Mohammad Hossein Dehghan1, Zahra Yavari1, Meissam Noroozifar1. 1. Department of Statistics, Department of Chemistry, and Renewable Energies Research Institute, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran.
Abstract
In this work, the catalytic activity of modified glassy carbon electrodes with xPd-yLaNi0.5Fe0.5O3-chitosan as an anodic catalyst for the polymeric fuel cell was investigated with cyclic voltammetry and controlled potential coulometry techniques; x and y are the mass loading of noble metal and mixed oxide, respectively. For the first time, the statistical regression mixed models were used to compare the electrocatalytic ability of nanocomposites in a fuel cell. The nonlinear regression model of y i,j = f(x i , (s j )) + ε i was considered and simulated, where X i is a random variable, s j is a covariate value, ε i is a normal random error variable, and θ is a P-dimensional vector of parameters of the mentioned model. A strategy to make a mixed model was proposed by using the maximum likelihood or mean square error methods. Then, the appropriate linear and nonlinear models were applied to the electrochemical results. The equations of current density vs time were obtained via the fitting and simulation of experimental data at different potentials and mass loadings of components. The amounts of transferred charge during the methanol oxidation were calculated vs time through the integration of mentioned equations at different potentials and mass loadings of components.
In this work, the catalytic activity of modified glassy carbon electrodes with xPd-yLaNi0.5Fe0.5O3-chitosan as an anodic catalyst for the polymeric fuel cell was investigated with cyclic voltammetry and controlled potential coulometry techniques; x and y are the mass loading of noble metal and mixed oxide, respectively. For the first time, the statistical regression mixed models were used to compare the electrocatalytic ability of nanocomposites in a fuel cell. The nonlinear regression model of y i,j = f(x i , (s j )) + ε i was considered and simulated, where X i is a random variable, s j is a covariate value, ε i is a normal random error variable, and θ is a P-dimensional vector of parameters of the mentioned model. A strategy to make a mixed model was proposed by using the maximum likelihood or mean square error methods. Then, the appropriate linear and nonlinear models were applied to the electrochemical results. The equations of current density vs time were obtained via the fitting and simulation of experimental data at different potentials and mass loadings of components. The amounts of transferred charge during the methanol oxidation were calculated vs time through the integration of mentioned equations at different potentials and mass loadings of components.
For
the last few decades, a significant percentage of research
on fuel cells was focused on noble-metal nanostructures as suitable
electrocatalysts toward the oxidation of liquid fuels with remarkable
features, including quantum, structure, size, and surface effects.[1−3] Up to now, platinum and ruthenium are regarded as effective electrocatalysts
toward liquid fuel oxidation.[4,5] In spite of this, some
main factors restricting the performance of such elements as electrocatalyst
are the minor availability, too much high price, susceptibility to
poisoning by the oxidation intermediates, and difficulty in durability
due to sintering and dissolution that may reduce the active area of
the electrocatalyst surface.[6,7] To overcome this bottleneck,
remarkable efforts have been made on introducing strong substitutes
for catalysts containing platinum and ruthenium to serve as the anode
electrode in the fuel cells.[8−10] As an appropriate alternative,
palladium is considered due to its comparatively low price and lower
poisoning.[11−14] In the following discussion are the investigations conducted for
the incorporation of mixed oxide-containing transition metals (M:
La, Sr, Mn, Fe,...) with a large number of oxygen vacancies in noble-metal
catalysts so that such oxides can be good candidates for replacing
noble metals in direct alcohol fuel cells as anodic electrodes.[15,16] The studies showed the decrease in the onset potential related to
an upgrade in the kinetics of alcohol electrooxidation. The adjacency
of metal particles can remove the intermediate poisoning on the surface
of the noble-metal particles. This proved that the selectivity and
catalytic efficiency are extremely dependent on both morphology and
size of the catalytic material. Therefore, the synthesis of noble
metal (Pt or Pd) and mixed oxide on nanoscale may be the fundamental
parameter affecting the performance of the noble-metal catalyst.[17]In our previous work,[18] we introduced
a novel anodic electrocatalyst for methanol oxidation in direct methanol
fuel cell as a type of polymeric fuel cell. The mentioned electrocatalyst
was the nanoscale LaNi0.5Fe0.5O3 particles
incorporated on Pd nanoparticles dispersed into chitosan (CH) polymer.In the present work, we prepared the mentioned nanocomposite at
different loadings of noble metal and mixed oxide dispersed into chitosan
polymer. The catalytic activity of glassy carbon (GC) electrodes modified
with xPd–yLaNi0.5Fe0.5O3–chitosan was investigated with
cyclic voltammetry and controlled potential coulometry techniques
at different potentials; x and y are the mass loadings of noble metal and mixed oxide, respectively.
