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                            Performance evaluation of a novel asymmetric capacitor using a light-weight, carbon foam supported nickel electrode
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Michigan Technological University Michigan Technological University

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Dissertations, Master's Theses and Master's
Reports

2011

Performance evaluation of a novel asymmetric capacitor using a Performance evaluation of a novel asymmetric capacitor using a

light-weight, carbon foam supported nickel electrode light-weight, carbon foam supported nickel electrode

Padmanaban Sasthan Kuttipillai
Michigan Technological University

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Copyright 2011 Padmanaban Sasthan Kuttipillai

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Kuttipillai, Padmanaban Sasthan, "Performance evaluation of a novel asymmetric capacitor using a light-
weight, carbon foam supported nickel electrode", Master's Thesis, Michigan Technological University,
2011.
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Page 2

PERFORMANCE EVALUATION OF A NOVEL ASYMMETRIC CAPACITOR

USING A LIGHT-WEIGHT, CARBON FOAM SUPPORTED NICKEL

ELECTRODE



by

Padmanaban Sasthan Kuttipillai





A THESIS


Submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

(Chemistry)













MICHIGAN TECHNOLOGICAL UNIVERSITY


2011





© 2011 Padmanaban Sasthan Kuttipillai

Page 42

32





In electrical engineering these two quantities, voltage and current, can be viewed as two

phase vectors (phasors) which have amplitude, either E or I, and frequency with an angle

of rotation .

Let us apply these concepts to the analysis of some simple circuits. Consider first a

pure resistance, R, across which a sinusoidal voltage, Et = E0 , is applied. Since

Ohm's law, E= IR, always holds, the current I is (Et/R) sin ( ), and it has the same phase

as the voltage, meaning the phase angle is zero, as shown in Fig. 3.4



Figure 3.4. Current and voltage response of AC signal for a resistor.40

Now we can apply those concepts to a pure capacitance, C. The fundamental

relation of interest is then, eqn. 3.12.

q = C E (3.12)


The current flow in the capacitor can be calculated by differentiating eqn. 3.12 with respect

to time to give eqn. 3.13.

dq/dt = C (dEt/dt) (3.13)

Page 43

33





The rate of change in charge is known as current, and by substituting eqn. 3.10 into

equation 3.13, eqn. 3.14 is obtained.

I = C E cos ( ) (3.14)


Current, I, can also be represented using eqn. 3.11 where = for a capacitor as written

in eqn. 3.15 and eqn. 3.16, where Xc = 1/( C) is the capacitive reactance.




I C



(3.15)

I Xc (3.16)



From equation 3.16 it is clear that the phase angle is and the current leads the

voltage in the capacitor, as shown in Fig.3.5.



Figure 3.5. Current and voltage response of a capacitor for an AC signal.40

In electrical circuit analysis, it is customary to use complex notation (j = 1) to

plot these quantities. The current phasor is usually plotted along the abscissa and the

Page 83

73



Cycle life

For cycle life testing of the capacitor, the cell has been cycled at 0.08 A/cm2. After

the 1500th cycle the specific capacitance started decreasing slowly, and by the end of cycle

4000, the capacitance dropped 8.8 % relative to cycle 1 (see Figure C.3.).

.

Figure C.3. Specific capacitance vs. cycle number.

Impedance Studies

Impedance studies were carried out using a model CH-660A Electrochemical Work

Station. (frequency range 1 mHz to 10 KHz); the AC signal amplitude was set at 0.005V.

The experimental and calculated impedance data for the cell is plotted in a Nyquist plot in

Fig. C.4. The equivalent circuit used for the impedance analysis is shown in Fig.3.8, and

the best fit circuit parameters calculated for this circuit are listed in Table 3. The

experimental error in the impedance data is 2.05 % for this model and the chi-squared

value is 4.20 x 10-4.

17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

0 500 1000 1500 2000 2500 3000 3500 4000

Sp
ec

ifi
c

Ca
pa

ci
ta

nc
e

(F
/g

)

Cycle Number

Page 84

74







Figure C.5. Experimental (red circles) and calculated (green squares) impedance data,
fitted with parameters in Table C.4.

Table C.4
Circuit parameters based upon fitting the impedance data in Fig. C.5 using

Conway’s circuit which includes pseudo-capacitance (refer Fig. 3.8).
Index Parameter Value

1 Inductance L ( Henri/cm2) 6.92E-6
2 Solution resistance Rs (Ohm/cm2) 1.734
3 Double layer
capacitance Cdl (F/cm

2) 1.071

4 Faradic resistance RF (Ohm/cm2) 0.5135
5 Pseudo-capacitance (C¢) (F/cm2) 4.125
6 Leakage resistance Rs’ (Ohm/cm2) 8.142



Z , Measured.
Z , Calculated.

Commercial Carbon Sheet Symmetric Capacitor
Model: LR(C(R(CR))) Wgt : Modulus

Z ' (ohm-sq. cm)
11 10 9 8 7 6 5 4 3 2 1 0

Z”

5

4

3

2

1

0

-1
6.64k 5.47k

811
1.43

143m
54.9m

37.4m
25.5m 21.1m

14.3m

9.77m
8.07m

6.64m
5.49m

4.54m

3.74m
3.09m

zz2.55m

2.1m
1.74m

1.43m
1.18m








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