Biomedical Engineering Reference
In-Depth Information
where superscripts “att” and “rep” denote attraction and repulsion respectively. The
consideration for the overall interactions mentioned above has been treated by the
Deryagin-Landau-Verwey-Overbeek theory [
32
]. In practice, it is not necessary
to consider all these contributions simultaneously. One shall here deal with
two
simpler situations
where the long-range potential arises from electrostatic
and/or
from steric repulsion contributions. Notice that the double-layer repulsion depends
on the ionic strength of the medium: the curves may show a high repulsive barrier at
low ionic strengths, a so-called secondary minimum at intermediate ionic strengths,
and a negligibly small barrier, or none at all, at higher ionic strengths. In the same
way, the form of the steric repulsion is determined by the nature of the interactions
between the adsorbed polymer chains and the solvent. A repulsive barrier of variable
range and a minimum of variable depth can result, depending on the solvent and the
temperature. The interaction between colloidal particles can be turned by changing
the ionic strength, pH of solutions, or adding polymers. This implies that the “phase
behavior” of such systems can be tuned by altering the above parameters.
Apart from the above-mentioned forces, the recent researches indicate that
the interaction between colloidal particles can be induced and controlled by an
alternating electric field (AEF) [
13
,
31
,
33
-
46
]. One can tune the interaction by
altering the frequency and/or the strength of the applied field. This effect can be
captured by
G
(other effects) in (
7.1
). In comparison with other stimuli, the electric
stimulus can be applied and switched off instantly without disturbing the original
solutions. Although the interactions between colloidal particles can be of many
kinds, they are basically functions of 1/
r
eq
(
r
eq
denotes the equilibrium distance
between two neighboring particles). This implies that for a given colloidal system,
the interaction between two adjacent particles is fixed once
r
eq
is constant. In other
words, the change of
r
eq
can reflect directly the change of interparticle interactions.
As tuning the frequency and field strength of an AC field is much easier to
achieve than other means, the following discussion will be mainly focused on the
control of the colloidal crystallization under an AC field (i.e., Fig.
7.1
)[
35
,
37
,
39
].
Nevertheless, not all ranges of frequency and intensity of the AC field can produce
a crystalline assembly of particles. There exists a finite frequency range with well-
defined lower and upper cut-off values of particle size, charge, ionic strength of the
solution, pH, etc., in which the effective control can be implemented (i.e., Fig.
7.1
).
The formation of various patterns is subject to the balance of the attractive and
repulsive forces. Here, the attractive force that can overcome the interparticle elec-
trostatic repulsion and enable 2D colloidal aggregation is suggested to be attributed
to electrohydrodynamic flow [
47
,
48
]. Fluid motion is set up by the interaction
between this free charge and the lateral electric field, which is caused by the
distortion of the applied field by the colloidal particles. A “phase diagram” of the
electrically controlled colloidal assembly under a constant temperature is given in
Fig.
7.1
.
The thermodynamic driving force for the phase transition (including biomineral-
ization and general crystallization) can be defined by
, referring to the difference