In the following discussion, for the first time, use of the nonlinear
regression model to analyze the behavior of prepared catalysts is
described asfor i = 1, 2,..., n and j =
1, 2,..., J;
where X is a random
variable, s is a covariate
value, ε is a normal random error
variable withand θ is a P-dimensional
vector of parameters
of the mentioned model and it can be modeled asfor l = 1, 2,..., P and j = 1, 2,..., J as
another regression model, where γ is the L-dimensional vector
of the parameters and e is a normal random error
variable withWe proposed a strategy to make a mixed model
by using the maximum likelihood or mean square error (MSE) methods.[19,20] For this, first, a regression model of θ on s, where j = 1, 2,..., J, was estimated. Then, the
new models were taken instead of each related parameter. To illustrate
the idea, studies were conducted by using the simulation method[21] and this strategy was applied to the electrochemical
results. To do this, assume according to the lth
parameter of the main regression model, a model of θ on s in the formfor j = 1, 2,..., J and l = 1, 2,..., P is
possible to estimate. Therefore, one can estimate the latter mentioned
model as followsfor l = 1,2,..., P orfor l = 1, 2,..., P and k ≥ 1.
Experimental
Section
All chemicals were purchased from Merck and employed
without further
purification. Chitosan with medium molecular weight (400 000
Da) was purchased from Fluka. All solutions were prepared in distilled
water.On the basis of our previous work,[18] the glassy carbon (GC) electrode was modified with palladium
nanoparticles
(A component) and LaNi0.5Fe0.5O3 (B
component) nanoparticles dispersed into chitosan (CH) polymer. These
modified electrodes have been denoted as GC/xA–yB–CH (x and y can
be 0, 0.8, 1.6, 2.4, 3.2, and 4 mg cm–2). Table offers the list of
all modified electrodes. The electrochemical behavior of modified
electrodes was investigated by SAMA Electroanalyser (Isfahan, Iran)
by using cyclic voltammetry and controlled potential coulometry techniques
in a three-electrode cell at room temperature (T =
301 K), for 500 s and different potentials. In this way, the working,
counter, and reference electrodes were the modified GC, platinum,
and Hg/HgO electrodes, respectively. A mixture of potassium hydroxide
solution with a known methanol concentration (1 M KOH + 1.54 M methanol)
was considered as the electrolyte.
Table 1
List of All Modified
Electrodes Employed
in the Present Study
mass loading
modified
electrode
Pd (mg cm–2) A component
LaNi0.5Fe0.5O3 (mg cm–2) B component
GC/A–4B–CH
0
4
GC/0.8A–3.2B–CH
0.8
3.2
GC/1.6A–2.4B–CH
1.6
2.4
GC/2.4A–1.6B–CH
2.4
1.6
GC/3.2A–0.8B–CH
3.2
0.8
GC/4A–0B–CH
4
0
Results and Discussion
Cyclic Voltammetry Investigations
The cyclic voltammograms
of methanol oxidation on different modified electrodes were recorded
at three potential ranges (Figure ). On the basis of Figure a, for the GC/0A–4B–CH electrode,
the peak of methanol oxidation appeared at 1.28 V. By increasing the
contribution of A to B component in the catalyst, the current density
was increased so the peak at 1.28 V was detected with difficulty.
