Supplementary Information Table S1. CB/PVDF porosity estimation. The values correspond to the average of a minimum of three measurements and the theoretical densities of PVDF and CB are assumed 1.49 g/cm 3 , and 1.90 g/cm 3 . Total Initia l Compresse d Init ial Fina l Final Theoreti cal Final Sampl e weigh t thickn ess thickness area area volum e volume porosi ty [mg] [ μm ¿ [ μm ¿ [mm 2 ] [mm 3 ] [mm 3 ] [mm 3 ] [%] 1 20.5 336.7 - 75.3 - 25.4 12.5 50.8 2 22.1 398.8 200.0 81.0 92.7 18.5 13.4 27.5 3 47.1 421.4 185.3 124. 8 160. 6 29.8 28.6 3.8 Table S2. PVDF volume expansion after 1 hour soaked in the electrolyte. Values correspond to the average of a minimum of three measurements. Sampl e Dry weig ht [mg] Dry thickn ess [ μm ¿ Dry area [mm 2 ] Dry volum e [mm 3 ] Dry densit y [mg/mm 3 ] Wet thickn ess [ μm ¿ Wet area [mm 2 ] Wet volum e [mm 3 ] Volume expans ion [%] 1 11.1 49.6 157. 0 7.8 1.43 54.3 187. 8 10.2 30.8 2 6.1 69.0 62.5 4.3 1.42 75.4 74.6 5.6 30.5 1
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Supplementary Information
Table S1. CB/PVDF porosity estimation. The values correspond to the average of a minimum of three measurements and the theoretical densities of PVDF and CB are assumed 1.49 g/cm3, and 1.90 g/cm3.
Total Initial Compressed Initial Final Final Theoretical FinalSample weight thickness thickness area area volume volume porosity
[mg] [μm¿ [μm¿ [mm2] [mm3] [mm3] [mm3] [%]1 20.5 336.7 - 75.3 - 25.4 12.5 50.82 22.1 398.8 200.0 81.0 92.7 18.5 13.4 27.53 47.1 421.4 185.3 124.8 160.6 29.8 28.6 3.8
Table S2. PVDF volume expansion after 1 hour soaked in the electrolyte. Values correspond to the average of a minimum of three measurements.
SampleDry
weight[mg]
Dry thickness
[μm¿
Dry area
[mm2]
Dry volume [mm3]
Dry density
[mg/mm3]
Wet thickness
[μm¿
Wet area
[mm2]
Wet volume[mm3]
Volume expansion
[%]1 11.1 49.6 157.0 7.8 1.43 54.3 187.8 10.2 30.82 6.1 69.0 62.5 4.3 1.42 75.4 74.6 5.6 30.5
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19Test #
0
10
20
30
40
50
60
70(a)
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
Test #
0
10
20
30
40
50
60
70(b)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19Test #
0
10
20
30
40
50
60
70(c)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Test #
0
10
20
30
40
50
60
70(d)
Figure S1. Reduced stiffness of individual tests for (a) dry NMC particles, (b) wet NMC particles, (c) dry NMC pellet and (b) wet NMC pellet. The red line indicates the median and the
bottom and top edges of the blue box indicate the 25th (Q 1) and 75th (Q 3) percentiles, respectively. The blue whiskers extend to S>Q 3+3 IQR and S<Q 1−3 IQR, and data points
outside this range are considered outliers (pop-in’s) and indicated by the red plus symbol.
2
Figure S2. Elastic modulus (a) and hardness (b) of PVDF film under dry and wet condition as a function of the indentation depth. The shaded areas represent the standard deviations.
3
0 500 1000 1500 20000
1
2
3
4 e=50.8% e=27.5% e=3.8%
Mod
ulus
[GP
a]
Indentation depth [nm]
a
0 500 1000 1500 2000
0.0
0.2
0.4
0.6
0.8
1.0 e=50.8% e=27.5% e=3.8%
Mod
ulus
[GP
a]
Indentation depth [nm]
b
0 500 1000 1500 20000.00
0.05
0.10
0.15
0.20 e=50.8% e=27.5% e=3.8%
Har
dnes
s[G
Pa]
Indentation depth [nm]
c
0 500 1000 1500 20000.00
0.05
0.10
Har
dnes
s[G
Pa]
Indentation depth [nm]
e=50.8% e=27.5% e=3.8%
d
Figure S3. Elastic modulus and hardness of CB/PVDF film of different porosities under dry (a, c) and wet condition (b, d) as a function of the indentation depth. The shaded areas represent the standard deviations.
