Biomedical Engineering Reference
In-Depth Information
If the curvature at time
t
= 0 is denoted by
κ
0
, then equation (6.70a) is further
generalized to
(
)
−=
(
)
(
)
+
κκ
E
ECRTneAlwtY
2
/*
(
)
1
−
exp.
−
tR
/
C
0
g
v
g
g g
g
g
(6.70b)
(
Π
/
YC
)
hw
Equations (6.70a) and (6.70b) are simple expressions for the time-dependent
curvature of the strip in an average and approximate fashion and clearly indicate
that the induced curvature is directly proportional to the imposed electric field, ;
is a nonlinear function of the capacitance of the gel strip,
C
g
, and cross-resistance,
R
g
; and is inversely proportional to the strip volume
V
g
= (
l
g
w
g
t
g
) and the Young
modulus of elasticity of the strip
Y.
These observations are in complete harmony with experimental results on the
bending of IPMNC strips. Figures 6.13, 6.14, and 6.15 display a number of simulations
for curvature versus capacitance
C
g
, electric field , resistance
R
g
, and time
t
.
Note that in figure 6.13 and subsequently in figures 6.14 and 6.15, the following
values were used for the parameters:
E
κ
E
E
E
= 20,000 {electric field imposed, V/m = J/C-m}
C
g
= 1000E-6 {capacitance, C/V, F = C/V, 200
µ
F}
R
= 8.314 {gas constant, Pa-m
3
/g-mol-K}
T
= 300 {absolute temperature, K}
V
g
= (
l
g
w
g
t
g
) = 2E-8 {sample volume, m
3
}
l
g
= 2 cm
w
g
= 0.5 cm
t
g
= 0.2 mm
Y
= 100E6 {modulus of the sample, Pa}
n
= +1 {valance charge}
e
= 1.602192E-19 {an electron charge, C}
A
v
= 6.022E23 {Avogadro's number, 1/mol}
R
g
= 100 {resistance, 100
Ω
= V/A; also C = A*sec}
δ
max
can be shown to be
approximately related to the absolute value of the curvature
In a cantilever mode, the maximum tip deflection
κ
E
by
2
2
δ
max
κ
=
(6.71)
E
2
l
+
δ
g
max
When combined with equation (6.70a), this results in the following equation
relating the maximum tip deflection of an IPMNC bending strip to the imposed
electric field, the time
t
, the strip cross-capacitance, the strip cross-resistance, the
strip volume, and the strip modulus of elasticity
Y
:
