Supporting Information
What are the practical limits for the specific surface area and
capacitance of bulk sp2 carbon materials?
Yanhong Lu1,2*, Guankui Long2, Long Zhang2, Tengfei Zhang2, Mingtao Zhang2, Fan Zhang2,
Yang Yang2, Yanfeng Ma2 & Yongsheng Chen2,*
1
School of Chemistry & Material Science, Langfang Teachers University, Langfang, Hebei,
065000, China
2
Key Laboratory of Functional Polymer Materials and Center for Nanoscale Science and
Technology, Institute of Polymer Chemistry, College of Chemistry, Nankai University, Tianjin,
300071, China
Corresponding: yschen99@nankai.edu.cn；luyanhong_2003@126.com;
1
Synthesis of various bulk sp2 carbon materials
Details for all the prepared materials are summarized in Table S1. An aqueous solution of the
different
carbon
sources,
including
the
phenol/formaldehyde
mixture
(PF,
phenol/formaldehyde weight ratio of 0.7), polyvinyl alcohol (PVA), sucrose, cellulose and
lignin was mixed with a GO aqueous suspension with different weight ratios of carbon source
to GO. As a typical example, the preparation of S@24GA is as follows. An aqueous solution
of sucrose (23 mL, 250 mg mL-1) and a GO aqueous suspension (47 mL, 5 mg mL-1) were
homogeneously mixed and stirred for 4 h and then transferred to a sealed 100 mL Teflonlined autoclave, and heated to 180 °C for 12 h. After the autoclave was cooled to room
temperature, the hydrothermal product was filtered, washed with distilled water and finally
dried in vacuum at 120 °C for 24 h. The intermediate hydrothermal product was mixed with
KOH activation agent at the weight ratio of 1:4, placed in a horizontal tube furnace and heated
from room temperature to 900 °C for 1 h at 5 °C min-1 under Ar. After cooling to room
temperature, the products were thoroughly washed with 0.1 M HCl to remove any inorganic
salts, and then washed with distilled water until the pH value reached 7. The final products
were obtained after drying in vacuum at 120 °C for 24 h.
Calculations of the stack height (Lc) and lateral size (La) of graphene domains in the sp2
carbon materials
The stack height Lc can be estimated from the XRD line broadening using the Scherrer
equation: Lc = Kλ / (βc × cosθ), where K is the shape factor which is equal to 0.89, λ is the
wave length of the X-ray radiation, βc is the full width at half height of the diffraction peaks
and θ is the Bragg angle. With Raman spectra, Lorentzian fitting was carried out to obtain the
positions and widths of the D and G bands. The size of graphene domains La (nm) can be
estimated using the equation La = (2.4 × 10-10) λ4 (ID / IG)-1, where λ is the laser energy in
nanometers, and ID and IG are the intensities of the D and G bands, respectively.
2
The estimated values of Lc and La of a series of sp2 carbon materials are shown in Table S2.
As can be seen from Table S2, the average domain height Lc of the optimized activation
products is found to be 0.7–0.8 nm, and the approximate dimensional size is around 5–6 nm
depending on the carbon source. These results suggest that the basic structural units in the
high SSA sp2 carbon materials are graphene sheets a few nanometers in size, most of which
should be wrinkled single-layer sheets with some few-layer, as observed earlier [1, 2].
Theoretical modeling and calculations
All DFT calculations were performed with the Gaussian 09 program package Full citation for
Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford CT, 2010.
M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G.
Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P.
Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K.
Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T.
Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers,
K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A.
Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J.
E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O.
Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V.
G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O.
Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox.
3
Construction of the effective ionic diameter (EID) model and calculation of effective
specific surface (E-SSA) and theoretical capacitance (Cth)
E-SSA, which is the accessible surface area for the electrolyte ions, was calculated according
to the cumulative DFT SSA, the PSD of the carbon materials and the electrolyte ion size. In
this work, the electrolyte ion sizes used to calculate the E-SSA in EMIMBF4, BMIMBF4 was
obtained using DFT calculations (B3LYP/6-31G*) [3, 4] and the cation sizes of EMIM+,
BMIM+ were found to be 0.752 and 1.107 nm, respectively, and the sizes of TEA+ in organic
system and K+ in aqueous system are 0.684 and 0.266 nm, respectively, following the
literature [5, 6]. Using the E-SSA, the theoretical capacitance was calculated. Before we could
do that, EID, the actual size of the electrolyte ions absorbed on the active material surface,
had to be known. For solvent free IL ions, the Cth could be obtained easily as there is no
solvation issue. However, for aqueous and organic electrolyte systems, the ion size depends
heavily on the solvation layer. With these provisos in mind, the bare electrolyte ion sizes
could not be used. Thus, a more general model was proposed as shown in Figures 1 and S1,
where the layers of solvent molecules around the ions were taken into account. Thus, the
actual electrolyte ion size, EID, was obtained as the sum of the naked ion size (obtained from
the van der Waals diameter) and the thickness of the shell of solvent molecules. With this
model, the EIDs of 1.0 M TEA+ in organic solvent AN and 6 M K+ in water were taken as
1.320 and 0.662 nm, respectively, following the literature [5-7]. Based on the EID model and
the method in our previous work [2], the corresponding Cth of representative materials in
several of the most widely studied electrolyte systems was calculated. The calculation was
based on equation (S1) [8]:
Cp 
 0 A
d
(S1)
4
where ε0 is vacuum permittivity which is 8.85×10-12 F m-1, ε is the relative dielectric
constant of the electrolyte, A is the E-SSA and d is the thickness of the electric double layer.