As seen from Figure b, the peak comparison for GC/4A–0B–CH and GC/3.2A–0.8B–CH
electrodes proved that the presence of B components shifted the potential
and current to more negative and higher values, respectively. By decreasing
the contribution of A to B component in the catalyst, the peak methanol
oxidation disappeared. Figure c shows the cyclic voltammograms of methanol oxidation on
different modified electrodes at a wider potential range. According
to this, there are two peak methanol oxidations (1.28 V for B component
and 0.43 V for A component, individually) at forward sweep for modified
electrodes. To include both peaks of methanol oxidation on such electrodes
with different contributions of A and B components, the potential
1.2 V was selected for the controlled potential coulometry technique.
Figure 1
Cyclic
voltammograms of methanol oxidation at (a) +0.5 to +1.5
V, (b) −1.0 to +0.7 V, and (c) −1.0 to +1.5 V vs Hg/HgO
on modified electrodes in 0.80 M methanol and 1.00 M KOH.
Cyclic
voltammograms of methanol oxidation at (a) +0.5 to +1.5
V, (b) −1.0 to +0.7 V, and (c) −1.0 to +1.5 V vs Hg/HgO
on modified electrodes in 0.80 M methanol and 1.00 M KOH.
Simulation Study
To study this approach,
the model
is defined aswhere is a random variable, the sample size n = 100,
the iteration number N = 1000,
the main random variable x = seq (0, 10, length = n), the fixed values of D = seq (1.8, 2.8,
length = 11), and the covariate values s = (2, 25,
50, 75, 100, 125, 150, 175, 200, 225, and 250). We assume that there
is a relation between the parameters and the covariate given by the
equationThe mixed model is
extracted asNot only is this a generalized model
but it
can also estimate the response variable according to optional values
of the covariate, i.e., s = 10, 40, and 230. We hope
the estimated model, with all mentioned models being significant,
can help us to forecast the response variable even in impossible situations.
We used the maximum likelihood estimator and mean square error (MSE)
methods to estimate the regression (linear and/or nonlinear) of the
involved models by usage R (SPSS) software. The results of the simulation
are subsequently stated. The estimated parameters are displayed in Table whereandThe curves
of estimated parameters are shown
in Figures and 3.
Table 2
Estimated Parameters
single models
general models
S
A
B
C
A
B
C
2
78.624 82
–26.237 80
2.922 020
80.93023
–27.123 25
3.069 766
25
113.523 39
–31.337 22
3.429 315
112.900 95
–31.000 21
3.397 758
50
152.139 06
–37.089 04
4.008 089
149.966 83
–36.578 75
3.905 945
75
192.271 20
–43.443 97
4.674 282
190.976 54
–42.737 10
4.572 127
100
235.479 65
–51.744 36
5.471 440
234.830 06
–50.975 26
5.396 304
125
282.504 34
–60.825 51
6.382 312
282.427 39
–60.793 23
6.378 474
150
332.452 32
–71.685 63
7.468 529
333.268 55
–72.191 02
7.518 639
175
385.991 24
–83.990 52
8.697 364
387.453 52
–85.168 62
8.816 798
200
444.877 12
–98.589 45
10.161 934
446.322 31
–99.126 03
10.272 952
225
507.882 04
–115.488 37
11.847 271
508.654 92
–115.863 26
11.887 099
250
576.417 46
–135.105 15
13.812 550
574.771 34
–134.580 30
13.659 241
Figure 2
Estimated parameter curves of (a) A, (b) B, and (c) C
vs a covariate
value (s).
Figure 3
(a) Scatter plot and curve estimations and (b)
the individual and
general estimations of variables.
Estimated parameter curves of (a) A, (b) B, and (c) C
vs a covariate
value (s).(a) Scatter plot and curve estimations and (b)
the individual and
general estimations of variables.