4
0.096
0.192
0.2890.248
Dry Wet Dry Wet
Particle Pellet
0.0
0.2
0.4
0.6
0.8
1.0
1.2
p=0.46
p=0.027
Val
id te
sts
ratio
[-]
a hmin = 50nm 25%~75% Range within 1.5IQR Median Line Mean
Frac
ture
toug
hnes
s [M
Pa
m1/
2 ]
0.0
0.2
0.4
0.6
0.8
1.0
0.104
0.2120.298 0.291
Dry Wet Dry Wet
Particle Pellet
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
p=0.88
p=0.007
Val
id te
sts
ratio
[-]
b hmin = 100nm
Frac
ture
toug
hnes
s [M
Pa
m1/
2 ]
0.0
0.2
0.4
0.6
0.8
1.0
0.126
0.2910.360
0.321
Dry Wet Dry Wet
Particle Pellet
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
p=0.011 p=0.48
Val
id te
sts
ratio
[-]
c hmin = 150nm
Frac
ture
toug
hnes
s [M
Pa
m1/
2 ]
0.0
0.2
0.4
0.6
0.8
1.0
Figure S4. Sensitivity of fracture toughness measurements on user-defined hmin. The ratio of valid (kept) number of tests to the total number of tests for each configuration is indicated by the
green square symbol (right y-axis).
5
a
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #1
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
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P [m
N]
Test #2
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
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0.2
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1
P [m
N]
Test #3
0 100 200h [nm]
0
10
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50
Sr [-
]
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0.5
1
1.5
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2.5
P [m
N]
Test #4
0 100 200 300h [nm]
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Sr [-
]
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1
2
3
P [m
N]
Test #5
0 100 200 300h [nm]
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Sr [-
]
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4
5
P [m
N]
Test #6
0 100 200h [nm]
0
10
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30
40
50S
r [-]
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P [m
N]
Test #7
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
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0.5
1
P [m
N]
Test #8
0 100 200 300h [nm]
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50
Sr [-
]
0
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4
P [m
N]
Test #9
0 100 200 300h [nm]
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50
Sr [-
]
0
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3
4
P [m
N]
Test #10
0 100 200h [nm]
0
10
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50
Sr [-
]
0
1
2
3
P [m
N]
Test #11
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #12
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #13
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #14
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #15
0 50 100 150 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #16
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
2
P [m
N]
Test #17
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #18
0 50 100h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
0.6
0.8
1
P [m
N]
Test #19
b
0 100 200h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #1
0 50 100 150h [nm]
0
0.1
0.2
0.3
0.4
0.5
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
P [m
N]
Test #2
0 50 100 150h [nm]
0
0.1
0.2
0.3
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Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
1
P [m
N]
Test #3
0 100 200h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #4
0 100 200 300h [nm]
0
0.2
0.4
0.6
0.8
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #5
0 100 200 300h [nm]
0
0.2
0.4
0.6
0.8
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
5
P [m
N]
Test #6
0 100 200h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #7
0 50 100 150h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #8
0 100 200 300h [nm]
0
0.05
0.1
0.15
0.2
0.25
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #9
0 100 200 300h [nm]
0
0.2
0.4
0.6
0.8
1
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #10
0 100 200h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #11
0 100 200h [nm]
0
0.05
0.1
0.15
0.2
0.25
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #12
0 100 200h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #13
0 50 100 150h [nm]
0
0.2
0.4
0.6
0.8
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #14
0 100 200h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
2.5
P [m
N]
Test #15
0 50 100 150 200h [nm]
0
0.1
0.2
0.3
0.4
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #16
0 100 200h [nm]
0
0.05
0.1
0.15
0.2
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
P [m
N]
Test #17
0 50 100 150h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #18
0 50 100h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
1
P [m
N]
Test #19
Figure S5. Test results for dry NMC pellet as a function of indentation depth. The right y axis shows the load (orange line). (a) A pop-in is detected when the reduced stiffness (blue straight
line) is larger than the Q 3+3 IQR cut-off (blue dashed line). (b) The first five data points following the pop-in (green line) are used for the calculation of the fracture toughness (blue
circle).
6
a
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #1
0 50 100h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #2
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
4
P [m
N]
Test #3
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
4
P [m
N]
Test #4
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #5
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
4
P [m
N]
Test #6
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #7
0 200 400 600h [nm]
0
10
20
30
40
50
Sr [-
]
0
2
4
6
8
P [m
N]
Test #8
0 200 400h [nm]
0
10
20
30
40
50
Sr [-
]
0
2
4
6
P [m
N]
Test #9
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
4
P [m
N]
Test #10
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
4
P [m
N]
Test #11
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #12
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #13
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
2
P [m
N]
Test #14
0 100 200 300h [nm]
0
10
20
30
40
50S
r [-]
0
1
2
3
P [m
N]
Test #15
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
P [m
N]
Test #16
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.1
0.2
0.3
0.4
P [m
N]
Test #17
0 50 100h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
P [m
N]
Test #18
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
4
P [m
N]
Test #19
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #20
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5P
[mN
]
Test #21
b
0 100 200 300h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #1
0 50 100h [nm]
0
0.05
0.1
0.15
0.2
0.25
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #2
0 100 200 300h [nm]
0
0.2
0.4
0.6
0.8
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #3
0 100 200 300h [nm]
0
0.1
0.2
0.3
0.4
0.5
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #4
0 100 200h [nm]
0
0.05
0.1
0.15
0.2
0.25 K
c [MP
a.m
1/2 ]
0
1
2
3
P [m
N]
Test #5
0 100 200 300h [nm]
0
0.05
0.1
0.15
0.2
0.25
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #6
0 100 200h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #7
0 200 400 600h [nm]
0
0.1
0.2
0.3
0.4
0.5
Kc [M
Pa.