In this work, room temperature ε was used because measurements were made at room
temperature, and ε values are found to be 14.8, 12.9, 9.65 and 13.4 for EMIMBF4, BMIMBF4,
1 M TEABF4/AN and 6 M KOH electrolyte systems, respectively [5, 9].
Note that the capacitance contribution of pores with diameters smaller than the size of
the solvated electrolyte ions but larger than that of the bare electrolyte ions was also included
as suggested in the literature [10-12]. A series of representative E-SSA and cumulative
specific capacitance values of GAC electrode materials in EMIMBF4, BMIMBF4,
TEABF4/AN and KOH electrolyte systems are listed in Tables S3–S7. Note that we only used
the cations for the estimation of Cth since all the corresponding anions are smaller than the
cations.
Similar to our previous report [2], the values of cumulative specific capacitance are quite
different from Cex because the actual relative dielectric constant of the electrolyte could
change due to many reasons such as the curvature of the pore surface, the temperature and
frequency dependenc of the relative dielectric constant. Therefore, the cumulative specific
capacitance of all the products in each electrolyte was normalized by the same degree to get
the normalized cumulative specific capacitance. The normalized cumulative specific
capacitances in EMIMBF4, BMIMBF4, TEABF4/AN and KOH electrolyte were divided by
2.3, 1.4, 1.15 and 2.5, respectively, to give what is defined as the theoretical specific
capacitance Cth, and a systematic comparison with Cex was obtained, as shown in Figures 3
and S2. From the results, an excellent agreement between Cex and Cth for all the products in
all electrolytes was observed, indicating that our model for the calculation of theoretical
specific capacitance is appropriate for SCs based on the different carbon materials in all the
studied electrolyte systems.
5
Calculation of the possible smallest stable graphene sheet size
To theoretically obtain the possible smallest stable graphene sheet (fragment) size,
geometrical optimization of all the graphene fragments with different sizes (different numbers
of carbon atoms) was performed at the B3LYP levels of theory with the 3-21G basis set [3, 4].
Frequency analysis was used at the same level of theory to check whether the optimized
geometrical structures were in stable states and to evaluate the zero-point vibration energy
(ZPE). With these graphene fragments, a thermodynamic calculation was used. The smallest
stable graphene fragment was then predicted under practical experimental conditions.
To calculate the Gibbs free energy change of the reaction, the gas phase reaction
enthalpy change ΔrH (g) at different temperatures is theoretically calculated. Assuming the
gasification enthalpy of the reactants is equal to the solidification enthalpy of the products,
ΔrH (g) could be used as the solid phase reaction enthalpy change ΔrH (s) of Equ. 1. In a
similar way, the gas phase reaction entropy change ΔrS (g) of equation (2), dominantly
provided by H2 with the value of 31.151 cal mol-1 K-1, could be used as the solid phase
reaction entropy change ΔrS (s). Based on ΔrH (s) and ΔrS (s), the Gibbs free energy change
ΔrG of the reaction in equation (2) at 900 °C could be obtained according to ΔrG = ΔrH - TΔrS.
Calculation of theoretical SSA for a given size graphene sheet
With a given graphene sheet size, the theoretical SSA of the sp2 carbon materials was
calculated from a simple Monte Carlo integration technique where the probe molecule is
“rolled” over the framework surface, and the probe radius is 1.82 Å (the kinetic radius of N2)
[13, 14]. Based on this method, the corresponding theoretical SSA of the bulk carbon
materials with 5 × 5–6 × 6 nm size graphene sheets would be ~ 3500–3700 m2 g-1.
6
Figure S1 Schematics of the packing mode of IL and solvated organic & aqueous electrolyte
ions in the pores of electrode materials and the corresponding utilized cylindrical pore surface.
Tightly stacked (a) IL and (b) solvated organic & aqueous electrolyte ions with complete
matching between the EID of the electrolyte ions and the pore size, (c) not tightly stacked
together due to mismatching. The d value is equal to the radius of the solvated ion. The black
regions of the pore circumference in (c) represent the unused or wasted cylindrical pore
surface.
7
Figure S2 Relationship between the experimental and theoretical specific capacitances of
various carbon materials in (a) EMIMBF4, (b) BMIMBF4, (c) TEABF4/AN and (d) KOH. In
each pair of the columns, the left is Cex and the right is Cth.
