Diffusion chain

One example of mapping by chain diffusion involved the case of lOmers of polyisoprene at 413 K. A dynamic mapping between a fully atomistic and a very simple coarse-grained model was demonstrated. Only chain stiffness was used to perform the mapping in that study. The local chain reorientation in both simulations was the same after the time scales had been determined by the diffusion coefficient. The decay times of the Rouse modes, however, were not equal, indicating that mapping by stiffness alone is too simplistic. 

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When compared to the early models that describe the adhesion of elastomers in the presence of interfacial chains, the central findings of this work, namely, observations b and d above, were quite surprising. In his recent work, de Gennes [102] pointed out that when a surface tethered chain diffuses into an elastomeric... 

In which X is the average monomer interpenetration distance, L is the contour length of interdiffused chains and n(t) is the number of chains diffused at time t. The time and molecular weight dependence of these molecular properties are given in Table 1. 

Once the chains become larger and larger, the dynamics of the melt slows down dramatically, due to the topological constraints imposed by the chains on each other. For the chain diffusion one observes a transition... 

Values of 0 required to fit the rate of copolymerization by the chemical control model were typically in the range 5-50 though values <1 are also known. In the case of S-MMA copolymerization, the model requires 0 to be in the range 5-14 depending on the monomer feed ratio. This "chemical control" model generally fell from favor wfith the recognition that chain diffusion should be the rate determining step in termination. 

It is important to realize that, even if the rate of termination is determined by the rates of chain diffusion, the chain end composition and the ratio of combination to disproportionation are not. Knowledge or prediction of the overall rate of termination offers little insight into the detailed chemistry of the termination processes not involved in the rale-determining step. 

Fig. 6.4. Vogel-Fulcher plot of the chain diffusion constants D for the three different polycarbonate modifications, as indicated in the figure, for N = 20 model monomers...

Since the possibility of direct melt intercalation was first demonstrated [11], melt intercalation has become a method of preparation of the intercalated polymer/ layered silicate nanocomposites (PLSNCs). This process involves annealing, statically or under shear, a mixture of the polymer and organically modified layered fillers (OMLFs) above the softening point of the polymer. During annealing, the polymer chains diffused from the bulk polymer melt into the nano-galleries between the layered fillers. 

This simple argument can yield the expected molecular weight dependence of both the single chain diffusion constant (in three dimensions) D and the viscosity 77. For in one reptation time the chain has moved on average one chain end-to-end distance R (N/Nj a, so... 

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

Consolidation and development of interlaminar bond strength for thermoplastic matrix composites have been modeled by two mechanisms intimate contact and autohesion. Intimate contact describes the process by which two irregular ply surfaces become smooth (Fig. 13.10). In areas in which the ply surfaces are in contact, autohesion occurs, and the long thermoplastic polymer chains diffuse across the ply boundaries. Filament winding with thermoplastic matrix materials is considered an on-line consolidation process in that local... 

A comparison of Eqs. 10.55 and 10.59 shows that the diffusivity of an isolated chain due to Brownian motion falls off more slowly with increasing chain size than the diffusivity of an entangled chain diffusing by the reptation mechanism. 

A well-defined amount of co-crystallization is possible across the interface of two adjacent crystals by annealing two stacked, completely wetted, solution-cast films of UHMW-PE [32]. It was found that doubling of the lamellae across the interface enhances the peel energy to such a level that the films could not be separated anymore. By contrast, pre-annealing one side of the film prohibited co-crystallization across the interface and these films could still be separated easily. It was therefore concluded that a limited amount of chain diffusion across the interface occurs during doubling of the lamellae, as facilitated by the well-defined structure of the interphase due to the adjacent reentry that occurs upon crystallization from solution. 

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