Junction dynamics elasticity

TABLE 5.2 Similarity Between Flory s Constrained Junction Model for Elasticity and the Coupling Model for Junction Dynamics... 

It will be obvious that the treatment of the present section can also be applied to the subchain model (77). As is well-known, this model where every junction point of subchains is assumed to interact with the surroundings, seems to provide a more realistic description of the dynamic behaviour of chain molecules than the simple model used in the proceeding paragraphs, viz. the elastic dumb-bell model where only the end-points of the chain are assumed to interact with the surrounding. One of the important assumptions of the subchain model is that every subchain should contain enough random links for a statistical treatment. From this it becomes evident that the derivations given above for a single chain, can immediately be applied to any individual subchain. In particular, those tensor components which were characterized by an asterisk, will hold for the individual subchains as well. 

Figure 4. Tunneling characteristics of an Al-AlOx-4-pyridine-COOH-Ag junction run at 1.4 K with a 1 mV modulation voltage, (a) Modulation voltage Vu across the junction for a constant modulation current Iu. This signal is proportional to the dynamic resistance of the sample, (b) Second harmonic signal, proportional to d2V/dI2. (c) Numerically obtained normalized second derivative signal G , dG/ dfeVJ, which is more closely related to the molecular vibrational density of states, (d) Normalized G0 dG/d(eVJ with the smooth elastic background subtracted out...

Fig. 8.47. Lomer-Cottrell junction as computed using three-dimensional elasticity representation of dislocation dynamics (adapted from Shenoy et al. (2000)).

For this we turn to a formahsm which allows us to study the dynamics of regular networks built from topologically complex cells (substructures). We let the cells (consisting of beads connected by elastic springs) have an arbitrary internal architecture, and require only that they be topologically identical to each other, see Fig. 9. Obviously, the regular networks built from Rouse chains which were considered in Sect. 5.2 also fall into this category in this case a cell of the network contains a junction and d Rouse chains directly attached to the junction (here d is the dimensionality of the network). 

Recent experimental advances reinforce the idea that the microscopic motions and the elastic properties can be usefully interrelated. For example, quasielastic neutron scattering measurements probe the motions of the network junctions [53,54]. Molecular dynamics simulations have also added new insight, for example, by demonstrating the existence of local constraints on the network chains at strand lengths less than the molecular weight necessary for chain entanglements [55]. Recently P NMR spin-lattice relaxation experiments on crosslinked rubber have been used to monitor specifically the dynamics of the network junctions [52,56]. 

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