8
Table S1 Preparation of various bulk sp2 carbon materials and the corresponding BET SSA
Weight ratio of
sp2 carbon
Activation
activation agent to
agent
hydrothermal
Carbon source
materials
Activation
BET
temperature
SSA /
/ °C
m2 g-1
product
RP20
-
-
-
-
1677
HXAC
-
-
-
-
1820
GAC
-
-
-
-
2654
GA
GO
KOH
4:1
900
1810
PA
PFa)
KOH
4:1
900
2074
BA
bitumen
KOH
4:1
900
2470
P@8GA
PF/GO = 8:1b)
KOH
4:1
900
2356
L@24GA
Lignin/GO = 24:1
KOH
4:1
900
3026
C@24GA
cellulose/GO = 24:1
KOH
4:1
900
3117
V@20GA
PVA/GO = 20:1
KOH
4:1
900
3192
S@24GA
sucrose/GO = 24:1
KOH
4:1
900
3271
P@16GA
PF/GO = 16:1
KOH
4:1
900
3523
P@16GA-8R
PF/GO = 16:1
KOH
8:1
900
2078
P@16GA-1100
PF/GO = 16:1
KOH
4:1
1100
1136
P@24GA-
PF/GO = 24:1
NaOH
4:1
900
2119
P@24GANaOH
P@24GAK2CO3
PF/GO = 24:1
K2CO3
4:1
900
1426
PF/GO = 24:1
ZnCl2
4:1
900
989
P@24GAZnCl2
P@24GAH3PO4
PF/GO = 24:1
H3PO4
4:1
900
651
PF/GO = 24:1
CaO
4:1
900
557
P@24GA-2R
CaO
P@24GA-3R
PF/GO = 24:1
KOH
2:1
900
1366
PF/GO = 24:1
KOH
3:1
900
2216
P@24GA
PF/GO = 24:1
KOH
4:1
900
3394
P@24GA-5R
PF/GO = 24:1
KOH
5:1
900
2613
P@24GA-6R
PF/GO = 24:1
KOH
6:1
900
2341
P@24GA-7R
PF/GO = 24:1
KOH
7:1
900
1700
P@24GA-8R
PF/GO = 24:1
KOH
8:1
900
1466
P@24GA-600
PF/GO = 24:1
KOH
4:1
600
1587
P@24GA-700
PF/GO = 24:1
KOH
4:1
700
2200
9
P@24GA-800
PF/GO = 24:1
KOH
4:1
800
2536
P@24GA-1000
PF/GO = 24:1
KOH
4:1
1000
2218
a)
PF = phenol and formaldehyde
b)
weight ratio
10
Table S2 The height (Lc) and lateral size (La) of the graphene domains
XRD results
Raman results
Lc / nm
La / nm
P@16GA
0.81
6.5
C@24GA
0.84
4.8
L@24GA
0.83
5.9
S@24GA
0.75
6.5
V@20GA
0.88
4.8
P@24GA
0.85
6.7
P@8GA
0.88
6.9
Products
11
Table S3 Detailed data for the calculation of E-SSA and the specific capacitance of (Cp) for
all the pores for the GAC electrode material in EMIMBF4 electrolyte. The cumulative specific
capacitance (Cc) is 320 F g-1.
DFT SSA /
Db) /
E-SSA /
Wa) / nm
UE-SSAe)
ηd)
nc)
2
m g
-1
nm
m2 g-1
Cpg) /
Cch) /
F g-1
F g-1
df) / nm
2
-1
/m g
0.500
685
0.752
0
0
0
0
0.536
0
0.752
0
0
0
0
0.590
0
0.752
0
0
0
0
0.643
0
0.752
0
0
0
0
0.679
0
0.752
0
0
0
0
0.733
97
0.752
0
0
0
0
0.804
149
0.752
149
1
0.935
139
0.376
48
48
0.858
7
0.752
7
1
0.877
6
0.376
2
50
0.929
0
0.752
0
1
0.809
0
0.376
0
50
1.001
0
0.752
0
1
0.751
0
0.376
0
50
1.090
120
0.752
120
1
0.690
82
0.376
29
79
1.179
154
0.752
154
1
0.638
98
0.376
34
113
1.269
73
0.752
73
1
0.593
43
0.376
15
128
1.358
36
0.752
36
1
0.554
20
0.376
7
135
1.483
61
0.752
61
1
0.507
31
0.376
11
146
1.591
60
0.752
60
2
0.709
42
0.376
15
161
1.716
38
0.752
38
3
0.855
33
0.376
11
172
1.859
45
0.752
45
4
0.952
43
0.376
15
187
2.002
54
0.752
54
4
0.823
45
0.376
16
203
2.162
64
0.752
64
5
0.895
57
0.376
20
223
2.341
58
0.752
58
6
0.942
54
0.376
19
242
2.520
55
0.752
55
7
0.980
54
0.376
19
261
2.734
56
0.752
56
8
0.991
56
0.376
19
280
12
2.949
37
0.752
37
8
0.890
33
0.376
12
292
3.181
27
0.752
27
9
0.902
25
0.376
9
300
3.431
24
0.752
24
11
0.997
23
0.376
8
308
3.699
13
0.752
13
12
0.986
12
0.376
4
313
4.003
8
0.752
8
13
0.966
7
0.376
3
315
4.325
5
0.752
5
14
0.946
5
0.376
2
317
4.664
3
0.752
3
16
0.986
3
0.376
1
318
5.040
2
0.752
2
17
0.954
2
0.376
1
319
5.433
1
0.752
1
19
0.976
1
0.376
0
319
5.880
1
0.752
1
21
