activation energy for short-distance diffusion of molecules at interfaces, the lower
the temperature, the smaller the crystal nucleation rate. The temperature depen-
dence of the overall nucleation rate will appear as a bell shape, as illustrated in
Fig.10.25. The crystallization during the cooling from high temperatures is
called hot crystallizationTcc; the crystallization during the heating from the glassy
state is called cold crystallizationTch. The nucleation agent mainly accelerates hot
crystallization, while the nucleation acceleration agent mainly accelerates cold
crystallization.
10.4.2 Microscopic Mechanism of Polymer Crystal Growth
The crystal growth process follows after primary nucleation. The characterization of
crystal growth rates is mainly through the measurements on the radiusRof the
spherulites or on the linear size of single-layer lamellar crystal as a function of timet,
using light scattering or microscopies. Correspondingly, the linear growth rate is
defined asv¼dR/dt.Normally,v appears independent tot,asillustratedin
Fig.10.26a, reflecting the interface-controlled crystal growth mechanism. The cur-
rent theoretical consensus on the kinetics of polymer crystal growth mainly regards
secondary nucleation as the rate-determining step at the interfaces, which exhibits the
critical free energy barrierDG*/DT^1. Indeed, the bell-shape curve of the crystal
growth rate versus temperatures is observed, as illustrated in Fig.10.25b.Duringhot
crystallization, three linear segments (according to (10.28)) with their slopes 2:1:2
occur on the curve of logarithmic linear crystal growth rates versus the reciprocal
supercooling, as illustrated in Fig.10.26b,calledtheregime-transitionphenomenon.
The linear growth rate actually reflects a net competition result between the
growth and the melting upon thermal fluctuations at the lateral surface of lamellar
crystals, as given by (Ren et al. 2010 )
Fig. 10.26 Illustration of (a) the linear sizes of crystallites showing constant growth rates with the
time evolution; (b) the logarithmic linear growth rate exhibiting three regimes on its temperature
dependence
212 10 Polymer Crystallization