Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysisстатья
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Дата последнего поиска статьи во внешних источниках: 25 ноября 2020 г.
Аннотация:In the application of classical nucleation theory (CNT) and all other theoretical models
of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after
the supercooled liquid or the glass have completed structural relaxation processes towards the
metastable equilibrium state. Only employing such an assumption, the thermodynamic driving force
of crystallization and the surface tension can be determined in the way it is commonly performed.
The present paper is devoted to the theoretical treatment of a different situation, when nucleation
proceeds concomitantly with structural relaxation. To treat the nucleation kinetics theoretically for
such cases, we need adequate expressions for the thermodynamic driving force and the surface
tension accounting for the contributions caused by the deviation of the supercooled liquid from
metastable equilibrium. In the present paper, such relations are derived. They are expressed via
deviations of structural order parameters from their equilibrium values. Relaxation processes result in
changes of the structural order parameters with time. As a consequence, the thermodynamic driving
force and surface tension, and basic characteristics of crystal nucleation, such as the work of critical
cluster formation and the steady-state nucleation rate, also become time-dependent. We show that
this scenario may be realized in the vicinity and below the glass transition temperature, and it may
occur only if diffusion (controlling nucleation) and viscosity (controlling the alpha-relaxation process)
in the liquid decouple. Analytical estimates are illustrated and confirmed by numerical computations
for a model system. The theory is successfully applied to the interpretation of experimental data.
Several further consequences of this newly developed theoretical treatment are discussed in detail.
In line with our previous investigations, we reconfirm that only when the characteristic times of
structural relaxation are of similar order of magnitude or longer than the characteristic times of crystal
nucleation, elastic stresses evolving in nucleation may significantly affect this process. Advancing the
methods of theoretical analysis of elastic stress effects on nucleation, for the first time expressions are
derived for the dependence of the surface tension of critical crystallites on elastic stresses. As the
result, a comprehensive theoretical description of crystal nucleation accounting appropriately for the
effects of deviations of the liquid from the metastable states and of relaxation on crystal nucleation
of glass-forming liquids, including the effect of simultaneous stress evolution and stress relaxation
on nucleation, is now available. As one of its applications, this theoretical treatment provides
a new tool for the explanation of the low-temperature anomaly in nucleation in silicate and polymer
glasses (the so-called “breakdown” of CNT at temperatures below the temperature of the maximum
steady-state nucleation rate). We show that this anomaly results from much more complex features of crystal nucleation in glasses caused by deviations from metastable equilibrium (resulting in changes
of the thermodynamic driving force, the surface tension, and the work of critical cluster formation,
in the necessity to account of structural relaxation and stress effects) than assumed so far. If these
effects are properly accounted for, then CNT appropriately describes both the initial, the intermediate,
and the final states of crystal nucleation.