0.984
1
0.376
0
319
6.344
1
0.752
1
23
0.988
1
0.376
0
320
6.845
0
0.752
0
25
0.985
0
0.376
0
320
7.399
0
0.752
0
27
0.975
0
0.376
0
320
7.988
0
0.752
0
30
0.995
0
0.376
0
320
8.632
0
0.752
0
32
0.974
0
0.376
0
320
9.311
0
0.752
0
35
0.981
0
0.376
0
320
10.061
0
0.752
0
38
0.979
0
0.376
0
320
10.866
0
0.752
0
42
0.995
0
0.376
0
320
11.723
0
0.752
0
45
0.983
0
0.376
0
320
12.653
0
0.752
0
49
0.987
0
0.376
0
320
13.671
0
0.752
0
53
0.983
0
0.376
0
320
14.761
0
0.752
0
58
0.992
0
0.376
0
320
15.941
0
0.752
0
63
0.994
0
0.376
0
320
17.210
0
0.752
0
68
0.990
0
0.376
0
320
18.586
0
0.752
0
74
0.994
0
0.376
0
320
20.069
0
0.752
0
80
0.992
0
0.376
0
320
21.660
0
0.752
0
87
0.997
0
0.376
0
320
23.393
0
0.752
0
94
0.994
0
0.376
0
320
25.252
0
0.752
0
102
0.997
0
0.376
0
320
13
27.271
0
0.752
0
110
0.994
0
0.376
0
320
29.451
0
0.752
0
119
0.993
0
0.376
0
320
31.792
0
0.752
0
129
0.995
0
0.376
0
320
34.330
0
0.752
0
140
0.999
0
0.376
0
320
37.064
0
0.752
0
151
0.996
0
0.376
0
320
40.031
0
0.752
0
164
1.000
0
0.376
0
320
43.230
0
0.752
0
177
0.998
0
0.376
0
320
46.679
0
0.752
0
191
0.996
0
0.376
0
320
50.396
0
0.752
0
207
0.999
0
0.376
0
320
54.417
0
0.752
0
224
1.000
0
0.376
0
320
58.760
0
0.752
0
242
0.999
0
0.376
0
320
63.442
0
0.752
0
261
0.997
0
0.376
0
320
68.499
0
0.752
0
282
0.997
0
0.376
0
320
73.968
0
0.752
0
305
0.998
0
0.376
0
320
79.865
0
0.752
0
330
0.999
0
0.376
0
320
86.245
0
0.752
0
356
0.997
0
0.376
0
320
93.126
0
0.752
0
385
0.998
0
0.376
0
320
100.560
0
0.752
0
416
0.998
0
0.376
0
320
108.566
0
0.752
0
450
1.000
0
0.376
0
320
117.233
0
0.752
0
486
0.999
0
0.376
0
320
126.580
0
0.752
0
525
0.999
0
0.376
0
320
136.677
0
0.752
0
567
0.999
0
0.376
0
320
147.596
0
0.752
0
613
1.000
0
0.376
0
320
159.355
0
0.752
0
662
1.000
0
0.376
0
320
172.079
0
0.752
0
715
0.999
0
0.376
0
320
185.804
0
0.752
0
772
0.999
0
0.376
0
320
200.619
0
0.752
0
834
0.999
0
0.376
0
320
216.632
0
0.752
0
901
1.000
0
0.376
0
320
233.913
0
0.752
0
973
0.999
0
0.376
0
320
14
a)
W: pore width
b)
D: diameter of EID of electrolyte ions
c)
n: number of electrolyte ions in one cylindrical pore
η: proportion of true E-SSA
d)
e)
UE-SSA: utilized E-SSA
f)
d: thickness of electric double layer
g)
Cp: specific capacitance contributed by the pores at the given pore size
h)
Cc: cumulative specific capacitance of all the pores below the given pore size
15
Table S4 Detailed data for the calculation of E-SSA and the specific capacitance of (Cp) for
all the pores for the GAC electrode material in BMIMBF4 electrolyte. The cumulative specific
capacitance (Cc) is 143 F g-1.
Cp /
Cc /
F g-1
F g-1
0
0
0
0
0
0
0
1.107
0
0
0
0
0
1.107
0
0
0
0
0.679
0
1.107
0
0
0
0
0.733
97
1.107
0
0
0
0
0.804
149
1.107
0
0
0
0
0.858
7
1.107
0
0
0
0
0.929
0
1.107
0
0
0
0
1.001
0
1.107
0
0
0
0
1.090
120
1.107
0
0
0
0
1.179
154
1.107
154
1
0.939
144
0.554
30
30
1.269
73
1.107
73
1
0.872
64
0.554
13
43
1.358
36
1.107
36
1
0.815
30
0.554
6
49
1.483
61
1.107
61
1
0.746
46
0.554
9
58
1.591
60
1.107
60
1
0.696
42
0.554
9
67
1.716
38
1.107
38
1
0.645
25
0.554
5
72
1.859
45
1.107
45
1
0.596
27
0.554
6
78
2.002
54
1.107
54
1
0.553
30
0.554
6
84
2.162
64
1.107
64
1
0.512
33
0.554
7
91
2.341
58
1.107
58
2
0.709
