Biomedical Engineering Reference
In-Depth Information
10
8
V/cm at the molecular level, which means a very large potential drop over a
distance defined by the Debye length of roughly 10-1000Å. The charged polyelec-
trolyte is therefore surrounded by the mobile counter-ions. Their experimental obser-
vation supported evidence of the model of an electric double layer formed by the
primary charge fixed on the polyelectrolyte and the diffuse layer of mobile counter-
ions in solution.
Yannas and Grodzinsky estimated the Debye length or effective thickness 1/
k
of the ionic layer surrounding the charged sites of individual fibrils. Using the
Poisson-Boltzmann equation with the linear Debye-Huckel approximation, the
Debye length becomes:
1
2
ε
kT
cz e
ii
1
κ
=
(1.18)
∑
22
i
where
c
i
is the concentration of the
i
th species
e
is the electronic charge
ε
is the dielectric constant
k
is Boltzmann constant
T
is the absolute temperature
z
is the valance
According to this equation, an increase in ionic strength results in a decrease in
Debye length. On the other hand, the observed drop in isometric force with ionic
strength should, in terms of the preceding model, result from a weakening of inter-
fibrillar repulsion and a corresponding decrease in lateral swelling. Grodzinsky and
Melcher (1976) modeled the electromechanical transduction of collagen and other
aqueous polyelectrolytes in membrane form. In their study, they coupled membrane
to mechanical load and observed the conversion of electrical to mechanical response
and vice versa. Their model represented membrane at interfibrillar level with cylin-
drical pores relating externally measured potentials, membrane deformations, current
flow, and mass fluxes to pore radius, fibril diameter, and polyelectrolyte charge.
Molecules of collagen, like other protein polyelectrolytes, possess many ioniz-
able groups capable of dissociating and attaining net charge in a variety of solvent
media. On the electrical side, this primary charge can give rise to intense local
electric fields as high as 10
8
V/cm. Therefore, collagen and other polyelectrolytes,
whether in the form of isolated molecules, fibers, or membranes, are susceptible to
interactions with externally applied fields. In addition, polyelectrolyte structures may
interact with each other through their own internal fields. On the mechanical side,
the fibril-electrolyte matrix composing macroscopic polyelectrolyte fibers and mem-
branes is often flexible and elastic in the hydrated state. Therefore, forces due to
electric fields can result in motion and deformation of the polyelectrolyte.