Real Data
For
real data, we consider the following
two conditions. First case: For constant potential at +1.2 V, the
proposed model was considered for experimental data of different percentages
of A and B to find a general model. The general model can predict
the value of the response variable (output) for each percentage of
A and B. Second case: For constant percentage of A and B, the proposed
model was considered for experimental data of different values of
the potential to find a general model. The general model can predict
the value of the response variable (output) for each applied potential.
According to the percentages of A and B components, several nonlinear
regressions of current density were chosen in J/(mA
cm–2) for these data. The exchanged charge over
this time based on the A-level percentage was pA × A and (1 – pA)
× B. Let pA = {0.00, 0.20, 0.40,
0.60, 0.80, 1.00} and t = {0.2,..., 300} per second.
The results are as follows and show that all models are significant.
The summary of the model equivalent to Pa = 0.00, Pb = 1.00 follows.Formula: J/(mA cm–2) ∼a + bT + cT2Residual standard error: 0.01307 on 1497 degrees of freedom;
achieved convergence tolerance: 2.257 × 10–8.The summary of the model equivalent to Pa = 0.20, Pb = 0.80 follows.Formula: J/(mA cm–2) ∼a + bT + cT2Residual standard error: 0.01829 on 1497 degrees of freedom;
achieved convergence tolerance: 1.377 × 10–8.The summary of the model equivalent to Pa = 0.40, Pb = 0.60 follows.Formula: J/(mA cm–2) ∼a + bT + cT2Residual standard error: 0.03095 on 1497 degrees of freedom;
achieved convergence tolerance: 7.564 × 10–9.The summary of the model equivalent to Pa = 0.60, Pb = 0.40 follows.Formula: J/(mA cm–2) ∼a + bT + cT2Residual standard error: 0.01874 on 1497 degrees of freedom;
achieved convergence tolerance: 2.055 × 10–8.The summary of the model equivalent to Pa = 0.80, Pb = 0.20 follows.Formula: J/(mA cm–2) ∼a + bT + cT2Residual standard error: 0.04067 on 1497 degrees of freedom;
achieved convergence tolerance: 8.595 × 10–9.The summary of the model equivalent to Pa = 1.00, Pb = 0.00 follows.Formula: J/(mA cm–2) ∼a + bT + cT2Residual standard error: 0.01956 on 1497 degrees of freedom;
achieved convergence tolerance: 1.165 × 10–8.By combining the parameter estimators from these modelsand putting them in the main model, the mixed
regression model was obtained. Finally, this nonlinear regression
model can easily estimate the response value, the current density, J/(mA cm–2), on the basis of the collaborated
participation of A percentage level (B percentage level) and time.Examples of regression models estimating the current density are
reported in Table . By combining the A and B levels such as PA × A and (1 – PA)
× B, the resulting robust model isTo have an estimation of exchanged charge
over time, we consider the values for t1 and t2 as displayed in Table .
Table 3
Individual
and General Regression
Models for Estimating the Current Density
Then, the fitting of the related graphs and calculation of the
exchanged charge over time intervals (Figure ) can be possible.
Figure 4
Current density vs time
curves on the basis of the experimental
and estimated data for (a) GC/0A–4B–CH, (b) GC/0.8A–3.2B–CH,
(c) GC/1.6A–2.4B–CH, (d) GC/2.4A–1.6B–CH,
(e) GC/3.2A–0.8B–CH, and (f) GC/4A–0B–CH
electrodes.
Current density vs time
curves on the basis of the experimental
and estimated data for (a) GC/0A–4B–CH, (b) GC/0.8A–3.2B–CH,
(c) GC/1.6A–2.4B–CH, (d) GC/2.4A–1.6B–CH,
(e) GC/3.2A–0.8B–CH, and (f) GC/4A–0B–CH
electrodes.These values are shown
in the following Tables –8. It is noteworthy that we considered the
logarithm of the response variable with a base of 10, as log[J/(mA cm–2)t/(s) ]; hence, it is easy to calculate the original response
variable, J/(mA cm–2), to use the
last mixed robust model by putting a new pA value and the time values to estimate the related response variable. Figure shows that the estimation
for PA=0.90 is reasonably located between
the two levels PA=0.80 and PA=0.10.
