Stretched state

Plotting U as a function of L (or equivalently, to the end-to-end distance r of the modeled coil) permits us to predict the coil stretching behavior at different values of the parameter et, where t is the relaxation time of the dumbbell (Fig. 10). When et < 0.15, the only minimum in the potential curve is at r = 0 and all the dumbbell configurations are in the coil state. As et increases (to 0.20 in the Fig. 10), a second minimum appears which corresponds to a stretched state. Since the potential barrier (AU) between the two minima can be large compared to kBT, coiled molecules require a very long time, to the order of t exp (AU/kBT), to diffuse by Brownian motion over the barrier to the stretched state at any stage, there will be a distribution of long-lived metastable states with different chain conformations. With further increases in et, the second minimum deepens. The barrier decreases then disappears at et = 0.5. At this critical strain rate denoted by ecs, the transition from the coiled to the stretched state should occur instantaneously. 

If e is now decreased, with the chain in the extended state, the dumbbell nevertheless stays in the stretched state where the potential is the lowest. The transition back to the coiled state occurs only when there is a single minimum on the potential energy curve, i.e. at et = 0.15. Since the critical strain-rate for the stretch-to-coil transition (esc) is much below the corresponding value for the coil-to-stretch transition (eca), the chain stretching phenomenon shows hysteresis (Fig. 11). 

In this mode the electrical charge is placed on the film in the stretched state (high capacitance). When the him is allowed to contract (low capacitance), the elastic stresses in the him work against the electric held pressure and thus increase the electrical energy. Figure 10.13 explains the basic mechanism. 

At a higher temperature T = 11.0, for flow rates near the transition rate c, the free-energy barrier between the coiled and stretched conformation is much lower than that for T = 9.0. The chain can therefore explore the phase space and jump back and forth from the coiled to the stretched state. Similar behavior has already been observed in [59] and [60]. Figure 27 illustrates this feature. 

Making the flow rate higher or lower will change from stable to metastable the folded or the stretched state, respectively. The effects of hysteresis associated with this first-order discontinuous transition play an important role in the formation of composite crystalline structures. 

Fig. 4. Two-angle fibers can be easily deformed via the bending and twisting of their linkers. This can be most easily seen for the special case of a planar zig-zag fiber under an external tension F, which extends the fiber via the bending of its linkers from its unperturbed state with contour length Lo (a) to a stretched state of length L>Lo (b).

Let us consider the system XCO with the mass of the fictitious atom X, mx, changing continously from 1 (X = H) to 3 (X = T). The resulting term energies of the three relevant excited vibrational states are depicted as functions of mx in Fig. 13. For m = 1 the two stretching states (1, 0, 0) and (0, 1, 0) are well separated in energy and the assignment provides no problem. The variation of mx in principle does not affect the C-O stretching frequency and to2 would stay constant (in a diabatic sense). On the other hand, the X-CO frequency scales approximately as 1 A/mx and therefore... 

It is possible to convert the essentially spherical PS particles just described into ellipsoids.18 58-62 First, the PS-PDMS composite is raised to a temperature well above the Tg of PS. It is then deformed, and cooled while in the stretched state. The particles are thereby deformed into ellipsoids, and retain this shape when cooled. Uniaxial deformations of the composite give prolate (needle-shaped) ellipsoids, and biaxial deformations give oblate (disc-shaped) ellipsoids.59,63 Prolate particles can be thought of as a conceptual bridge between the roughly spherical particles used to reinforce elastomers and... 

In Fig. 3 the sheet is macroscopically stretched as indicated by the arrows. As a consequence, transversal contraction takes place perpendicular to the stretching direction. Wrinkles will appear in the macroscopically stretched state and - provided the system is linearly elastic and no plastic deformations occur - disappear upon relaxation [22],... 

In Fig. 4 the film was wrinkle-free in the macroscopically stretched state (e.g., it could be prepared on a stretched substrate, as in some of the cases explained below). Now wrinkles are formed as the macroscopic tension is relaxed and remain... 

Dynamic Mechanical Properties. Figure 15 shows the temperature dispersion of isochronal complex, dynamic tensile modulus functions at a fixed frequency of 10 Hz for the SBS-PS specimen in unstretched and stretched (330% elongation) states. The two temperature dispersions around — 100° and 90°C in the unstretched state can be assigned to the primary glass-transitions of the polybutadiene and polystyrene domains. In the stretched state, however, these loss peaks are broadened and shifted to around — 80° and 80°C, respectively. In addition, new dispersion, as emphasized by a rapid decrease in E (c 0), appears at around 40°C. The shift of the primary dispersion of polybutadiene matrix toward higher temperature can be explained in terms of decrease of the free volume because of internal stress arisen within the matrix. On the other... 

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