41
0.554
8
99
2.520
55
1.107
55
3
0.860
47
0.554
10
109
2.734
56
1.107
56
4
0.953
53
0.554
11
120
E-SSA /
DFT SSA /
D/
m2 g-1
nm
m g
0.500
685
1.107
0
0.536
0
1.107
0.590
0
0.643
W / nm
UE-SSA /
η
n
2
d / nm
m2 g-1
-1
16
2.949
37
1.107
37
4
0.821
31
0.554
6
126
3.181
27
1.107
27
5
0.897
24
0.554
5
131
3.431
24
1.107
24
6
0.949
22
0.554
5
136
3.699
13
1.107
13
7
0.984
12
0.554
3
138
4.003
8
1.107
8
8
0.999
8
0.554
2
140
4.325
5
1.107
5
8
0.895
5
0.554
1
141
4.664
3
1.107
3
9
0.907
3
0.554
1
142
5.040
2
1.107
2
11
1.000
2
0.554
0
142
5.433
1
1.107
1
12
0.989
1
0.554
0
142
5.880
1
1.107
1
13
0.969
1
0.554
0
142
6.344
1
1.107
1
14
0.950
1
0.554
0
142
6.845
0
1.107
0
16
0.989
0
0.554
0
143
7.399
0
1.107
0
17
0.958
0
0.554
0
143
7.988
0
1.107
0
19
0.978
0
0.554
0
143
8.632
0
1.107
0
21
0.987
0
0.554
0
143
9.311
0
1.107
0
23
0.991
0
0.554
0
143
10.061
0
1.107
0
25
0.987
0
0.554
0
143
10.866
0
1.107
0
27
0.978
0
0.554
0
143
11.723
0
1.107
0
30
0.998
0
0.554
0
143
12.653
0
1.107
0
32
0.979
0
0.554
0
143
13.671
0
1.107
0
35
0.983
0
0.554
0
143
14.761
0
1.107
0
38
0.982
0
0.554
0
143
15.941
0
1.107
0
42
0.999
0
0.554
0
143
17.210
0
1.107
0
45
0.986
0
0.554
0
143
18.586
0
1.107
0
49
0.989
0
0.554
0
143
20.069
0
1.107
0
53
0.986
0
0.554
0
143
21.660
0
1.107
0
58
0.995
0
0.554
0
143
23.393
0
1.107
0
63
0.997
0
0.554
0
143
25.252
0
1.107
0
68
0.993
0
0.554
0
143
17
27.271
0
1.107
0
74
0.997
0
0.554
0
143
29.451
0
1.107
0
80
0.995
0
0.554
0
143
31.792
0
1.107
0
87
1.000
0
0.554
0
143
34.330
0
1.107
0
94
0.998
0
0.554
0
143
37.064
0
1.107
0
101
0.990
0
0.554
0
143
40.031
0
1.107
0
110
0.996
0
0.554
0
143
43.230
0
1.107
0
119
0.996
0
0.554
0
143
46.679
0
1.107
0
129
0.998
0
0.554
0
143
50.396
0
1.107
0
139
0.994
0
0.554
0
143
54.417
0
1.107
0
151
0.999
0
0.554
0
143
58.760
0
1.107
0
163
0.997
0
0.554
0
143
63.442
0
1.107
0
176
0.995
0
0.554
0
143
68.499
0
1.107
0
191
0.999
0
0.554
0
143
73.968
0
1.107
0
206
0.997
0
0.554
0
143
79.865
0
1.107
0
223
0.998
0
0.554
0
143
86.245
0
1.107
0
241
0.998
0
0.554
0
143
93.126
0
1.107
0
261
1.000
0
0.554
0
143
100.560
0
1.107
0
282
1.000
0
0.554
0
143
108.566
0
1.107
0
304
0.997
0
0.554
0
143
117.233
0
1.107
0
329
0.999
0
0.554
0
143
126.580
0
1.107
0
355
0.997
0
0.554
0
143
136.677
0
1.107
0
384
0.999
0
0.554
0
143
147.596
0
1.107
0
415
0.999
0
0.554
0
143
159.355
0
1.107
0
448
0.998
0
0.554
0
143
172.079
0
1.107
0
484
0.998
0
0.554
0
143
185.804
0
1.107
0
523
0.998
0
0.554
0
143
200.619
0
1.107
0
565
0.998
0
0.554
0
143
216.632
0
1.107
0
611
0.999
0
0.554
0
143
233.913
0
1.107
0
660
0.999
0
0.554
0
143
18
Table S5 Detailed data for the calculation of E-SSA and the specific capacitance of (Cp) for
all the pores for the GAC electrode material in 1M TEABF4/AN electrolyte. The cumulative
specific capacitance (Cc) is 169 F g-1.
E-SSA /
Cp /
D/
m2 g-1
nm
m g
0.500
685
0.684a)
0
0
0
0
0.536
0
0.684
0
0
0
0
0.590
0
0.684
0
0
0
0
0.643
0
0.684
0
0
0
0
0.679
0
0.684
0
0
0
0
0.733
97
0.684
97
1
0.934
90
0.342
23
23
0.804
149
0.684
149
1
0.851
126
0.342
32
54
0.858
7
0.684
7
1
0.797
5
0.342
1
55
0.929
0
0.684
0
1
0.736
0
0.342
0
55
1.001
0
0.684
0
1
0.683
0
0.342
0
55
1.090
120
0.684
120
1
0.627
75
0.342
19
74
1.179
154
0.684
154
1
0.580
89
0.342
22
96
1.269
73
0.684
73
1
0.539
39
0.342
10
106
1.358
36
1.320b)
36
1
0.972
35
0.660
5
111
1.483
61
1.320
61
1
0.890
55
0.660
7
118
1.591
60
1.320
60
1
0.830
50
0.660
6
124
1.716
38
1.320
38
1
0.769
30
0.660
4
128
1.859
45
1.320
45
1
0.710
32
0.660
4
132
2.002
54
1.320
54
1
0.659
36
0.660
5
137
2.162
64
1.320
64
1
0.610
39
0.660
5
142
2.341
58
1.320
58
1
0.564
32
0.660
4
146
2.520
55
1.320
55
1
0.524
29
0.660
4
150
2.734
56
1.320
56
2
0.767
43
0.660
6
156
W / nm
UE-SSA /
Cc /
DFT SSA /
η
n
2
d / nm
m2 g-1
-1
19
F g-1
F g-1
2.949
37
1.320
37
3
0.903
34
0.660
4
160
3.181
27
1.320
27
3
0.753
21
0.660
3
163
3.431
24
1.320
24
4
0.860
20
0.660
3
165
3.699
13
1.320
13
5
0.936
12
0.660
2
167
4.003
8
1.320
8
6
0.983
8
0.660
1
168
4.325
5
1.320
5
6
0.869
4
0.660
1
168
4.664
3
1.320
3
7
0.905
3
0.660
0
169
5.040
2
1.320
2
8
0.924
2
0.660
0
169
5.433
1
1.320
1
9
0.936
1
0.660
0
169
5.880
1
1.320
1
10
0.935
1
0.660
0
169
6.344
1
1.320
1
11
0.931
0
0.660
0
169
6.845
0
1.320
0
13
0.999
0
0.660
0
169
7.399
0
1.320
0
14
0.976
0
0.660
0
169
7.988
0
1.320
0
15
0.952
0
0.660
0
169
8.632
0
1.320
0
17
0.983
0
0.660
0
169
9.311
0
1.320
0
18
0.951
0
0.660
0
169
10.061
0
1.320
0
20
0.966
0
0.660
0
169
10.866
0
1.320
0
22
0.972
0
0.660
0
169
11.723
0
1.320
0
24
0.972
0
0.660
0
169
12.653
0
1.320
0
26
0.967
0
0.660
0
169
13.671
0
1.320
0
29
0.989
0
0.660
0
169
14.761
0
1.320
0
31
0.971
0
0.660
0
169
15.941
0
1.320
0
34
0.979
0
0.660
0
169
17.210
0
1.320
0
37
0.980
0
0.660
0
169
18.586
0
1.320
0
41
0.999
0
0.660
0
169
20.069
0
1.320
0
44
0.987
0
0.660
0
169
21.660
0
1.320
0
48
0.993
0
0.660
0
169
23.393
0
1.320
0
52
0.991
0
0.660
0
169
25.252
0
1.320
0
56
0.984
0
0.660
0
169
20
27.271
0
1.320
0
61
0.989
0
0.660
0
169
29.451
0
1.320
0
66
0.987
0
0.660
0
169
31.792
0
1.320
0
72
0.994
0
0.660
0
169
34.330
0
1.320
0
78
0.994
0
0.660
0
169
37.064
0
1.320
0
85
1.000
0
0.660
0
169
40.031
0
1.320
0
92
0.999
0
0.660
0
169
43.230
0
1.320
0
99
0.993
0
0.660
0
169
46.679
0
1.320
0
107
0.992
0
0.660
0
169
50.396
0
1.320
0
116
0.994
0
0.660
0
169
54.417
0
1.320
0
126
0.998
0
0.660
0
169
58.760
0
1.320
0
136
0.995
0
0.660
0
169
63.442
0
1.320
0
147
0.995
0
0.660
0
169
68.499
0
1.320
0
159
0.995
0
0.660
0
169
73.968
0
1.320
0
172
0.995
0
0.660
0
169
79.865
0
1.320
0
186
0.996
0
0.660
0
169
86.245
0
1.320
0
202
1.000
0
0.660
0
169
93.126
0
1.320
0
218
0.998
0
0.660
0
169
100.560
0
1.320
0
236
1.000
0
0.660
0
169
108.566
0
1.320
0
255
1.000
0
0.660
0
169
117.233
0
1.320
0
275
0.997
0
0.660
0
169
126.580
0
1.320
0
297
0.997
0
0.660
0
169
136.677
0
1.320
0
321
0.997
0
0.660
0
169
147.596
0
1.320
0
347
0.997
0
0.660
0
169
159.355
0
1.320
0
375
0.998
0
0.660
0
169
172.079
0
1.320
0
406
1.000
0
0.660
0
169
185.804
0
1.320
0
438
0.998
0
0.660
0
169
200.619
0
1.320
0
474
1.000
0
0.660
0
169
216.632
0
1.320
0
512
1.000
0
0.660
0
169
233.913
0
1.320
0
553
0.999
0
0.660
0
169
21
the diameter of bare TEA+
a)
the diameter of solvated TEA+ in AN system[5]
b)
22
Table S6 Detailed data for the calculation of E-SSA and the specific capacitance of (Cp) for
all the pores for the GAC electrode material in KOH electrolyte. The cumulative specific
capacitance (Cc) is 683 F g-1.
