquid, 4 V s−1 [10]

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