Biomedical Engineering Reference
In-Depth Information
complexation to one block can cause a significant increase in
dielectric contrast and a corresponding increase in the electric field
alignment response [40, 41]. Tsori
have also proposed that
mobile ions contained in the copolymer contribute a further free
energy reduction for domain alignment [42]. Electric fields can also
induce complete phase morphology changes such as the spheres-to-
cylinder transition observed by Xu
et al.
. [43].
In a thin film, a vertical electric field such as that applied in a
parallel-plate capacitor geometry drives a standing alignment of
L
et al
microdomains. There is, therefore, a competition between
the electric field and the surface fields that favor parallel domain
alignment (
or
C
). The free energy of Eq. 2.7 is modified in a simple
model to include distinct contributions from the surface interactions
and the electric field response:
L
or
C
1
2
F
=
F
+
F
+
F
=
F
− �
Vel ε
(
r
) |
E
(
r
)|
2
.
dV
+�
A σ
(
,
)
dA
,
0
el
surf
0
(2.9)
where
F
contains a surface integral of σ(
,
) from interfacial
surf
interactions over the substrate area
is the sample volume
(extending out from the surface) over which the surface and
electric field alignment forces are in competition, driving alignment
perpendicular or parallel to the electric field, respectively. In the
notation of Eq. 2.8, there is a critical field at which Δ
A
.
V
el
F
= −Δ
F
and
el
surf
the two contributions are balanced. Thurn-Albrecht
et al.
found
that
was independent of the film thickness, indicating a finite
boundary layer at the substrate at which
V
el
F
is able to dominate
surf
F
[32]. Slightly below the threshold field, the
C
boundary layer
el
coexists with
in the rest of the film. Only above the threshold does
the electric field dominate everywhere and produce “complete”
alignment, i.e.,
C
microdomains that pass continuously from
surface to substrate. Detailed theoretical studies have described
the orientation of lamellar microdomains in symmetric BCP thin
films taking into account the competition between electric (
C
) and
surface fields [35, 44]. In the strong segregation regime, there are
two critical fields
E
E
and
E
when there are strong, preferential
1
2
interfacial interactions. For
E
<
E
, surface fields dominate and an
L
1
morphology is favored, while for
E
>
E
, the electric field dominates
2
 
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