measured values of thermodynamic response functions such as heat
capacity, thermal expansion coefficient, and compressibility fall
from those of a liquid to those of a solid. The glass transition is
typically detected calorimetrically by an observed drop in heat
capacity during cooling. In contrast, thermodynamic state variables
such as volume, energy, and entropy do not change during the glass
transition. Only their slope as a function of temperature undergoes
change [2].
Although the glass transition is a material phase change (liquid
to solid), it is not a thermodynamic phase change from one equilibrium state to another. The glass transition is a kinetic phenomenon in which viscosity delays intermolecular rearrangements that
are thermodynamically favored. In essence, vitrification “locks in” a
non-equilibrium thermodynamic state. As cooling rates are varied
by orders of magnitude, measured glass transition temperatures can
vary by several degrees Celsius [197], with slower cooling rates
resulting in lower measured glass transition temperatures. This is
due to the kinetic nature of the glass transition. Slower cooling rates
provide more time for intermolecular rearrangements that release
heat, contract volume, and otherwise approach equilibrium before
rising viscosity stops liquid-like behavior.
The measured decrease in heat capacity that occurs during
passage below the glass transition temperature provides a more
abstract interpretation of the glass transition. The heat capacity of
a liquid above the glass transition temperature is greater than that
of a crystal at the same temperature. Entropy varies as heat flow
divided by temperature. Therefore, during cooling, the entropy of a
liquid decreases faster than the entropy of a crystal of the same
composition. This leads to a projected temperature called the
Kauzmann temperature (T K ) below which the liquid is extrapolated
to have a lower entropy than the crystal [198]. Since a disordered
liquid state is supposed to have higher entropy than an ordered
crystal, cooling a liquid to T K would create a paradox. The decrease
in heat capacity at the glass transition prevents this thermodynamic
paradox. Although kinetic in nature, the eventual occurrence of a
glass transition can be viewed as a thermodynamic necessity for
crystallizable liquids with a Kauzmann temperature greater than
absolute zero.
As mentioned above, thermodynamic non-equilibrium is
intrinsic to glasses at the time of their formation. Lack of equilibrium pertains to the glassy phase in which cryopreserved cells are
suspended irrespective of whether cryopreservation is by freezing
or vitrification.
Four types of non-equilibrium state are noteworthy in the
context of cryopreservation. First, there is vapor pressure
non-equilibrium between ice and the unfrozen sample volume.
This is important for cryopreservation by vitrification because the
aim is for the sample to remain substantially free of ice during
cooling and storage despite strong thermodynamic driving forces
Principles of Vitrification
45
capacity, thermal expansion coefficient, and compressibility fall
from those of a liquid to those of a solid. The glass transition is
typically detected calorimetrically by an observed drop in heat
capacity during cooling. In contrast, thermodynamic state variables
such as volume, energy, and entropy do not change during the glass
transition. Only their slope as a function of temperature undergoes
change [2].
Although the glass transition is a material phase change (liquid
to solid), it is not a thermodynamic phase change from one equilibrium state to another. The glass transition is a kinetic phenomenon in which viscosity delays intermolecular rearrangements that
are thermodynamically favored. In essence, vitrification “locks in” a
non-equilibrium thermodynamic state. As cooling rates are varied
by orders of magnitude, measured glass transition temperatures can
vary by several degrees Celsius [197], with slower cooling rates
resulting in lower measured glass transition temperatures. This is
due to the kinetic nature of the glass transition. Slower cooling rates
provide more time for intermolecular rearrangements that release
heat, contract volume, and otherwise approach equilibrium before
rising viscosity stops liquid-like behavior.
The measured decrease in heat capacity that occurs during
passage below the glass transition temperature provides a more
abstract interpretation of the glass transition. The heat capacity of
a liquid above the glass transition temperature is greater than that
of a crystal at the same temperature. Entropy varies as heat flow
divided by temperature. Therefore, during cooling, the entropy of a
liquid decreases faster than the entropy of a crystal of the same
composition. This leads to a projected temperature called the
Kauzmann temperature (T K ) below which the liquid is extrapolated
to have a lower entropy than the crystal [198]. Since a disordered
liquid state is supposed to have higher entropy than an ordered
crystal, cooling a liquid to T K would create a paradox. The decrease
in heat capacity at the glass transition prevents this thermodynamic
paradox. Although kinetic in nature, the eventual occurrence of a
glass transition can be viewed as a thermodynamic necessity for
crystallizable liquids with a Kauzmann temperature greater than
absolute zero.
As mentioned above, thermodynamic non-equilibrium is
intrinsic to glasses at the time of their formation. Lack of equilibrium pertains to the glassy phase in which cryopreserved cells are
suspended irrespective of whether cryopreservation is by freezing
or vitrification.
Four types of non-equilibrium state are noteworthy in the
context of cryopreservation. First, there is vapor pressure
non-equilibrium between ice and the unfrozen sample volume.
This is important for cryopreservation by vitrification because the
aim is for the sample to remain substantially free of ice during
cooling and storage despite strong thermodynamic driving forces
Principles of Vitrification
45