During cooling, ice growth will be limited by the small number
of nuclei (typically those arising from heterogeneous nucleation)
that form at higher temperatures where the growth rate is significant. Nucleation continues and accelerates during cooling until T G
is passed, but at those temperatures, the nuclei are too cold to grow.
Upon warming, nucleation resumes when the temperature range
near T G is again traversed. A sample will therefore be much more
extensively nucleated during warming than during most of the
cooling process [2, 217, 224], and consequently there will be
many more growing nuclei during warming than during cooling.
This means that total ice development is much more rapid during
warming, and hence warming rates required to avoid significant
devitrification are found to be far higher than cooling rates initially
required to achieve vitrification (e.g., [43, 225]). For glycerol,
propylene glycol, and ethylene glycol, as the critical cooling rate
increases from 10
C/min to 100
C/min, the critical warming rate
increases from ~10
2 to 10
3 C/min to ~10
5 to 2 Â 10
7 C/min
[18, 89] (a 5-log increase for ethylene glycol and glycerol and
around a 3-log increase for propylene glycol). Fahy found that for
vitrification solutions of propylene glycol and Me 2 SO, which vitrify
at about 10
C/min, the critical warming rate is 1000
C/min
(ignoring the effect of the carrier on the latter) [226, 227].
A mathematical relationship between the critical cooling rate
and the critical warming rate has recently been found [20, 228]. If
v cw is the critical warming rate and v cc is the critical cooling rate, it
has been empirically determined that
logðv cw =v cc Þ ¼ y o þ að1 À e
Àbv cc Þ,
where y o , a, and b are empirical constants that vary from cryoprotectant to cryoprotectant. Examples are shown in Fig. 4 and indicate that cryoprotectants that have significantly different glassforming properties (e.g., Me 2 SO vs. ethylene glycol or
glycerol vs. 2,3-butanediol) may have virtually identical relationships between v cw and v cc , for reasons yet to be elucidated.
Injury caused by devitrification presumably depends on both
the total amount of ice formed and on the sizes of the resulting
crystals. The amount of ice formed depends on the warming rate
[142] and the difference between the concentration of cryoprotectant used for vitrification or otherwise present in and around the
cells and the equilibrium concentration at the temperature of devitrification [20, 229] (Fig. 5). Recrystallization generally proceeds in
proportion to t
1/3 [230] where t is time. Recrystallization tends to
be slower than devitrification, but can still be quite rapid, apparently requiring warming at 5000 [231] to 100,000
C/min
[200, 232] to outrun its biological effects in some cases.
Critical warming rates can be quantified by the method of
Boutron in which DSC thermograms are obtained during warming
50
Gregory M. Fahy and Brian Wowk
of nuclei (typically those arising from heterogeneous nucleation)
that form at higher temperatures where the growth rate is significant. Nucleation continues and accelerates during cooling until T G
is passed, but at those temperatures, the nuclei are too cold to grow.
Upon warming, nucleation resumes when the temperature range
near T G is again traversed. A sample will therefore be much more
extensively nucleated during warming than during most of the
cooling process [2, 217, 224], and consequently there will be
many more growing nuclei during warming than during cooling.
This means that total ice development is much more rapid during
warming, and hence warming rates required to avoid significant
devitrification are found to be far higher than cooling rates initially
required to achieve vitrification (e.g., [43, 225]). For glycerol,
propylene glycol, and ethylene glycol, as the critical cooling rate
increases from 10
C/min to 100
C/min, the critical warming rate
increases from ~10
2 to 10
3 C/min to ~10
5 to 2 Â 10
7 C/min
[18, 89] (a 5-log increase for ethylene glycol and glycerol and
around a 3-log increase for propylene glycol). Fahy found that for
vitrification solutions of propylene glycol and Me 2 SO, which vitrify
at about 10
C/min, the critical warming rate is 1000
C/min
(ignoring the effect of the carrier on the latter) [226, 227].
A mathematical relationship between the critical cooling rate
and the critical warming rate has recently been found [20, 228]. If
v cw is the critical warming rate and v cc is the critical cooling rate, it
has been empirically determined that
logðv cw =v cc Þ ¼ y o þ að1 À e
Àbv cc Þ,
where y o , a, and b are empirical constants that vary from cryoprotectant to cryoprotectant. Examples are shown in Fig. 4 and indicate that cryoprotectants that have significantly different glassforming properties (e.g., Me 2 SO vs. ethylene glycol or
glycerol vs. 2,3-butanediol) may have virtually identical relationships between v cw and v cc , for reasons yet to be elucidated.
Injury caused by devitrification presumably depends on both
the total amount of ice formed and on the sizes of the resulting
crystals. The amount of ice formed depends on the warming rate
[142] and the difference between the concentration of cryoprotectant used for vitrification or otherwise present in and around the
cells and the equilibrium concentration at the temperature of devitrification [20, 229] (Fig. 5). Recrystallization generally proceeds in
proportion to t
1/3 [230] where t is time. Recrystallization tends to
be slower than devitrification, but can still be quite rapid, apparently requiring warming at 5000 [231] to 100,000
C/min
[200, 232] to outrun its biological effects in some cases.
Critical warming rates can be quantified by the method of
Boutron in which DSC thermograms are obtained during warming
50
Gregory M. Fahy and Brian Wowk