Primary nucleation rate

Interestingly, this barrier does not depend on chain length. This result coincides with experimental observations on the primary nucleation rate of bulk polymers [128-130]. For secondary nucleation of crystallization on a smooth growth front, a similar free-energy expression can be obtained for 2D nucleation ... 

The molecular weight (M) dependence of the steady (stationary) primary nucleation rate (I) of polymers has been an important unresolved problem. The purpose of this section is to present a power law of molecular weight of I of PE, I oc M-H, where H is a constant which depends on materials and phases [20,33,34]. It will be shown that the self-diffusion process of chain molecules controls the Mn dependence of I, while the critical nucleation process does not. It will be concluded that a topological process, such as chain sliding diffusion and entanglement, assumes the most important role in nucleation mechanisms of polymers, as was predicted in the chain sliding diffusion theory of Hikosaka [14,15]. 

The metastable zone width can also be reduced by the application of US. The apparent order of nucleation or growth is deoreased by US. Based on available evidence, the metastable zone width can be reduced simply by applying a low US power. Thus, US decreases the apparent order of the primary nucleation rate and increases the rate of appearance of the solid. Seemingly, US modifies the meohanism of nucleation itself as its presence strongly reduces the apparent order of nuoleation. 

Umemoto, S. et al.. Molecular weight dependence of primary nucleation rate of poly(ethylene succinate), J. Macromol. ScL, Part B Phys. 42, 421 30, 2003. 

In the above equation, J is the primary nucleation rate that is assumed to be the dominant nucleation mechanism. The boundary condition at the entrance is... 

Figure 10.14 Effect of the number of seeds on primary nucleation rate in a controlled cooling batch crystallization. Computer simulation results for citric acid, as reported by Bohlin and Rasmuson (1992a).

If nanometer-scale crystals are required, a tiny crystal size can be obtained by applying very high primary nucleation rates, which require extremely strong supersaturations. Such high levels of supersaturation can be achieved through... 

Fig. 19.1. Temperature dependencies of the primary nucleation rate (I) (A) and the linear crystal growth rate (G) (Q) for poly(ethylene succinate) (PEISU) [14] with a molecular weight (M) of 8,770. The solid and broken lines are results from the best fitting procedure for G based on Eq. (19.2) and for I based on Exj. (19.11) by the Arrhenius and the WLF expressions of the molecular transport term, respectively...

Molecular weight dependence of primary nucleation rate can be expressed by number of molecules (N ), diffusion of molecules (D ) and formation of critical nucleus (4iFi) according to the following equation ... 

Nucleation includes primary as well as secondary nucleation. In primary nucleation, there is spontaneous generation of new particles in the absence of existing particles. Secondary nucleation includes the formation of nuclei in the neighborhood of an existing particle, and those microparticles that are formed by breakage by impact with the impeller or the container walls (in other words, first-order processes), or by particle-particle collisions (second-order processes). Denoting the supersaturation at time t by cr(t), we may represent the primary nucleation rate by the particle growth... 

Figure 6.31 Model tor regime II growth showing multiple nucleation. The quantity S represents the mean separation between the primary nuclei, and S denotes the mean distance between the associated niches. The primary nucleation rate is and the substrate completion rate is g. The overall observable growth rate is G//. Reptation tube contains molecule being reeled at rate ronto substrate (75).

Figure 11.6 Schematic plots for the primary nucleation rate (I) and crystal growth rate (G) as a function of the isothermal crystallization (or nucleation) temperature. Adapted from Lorenzo and Muller [60].

Refs [56,64,68,72]). Supernucleation accelerates the primary nucleation rate and contributes to increase the overall crystallization kinetics. 

Ani primary nucleation rate constant parameter [length/time]... 

Fig. 9.100 Plot of log of primary nucleation rate, N, against (AT) for linear polyethylene fractions of indicated molecular weights. (From Ghosh et al. (334))...

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