Biomedical Engineering Reference
In-Depth Information
The mean Coulomb attraction or repulsion force associated with the mean field
R
*
(
r
,
Z
) is given by
F
(
r
,
Z
) such that:
2
**
FrZ
(, )
=
kqrR rZ
(, )
(5.14)
where
k
is a constant of proportionality,
r
*
is the mean radius of the gel strip, and
q
corresponds to total charge between a pair of adjacent ionic surfaces in the gel
sample.
Thus,
q
= (4/3)
b
-1
is the average density of the gel sample.
This force is repulsive (positive) or attractive (negative) according to whether like
or unlike charges lie in the adjacent rows of charges. Experimental observations on
bending of ionic gels in the presence of a voltage gradient generally indicate no
gross motion in the direction of the field, suggesting that the force field
F
(
r
,
Z
) along
the long axis of the gel may be nonuniformly distributed. In fact, the nature of
F
(
r
,
Z
), namely:
ρπ
r
3
Q
, where
ρ
∞
∑
2
π
mr
b
FrZ
(, )
=
32
π
krqb
*
23
−
mK
cos(
2
π
mZ
/
b
)
(5.15)
1
m
=
135
,, .
suggests that even a one-term series solution gives rise to a possible solution, namely:
2
π
r
(
)
=
*
23
−
FrZ
(, )
32
π
krqb
K
cos
2
π
Zb
/
(5.16)
1
1
b
This implies that one possible force configuration is when ions are located at
the outskirts of the sample with mobile ions located in the middle.
The solution for the force field given by equation (5.16) is quite capable of
creating a nonhomogeneous deformation field is the cylindrical sample. This then
allows the designer to robotically control such deformations in ionic gels by means
of a voltage controller or, conversely, to measure the mechanical deformation of gels
by the voltage produced due to such deformations. In this sense, the gel body
becomes a large strain or deformation sensor.
5.4.3
E
LECTRICALLY
C
ONTROLLABLE
I
ONIC
P
OLYMERIC
G
ELS
AS
A
DAPTIVE
O
PTICAL
L
ENSES
Reversible change in optical properties of ionic polymeric gels, PAMPS, and poly-
acrylic acid plus sodium acrylate cross-linked with bisacrylamide (PAAM), under
the effect of an electric field is reported. The shape of a cylindrical piece of the gel,
with flat top and bottom surfaces, changed when affected by an electric field. The
top surface became curved and the sense of the curvature (whether concave or
convex) depended on the polarity of the applied electric field. The curvature of the
surface changed from concave to convex and vice versa by changing the polarity of
the electric field.