E-SSA /
Cp /
D/
m2 g-1
nm
m g
0.500
685
0.266a)
685
1
0.532
364
0.133
325
325
0.536
0
0.266
0
1
0.496
0
0.133
0
325
0.590
0
0.266
0
1
0.451
0
0.133
0
325
0.643
0
0.266
0
1
0.413
0
0.133
0
325
0.679
0
0.662b)
0
1
0.975
0
0.331
0
325
0.733
97
0.662
97
1
0.903
87
0.331
31
356
0.804
149
0.662
149
1
0.823
122
0.331
44
400
0.858
7
0.662
7
1
0.772
5
0.331
2
402
0.929
0
0.662
0
1
0.712
0
0.331
0
402
1.001
0
0.662
0
1
0.661
0
0.331
0
402
1.090
120
0.662
120
1
0.607
73
0.331
26
428
1.179
154
0.662
154
1
0.561
86
0.331
31
459
1.269
73
0.662
73
1
0.522
38
0.331
14
472
1.358
36
0.662
36
2
0.800
29
0.331
10
483
1.483
61
0.662
61
3
0.896
55
0.331
20
502
1.591
60
0.662
60
3
0.758
45
0.331
16
519
1.716
38
0.662
38
4
0.865
33
0.331
12
531
1.859
45
0.662
45
5
0.934
42
0.331
15
546
2.002
54
0.662
54
6
0.988
54
0.331
19
565
2.162
64
0.662
64
6
0.873
56
0.331
20
585
2.341
58
0.662
58
7
0.903
52
0.331
19
604
2.520
55
0.662
55
8
0.928
51
0.331
18
622
2.734
56
0.662
56
9
0.932
52
0.331
19
641
W / nm
UE-SSA /
Cc /
DFT SSA /
η
n
2
d / nm
m2 g-1
-1
23
F g-1
F g-1
2.949
37
0.662
37
10
0.935
35
0.331
13
653
3.181
27
0.662
27
11
0.932
25
0.331
9
662
3.431
24
0.662
24
13
0.999
24
0.331
8
671
3.699
13
0.662
13
14
0.980
12
0.331
4
675
4.003
8
0.662
8
15
0.953
7
0.331
3
678
4.325
5
0.662
5
17
0.984
5
0.331
2
680
4.664
3
0.662
3
18
0.953
3
0.331
1
681
5.040
2
0.662
2
20
0.967
2
0.331
1
681
5.433
1
0.662
1
22
0.975
1
0.331
0
682
5.880
1
0.662
1
24
0.972
1
0.331
0
682
6.344
1
0.662
1
26
0.967
1
0.331
0
682
6.845
0
0.662
0
29
0.991
0
0.331
0
682
7.399
0
0.662
0
31
0.972
0
0.331
0
682
7.988
0
0.662
0
34
0.980
0
0.331
0
682
8.632
0
0.662
0
37
0.980
0
0.331
0
683
9.311
0
0.662
0
40
0.976
0
0.331
0
683
10.061
0
0.662
0
44
0.988
0
0.331
0
683
10.866
0
0.662
0
48
0.992
0
0.331
0
683
11.723
0
0.662
0
52
0.992
0
0.331
0
683
12.653
0
0.662
0
56
0.985
0
0.331
0
683
13.671
0
0.662
0
61
0.989
0
0.331
0
683
14.761
0
0.662
0
66
0.987
0
0.331
0
683
15.941
0
0.662
0
72
0.994
0
0.331
0
683
17.210
0
0.662
0
78
0.994
0
0.331
0
683
18.586
0
0.662
0
84
0.988
0
0.331
0
683
20.069
0
0.662
0
92
1.000
0
0.331
0
683
21.660
0
0.662
0
99
0.994
0
0.331
0
683
23.393
0
0.662
0
107
0.993
0
0.331
0
683
25.252
0
0.662
0
116
0.995
0
0.331
0
683
24
27.271
0
0.662
0
126
0.998
0
0.331
0
683
29.451
0
0.662
0
136
0.996
0
0.331
0
683
31.792
0
0.662
0
147
0.996
0
0.331
0
683
34.330
0
0.662
0
159
0.996
0
0.331
0
683
37.064
0
0.662
0
172
0.996
0
0.331
0
683
40.031
0
0.662
0
186
0.996
0
0.331
0
683
43.230
0
0.662
0
201
0.996
0
0.331
0
683
46.679
0
0.662
0
218
0.999
0
0.331
0
683
50.396
0
0.662
0
235
0.996
0
0.331
0
683
54.417
0
0.662
0
254
0.996
0
0.331
0
683
58.760
0
0.662
0
275
0.998
0
0.331
0
683
63.442
0
0.662
0
297
0.997
0
0.331
0
683
68.499
0
0.662
0
321
0.998
0
0.331
0
683
73.968
0
0.662
0
347
0.998
0
0.331
0
683
79.865
0
0.662
0
375
0.998
0
0.331
0
683
86.245
0
0.662
0
405
0.998
0
0.331
0
683
93.126
0
0.662
0
438
0.999
0
0.331
0
683
100.560
0
0.662
0
473
0.998
0
0.331
0
683
108.566
0
0.662
0
511
0.998
0
0.331
0
683
117.233
0
0.662
0
552
0.998
0
0.331
0
683
126.580
0
0.662
0
597
1.000
0
0.331
0
683
136.677
0
0.662
0
645
1.000
0
0.331
0
683
147.596
0
0.662
0
696
0.999
0
0.331
0
683
159.355
0
0.662
0
752
0.999
0
0.331
0
683
172.079
0
0.662
0
813
1.000
0
0.331
0
683
185.804
0
0.662
0
878
1.000
0
0.331
0
683
200.619
0
0.662
0
948
1.000
0
0.331
0
683
216.632
0
0.662
0
1024
1.000
0
0.331
0
683
233.913
0
0.662
0
1106
1.000
0
0.331
0
683
25
the diameter of bare K+ [6]
a)
the diameter of solvated K+ in aqueous system [7]
b)
26
Table S7 DFT SSA, E-SSA and the corresponding Cth of various sp2 carbon materials in
different electrolyte systems for several of the representative bulk sp2 materials prepared in
this work.
