Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 75

Fig. 3.11 Schematic
representation of molecular
mobility in the glass phase.
The letters ʱ and ʲ repre-
sent molecules respectively
involved in cooperative and
noncooperative motion. The
open area is a mobility island

that contains significant density fluctuations (Fig. 3.11 ). The lower density areas
form the mobility islands [ 31 ] inside the glass. As a result, the molecules of the
glass phase find themselves in a variety of the spatial situations of different crowd-
edness. Those, stuck in highly congested situations, can only move cooperatively,
i.e., together with moving the closest neighbors. The respective motion is termed
the ʱ -process (relaxation). This is a slow process characterized by high activation
energy whose value is typically on the order of hundreds of kilojoules per mole.
On the other hand, the molecules located in the vicinity of the mobility islands can
move rather freely, i.e., in a noncooperative manner. The respective motion is re-
ferred to as the ʲ -process (relaxation) or Johari-Goldstein process. This process is
fast and its activation energy amounts to several tens of kilojoules per mole.
When glass relaxes toward the equilibrium supercooled liquid structure, the
overall process would occur generally via both cooperative and noncooperative
motion. However, one particular mechanism may dominate depending on tempera-
ture or the stage of relaxation. Since cooperative and noncooperative processes can
occur in parallel with each other, at any given temperature, the kinetics of relaxation
is dominated by the fastest process, i.e., a process having the smallest relaxation
time, ˄ . Cooperative and noncooperative processes have distinctly different tem-
perature dependencies of the relaxation time. Noncooperative processes, such as
ʲ -relaxation, obey the Arrhenius equation:

E
RT

(3.14)

τ= C exp ,