Chain sliding diffusion

Fig-1 Schematic illustration of the crystallization and melting processes of polymers. The crystallization process corresponds to processes of disentanglement and chain sliding diffusion. The melting process is the reverse of the crystallization process. Between equilibrium melt and ideal crystal, there exists metastable melt and crystal. Cross marks indicate entanglement... 

Hikosaka presented a chain sliding diffusion theory and formulated the topological nature in nucleation theory [14,15]. We will define chain sliding diffusion as self-diffusion of a polymer chain molecule along its chain axis in some anisotropic potential field as seen within a nucleus, a crystal or the interface between the crystalline and the isotropic phases . The terminology of diffusion derives from the effect of chain sliding diffusion, which could be successfully formulated as a diffusion coefficient in our kinetic theory. 

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]. 

Topological Nature and Chain Sliding Diffusion in Polymer Nucleation... 

There are three kinds of diffusion (i) within the isotropic phase (ii) the interface (between the isotropic and the crystalline phases) and (iii) the crystalline phase. In the case of a polymer system, the topological nature of polymer chains assumes an important role in all three kinds of diffusion, which has been shown in the chain sliding diffusion theory proposed by Hikosaka [14,15]. It is obvious that any nucleus (a primary nucleus and a two-dimensional nucleus) and a crystal can not grow or thicken without chain sliding diffusion. 

Fig. 20 Chain sliding diffusion model of primary nucleation. Polymer chains are rearranged from Gaussian shape within the melt into a nucleus through chain sliding diffusion within the nucleus and disentanglement within the interface. Bottom graph indicates change in free energy of the nucleus against N...

As shown in Fig. 1, chain sliding diffusion becomes difficult due to pinning effect within the interface between a nucleus and the melt. Since Jo is proportional to the topological diffusion constant D, D is related to ve from Eq. 62,... 

The free energy necessary for the formation of a critical nucleus AG in both primary and secondary nucleation processes does not depend on Mn, i.e., AG ps const, while only the diffusion coefficient D depends on Mn, i.e., I ex D(Mn). Therefore, the Mn dependences of I and V are not controlled by the formation process of a critical nucleus but are mainly controlled by the chain sliding diffusion process. 

Hikosaka, M., Watanabe, K., Okada, K. and Yamazaki, S. Topological Mechanism of Polymer Nucleation and Growth - The Role of Chain Sliding Diffusion and Entanglement. Vol. 191, pp. 137-186. 

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