m1/
2 ]
0
2
4
6
8
P [m
N]
Test #8
0 200 400h [nm]
0
0.1
0.2
0.3
0.4
Kc [M
Pa.
m1/
2 ]
0
2
4
6
P [m
N]
Test #9
0 100 200 300h [nm]
0
0.1
0.2
0.3
0.4
0.5
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #10
0 100 200 300h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4 P
[mN
]
Test #11
0 100 200h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #12
0 100 200 300h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #13
0 100 200h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
P [m
N]
Test #14
0 100 200 300h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #15
0 50 100 150h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #16
0 50 100 150h [nm]
0
0.02
0.04
0.06
Kc [M
Pa.
m1/
2 ]
0
0.1
0.2
0.3
0.4
P [m
N]
Test #17
0 50 100h [nm]
0
0.5
1
1.5
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #18
0 100 200 300h [nm]
0
0.1
0.2
0.3
0.4
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #19
0 100 200h [nm]
0
0.2
0.4
0.6
0.8
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #20
0 50 100 150h [nm]
0
0.1
0.2
0.3
0.4
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #21
Figure S6. Test results for wet NMC pellet as a function of indentation depth. The right y axis shows the load (orange line). (a) A pop-in is detected when the reduced stiffness (blue straight
line) is larger than the Q 3+3 IQR cut-off (blue dashed line). (b) The first five data points following the pop-in (green line) are used for the calculation of the fracture toughness (blue
circle).
7
a
0 200 400h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
P [m
N]
Test #1
0 50 100h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.05
0.1
0.15
P [m
N]
Test #2(negative crack)
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
P [m
N]
Test #3
0 200 400h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
4
P [m
N]
Test #4
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
P [m
N]
Test #5
0 50 100h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.05
0.1
P [m
N]
Test #6
0 100 200 300h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
2
P [m
N]
Test #7
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
P [m
N]
Test #8
0 200 400h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #9
0 50 100h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
0.6
P [m
N]
Test #10
0 200 400h [nm]
0
10
20
30
40
50
Sr [-
]
0
2
4
P [m
N]
Test #11(no pop-in)
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #12
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]0
0.2
0.4
0.6
0.8
P [m
N]
Test #13
0 50 100h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
P [m
N]
Test #14
0 100 200h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #15
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #16
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #17
0 200 400h [nm]
0
10
20
30
40
50
Sr [-
]
0
1
2
3
P [m
N]
Test #18
0 50 100 150h [nm]
0
10
20
30
40
50
Sr [-
]
0
0.2
0.4
0.6
P [m
N]
Test #19
b
0 200 400h [nm]
0
0.02
0.04
0.06
0.08
Kc [M
Pa.
m1/
2 ]
0
1
2
P [m
N]
Test #1
0 50 100h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
0.05
0.1
0.15
P [m
N]
Test #2(negative crack)
0 100 200h [nm]
0
0.02
0.04
0.06
0.08
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #3
0 200 400h [nm]
0
0.05
0.1
0.15
Kc [M
Pa.
m1/
2 ]
0
1
2
3
4
P [m
N]
Test #4
0 50 100 150h [nm]
0
0.05
0.1
0.15
0.2
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #5
0 50 100h [nm]
0
2
4
Kc [M
Pa.
m1/
2 ]
10-3
0
0.05
0.1
P [m
N]
Test #6
0 100 200 300h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
2
P [m
N]
Test #7
0 50 100 150h [nm]
0
0.02
0.04
0.06
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
P [m
N]
Test #8
0 200 400h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #9
0 50 100h [nm]
0
0.1
0.2
0.3 K
c [MP
a.m
1/2 ]
0
0.2
0.4
0.6
P [m
N]
Test #10
0 200 400h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
2
4
P [m
N]
Test #11(no pop-in)
0 100 200h [nm]
0
0.05
0.1
0.15
0.2
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #12
0 100 200h [nm]
0
0.02
0.04
0.06
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #13
0 50 100h [nm]
0
0.05
0.1
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
P [m
N]
Test #14
0 100 200h [nm]
0
0.05
0.1
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #15
0 50 100 150h [nm]
0
0.1
0.2
0.3
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #16
0 50 100 150h [nm]
0
0.05
0.1
0.15
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #17
0 200 400h [nm]
0
0.1
0.2
0.3
0.4
Kc [M
Pa.