Table 5
Integrated Charge Exchanged over Time
Intervals for PA=0.00
∫t1t2f(t) dt
PA=0.00
t2
t1
0.00
90.16
135.26
171.49
202.93
231.24
257.27
281.56
304.45
326.17
346.91
366.81
385.97
404.48
0.00
0.00
45.10
81.33
112.77
141.08
167.11
191.40
214.28
236.01
256.75
276.65
295.81
314.32
0.00
0.00
0.00
36.22
67.67
95.97
122.01
146.30
169.18
190.91
211.65
231.55
250.71
269.22
0.00
0.00
0.00
0.00
31.44
59.75
85.79
110.07
132.96
154.68
175.43
195.33
214.49
233.00
0.00
0.00
0.00
0.00
0.00
28.31
54.34
78.63
101.52
123.24
143.98
163.88
183.04
201.55
0.00
0.00
0.00
0.00
0.00
0.00
26.04
50.32
73.21
94.93
115.68
135.57
154.74
173.25
0.00
0.00
0.00
0.00
0.00
0.00
0.00
24.29
47.17
68.90
89.64
109.54
128.70
147.21
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
22.88
44.61
65.35
85.25
104.41
122.92
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
21.72
42.47
62.37
81.53
100.04
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
20.74
40.64
59.80
78.31
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
19.90
39.06
57.57
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
19.16
37.67
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
18.51
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Table 8
Integrated Charge Exchanged over Time
Intervals for PA=1.00
∫t1t2f(t) dt
PA=0.60
t2
t1
0.00
592.18
801.92
957.54
1085.94
1197.29
1296.68
1387.13
1470.56
1548.31
1621.34
1690.36
1755.94
1818.51
0.00
0.00
209.74
365.36
493.76
605.11
704.50
794.95
878.38
956.13
1029.16
1098.18
1163.76
1226.33
0.00
0.00
0.00
155.62
284.02
395.37
494.76
585.21
668.64
746.39
819.42
888.44
954.02
1016.59
0.00
0.00
0.00
0.00
128.40
239.75
339.14
429.59
513.02
590.77
663.80
732.82
798.40
860.97
0.00
0.00
0.00
0.00
0.00
111.34
210.74
301.19
384.62
462.37
535.40
604.42
670.00
732.57
0.00
0.00
0.00
0.00
0.00
0.00
99.40
189.84
273.28
351.03
424.06
493.08
558.65
621.22
0.00
0.00
0.00
0.00
0.00
0.00
0.00
90.45
173.88
251.63
324.66
393.68
459.26
521.83
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
83.43
161.18
234.21
303.23
368.81
431.38
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
77.75
150.78
219.80
285.38
347.94
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
73.03
142.05
207.63
270.19
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
69.02
134.60
197.17
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
65.58
128.14
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
62.57
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Figure 5
Graphs of the current density vs time for methanol oxidation
at
1.2 V potential by (a) the individual and general models and forecasting
for the new 90 % of the A component and (b) the experiment vs its
statistical general estimation for PA =
0.9 and PB = 0.10.
