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Question 4 ( 4 0 points ) One type of Li - ion battery includes a graphite negative electrode and manganese dioxide spinel positive electrode,

Question 4(40 points)
One type of Li-ion battery includes a graphite negative electrode and manganese dioxide spinel
positive electrode, described by the following reactions (written in the discharge direction):
LixC6xLi++xe--+C6(negative)
xLi++xe--+Mn2O4LixMn2O4(positive)
The electrolyte consists of an organic solvent that contains a binary LiPF6 lithium salt, where the
anion is PF6. Assume a one-dimensional cell with the cathode located at x=0 and the anode
located at x=L. The following properties are known:
DLi+=1.810-10m2s-1
DPF6-=2.610-10m2s-1
t+=0.4
For our purposes here, we assume that the electrodes are flat surfaces, and that they are separated
by an electrolyte-containing separator that is 25m thick. The initial concentration of LiPF6 in
the electrolyte is 1.0M. The parameters given in the question are for transport in the separator.
a) In which direction does the current in solution flow during discharge? Is this positive or
negative relative to the x-direction? (10 points)
b) Where is the concentration highest, at x=0 or x=L?(10 points)
c) What is the concentration difference across the separator if a cell with a 2cm5cm
electrode is operated at a current of 10mA? Is this difference significant? (15 points)
d) Briefly describe how you would calculate the cell potential for a constant current
discharge of this cell if the current is known and the concentration variation is known.
The potential that would be measured is between the current collectors of the cathode and
anode during discharge. You do not need to include all the equations that you would use.
The important thing is that you know and are able to identify the factors that contribute to
the measured cell potential, and that you know the process by which you might determine
their values. (5 points)
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