Biomedical Engineering Reference
In-Depth Information
where
a
i
,and
C
i
denote the activity and concentration of species
i
, respectively, and
i
1) of the chemical potential of species
i
.This
then gives rise to the thermodynamic driving force
denotes the standard state (
a
i
D
kT
D
ln
a
i
a
ln
C
i
C
(7.4)
eq
i
eq
i
eq
i
;C
eq
i
where
are, respectively, the equilibrium activity and concentration of
species
i
. If we define the supersaturation for crystallization as
a
eq
i
/=a
eq
i
.C
i
C
eq
i
/=C
eq
D
.a
i
a
(7.5)
i
(
7.4
) can then be rewritten as
kT
D
ln
.1
C
/
Š
.
if
<<1/
(7.6)
For colloidal crystallization, the similar relationship can be found. If the inter-
action between the particles in the crystal phase remains constant at different field
strength and frequencies, the supersaturation can be given by (
7.6
)
D
(
-
m
)/
m
(
m
represent the actual concentration and the equilibrium concentration
of the solute, respectively). For more precise definition of supersaturation in
biomineralization, refer to Chap. 3.
and
7.3
Simulations of Nucleation and Crystal Growth
in Biomineralization
Similar to the crystallization of other materials, 3D crystallization of biominerals
occurs via (1)
the nucleation
,followedby(2)
the growth
of crystals. Nucleation
will determine whether and when a mineral (crystalline) phase will occur and the
correlation with its surroundings. It will also determine the total number and the
average size of crystalline particles occurring in the system eventually. On the other
hand, the growth of crystals will to a large extent determine the size, morphology,
and perfection of crystals. Therefore, the understanding of the governing mechanism
will allow us to acquire the knowledge on how organisms can exercise the effective
control and on the engineering of biomineral crystalline materials. In this regard,
how the colloidal crystallization can be controlled electrically can be applied to
model the general process of nucleation and biomineralization-related phenomena,
i.e., multistep/phase crystallization, anti-templating effect, etc.
