Isoenergetic chains

Finally, making use the equation of state of Eq. (28) one can demonstrate that the linear thermal expansion coefficient depends on the deformation as follows (for isoenergetic chains)26 211... 

These expressions show that a deformed polymer network is an extremely anisotropic body and possesses a negative thermal expansivity along the orientation axis of the order of the thermal expansivity of gases, about two orders higher than that of macromolecules incorporated in a crystalline lattice (see 2.2.3). In spite of the large anisotropy of the linear thermal expansivity, the volume coefficient of thermal expansion of a deformed network is the same as of the undeformed one. As one can see from Eqs. (50) and (51) Pn + 2(iL = a. Equation (50) shows also that the thermoelastic inversion of P must occur at Xim (sinv) 1 + (1/3) cxT. It coincides with F for isoenergetic chains [see Eq. (46)]. 

Within the class of polymer crystals having, ideally, long-range positional order for all the atoms, different crystalline forms (polymorphs) may arise as a result of having different almost isoenergetic macromolecular conformations (of the main chain, in most known cases) or as a result of different, almost isoenergetic modes of packing of macromolecules with identical conformations [1-3]. 

When two trans-polyacetylene chains with different phases are put together, an obvious disturbance occurs in the standard conjugation pattern. The bond alternation defect that appears is known as a neutral soliton (Fig. 1.7). This kind of quasi-particle has an unpaired electron but is electrically neutral and is isoenergetically mobile along the polymer chain in both directions. This soliton gives rise to a state in the middle of the otherwise empty energy gap that can be occupied by zero, one or two electrons (Fig. 1.8). 

The nonconventional N-H Au- hydrogen bond coexists with the conventional one in the ammonia dimer when the latter forms with An- the complex Air-fNth 1 on the PES of Au--(NH3)2 (see Figure 2). This latter is quasi isoenergetic to the chain complex Au--(NH3)2n the small energy difference, AEj.jj, between Au -(NH3)2I and Au--(NH3 )2H amounts to only — 0.34kcal mol-1. Since ASi-n° = —11.19cal K-1 mol-1, the order of stability of these complexes is reversed at T > 30 K. 

Polymorphism is observed relatively frequently in long-chain macromolecules, for which approximately isoenergetic structures exist. The stable... 

Polymorphism is observed relatively frequently in long-chain macromolecules, for which approximately isoenergetic structures exist. The stable crystal form of poly(ethylene), for example, possesses an orthorhombic lattice, but on elongation, triclinic and monoclinic modifications are observed. Three modifications are known in it-poly(propylene) a (monoclinic), P (pseudohexagonal), and y (triclinic). Since the molecules are in a 31 helix conformation in all the modifications, differences in the packing of the chain must be responsible for this polymorphism. The three modifications appear at varying crystallization temperatures. In it-poly(butene-l), however, the various modifications correspond to different kinds of helix, so that variations in conformation must be important (see also Table 5-5). 

The eclipsed and staggered chain orientations were found by Bormann-Rochotte to be nearly isoenergetic for the transition state for stereoregular isotactic propylene insertion into a stereoregular... 

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