m1/
2 ]
0
1
2
3
P [m
N]
Test #18
0 50 100 150h [nm]
0
0.2
0.4
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
P [m
N]
Test #19
Figure S7. Test results for dry NMC particles as a function of indentation depth. The right y axis shows the load (orange line). (a) A pop-in is detected when the reduced stiffness (blue straight
line) is larger than the Q 3+3 IQR cut-off (blue dashed line). (b) The first five data points following the pop-in (green line) are used for the calculation of the fracture toughness (blue
circle).
8
a
0 100 200 300 400 500h [nm]
0
20
40S
r [-]
0
2
4
6
P [m
N]
Test #1(no pop-in)
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #2
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
P [m
N]
Test #3
0 100 200 300 400 500h [nm]
0
20
40
Sr [-
]
0
2
4
6
P [m
N]
Test #4(no pop-in)
0 50 100 150 200h [nm]
0
20
40
Sr [-
]
0
0.5
1
P [m
N]
Test #5
0 50 100 150 200h [nm]
0
20
40
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #6
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.5
1
P [m
N]
Test #7
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
P [m
N]
Test #8
0 100 200 300h [nm]
0
20
40
Sr [-
]
0
1
2
3
P [m
N]
Test #9
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.5
1
P [m
N]
Test #10
0 100 200h [nm]
0
20
40
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #11
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
P [m
N]
Test #12
0 100 200 300 400 500h [nm]
0
20
40
Sr [-
]
0
2
4
6
P [m
N]
Test #13(no pop-in)
0 100 200 300h [nm]
0
20
40
Sr [-
]
0
1
2
P [m
N]
Test #14
0 50 100 150 200h [nm]
0
20
40
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #15
0 100 200 300h [nm]
0
20
40
Sr [-
]
0
0.5
1
1.5
P [m
N]
Test #16
0 50 100 150 200h [nm]
0
20
40
Sr [-
]
0
0.5
1
P [m
N]
Test #17
0 100 200 300h [nm]
0
20
40
Sr [-
]
0
1
2
P [m
N]
Test #18
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #19
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.5
1
P [m
N]
Test #20
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #21
0 50 100 150 200h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #22
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #23
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #24
0 50 100 150h [nm]
0
20
40
Sr [-
]
0
0.2
0.4
0.6
P [m
N]
Test #25
b
0 200 400h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
2
4
6
P [m
N]
Test #1(no pop-in)
0 50 100 150h [nm]
0
0.05
0.1
0.15
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #2
0 50 100 150h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
P [m
N]
Test #3
0 100 200 300 400 500h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
2
4
6
P [m
N]
Test #4(no pop-in)
0 100 200h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #5
0 100 200h [nm]
0
0.2
0.4
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #6
0 50 100 150h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #7
0 50 100 150h [nm]
0
0.05
0.1
0.15
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
P [m
N]
Test #8
0 100 200 300h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
1
2
3 P
[mN
]
Test #9
0 50 100 150h [nm]
0
0.05
0.1
0.15
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #10
0 100 200h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #11
0 50 100 150h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
P [m
N]
Test #12
0 200 400h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
2
4
6
P [m
N]
Test #13(no pop-in)
0 100 200 300h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
1
2
P [m
N]
Test #14
0 100 200h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #15
0 100 200 300h [nm]
0
0.01
0.02
0.03
Kc [M
Pa.
m1/
2 ]
0
0.5
1
1.5
P [m
N]
Test #16
0 50 100 150 200h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #17
0 100 200 300h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
1
2
P [m
N]
Test #18
0 50 100 150h [nm]
0
0.2
0.4
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #19
0 50 100 150h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
0.5
1
P [m
N]
Test #20
0 50 100 150h [nm]
0
0.2
0.4
0.6
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #21
0 50 100 150 200h [nm]
0
0.05
0.1
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #22
0 50 100 150h [nm]
0
0.1
0.2
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #23
0 50 100 150h [nm]
0
0.5
1
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
0.8
P [m
N]
Test #24
0 50 100 150h [nm]
0
0.2
0.4
Kc [M
Pa.
m1/
2 ]
0
0.2
0.4
0.6
P [m
N]
Test #25
Figure S8. Test results for wet NMC particles as a function of indentation depth. The right y axis shows the load (orange line). (a) A pop-in is detected when the reduced stiffness (blue straight
line) is larger than the Q 3+3 IQR cut-off (blue dashed line). (b) The first five data points following the pop-in (green line) are used for the calculation of the fracture toughness (blue
circle).
9
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