For the mechanism of isothermal bulk crystallization of high polymers

beside the nucleation and growth steps

the unimpingement of growing crystal aggregates should be taken into account for the modification of the Avrami equation. Starting from Poisson distribution function of growing crystal aggregates

the probability of the unimpinging ones should be P(0)+P(1)

then the Q-modified Avrami equation thus derived can be expressed as Q(V0)=Ln[1-Ln(1-V0])+(?)-1.3179=K(?)where V0 represents the volume fraction of crystal aggregates at crystallization time t at a given temperature

while the exponent n on t relates to the mode of nucleation and growth

and Kq is the corresponding shape factor.This Q-modified one is verified satisfactory by the isothermal bulk crystallization of lanthanide catalytically polymerized polybutadiene(Ln-PB)

polyisoprene(Ln-PIR) and their copolymers(Ln-PB/IR).Furthermore

the proposed mechanism is well identified by the change of morphological state during the course of crystallization of the corresponding cast film of Ln-PB/TR(92/8) at-60°(Fig.1).Upon examination of the influence of the number of entanglement on crystallization rate

it reveals the existence of two stages of entanglementation

the primary and the econdary ones(Fig.19) The equation for dependence of molecular weight and entanglement on bulk crystallization rate has been derived as Eq.13 or 18 for Ln-PB

and verified by the experimental rate date of well fractionated Ln-PB samples crystallized at-9.1 to -15℃(Fig.20).