Biomedical Engineering Reference
In-Depth Information
In corresponding to the Bravais-Friedel-Donnay-Harker law, in the Hartman-
Perdok theory, the growth rate of F-faces is taken proportional to the attachment
energy
E
att
/
E
att
R
hkl
hkl
;
(2.30)
E
latt
D
E
att
hkl
C
E
slice
hkl
;
(2.31)
where
E
latt
denotes the lattice energy of crystals, E
slice
hkl
is the slice energy or 2D
lattice energy of face (
hkl
). The slice energy refers to the amount of energy contained
in that growth layer and
E
att
, the attachment energy, refers to the quantity of energy
released when a new growth layer becomes attached to the crystal. According to
(
2.30
), the most favorable molecular composition of a primary surface is the one
with the smallest attachment energy [
70
-
72
]. The implication of (
2.30
)and(
2.31
)
is that the larger the slice energy (equivalent to smaller attachment energy), the
smaller the growth rate and the more crucial the face [
71
,
72
].
The PBC theory precisely identified the mechanisms by which AFPs alter the
ice morphology as reported by Strom et al. [
44
,
79
,
80
]. These works overcome
the drawback of most other studies in which randomly obtained planar cut surfaces
are selected. In fact, crystallographically valid flat surfaces need not be planar cut
slices of the structure. Both the AFP-ice interaction and the molecular equilibrium
distribution in the AFP-ice-water system depend crucially on the detailed definition
of the simulated ice crystal substrates.
The morphological modification caused by external factors can be assessed from
knowledge of the growth conditions, that is, usually the surrounding liquid, often
containing influential molecular species. Such species may exert an even stronger
morphological effect than the liquid itself, as is the case with the AFP (cf. Fig.
2.15
).
The slice energies of the low index (
hk
0) and (
h
0
l
) secondary surfaces are
characterized by relatively high slice energies, comparable to those of the primary
surfaces. The main impediment to the appearance of some secondary prismatic and
pyramidal facets on the growth form of ice would not likely arise from a modest
deficit in the energy of the surface bonding pattern. That impediment is rather due to
the lack of bonding in a second lattice direction transverse to the single existing one.
As mentioned before, crystals are only bounded by F faces, not by S or K faces.
It is surprising to see some S faces can occur on the morphology of ice crystals
when some AFPs and AFGPs are added [
31
]. It was found that these AFPs and
AFGPs can turn the S faces into pseudo âFâ faces surface bridging. According to
theworkbyStrometal.[
44
], the fish-type ice binding surface stabilizes a secondary
surface by introducing effectively a second strong-bonding direction to intersect
with the existing one. This is schematically illustrated in Fig.
2.18
. Some of the
surface molecular compositions available for engagement will offer a better match
than others to the ice binding surface structure. The selection of the face indices
of the reconstructed surface occurs by identifying the particular surface molecular
composition that offers the best structural match or the strongest interaction with
