24
-
FREEZE—DRYING
The accuracy of computed values of rc is limited by the assumption that the embryo is
spherical and that a value of CSL exists which is independent of crystallographic orienta—
tion.
’
A drop of pure water supercooled to temperature T… Will therefore freeze should it
contain an ice crystal with radius greater than the equilibrium radius rc. The random
motion of the molecules may eventually enable this nucleus to form to give homogeneous
nucleation.
The probability of this event is proportional to drop volume and the time
,_
for which the drop is supercooled. It can be shown to increase rapidly With decreasing
.
temperature. Curve (19) (gure 2) is consistent With this theory, for drops freezing within
0.5 seconds of reaching the temperature specied.
Alternatively a solid nucleus in suspension or a solid surface may provide a nucleus of
suîcient size and similarity to ice to allow growth to begin (heterogeneous nucleation).
Nucleation Of distilled water in drops of radius greater than about 10 microns takes place
by this process. The observed exponential increase of freezing nuclei with supercooling
'_
may be interpreted in terms of nucleus size — there are more small particles present,
which will nucleate at lower temperatures. Size is not the only parameter which inuences
the temperature at which a particle will nucleate. This other parameter is aNL, the
surface energy between the nucleus and the liquid. This will approach CSL, the
fÏ
value between ice and the liquid as the molecular properties of the nucleus become closer
to those of ice.
In practice this means that the most effective freezing nucleus will have
a crystalline structure and lattice spacing similar to ice With similar binding forces and
_
atomic polarisabity.
Since the freezing behaviour of a given sample of water will be determined by the size
distribution and chemical composition of the particulates, it is possible that processes
may take place which will change, for example, the size distribution, so that the exponential
relationship fails. This could happen if there were no nuclei at all in a particular size
interval, when the freezing characteristics wOuld be quite different from that of figure 2 a.
NUCLEATIÛN OF ICE CRYSTALS FROM THE VAPOUR
Greater physical insight into the nucleation process can beobtained from a study of
the nucleation of ice crystals direct from the vàpour onforeign substrate crystals. Using
an equation similar to [1] we may computethe critical radius for aliquid drop to grow
from the vapour. An estimate of the ratio% gives a value greater for the vapeur-solid
transition
for the vérp0ur—liquid,, tranSi—ti0n.
…
—
……
At— 40°C
=85À
-
-
“_ "_
,_
——
4°C
‘
u—‘rc
.
' —
These values’ are less than the corresponding values
that water drops Will
fOrm before ice crystals as the supersaturatiqn of
vapouriSÿicreased.
_
This conclusion is
409C.Whenthehqu1d:drops
freeze so quickly that“ Ïit—isno longer
to determine
.
rst. In the caSe of ice c}rystals"nuclçæatigbh
appears
-
FREEZE—DRYING
The accuracy of computed values of rc is limited by the assumption that the embryo is
spherical and that a value of CSL exists which is independent of crystallographic orienta—
tion.
’
A drop of pure water supercooled to temperature T… Will therefore freeze should it
contain an ice crystal with radius greater than the equilibrium radius rc. The random
motion of the molecules may eventually enable this nucleus to form to give homogeneous
nucleation.
The probability of this event is proportional to drop volume and the time
,_
for which the drop is supercooled. It can be shown to increase rapidly With decreasing
.
temperature. Curve (19) (gure 2) is consistent With this theory, for drops freezing within
0.5 seconds of reaching the temperature specied.
Alternatively a solid nucleus in suspension or a solid surface may provide a nucleus of
suîcient size and similarity to ice to allow growth to begin (heterogeneous nucleation).
Nucleation Of distilled water in drops of radius greater than about 10 microns takes place
by this process. The observed exponential increase of freezing nuclei with supercooling
'_
may be interpreted in terms of nucleus size — there are more small particles present,
which will nucleate at lower temperatures. Size is not the only parameter which inuences
the temperature at which a particle will nucleate. This other parameter is aNL, the
surface energy between the nucleus and the liquid. This will approach CSL, the
fÏ
value between ice and the liquid as the molecular properties of the nucleus become closer
to those of ice.
In practice this means that the most effective freezing nucleus will have
a crystalline structure and lattice spacing similar to ice With similar binding forces and
_
atomic polarisabity.
Since the freezing behaviour of a given sample of water will be determined by the size
distribution and chemical composition of the particulates, it is possible that processes
may take place which will change, for example, the size distribution, so that the exponential
relationship fails. This could happen if there were no nuclei at all in a particular size
interval, when the freezing characteristics wOuld be quite different from that of figure 2 a.
NUCLEATIÛN OF ICE CRYSTALS FROM THE VAPOUR
Greater physical insight into the nucleation process can beobtained from a study of
the nucleation of ice crystals direct from the vàpour onforeign substrate crystals. Using
an equation similar to [1] we may computethe critical radius for aliquid drop to grow
from the vapour. An estimate of the ratio% gives a value greater for the vapeur-solid
transition
for the vérp0ur—liquid,, tranSi—ti0n.
…
—
……
At— 40°C
=85À
-
-
“_ "_
,_
——
4°C
‘
u—‘rc
.
' —
These values’ are less than the corresponding values
that water drops Will
fOrm before ice crystals as the supersaturatiqn of
vapouriSÿicreased.
_
This conclusion is
409C.Whenthehqu1d:drops
freeze so quickly that“ Ïit—isno longer
to determine
.
rst. In the caSe of ice c}rystals"nuclçæatigbh
appears