Page 320 - Handbook of Battery Materials

290 11 Separators

and substitution into Equation 11.2 gives:
1 l s 1 d
R(separator) = · −
σ q s σ q
1 T d
= dT · −
σ qP q
1 d T 2
= − 1
σ q P
2
T
= R(electrolyte) − 1
P
2
T
R sep = R el − 1
P
1 d
with R el = · (11.6)
σ q
This formula shows the factorial effect of the separator on the electrical resistance;
2
the measured resistance of the electrolyte-filled separator is the (T /P)-fold multiple
2
of the electrolyte resistance without the separator; by definition, T /P ≥ 1.
With increasing tortuosity factor T and lower porosity P, R increases sharply.
The electrical resistance of a separator is proportional to the thickness d of the
membrane and is subject to the same dependence on temperature or concentration
as the electrolyte itself.
◦
For sulfuric acid (H 2 SO 4 ) of specific density 1.28 g cm −3 at 25 C, the specific
resistance (l/σ)is1.26 cm; using this value in the Equation 11.6 and selecting
values typical for polyethylene starter battery separators at d = 0.25 mm, P = 0.6,
2
and T = 1.3, the electrical resistance for 1 cm of separators area results in
0.025 cm 1.3 2
R sep = 1.26 cm − 1
1cm 2 0.6
= 0.057
Usually the electrical resistance of a separator is quoted in relation to area; in the
2
above case it is 57 m cm . In order to quote it for other areas, because of the
parallel connection of individual separator areas, Kirchhoff’s law has to be taken
into account:
1 1 1
= + + ...
R total R 1 R 2
or, as all R i are equal,

1
R total = R n
n
2 2
Applying this to the above example for an area of 1 in = 6.45 cm , the result is R =
2
8.8m in . Taking an example from starter-lighting-ignition (SLI) battery practice,
one cell with six positive and seven negative electrodes of typical 114 mm × 147 mm
◦
size with the above separator shows a resistance of 28.3 × 10 −6 at 25 C, or close
◦
to 75 × 10 −6 at −18 C. For a cold crank current of 320 A and six cells in series in