DFT
KOH
EMIMBF4
BMIMBF4
TEABF4/AN
2
bulk sp carbon
SSA
E-SSA
Cth
E-SSA
Cth
E-SSA
Cth
E-SSA
Cth
m2 g-1
m2 g-1
F g-1
m2 g-1
F g-1
m2 g-1
F g-1
m2 g-1
F g-1
P@16GA-1100
760
760
101
582
75
422
54
614
73
RP20
1255
1255
160
739
96
415
46
817
112
GA
1361
1361
179
748
98
544
70
781
92
HXAC
1035
1035
119
846
101
483
53
935
124
PA
1486
1486
191
956
116
390
44
1009
129
P@8GA
1571
1571
195
1058
129
654
74
1088
132
BA
1508
1508
195
1230
163
1034
134
1305
146
GAC
1934
1934
273
1153
139
878
102
1250
147
P@24GA
1779
1779
234
1439
196
1125
143
1509
182
L@24GA
1952
1952
254
1558
215
1347
179
1636
184
S@24GA
2105
2105
278
1631
209
1402
179
1738
195
P@16GA
2224
2224
290
1686
216
1391
176
1759
192
materials
27
Table S8 The Cex of various sp2 carbon materials in different electrolyte systems
6 M KOH
EMIMBF4
Cex
materials
BMIMBF4
Cex
materials
F g-1
P@16GA-
P@16GA-
1100
P@16GA-
R
53
1100
P@16GA171
Cex
materials
F g-1
71
1100
P@16GA-
Cex
materials
F g-1
92
1 M TEABF4/AN
F g-1
P@16GA1100
53
P@16GA125
8R
102
GA
92
8R
RP20
143
RP20
91
RP20
45
RP20
94
P@8GA
209
P@8GA
136
P@8GA
80
P@8GA
119
GAC
244
GAC
139
GAC
108
GAC
140
P@24GA
212
PA
120
PA
38
PA
112
S@24GA
281
S@24GA
216
GA
75
S@24GA
197
P@16GA
296
P@16GA
231
P@24GA
144
P@16GA
202
BA
183
L@24GA
213
BA
133
V@20GA
174
28
Table S9 Reaction Gibbs free energy change ΔrG per carbon atom of different
aromatic/polyaromatic compounds.
Aromatic/polyaromatic
Number of carbon atoms
ΔrG/n / kcal mol-1
compound
(n)
benzene
6
-2.08
naphathlene
10
-1.14
anthracene
14
-0.79
phenanthrene
14
-0.90
pyrene
16
-0.77
graphene0505
20
-0.58
Coronene
24
-0.48
graphene1010
54
-0.21
graphene1515
104
-0.14
graphene2020
170
-0.09
graphene2525
252
-0.06
29
Table S10 The corresponding best capacitance in different electrolyte systems for the E-SSA
limit of about 3500–3700 m2 g-1 based on the linear relationship between capacitance and ESSA.
Electrolyte system
Linear relationship
Capacitance / F g-1
EMIMBF4
Y = 0.144 X - 19.2
484.8–513.6
KOH
Y = 0.141 X - 24.4
469.1–497.3
BMIMBF4
Y = 0.137 X - 8.96
470.5–497.9
TEABF4/AN
Y = 0.122 X - 11.5
415.5–439.9
30
References
1 Zhang L, Zhang F, Yang X, et al. Porous 3d graphene-based bulk materials with exceptional
high surface area and excellent conductivity for supercapacitors. Sci Rep, 2013, 3.
2 Zhang L, Yang X, Zhang F, et al. Controlling the effective surface area and pore size
distribution of sp2 carbon materials and their impact on the capacitance performance of
these materials. J Am Chem Soc, 2013, 135(15): 5921-5929
3 Becke AD. Density‐functional thermochemistry. Iii. The role of exact exchange. J Chem
Phys, 1993, 98(7): 5648-5652
4 Lee C, Yang W, Parr RG. Development of the colle-salvetti correlation-energy formula into
a functional of the electron density. Phys Rev B, 1988, 37(2): 785-789
5 Huang J, Sumpter BG, Meunier V. A universal model for nanoporous carbon supercapacitors
applicable to diverse pore regimes, carbon materials, and electrolytes. Chem-Eur J, 2008,
14(22): 6614-6626
6 Israelachvili JN. Intermolecular and surface forces, third edition, USA: Academic Press,
2011. 79
7 Volkov AG, Paula S, Deamer DW. Two mechanisms of permeation of small neutral
molecules and hydrated ions across phospholipid bilayers. Bioelectrochem Bioenerg, 1997,
42(2): 153-160
8 Simon P, Gogotsi Y. Materials for electrochemical capacitors. Nat Mater, 2008, 7(11): 845854
9 Singh T, Kumar A. Static dielectric constant of room temperature ionic liquids: Internal
pressure and cohesive energy density approach. J Phys Chem B, 2008, 112(41): 1296812972
10 Chmiola J, Yushin G, Gogotsi Y, et al. Anomalous increase in carbon capacitance at pore
sizes less than 1 nanometer. Science, 2006, 313(5794): 1760-1763
11 Ania CO, Pernak J, Stefaniak F, et al. Polarization-induced distortion of ions in the pores of
carbon electrodes for electrochemical capacitors. Carbon, 2009, 47(14): 3158-3166
12 Lin R, Taberna PL, Chmiola J, et al. Microelectrode study of pore size, ion size, and
solvent effects on the charge/discharge behavior of microporous carbons for electrical
double-layer capacitors. J Electrochem Soc, 2009, 156(1): A7-A12
13 Dueren T, Millange F, Ferey G, et al. Calculating geometric surface areas as a
characterization tool for metal-organic frameworks. J Phys Chem C, 2007, 111(42): 1535015356
31
14 Connolly ML. Solvent-accessible surfaces of proteins and nucleic acids. Science, 1983,
221(4612): 709-713
32