Rotational isomeric mechanisms of flexibility

Fig. 12. Freely jointed diain (a), persistent chain (b), and chain with a rotational-isomeric mechanism of flexibility (c).

The rotational isomeric mechanism of flexibility is basically characteristic of carbon-carbon chains [28, 29]. The simplest model of the polymer chain which illustrates the basic features of the rotational isomeric mechanism of flexibility is shown in Fig. 1.2c [30]. In this model, the polymer chain is represented as a sequence of units of length a and characteristic thickness d, each of which can be in either the trans position (step forward) or in the gauche position (kink in valence angle Yq)- The sites of the kinks are not fixed, as they can appear with the same probability p in each stq> (p Kuhn segment of this model of the chain I by the relation [31]... 

Angles Yo ar usually greater than 26° for real chains. For this reason, nematic ordering should take place for them according to the first mechanism described above. The physical reason for this is that for the pure rotational isomeric mechanism of flexibility (cf. Fig. 1.2c), the losses in the orientational... 

It can thus be concluded that in consideration of the small persistent component of the flexibility, the anomalous features of nematic ordering in a solution of rotational-isomer chains (broad region of separation, high value of the order parameter at the transition point) are preserved (since v 1), but are manifested in a less pronounced form, as for the pure rotational-isomeric mechanism of flexibility. 

The diffo ence in the character of the nematic ordering in solutions of semiflexible macromolecules with diffaent mechanisms of flexibility is not only manifested in the thermodynamic characteristics of the phase transition itself, but also in the conformations of the polymer chains in the liquid-crystalline phase. For example, the dependences of the root-mean-square distance between chain ends (/ 2) on the concentration of polymer in the solution for semiflexible freely jointed and persistent chains calculated in [43,44] are shown in Fig. 1.4. Note that for the freely jointed model, the value of (jf) is almost independent of the concentration of the solution in the anisotropic phase (i.e., orientation of the segments but not uncoiling of the macromolecules takes place), while for a solution of persistent chains, the increase in (/ ) in the anisotropic phase with an increase in the concentration is very signiflcant (exponential). A solution of chains with the rotational-isomeric mechanism of flexibility (cf. Fig. 1.2c) behaves analogously in this case, as demonstrated in [35], in the... 

The following three mechanisms of polymer chain flexibility are the best known in polymer physics freely jointed persistence, and rotational isomeric mechanisms [27]. The freely jointed mechanism corresponds to the simplest freely jointed model of a semiflexible polymer chain in which the chain is in the form of a sequence of hinged, long, rigid rods of length I and diameter d, with I d (Fig. 1.2a). In the persistence mechanism, the flexibility is due to gradual accumulation of the effect of small vibrations of valence angles, bonds, etc. A... 

The flexibility and extensibility of a crosslinked epoxy network are determined by the available glassy-state free volume. If the free volume is insufficient to allow network segmental extensibility via rotational isomeric changes then the brittle mechanical response of the epoxy glass is not controlled by the network structure but rather by macroscopic defects such as microvoids. For epoxies with sufficient free volume that allows plastic network deformation the mechanical response is controlled by the network structure. 

The theory of relaxation spectra in polarized luminescence for various dynamic models of a flexible polymer chain has been developed by several groups of workers. Wahl has proposed a theory for the model of Gaussian subchains. The authors and coworkers used dynamic chain models consisting of rigid or deformable elements with continuous visco-elastic mechanism of mobility and rotational-isomeric lattice chain... 

If it is assumed that the chain is flexible, that is that the barrier between conformational states is sufficiently low that rapid interchange can occur, then the time averaged shape of the polymer will be described by the distribution between the available conformations. This allows a statistical mechanical analysis, called the rotational isomeric model. This indicates that the population of the gauche states causes the chain to adopt a random quasi-spherical shape and not the often pictured zigzag extended aU trans form. The analysis allows calculation of two fundamental parameters the radius of gyration, which is the size of the polymer molecule if it were to undergo free internal rotation, and the related end-to-end distance. These quantities define the shape of the isolated polymer... 

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