Chain end motion

It has been suggested (94) that the small peak at 170°K. (102 c.p.s.) for polyoxymethylene is caused by chain end motion. However, little proof has been put forward, and further investigations are needed. 

Figure 5.5. Sources of free volume for plasticization A, chain end motion B, side chain motion, C, main chain Crankshaft , D, external plasticizer motion. [Adapted, by permission, Kern Sears J, Darby J R, The Technology of Plasticizers, John Wiley ...

Reaction diffusion (also called residual termination). Chain end motion by addition of monomer to the chain end. 

To the extent that the segmental friction factor f is independent of M, then Eq. (2.56) predicts a first-power dependence of viscosity on the molecular weight of the polymer in agreement with experiment. A more detailed analysis of f shows that segmental motion is easier in the neighborhood of a chain end because the wagging chain end tends to open up the structure of the melt and... 

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

HDH/DHD interface. If the motion of the polymer was the same for each portion of the molecule, i.e., isotropic, the concentration of deuterium across the interface would remain constant. However, if the monomer motion is anisotropic, such as with reptation, where the chain ends lead the centers, a high amplitude ripple in the concentration profile, as described below will be displayed. For a reptating chain, lateral motion of the central segment of the chain is permitted up to depths approximating the tube diameter, after which the central segments must follow the chain ends in a snake-like fashion. 

More complex models for diffusion-controlled termination in copolymerization have appeared.1 tM7j Russo and Munari171 still assumed a terminal model for propagation but introduced a penultimate model to describe termination. There are ten termination reactions to consider (Scheme 7.1 1). The model was based on the hypothesis that the type of penultimate unit defined the segmental motion of the chain ends and their rate of diffusion. 

With the boundary conditions that the chain ends are free of forces, Eq. (13) is readily solved by cos-Fourier transformation, resulting in a spectrum of normal modes. Such solutions are similar, e.g. to the transverse vibrational modes of a linear chain except that relaxation motions are involved here instead of periodic vibrations. 

Simulation programs for the ESR line shapes of peroxy radicals for specific models of dynamics have been developed for the study of oxidative degradation of polymers due to ionizing radiation [66]. The motional mechanism of the peroxy radicals, ROO, was deduced by simulation of the temperature dependence of the spectra, and a correlation between dynamics and reactivity has been established. In general, peroxy radicals at the chain ends are less stable and more reactive. This approach has been extended to protiated polymers, for instance polyethylene and polypropylene (PP) [67],... 

B. The mean vector connecting the chain ends is deformed affinely. The crosslink junctions fluctuate according to the theory of Brownian motion (2, 5, 7) ... 

The chain tension arises in a physical way at timescales short enough for the tube constraints to be effectively permanent, each chain end is subject to random Brownian motion at the scale of an entanglement strand such that it may make a random choice of exploration of possible paths into the surrounding melt. One of these choices corresponds to retracing the chain back along its tube (thus shortening the primitive path), but far more choices correspond to extending the primitive path. The net effect is the chain tension sustained by the free ends. 

The simplest case of comb polymer is the H-shaped structure in which two side arms of equal length are grafted onto each end of a linear cross-bar [6]. In this case the backbones may reptate, but the reptation time is proportional to the square of Mj, rather than the cube, because the drag is dominated by the dumb-bell-like frictional branch points at the chain ends [45,46]. In this case the dependence on is not a signature of Rouse motion - the relaxation spectrum itself exhibits a characteristic reptation form. The dynamic structure factor would also point to entangled rather than free motion. 

It was straightforward to apply the TRMC technique to study on-chain charge transport to ladder-type poly-phenylene (LPPP) systems because covalent bridging between the phenylene rings planarizes the chain skeleton, eliminates ring torsions, and reduces static disorder. One can conjecture that in these systems intra-chain motion should be mostly limited by static disorder and chain ends. To confirm this... 

Tanaka et al. have studied the surface molecular motions of PS films coated on a solid substrate by lateral force microscopy and revealed that the Tg at the surface was much lower than the corresponding bulk one [148]. Possible reasons for this included an excess free volume induced by localized chain ends, a reduced cooperativity for of-relaxation process, a reduced entanglement, and a unique chain conformation at the surface. For comparison, they examined surface relaxation behavior of high-density PMMA brushes. 

The simulation results indicate that helix reversals form and migrate easily in PTFE crystal structures. Their motion in neighboring chains can be coupled. In simulations at both temperatures, the reversal bands formed mostly at chain ends where torsional motion was relatively unrestricted, but also were observed to form in the center of some of the helices. This latter point of origin, though more energetically and mechanistically difficult (because it involves coordinated motion... 

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