Graphs of the current density vs time for methanol oxidation
at
1.2 V potential by (a) the individual and general models and forecasting
for the new 90 % of the A component and (b) the experiment vs its
statistical general estimation for PA =
0.9 and PB = 0.10.At first, we consider the fixed percentages pA = 0.40 (pB = 0.60)
and pB = 0.80 (pB = 0.20)
of A and B, respectively. Let the applied potential be considered
as E = {0.2, 0.4, 0.6, 0.8, 1.00, 1.2}. It was chosen
by several nonlinear regressions of current density, J/(mA cm–2), for these data. The exchanged charge
over this time was measured on the basis of the measures mentioned
above at t = {0.2,..., 300} per second. The results
are as follows and show that all models are significant.For
example, following is the summary of the model equivalent to PA = 0.40, PB = 0.60,
and E = 0.2 V.Formula: J/(mA
cm–2) ∼a + bT + cT2Residual standard error: 0.006902 on 2494 degrees of freedom.A convergence tolerance of 1.754 × 10–8 was
achieved. By combining the parameters’ estimators from these
modelsand putting them in the
main model, the mixed
regression model was obtained. Finally, this nonlinear regression
model can easily estimate the response value, the current density, J/(mA cm–2), on the basis of the participation
potential level and the time.Examples of regression models
to estimate the current density are
reported in Tables and 10. By combining the fixed mentioned
levels of A and B and potential levels, the resulting robust model
isHence, the fitting of the related graphs and
calculation of the exchanged charge over time intervals (Figure and 7) can be possible.
Table 9
Individual and General Regression
Models for Estimating the Current Density for PA = 0.40 and PB = 0.60
Graphs of (a) real and general estimation results
and (b) real
and individual results for 40 A and 60 B.
Figure 7
Graphs of (a) real and general estimation results and (b) real
and individual results for 80 A and 20 B.
Graphs of (a) real and general estimation results
and (b) real
and individual results for 40 A and 60 B.Graphs of (a) real and general estimation results and (b) real
and individual results for 80 A and 20 B.
Conclusions
In this work, the catalytic
activity of modified glassy carbon
electrodes with xPd–yLaNi0.5Fe0.5O3–chitosan as an anodic
catalyst toward methanol oxidation was investigated with cyclic voltammetry
and controlled potential coulometry techniques; x and y are the mass loading of noble metal and mixed
oxide, respectively. The results of the simulation method to extract
a suitable mixed model and robust model show that on the basis of
the skill of the statistician, this strategy usually works well. It
would be better, before starting the related trials, to consult a
statistician, and the points of the covariate values should be more.
For example, it is impossible to repeat the trials for all arbitrary
percentages of the A and B components without spending time and chemicals.
But with the use of this method, the same results can be obtained
with less expense and time. Although we can estimate the regression
model for each value of the percentage, it is possible to estimate
the regression model for another new value of percentage; meaning,
not only by use of the mixed model can we estimate the response variable
for all possible percentage values but we can also forecast it for
each arbitrary value of the covariate {PA|0 ≤ PA ≤ 1}.
Table 6
Integrated
Charge Exchanged over Time
Intervals for PA=0.40
∫t1t2f(t) dt
PA=0.40
t2
t1
0.00
190.18
272.63
336.56
390.82
438.86
482.47
522.70
560.25
595.60
629.12
661.05
691.62
720.99
0.00
0.00
82.45
146.38
200.64
248.68
292.28
332.51
370.07
405.42
438.93
470.87
501.44
530.81
0.00
0.00
0.00
63.93
118.19
166.23
209.84
250.07
287.62
322.97
356.49
388.42
418.99
448.36
0.00
0.00
0.00
0.00
54.26
102.30
145.91
186.14
223.69
259.04
292.55
324.49
355.06
384.43
0.00
0.00
0.00
0.00
0.00
48.04
91.65
131.88
169.43
204.78
238.30
270.23
300.80
330.17
0.00
0.00
0.00
0.00
0.00
0.00
43.60
83.84
121.39
156.74
190.25
222.19
252.76
282.13
0.00
0.00
0.00
0.00
0.00
0.00
0.00
40.23
77.78
113.14
146.65
178.59
209.16
238.53
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
37.55
72.91
106.42
138.36
168.93
198.30
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
35.36
68.87
100.81
131.38
160.75
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
33.51
65.45
96.02
125.39
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
31.94
62.51
91.88
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
30.57
59.94
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
29.37
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Table 7
Integrated Charge Exchanged over Time
Intervals for PA=0.60
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7