Cooling rate dependence of T[sub g]—caused by clustering
Istvan Pócsik, Margit Koós · AIP conference proceedings · 1999
In liquid (amorphous) matter the equilibrium number of the active motional degrees of freedom is determined by a cluster structure. These clusters are groups of atoms, which remains connected to each other for some characteristic time. The size of these clusters is very small near the boiling temperature, but it increases on cooling. Because these clusters are re-arranging continuously i.e. they are in a dynamical equilibrium, a cluster life-time can be defined, which also depends on temperature, increasing on cooling. With the only exemption of helium, each other matter solidifies on low temperatures, so it is only a matter of temperature and cooling rate, that these matters can be cooled more quickly, than what the dynamical equilibrium of their cluster structure is able to follow, and the actual equilibrium will be quenched for lower temperatures. Varying the cooling rate we can prepare a set of samples, in which different thermal equilibria, corresponding to different temperatures are quenched. The active motional degrees of freedom at lower temperatures are the basic vibrational mode of these clusters. The vibrational frequency of the clusters is inversely proportional to their size. To each cluster of diameter l, have a vibrational frequency v, and a temperature T, where thermal excitation falls below the energy of this vibration, which vibration freezes on further cooling. We can expect, that a quickly cooled sample, having smaller clusters with higher vibrational frequency will freeze at relatively higher temperature, than the samples cooled slower, having larger clusters and lower vibrational frequencies, which freeze at lower temperature. This freezing process will be detected as a step-like decrease of the specific heat, what is usually known, as the glassy transition, Tg.