Two-Step Entangling Model

Sections 4.1 and 4.2 introduced nucleation by reviewing CNT. Section 4.3 discussed observation of nano-nucleation by means of SAXS.The correct size distribution f(N, t) and 2D shape (kinetic parameters) of a nano-nucleus are obtained simultaneously by analyzing SAXS intensity Ix(q, t) using the extended Guinier plot method. f N, t) is shown to decrease with the increase of N for each t. f(N, i) increases with the increase of t and saturates for each N. With the increase of t,f(N, t) 

The free energy of the end surface ( 7e) of the nanonucleus (cTe(nano)) is much smaller than that of the macro-crystal (cTe(macro)), that is, 7e(nano) (1/5) (76(macro). Here, macro-crystal means the macroscopic crystal. We conclude that the nano-nucleus shows significant fluctuation with respect to size and shape and repeats frequent generation and disappearance. In the case of macro-crystals, it is well known that surface particles are thermodynamically reconstructed into smooth and flat surfaces by surface diffusion, which is a type of Ostwald ripening that results in large (7e(macro). 

We describe the direct observation of the degree of supercooling (AT) dependence of f(N, t) by means of SAXS. f(N, t) increases rapidly with the increase of t at large AT, while f(N, t) increases more slowly at small AT. We obtain AT dependence of the onset time r(A7 defined as the extrapolated time of the linearly increasing f(N, t) with t. We describe the empirical formula by ir AT) oc exp[-yAT], where 7 is a constant that is, nucleation becomes impossible when AT approaches 0. We conclude that nucleation controls the induction period of crystallization, rather than the spinodal decomposition process. 

The relationship between nano-nucleation and macro-crystallization has been studied. We obtain the AT dependence of nucleation rate (I) of a macro-crystal whose size is more than 1 pm by optical microscopy. We describe the empirical formula by /(AT) exp[-C7AT], where C is a constant. We obtain t and I by using the AT dependence of fiN, t) proportional to the net flow of nucleation (/), that is, t °c / as the zero-th approximation. This shows that the critical nano- 

Section 4.6 described the essential role of epitaxy in heterogeneous nucleation by formulating and confirming a relationship, / /q oe Cna/ na, where I is the nucleation rate of polymer crystals, lo is a prefactor of I, Cna is the concentration of NA in the mixture of NA and 

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