(vapor pressure non-equilibrium) favoring ice growth. Unequal
vapor pressures between ice crystals of different size also play a
role in ice recrystallization [39, 199], which can damage cells
during rewarming of frozen samples or vitrified samples that form
ice during rewarming [172, 200, 201]. Second, there is chemical
non-equilibrium, in the sense of chemical instability and change. At
relatively high temperatures, chemical or protein conformational
changes in cells are able to proceed beyond the controls of normal
metabolism, but these changes can be slowed and ultimately
arrested as temperatures decline and increasing viscosity combined
with insufficient activation energies prevents chemical reactions.
Chemical non-equilibrium may relate to the rate of viability loss
during cooling. Third, there is chemical potential non-equilibrium.
Non-equilibrium of cryoprotectant concentration between different regions of a vitrified sample [22] or across the cell membrane
[105, 202] can make the difference between satisfactory and unsatisfactory
preservation.
Fourth,
there
is
mechanical
non-equilibrium. Mechanical non-equilibrium is relevant to
mechanical stress and strain during cryopreservation, which is an
especially important consideration for large samples such as tissues
and organs, and is discussed in more detail in Subheading 2.7.
2.3 Ice Nucleation
Ice formation begins with a process called nucleation [203]. There
are two kinds of nucleation, homogeneous and heterogeneous.
During nucleation, water molecules begin organizing into the
structure of ice on a nanometer scale. The resulting nascent ice
crystals, or ice nuclei, tend to be unstable. In accordance with the
Gibbs-Thomson equation [204], ice crystals of small size have low
melting temperatures (high vapor pressure) caused by sharp curvature of the crystal surface. Consequently, newly formed ice nuclei
tend to melt at any temperatures warmer than about À38
C in
pure water. This defines the homogeneous nucleation temperature
(T h ), the lowest temperature to which small [36, 205] samples can
be cooled under normal conditions without ice formation and the
highest temperature at which small samples are likely to form ice
when preexisting ice crystals or contaminants that mimic ice crystals
(heterogeneous nucleators, discussed below) are absent [36, 87,
205–208]. As shown in Fig. 3, T h decreases with increasing solute
concentration [110].
Ice can form at temperatures above T h in the presence of
heterogeneous nucleators [36, 203, 209]. Heterogeneous nucleators are particles or surfaces that mimic the structure of ice on a
molecular scale or otherwise induce water to assume a more ice-like
configuration with a larger radius of curvature. Ice crystals with a
larger radius of curvature upon their initial formation have a lower
surface energy, allowing them to avoid melting at warmer temperatures [209]. The most potent heterogeneous nucleators can cause
ice to form at temperatures only 1
C below T m [210, 211]. Heterogeneous nucleators are ubiquitous environmental contaminants
46
Gregory M. Fahy and Brian Wowk
vapor pressures between ice crystals of different size also play a
role in ice recrystallization [39, 199], which can damage cells
during rewarming of frozen samples or vitrified samples that form
ice during rewarming [172, 200, 201]. Second, there is chemical
non-equilibrium, in the sense of chemical instability and change. At
relatively high temperatures, chemical or protein conformational
changes in cells are able to proceed beyond the controls of normal
metabolism, but these changes can be slowed and ultimately
arrested as temperatures decline and increasing viscosity combined
with insufficient activation energies prevents chemical reactions.
Chemical non-equilibrium may relate to the rate of viability loss
during cooling. Third, there is chemical potential non-equilibrium.
Non-equilibrium of cryoprotectant concentration between different regions of a vitrified sample [22] or across the cell membrane
[105, 202] can make the difference between satisfactory and unsatisfactory
preservation.
Fourth,
there
is
mechanical
non-equilibrium. Mechanical non-equilibrium is relevant to
mechanical stress and strain during cryopreservation, which is an
especially important consideration for large samples such as tissues
and organs, and is discussed in more detail in Subheading 2.7.
2.3 Ice Nucleation
Ice formation begins with a process called nucleation [203]. There
are two kinds of nucleation, homogeneous and heterogeneous.
During nucleation, water molecules begin organizing into the
structure of ice on a nanometer scale. The resulting nascent ice
crystals, or ice nuclei, tend to be unstable. In accordance with the
Gibbs-Thomson equation [204], ice crystals of small size have low
melting temperatures (high vapor pressure) caused by sharp curvature of the crystal surface. Consequently, newly formed ice nuclei
tend to melt at any temperatures warmer than about À38
C in
pure water. This defines the homogeneous nucleation temperature
(T h ), the lowest temperature to which small [36, 205] samples can
be cooled under normal conditions without ice formation and the
highest temperature at which small samples are likely to form ice
when preexisting ice crystals or contaminants that mimic ice crystals
(heterogeneous nucleators, discussed below) are absent [36, 87,
205–208]. As shown in Fig. 3, T h decreases with increasing solute
concentration [110].
Ice can form at temperatures above T h in the presence of
heterogeneous nucleators [36, 203, 209]. Heterogeneous nucleators are particles or surfaces that mimic the structure of ice on a
molecular scale or otherwise induce water to assume a more ice-like
configuration with a larger radius of curvature. Ice crystals with a
larger radius of curvature upon their initial formation have a lower
surface energy, allowing them to avoid melting at warmer temperatures [209]. The most potent heterogeneous nucleators can cause
ice to form at temperatures only 1
C below T m [210, 211]. Heterogeneous nucleators are ubiquitous environmental contaminants
46
Gregory M. Fahy and Brian Wowk