Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 63

Fig. 3.1 Temperature
dependence on the Gibbs free
energy for solid, liquid, gas,
and glass phases at constant
pressure
temperature, the whole bulk of one phase would convert entirely to another phase.
However, the processes of vaporization and sublimation occur to some extent well
below their respective transition temperatures. This is an entirely surface phe-
nomenon. Because the surface molecules are bound to fewer neighbors than the
molecules in the bulk, they have higher mobility and through fluctuation can gain
enough energy to leave the surface. As long as the condensed substance is enclosed
in a container whose volume is not much larger than the volume of the substance,
the process would continue until the vapor phase saturates, i.e., its pressure reaches
an equilibrium value at a given temperature. Otherwise, it will continue until the
condensed phase is gone. Similarly, the higher mobility of the surface layer in the
crystal melts at a temperature lower than T m , while the bulk of the crystal remains
solid indefinitely.
From the equilibrium standpoint, the reverse transitions are supposed to happen
at the same temperature as the forward ones, i.e., condensation of vapor to crystal at
T s , condensation of vapor to liquid at T b , and crystallization of liquid at T m . In real-
ity, all these processes occur at markedly lower temperatures because of a signifi-
cant energy barrier to nucleation, i.e., the energy of creating the surface of a nucleus
of the new condensed phase [ 3 , 4 ]. The barrier can only be overcome when Δ G
(Fig. 3.1 ) is negative enough to outweigh the surface energy of the new phase, i.e.,
when the fluid phase is supercooled below the equilibrium transition temperature,
at which Δ G is zero.
An important property of supercooled or metastable liquids [ 3 ] is their ability to
form the glass phase. While thermodynamic drive toward crystallization increases
with decreasing temperature, the molecular mobility becomes increasingly slower.
At certain temperature, T g (Fig. 3.1 ), the molecular mobility becomes so slow that
the supercooled liquid cannot maintain the equilibrium liquid structure at a given
rate of cooling. At this point, the supercooled liquid turns into a glass, and the re-
spective temperature is taken as the glass transition temperature. The glass is a non-
equilibrium phase and, thus, its Gibbs energy is larger than that of the supercooled
liquid. Therefore, the glass is bound to relax continuously toward the supercooled
liquid. Unlike the equilibrium phases, the glass cannot coexist in equilibrium with
any other phases, and for that reason, the glass transition temperature can never be